Continuous emulsion polymerization in a pulsed packed column Citation for published version (APA): Hoedemakers, G. F. M. (1990). Continuous emulsion polymerization in a pulsed packed column Eindhoven: Technische Universiteit Eindhoven DOI: 10.6100/IR329856 DOI: 10.6100/IR329856 Document status and date: Published: 01/01/1990 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected]providing details and we will investigate your claim. Download date: 13. May. 2019
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Continuous emulsion polymerization in a pulsed packedcolumnCitation for published version (APA):Hoedemakers, G. F. M. (1990). Continuous emulsion polymerization in a pulsed packed column Eindhoven:Technische Universiteit Eindhoven DOI: 10.6100/IR329856
DOI:10.6100/IR329856
Document status and date:Published: 01/01/1990
Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:
www.tue.nl/taverne
Take down policyIf you believe that this document breaches copyright please contact us at:
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, Prof. ir. M. Tels, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen op
dinsdag 17 april 1990 om 16.00 uur
door
GUILLAUME FRANCISCUS MARIA HOEDEMAKERS
geboren te Geleen
druk: wibro dissertatiedrukkerij, heimond
Dit proefschrift is goedgekeurd door de promotoren:
Prof. dr. ir. D. Th oen es Prof. dr. ir. A.L. German
Aan mijn ouders.
Het in dit proefschrift beschreven onderzoek werd mogelijk gemaakt dankzij
financiële ondersteuning van DSM Research B.V., Geleen.
SUMMARY
Continuous emulsion polymerization on a technica! scale is mostly carried out in
continuous stirred tank reactors (CSTRs). This reactor type, however, bas some
disadvantages that make it less suitable for general applications on a large scale.
One of the main prohlems is the partiele formation. A CSTR bas shown to produce much
fewer particles per unit volume than a batch reactor operated under the same
conditions. Por example, for styrene emulsion polymerization the maximum attainable
number of formed polymer particles per unit volume in a CSTR is only 57 % of that
formed in a batch reactor under the same conditions. Consequently, the
polymerization rate in a CSTR is also lower. A second problem often encountered in a
CSTR is the occurrence of large sustained oscillations in conversion and partiele
numbers. This phenomenon is often observed in the polymerization of monomers such as
vinyl acetate or methyl methacrylate, where relatively high rates of radical
desorption from the polymer particles take place. It was found earlier that both
problems are caused by the large residence time distribution in a CSTR, and can be
avoided when a plug flow type reactor is used instead.
This thesis describes the development of a new reactor type in which the above
mentioned disadvantages are avoided. This reactor is a pulsed packed column: a
packed tubular reactor in which velocity fluctuations are introduced by pulsation.
This causes the flow to be locally turbulent, which provides proper emulsification
of the monomer, efficient transport of the heat of reaction to the reactor wan by
good radial mixing, without the risk of reactor fouling.
The residence time distribution in the pulsed packed column bas been examined for
random stacked Raschig rings and for structured Sulzer SMV8-DN50 intemals. lt
appears that the axial dispersion coefficient is determined by three effects
originating from the nett flow rate, the pulsation velocity and the packing
structure, respectively. The axial dispersion in the structured packing was much
lower than in the Raschig rings packing. This could be attributed to the regular
structure of the Sulzer packing.
The results of the measurements of the residence time distribution are used to
explain results of emulsion polymerization experiments of styrene in the pulsed
packed column. The polymerization reaction was studied by measuring conversion and
numbers of formed polymer particles at . different positions in the column as a
function of mean residence time, pulsation conditions and packing type. The results
were compared with the performances of a batch reactor and of a CSTR. lt appears
that at low pulsation rates the pulsed packed column behaves like a batch reactor.
At relatively large pulsation rates the number of forrned polymer particles and the
conversion decrease, but are still considerably higher than those obtained in a
CSTR. Molecular weights of the column products did not show significant deviations
from those of batch products. The residence time distribution in the column could be
varied by varying the pulsation velocity (reflected by the axial dispersion
coefficient), the flow rate or both. The importance of axial dispersion relative to
the velocity of the liquid is expressed in the dimensionless Peclet-number. It has
been shown that a Peclet-number related to the section of the column in which the
partiele formation takes place (Pe1) is the best criterion for descrihing the
performance of the reactor. Experimental results of the different column packing
types, mentioned before, could be reduced to one common denominator by the usè of
Per For the emulsion polymerization of styrene in a pulsed packed column, a reactor
model is developed, descrihing the performance of the column both qualitatively and
quantitatively. It appeared that the best model of a pulsed packed column is based
on plug flow with axial dispersion.
A study of the styrene droplet sizes in emulsions, prepared in a batch reactor and
in a pulsed packed column, showed that almost all measured droplet diameters were in
the range 1-10 J.lm. From this it follows that the chance of polymerization in
dropiets can be regarded to be negligible. An analysis of the dependenee of the
droplet sizes on the energy dissipation in the reactors showed, that the mean
droplet diameter was determined only by break up of the dropiets and not by
coalescence of the droplets. Coalescence of the dropiets was prevented by the
emulsifier present at the monomer/water interfaces.
Besides aspects of macromolecular chemistry and chemica! reaction engineering also
aspects of colloid and interfacial chemistry play a role in the emulsion
polymerization process. Partiele numbers and conversion strongly depend on the
emulsifier used and on the ionic strength of the emulsion. The emulsion
polymerization of styrene emulsified with a rosin acid soap and carried out at high
electrolyte concentrations showed a decline in the number of polymer particles
during the course of the polymerization, which was caused by coagulation and
coalescence of the particles. The coalescence of the particles strongly influences
the polymerization kinetics: it appeared that the number of polymer particles in the
final latex depends on the type and concentration of the emulsifier, the monomer and
electrolyte concentration and the energy dissipation, but was almost independent of
initiator concentration and temperature.
SAMENVATTING
Continue emulsiepolymerisatie wordt ~p technische schaal voomarnelijk uitgevoerd in
continu doorstroomde geroerde tank reaktaren (CSTR's). Dit reaktor type heeft echter
een aantal nadelen welke het minder geschikt maken voor toepassing op grote schaaL
Een van de belangrijkste problemen is de deeltjesvorming. In eerdere onderzoeken is
gebleken dat een CSTR beduidend minder polymeerdeeltjes per volume-eenheid latex
produceert dan een batch reaktor, bedreven onder dezelfde reaktiecondities. Voor de
emulsie- polymerisatie van styreen bijvoorbeeld bedraagt het maximale aantal
geproduceerde polymeerdeeltjes in een CSTR slechts 57 % van dat in een batch
reaktor, bij gelijke reaktiecondities. Dientengevolge zal de polymerisatiesnelheid
in een CSTR ook aanmerkelijk lager zijn dan in een batch reaktor. Een tweede
probleem dat vaak voorkomt in een CSTR is het optreden van grote oscillaties in
conversie en deeltjesaantallen. Dit fenomeen wordt vaak waargenomen bij de
polymerisatie van monomeren zoals vinylacetaat en methylmethacrylaat, welke relatief
grote snelheden van radicaaldesorptie uit de polymeerdeeltjes vertonen. In eerdere
onderzoeken is gevonden dat beide bovengenoemde problemen worden veroorzaakt door de
grote verblijfrijdspreiding in een CSTR, en kunnen worden voorkomen bij gebruik van
een propstroomreaktor.
Dit proefschrift beschrijft de ontwikkeling van een nieuw reaktortype, waarin
bovengenoemde problemen niet optreden. Deze reaktor is een gepulseerde gepakte
kolom: een gepakte buisreaktor waarin ten gevolge van pulsatie van de vldeistof
snelheidsfluctuaties worden geïntroduceerd. Deze snelheids- fluctuaties zorgen
ervoor dat de vloeistofstroming lokaal turbulent wordt, hetgeen een goede
emulsificatie van het monomeer, efficient transport van de reaktiewarmte naar de
reaktorwand door een goede radiale menging, en minimale kans op reaktorvervuiling
garandeert.
De verblijflijdspreiding in de gepulseerde gepakte kolom is onderzocht voor random
gepakte Raschig ringen en voor gestruktureerde Sulzer SMV8-DN50 intemals. Het
blijkt dat de axiale dispersiecoëfficiënt wordt bepaald door drie effekten,
afkomstig van respectievelijk de netto vloeistofstroming, de pulsatiesnelheid en de
pakkingstruktuur. De axiale dispersie in de Sulzer pakking is veel kleiner dan in de
Raschig ringen pakking, hetgeen toegeschreven kan worden aan de regelmatige
struktuur van de Sulzer pakking.
De resultaten van de verblijftijdspreidingsmetingen zijn gebruikt om resultaten van
emulsiepolymerisatie experimenten van styreen in de gepulseerde gepakte kolom te
verklaren. De polymerisatiereaktie is bestudeerd door het meten van conversie en
aantal gevormde polymeerdeeltjes op verschillende posities in de kolom als functie
van de gemiddelde verblijftijd, de pulsatiecondities en het pakking type. De
resultaten zijn vergeleken met de prestaties van een batch reaktor en van een CSTR.
Het blijkt dat bij geringe pulsatiesnelheden de gepulseerde gepakte kolom zich
gedraagt als een batch reaktor. Bij relatief grote pulsatiesnelheden nemen de
conversie en het aantal gevormde polymeerdeeltjes af, echter beiden blijven
aanzienlijk groter dan in een CSTR. Molekuulgewichten van de kolomprodukten blijken
niet significant af te wijken van de molekuulgewichten van batch produkten. De
verblijftijdspreiding in de kolom werd gevarieerd door variatie van de
pulsatiesnelheid (weergegeven door de axiale dispersiecoëfficiënt), de netto
stroomsnelheid van de vloeistof, of beiden. De relatieve bijdrage van de axiale
dispersie tot de verblijftijd- spreiding ten opzichte van die van de netto
stroomsnelheid wordt tot uitdrukking gebracht in het dimensieloze Pecletgetal. Het
is gebleken, dat een Peeletgetal gerelateerd aan de kolomsectie waarin de
deeltjesvorming plaats vindt (Pe1) het optimale criterium is voor het beschrijven
van de prestaties van de reaktor. Experimentele resultaten van de verschillende
kolompakkingtypen kunnen onder een gemeenschappelijke noemer worden gebracht door
het gebruik van Pet
Voor de emulsiepolymerisatie van styreen in een gepulseerde gepakte kolom is een
reaktormodel ontwikkeld, dat de prestaties van· de kolom zowel kwalitatief als
kwantitatief beschrijft. Het is gebleken dat het beste model voor een gepulseerde
gepakte kolom is gebaseerd op propstroom met axiale dispersie.
Een studie naar de druppelgrootte van styreendruppels in emulsies in een batch
reaktor en in een gepulseerde gepakte kolom laat zien dat vrijwel alle gemeten
druppelgroottes in de range 1-10 ~-tm liggen, hetgeen impliceert dat de kans op
polymerisatie in de druppels als verwaarloosbaar moet worden geacht. De gevonden
afhankelijkheid van de druppelgrootte van de energiedissipatie in de reaktoren toont
aan dat de gemiddelde druppeldiameter alleen bepaald wordt door opbreken van de
druppels en niet door coalescentie van de druppels. Coalescentie wordt verhinderd
door de aanwezigheid van emulgatormolekulen op het monomeer/water fasegrensvlak.
Naast polymeerchemische en reaktorkundige aspekten spelen ook colloïdchemische
aspekten een belangrijke rol bij emulsiepolymerisatieprocessen. Deeltjes- aantallen
en conversie hangen in sterke mate af van de gebruikte emulgator en van de
ionensterkte van de emulsie. De emulsiepolymerisatie van styreen geëmulgeerd met een
rosin acid soap en uitgevoerd bij hoge elektroliet- concentraties vertoont een
afname van het deeltjesaantal tijdens het verloop van de polymerisatie, hetgeen
veroorzaakt wordt door coagulatie en coalescentie van de polymeerdeeltjes. De
coalescentie van de deeltjes heeft een grote invloed op de polymerisatiekinetiek:
het blijkt dat het aantal polymeerdeeltjes in de eindlatex afuankelijk is van type
en concentratie van de emulgator, monomeer- en elektrolietconcentratie en
energiedissipatie, maar vrijwel onafuankelijk van initiatorconcentratie en
temperatuur.
T ABLE OF CONTENTS
List of symbols
Chapter 1:Jntroduction
1.1. Continuous emulsion polymerization
1.2. Specific problems of emulsion polymerization in a CSTR
1.3. A new reactor type for continuous emulsion polymerization
1.4. Contents of this thesis
1.5. References
Chapter 2: Axial mixing in a pulsed packed cqlumn
2.1. Introduetion
2.2. Theory
2.2.1. Characterization of the axial dispersion coefficient
2.2.2. The parameters <p1, <p2 and K2 2.3. Experimental
2.3.1. Solution of the dispersion equation
2.3.2. Determination of the dispersion coefficient
2.4. Results and discussion
2.4.1. Raschig rings
2.4.2. Sulzer SMV8-DN50 packing
2.4.3. Possible influence of latex properties on axial mixing
2.5. Conclusions
2.6. References
Chapter 3: Mechanism and kinetics of emulsion polymerization
3.1. Introduetion
3.2. Polymerization mechanism
3.3. Polymerization kinetics
3.3.1. Smith-Ewart model
3.3.1.1. Nucleation of polymer particles
3.3.1.2. Polymerization rate per partiele
3.3.2. Nomura !ind Harada model
1
5
11
ll
11
13
15
16
17 17
17
19
22
26
27 30
33
33
37 43
44
46
47
47
47
48
49
49
50
53
3.3.2.L Nocteation and number of formed polymer particles 55
3.3.2.2. Rate of polymerization and partiele growth 58
3.3.2.3. Average number of radicals per partiele 59
3.4. References 61
Chapter 4: Emulsion polymerization of styrene in a pulsed packed column 63
4.1. Introduetion 63
4.2. Comparison of reactor types 64
4.2.1. Partiele formation 64
4.2.2. Partiele size distributions 67
4.2.3. Molecular weight properties 70
4.3. Experimental 71
4.4. Results and discussion 75
4.4.1. Comparison of reactor types 78
4.4.2. Number of polymer particles formed 84
4.4.3. Partiele size distributions 89
4.4.4. Molecular weights 92
4.5. Conclusions 94
4.6. References 94
Chapter 5: Reactor model for the emulsion polymerization of styrene in a
pulsed packed column 97
5 .I. Introduetion 97
5.2. Plug flow with axial dispersion model 98
5.2.1. Mass balances 98
5.2.2. Kinetic equations 99
5.2.3. Solutions of the differential equations 102
5.2.4. Comparison of theory with experiments for a PPC 104
5.3. Tanks in series model 106
5.3.1. Mass balances and kinetic equations 107
5.3.2. Partiele size distributions 109
5.3.3. Comparison of theory with experiments for a series of CSTRs 113
5.3.3.1. Numbers of formed polymer particles 114
5.3.3.2. Partiele size distributions
5.3.3.3. Conversion
5.3.6. Comparison of theory with experiments for a PPC
2
117
121
123
5.4. Conclusions
5.5. References
125
126
Chapter 6: Coagulation effects during the emulsion polymerization
of styrene emulsified with a rosin 'acid soap 127
6.1. Introduetion 127
6.2. Coagulation during an emu1sion polymerization 129
6.2.1. Stability of polymer particles 129
6.2.2. Mechanisms of coagulation 133
6.2.2.1. Brownian coagulation 134
6.2.2.2. Shear coagulation 135
6.2.2.3. Brownian coagulation versus shear coagulation 136
6.2.2.4. Surface coagulation 136
6.3. Ex perimental 138
6.4. Results and discussion 140
6.4.1. Preliminary experiments 140
6.4.2. Variàtion of emulsifier concentration 142
6.4.3. Variation of initiator concentration 153
6.4.4. Variation of monomer concentration 156
6.4.5. Variation of temperature 161
6.4.6. Influence of shear rate 165
6.4.6.1. Influence of shear rate in stirred tanks,
in batch reaelions 165
6.4.6.2. lnfluence of shear rate in pulsed packed column 172
6.4.7. Variation of electrolyte concentration 176
6.4.8. Influence of residence time distribution 181
6.5. Conclusions 186
6.6. References 187
Chapter 7: Monomer droplet si zes in styrene emulsion polymerization 191
7 .1. Introduetion 191
7 .2. Liquid-liquid dispersions 192
7 .2.1. Break-up of dropiets 192
7 .2.2. Coalescence of dropiets 194
7.2.3. Simultaneous break-up and coalescence 195
7 .2.4. Energy dissipation in an agitated vessel 197
3
7.2.5. Energy dissipation in a pulsed packed column 200
7.3. EKperimental 202
7.4. Results and discussion 203
7.4.1. Droplet sizes in an agitated vessel 204
7.4.2. Infiuence of emulsifier 209
7.4.3. Droplet sizes in a pulsed packed column 214
7.5. Conclusions 216
7.6. References 217
Appendices
A.l. General solution of the recurrent equations 219
A.2. Dynamic light scattering 227
A.3. Laser diffraction speetrometry 231
A.4. Parameters for styrene emulsion polymerization 233
A.5. Length of the partiele nucleation period in a pulsed packed column 235
4
a
c
D
Dm
Dw de
dm
dmax d . nun dp
dr d p,w E
Ea E.
1
~ EP Es
eo F
f
[I]
LIST OF SYMBOLS
column cross-sectionat area
total surface area of all polymer particles
argument of Bessel function
distance between centers of two particles (chapter 6)
surface area occupied by an emulsifier molecule
number of impeller blades
impeller distance to tank bottorn
tracer concentration
impeller diameter
local conveelion coefficient (chapter 2)
molecular diffusion coefficient
diffusion coefficient
column diameter
diameter of micelle
maximum stabie droplet diameter
minimum stabie droplet diameter
diameter of polymer partiele
diameter of packing partiele
weight average diameter of polymer particles
axial dispersion coefficient
adhesion energy
activation energy for initiator decomposition
kinetic energy
activation energy for propagation reaction
surface energy
charge of a proton
feed rate
frequency of pulsation
initiator efficiency in radical formation
friction factor
acceleration of gravity
gel-effect correction factor
height of packed bed
distance between two particles (chapter 6)
initiator concentration
5
m
m
m
m
m
m
m
m2/s
kJ
kJ/kmol
kJ
klikmol
kJ
c m3/s -1 s
m
m
kmo11m3
H20
baffle width
Brownian coagulation rate
shear coagulation rate
number of mixing stages in series
Langmuir adsorption equilibrium constant
surface coagulation rate constant
Boltzmann constant
radkal desorption rate constant
rate constant of formation of initiator radicals
propagation rate constant
rate constant of terminalion
radical absorption rate constant for particles
radical absorption rate constant for micelles
column length I length of packed bed
length of impeller blade
I length of the column section in which the
[M]
N
[N]
[N]w
[N"]
[Nt]
MNlj
Na
Np
Nt
partiele nucleation takes place
overall monoroer concentration
aggregation number of a micelle
number average molecular weight
monoroer concentration in polymer partiele
weight average molecular weight
molecular weight of monoroer
number of micelles per unit volume
rotational impeller speed
number of polymer particles per unit volume
number of polymer particles calculated from d p,w
number of active polymer particles
number of dead polymer particles
number of polymer particles formed in j-th reactor
A vogadros constant
power number
number of ideally mixed tanks in series
n time-average number of radicals per partiele
n. 1
bulk concentration of ions of type i
6
m -1 -3
s .m H20
-1 -3 s .m H20
m3
m/s
J/K -1 s -1 s
m3/(kmol.s)
m3/(kmol.s)
m3t(kmol.s) 3/ m (kmol.s)
m
m
m
kmoVm3
H20
kg!m3
-3 m H20
s -1
-3 m H20
-3 m H2o
-3 m H2o
-3 m H20
m -3 H20
kmor 1
-3 m H20
Q
R
[R"]
power input
concentration of radical chains
pressure drop
Peelet-number related to the column length
Peelet-number related to the column section in
which the partiele nueleation takes place
amount of injected tracer
number of baffle plates
radical concentration
Re Reynolds number
R. I
(S]
s
T
u
rate of formation of polymer particles
overall polymerization rate
rate of polymerization in one polymer partiele
partiele radius
emulsifier concentration
stroke length of pulsation
temperature
tank diameter
time
interstitial liquid velocity
superficial velocity
mean square of the relative velocity fluctuations
between two diametrically opposite points on the
surface of a droplet
volume
attraction potential
specific volume of monomer
specific volume of polymer
repulsion potendal
volume of tank
velocity
Kolmogoroffs velocity scale for turbulence
volume of a polymer partiele
width of impeller blade
W hr stability factor for Brownian coagulation
We Weber number
7
J/s . 3
kmoVm H20
N/m2
kg
kmoVm3 H20
-1 -3 s m H20
kmoV(s.m3 H2~)
kmoVs
m
kmoVm3
m
s
mis mis
m2/s2
m3
V
m3/kg
m3/kg
V m3
mis mis m3
m
W ,, stability factor for shear coagulation s
w 0
.607
width of response curve at 0.607 height
[x+] I I . e ectro yte concentratton
Xm monomer conversion
z height * z height of partiele nucleation section
zi valency of ion of type i
Greek symbols
a.0 capture efficiency
~ partiele growth parameter
X constant (in Smith-Ewart relation)
E
~ Er.Eo
q>d
q>mon
q>pol q>l
q>2 <I>
y
TJ
energy dissipation per unit time and mass
bed porosity
permittivity of suspension
volume fraction disperse phase
weight fraction monomer in partiele
weight fraction polymer in partiele
constant ( chapter 2)
constant (chapter 2)
average fraction of liquid being subject to pulsation
shear rate
skewness of response curve (chapter 2)
dynamic viscosity
Kolmogoroffs length scale for turbulence
viscosity of the emulsion
relative viscosity (= TJe/TJsm)
viscosity of the suspension medium
volume fraction disperse phase (chapter 2)
surface potential
reciprocal thick:ness of the double layer
constant (chapter 2)
constant (chapter 2)
constant (chapter 2)
London wave length
growth rate of a polymer partiele
8
s
m
m
W/kg
F/m
-1 s
kg/(m.s)
m
kg/(m.s)
kg/(m.s)
V -1 m
V
* 't
e
kinematic viscosity
density
radical absorption rate
generation rate of radicals
surface tension
standard deviation ( chapter 2)
mean residence time
mean residence time in partiele nucleation section
fraction of the surface area of the polymer
particles occupied by emulsifier molecules
frequency (=2.1t.f)
age of a polymer partiele (chapter 5)
dimensionless time t/'t (chapter 4)
zeta potential (chapter 6)
effectiveness factor for particles relative to
micelles in absorption of radicals
effectiveness factor for radical absorption
effectiveness factor for radical absorption
effectiveness factor for radical absorption
effectiveness factor for radical absorption
Subscripts
b bulk zone
c continuous phase
CMC critica! micelle concentration
d disperse phase
f feed stream
impeller zone
j exit stream of j-th reactor
m micellar
mon monomer
p polymer partiele
pol polymer
0 feed stream
1 exit stream of first reactor
9
m2ts kglm3
krnoV(s.m3 H20)
krnoV(s.m3 H2J
N/m
s
s
s
rad/s
s
V
kmol
krnol
krnoVm
kmoVm2
kmoVm3
lO
Chapter 1. Introduetion
1.1. Continuons emulsion polymerization
Emulsion polymerization is one of the four major types of free radical
polyrnerization. Some of the main reasons why emulsion polymerization is used instead
of bulk, solution or suspension polymerization are:
- several products such as paints and adhesives are used in latex form;
- the low viscosity of the latex makes handling of the product and removal of the
heat of reaction relatively easy;
- with emulsion polymerization it is possible to produce a high molecular weight
polymer at high reaction rates.
Emulsion polymerization reacrions are mostly carried out in batch reactors. They are
easy to operate and there is a large amount of information about these reactor
systems available in literature. Recently there bas been considerable interest in
the use of continuous reactor systems for emulsion polymerization. Economie
incentives and better possibilities for controlling product quality are the main
motives in the development of continuous emulsion polymerization processes. However,
there are some limitations to the use of continuous reactors. Continuous systems are
only paying when rather long run times can he achieved. Latexes that foul badly and
cause frequent shutdowns are preferably produced in batch reactors. Likewise,
continuous reactors are not practical for product distributions which require
frequent recipe changes. On the other hand process economics tend to become more
favorable for continuous reactors as production run-times increase.
Most commercial emulsion polymerization processes consist of· a series of continuous
stirred tank reactors (CSTRs) [1-3]. The early systems comprised 10 to 15 equal
sized reactors in series. More recent processes consist of only 2 to 5 reactors in
series. Tubular reactor systems are rarely used in continuous emulsion
polymerization. Although sorne tubular reactors have been used in kinetic studies
{4-6] they have not been commercialized. Recently a continuous tubular-loop process
bas been developed and patented [7,8]. The residence time distribution of this
reactor type is nearly identical with that of a single CSTR. However a .continuous
tubular reactor offers the advantage of a large heat transfer area per unit volume.
1.2. Specitic problems of emulsion polymerization in a CSTR
The reactor system that is mostly used in continuous emulsion polymerization is a
11
series of CSTRs. Although this operation method is already, used in the co~mercial
production of rubber latices, the system has some disadvantages which prevent it to
be used on a large scale for general applications.
First there is the problem of partiele formation. In a series of CSTR's the first
CSTR can be regarded as the reactor in which the partiele formation takes place: the
seeding reactor. Because the rate of polymerization is usually proportional to the
number of polymer particles present, it is important to optimize the number of
particles that is formed in the first reactor. However, a CSTR as the first reactor
has shown to produce a much lower number of polymer particles than a batch reactor
operated under the same conditions. Nomura et al [9,101 have theoretically shown the
existence of a maximum in the number of polymer particles for styrene emulsion
polymerization at a certain low value of the mean residence time of the CSTR.
According to their theory, which was in good agreement with their experiments, this
maximum number is only 57 % of the number of polymer particles, per unit volume,
formed in a batch reactor. The same value for this maximum is obtained by Poehlein
[2 1 who based his calculation on a model of Gershberg and Longfield [11 1. This
relatively low number of polymer particles is mainly caused by the large residence
time distribution in a CSTR. This causes large particles to be mixed up with freshly
added emulsifier. As a result a large amount of the emulsifier is consumed for
covering the surface of the large particles. Therefore only part of the emulsifier
is available for the generation of new particles.
A second problem of a CSTR used for a continuous emulsion polymerization is that in
a CSTR sustained oscillations in conversion and partiele number often are observed.
These oscillations mostly result in large fluctuations in product quality with time.
Kiparissides et al [ 12,/31 suggested the following mechanism for the sustained
oscillations. The emulsifier used in an emulsion polymerization is mainly needed for
two purposes. The frrst one is the formation of emulsifier micelles from which
polymer particles are formed. The second purpose is the surface coverage of the
polymer particles ~ith emulsifier to stabilize those particles. The sustained
oscillations are. caused by a competition between the formation of micelles and the
surface coverage, in the frrst CSTR of the cascade. At the beginning of the reaction
a rapid generation of a large number of particles and surface area consumes . the
available emulsifier. The rate of emulsifier consumption for surface coverage
exceeds the feed rate of emulsifier to the reactor and the emulsifier micelles
disappear quickly. The partiele generation rate decreases and will he close to zero
for a eertaio period., The. duration of this period depends on the feed rate of
emulsifier, the washout rate of polymer particles and the growth of the total
partiele surface. Eventually the emulsifier concentration saturates the partiele
12
surface and emulsifier micelles are formed again for partiele generation. This
mechanism leads to fluctuations in the number of particles, polymerization rate and
conversion.
According to PenHdis { 14] sustained oscillations is a phenomenon which is
characteristic of the continuous emulsion polymerization of monoroers that show a
high rate of radical desorption from the latex partieles. These high rates of
desorption of radicals lead to very rapid homogeneous partiele nueleation and to low
partiele growth rates due to the low radical concentration in small particles. The
growth increases with partiele size, and it is this factor that contributes to the
instability. Rawlings and Ray {15-18] have modelled the occurrence of oscillations
during the emulsion polymerization in a CSTR. Their detailed model prediets that for
monoroers showing no desorption of radicals from the polymer particles, no
oscillations can he expected. For monoroers that show a strong dependenee of the
average numher of radicals per partiele on the partiele size (high rates of radical
desorption) the model prediets large sustained oscillations.
It was found that both problems can he avoided by replacing the CSTR by a plug flow
type reactor, that is characterized hy the absence of residence time distrihution.
For this reactor type Nomura et al {9.10] have shown that the numher of particles
per unit volume can then he increased up to the batch level. They also showed, in
accordance with results of Greene et al {19], that this can avoid the prohlem of the
sustained oscillations often ohserved in a CSTR.
1.3. A new reactor type for continuons emulsion polymerization
Designing a plug flow type reactor that is suitahle for an emulsion polymerization
is quite complicated. The liquid flow in a plug flow reactor has to he turbulent,
for three reasons:
(I) to avoid coalescence and creaming up of the monoroer dropiets (deemulsification);
(2) to prevent reactor fouling and wall polymerization;
(3) to obtain sufficient radial mixing to remove the heat of reaction through the
reactor wall and thus to avoid radial temperature profiles.
The frrst and last reasons are especially important in sealing up of the reactor
system. Because of the requirement of a turbulent flow in the reactor, it is not
feasible to use an ordinary tuhular reactor as the seeding reactor. In such a
reactor the required turhulence can only he realized at very high liquid velocities.
In emulsion polymerizations, where long reaction times are necessary to ohtain a
high conversion, this would lead to the application of a numher of extremely long
13
tubes, in parallel, which is unpr!lctical.
If we examine the plug flow type reactors that have been used recently in continuous
emulsion polymerization processes, it appears that sealing up is difficult for
almost all systems. Greene e.a. [19] have used a spiralized teflon tube, in which
they created plug flow by alternately injecting nitrogen and emulsion in plugs.
Ghosh and Forsyth [4] and Lee and Forsyth [5] used spiralized stainless steel tubes
with outer diameters of l/2-inch and l/4-inch, respectively. Lin and Chiu [20] used
a static mixer with 20 elements in a cylindrical pipe (Toray Hi-mixer) in order to
avoid deemulsification.
A new reactor type, that can be scaled up rather easily and in which the probienis of
deemulsification and heat transfer could be minimized, is a pulsed packed column
(PPC). Until now a PPC was mainly used in extraction processes [21], where it was
successful because of its ability to combine the properties of a turbulent flow and
a reasonable plug flow. In one example the PPC was used as a chemica! reactor [22].
Figure 1.1 shows a schematic drawing of a pulsed packed column. The column is filled
with a packing material, e.g. Raschig rings, of a size that is small as compared
sieve plate
packing
feed
pulsator
Figure 1.1. Schematic drawing of a pu/sed packed column.
14
with the column diameter. At the top of the column there is a gas-Iiquid interface.
The pulsator is positioned at the bottorn of the column. The most simple
configuration of a pulsator is a plunger pump from Which the valves have been
removed. The suction pipe of the plunger pump is blocked with a blind flange, and
the pressure pipe is connected to the column. The stroke length and the frequency of
the pulsation can be adjusted and are independent of the feed rate. Because of this
construction it is possible to maintain turbulent flow conditions and to keep the
monomer emulsified even at very low feed rates, while axial mixing is limited. This
makes a PPC not only suitable as a seeding reactor, but it can also he used as a
reactor for emulsion polymerizations, up to high conversions.
1.4. Contents of this thesis
In this thesis the performances of the PPC in styrene emulsion polymerization are
compared with those of the conventional reactor types: a CSTR and a batch reactor.
Especially the influence of residence time distribution on the emulsion
polymerization is exarnined.
In chapter 2 the axial mixing in the PPC is measured and modelled.
Chapter 3 gives a brief review of the mechanism and kinetics of styrene emulsion
polymerization.
Chapter 4 is dedicated to the emulsion polymerization of styrene in the PPC. A
classica! recipe was used with sodium dodecylsulfate as emulsifier and sodium
persulfate as free-radical initiator.
In chapter 5 an attempt is made to model the PPC for the styrene system that was
used in chapter 4.
A different recipe with a rosin acid soap as emulsifier and used to test the PPC, is
described in chapter 6. Rosin acid soap is an emulsifier often used in commercial
emulsion polymerization processes, especially in diene polymerizations. The first
part of Chapter 6 describes the batch kinetics, showing that Iimited coagulation of
the particles occurs during the polymerization, which strongly affects the overall
reaction rate. The polymerization of the styrene-rosin acid soap system in the PPC
is examined in the second part of chapter 6.
Finally, in chapter 7 results are presenled of the measurement of droplet sizes of
the monomer dropiets present in the styrene emulsions prepared in the reactor types
examined.
15
l.S. References
1. G.W.Poeh1ein, Br. Po1ym. J., 14, 153, (1982) 2. G.W.Poeh1ein, "Emu1sion Po1ymerization", I.Piirma ed., Academie Press, New York,
341, (1976) 20. C.C.Lin, W.Y.Chiu, J. Appl. Polym. Sci., 27, 1977, (1982) 21. AJ.F.Simons, "Steady-state and Transient Behaviour of Systems in Pulsed Packed
Columns for Liquid-liquid Extraction", Ph.D. Thesis, Geleen, The Netherlands, (1987)
22. AJ.F.Simons, Chem. Ind., nr. 19, Oct. 7, 748, (1978)
16
Chapter 2. Axial mixing in a pulsed packed column
2.1. Introduetion
Knowledge of the mixing in chemica! reactors is necessary for an optima! operation
of processes on a large scale. Considering processes in packed columns, one of the
most important physical phenomena is the axial dispersion (or axial mixing), since
this axial dispersion flattens the axial concentration profile, generally resulting
in a decrease of the performance of the process carried out in the column. For
emulsion polymerization processes the reactor performance can be expressed in terms
of numbers of formed polymer particles. This number of formed polymer particles is
strongly affected by the residence time distribution of the reactor system. For a
pulsed packed column the residence time distribution is determined by the axial
mixing.
The axial dispersion in single-phase flow through a pulsed packed column is scarcely
examined yet. Spaay et al f 1] were the first to do some modelling work in this
field. Later Simons [2] and Göebel et al [3] extended this work.
2.2. Theory
The two most simple, and therefore mostly used (one parameter) roodels for the
description of the axial mixing in packed columns are:
- the "ideally mixed tanks in series" model and
- the "plug flow with axial dispersion" model.
The first model describes the mixing in the column as being caused by several
ideally mixed tanks connected in series. The parameter used for the description of
the mixing behaviour is the number of mixed tanks.
The second model explains the mixing as being caused by plug flow on which some
axial dispersion is superimposed. The dispersion can be considered as a process
analogous to diffusion and is characterized by a dispersion coefficient E, which 1s
an equivalent of the molecular diffusion coefficient D. The axial dispersion is
mostly described by the Peelet number, P~:
(2.1)
where u stands for the mean velocity of the liquid in the interstitial space and L
for the length of the packed bed. A value of u can be obtained from the superficial
17
liquid velocity u0 with:
(2.2)
m which eb represents the bed porosity.
For PeL >> l (e.g. PeL > 10) the two models are practically equivalent, so that the
axial mixing can be described by a series of Nt ideally mixed tanks [4}, where:
(2.3)
Although in case of low backmixing both models are mathematically equivalent
approximations for the mixing behaviour, only the plug flow with axial dispersion
model gives physical insight into the mixing process in the column.
A mass balance for a tracer component over a short distance (ax) of the column gives
the so-called dispersion equation (figure 2.1):
ac 8f
2 E a c ac ·:-z u.ax a x
where t is the time and x is the distance.
x C(x)
U flow
x+6x
C(x+~x)
(2.4)
Figure 2.1. Schematic drawing of a small part 6x of the column.
Solutions of this (second order) differential equation can be used to predict the
performance of the column with regard to tracer experiments. The results of these
18
tracer experiments can be used to determine the axial dispersion coefficient.
2.2.1. Characterization of the axial dispersion eoemeient
One of the most striking characteristics of the dispersion coefficient m pulsed
packed columns is a drop in E when the pulsation is increased starting from zero
{3]. After achieving a minimum value, E increases with increasing pulsation velocity
(figure 2.2, based on our experiments). The pulsation is mostly expressed as a
so-called pulsation velocity, i.e. the product of the stroke length of pulsation, s,
and the frequency of pulsation, f.
- 3 00
............ N
8 -.... 2 0 ........
....
w
QL---~----~--~----~----
0 2 3 4 5
s.f * 102 (m/s)
Figure 2.2. Experimentally determined dependenee of the axial dispersion coefficient
on the pulsation velocity (sf), at a constant interstitial velocity u.
For the characterization of E the axial dispersion in an empty tube is considered
frrst. Aris [5} found that for a constant molecular diffusion coefficient the axial
dispersion coefficient follows from:
E
2 2 "o· u .de Dm+ -...,o....--m-- (2.5)
19
where:
Dm = molecular diffusion coefficient
de "" column diameter
u = average interstitial velocity
KO constant
The dispersion coefficient is determined by the molecular diffusion on the one hand
and by the radial velocity profile on the other hand. The second term on the
right-hand side of equation (2.5) is called the Taylor diffusion coefficient and
represents the influence of the combination of radial molecular diffusion and · the
velocity profile on axial dispersion. For laminar flow KO has a value of 1/192 [3}.
In packed beds the disorientated movement of liquid elements through the bed (Eddy
diffusion) should also he considered. One can account for these motions by
introducing a local conveelion coefficient D (or eddy diffusivity) [3}. In fact,
both the molecular diffusion coefficient and the local conveelion coefficient have
to he added. However, since D >>Dm (Dis of order w-4 m2/s and Dm of order w-9
m2/s), the molecular diffusion coefficient is negligible. If the column diameter de
of equation (2.5) is replaced by K 1.dr, (where dr is the diameter of a packing
particle) the following equation results:
E (2.6)
where:
D = local convection coefficient
d = characteristic diameter of a pacldng partiele r 2
1<2, Ko·KJ
It is assumed that the local convection coefficient D is related to u and dr:
(2.7)
where <pi is assumed to he constant for turbulent flow. Combination of (2.6) and
(2.7) gives:
(2.8)
20
Several investigators [6,7] have found this proportionality between E and u.dr
Figure 2.3. A.xial dispersion coefficient as a function of the product u.d for r packed columns, in the absence of pulsation.
Raschig rings (our experiments): (D) d = JO mm; (A) d = 6 mm. r r The dashed lines indicate the results for granular beds {6,7].
For pulsed packed columns the contributions of the pulsation velocity (s.f) and the
liquid velocity (u) originating from the net mass flow through the column, to the
local convective diffusion coefficient are assumed to be additive. This results in
the following relation for D in pulsed packed columns:
(2.9)
where the term <p2.s.f.dr represents the influence of pulsation. Also <p2 is assumed
to be constant. Later in this chapter it will be shown that this is not always so.
Combination of the equations (2.6) and (2.9), as proposed first by Göebel et al {3],
gives:
2 2 1C2.u . dr
E = <pl.u.d + <p2.s.f.d + <p d <p f d r r l.u. r+ 2.s .. r
21
(2.10)
or in a dimensionless form:
(2.11)
Equation (2.11) describes the behaviour of E corresponding to figure 2.2. The
initial decrease of E is caused by an improved radial mixing. This diminishes the
contribution of the velocity profile to the axial dispersion. The contributions of
the separate terms of equation (2.11) to the axial dispersion coefficient are shown
in figure 2.4.
s * t 1 u
Figure 2.4. Dimensionless dispersion coefficient according to equation (2.llb).
a <f'J + <p2(s.j)lu; b = Kl(<f'J + <p2(sf)lu); c = El(u.d/
2.2.2. The parameters <f'p <p2 and K2
Equation (2.11) describes the axial mixing coefficient as the sum of the influence
of net flow, pulsation, and the radial velocity profile. The contribution of each
separate term in equation (2.11) to the axial dispersion is determined by the
parameters <p1, <p2 and ~·
Göebel et al [3], who first proposed equation (2.11), considered all parameters <p
and K as constants. These authors determined the parameter ~ from the minimum value
of E (Emin): equating lhe first derivative of expression (2.11) to zero:
22
leads to the following relation between s.f/u, cp1 and cp2 :
s.f u
Combination of the equations (2.11) and (2.13) gives:
E . r--' min = 2.'1/ K~ ~ 2
(2.12)
(2.13)
(2.14)
With this equation, the parameter 1e2 can be found from experimental data.
The parameters cp1 and cp2 were obtained by curve-fitting of experimental determined
values of E to equation (2.11). Göebel et al did not mention any dependenee of these
parameters on the pulsation velocity (neither on the stroke length nor on the
frequency). The pulsation range in which Göebel et al have measured was close to the
minimum E-value, i.e. at low pulsation velocities.
A slightly different expression for E than that given by equation (2.11) was used by
Spaay et al [ 1 ]:
(2.15)
The Taylor diffusion term was not taken into account by these authors. Therefore,
equation (2.15) is only valid for high pulsation velocities, and this is indeed the
range where Spaay et al did most of their measurements. For cp2 a characteristic
dependenee on the stroke length of pulsation was found. This is shown in figure 2.5.
The coefficient cp2 frrst increases with increasing stroke length and finally a
constant value cp2 is attained. ,max
According to Spaay et al [1] the coefficient cp1 may be given as a function of both
cp2 and the pulsation velocity (s.f):
(2.16)
23
0.70 0 0
0 .. .. • 0.60 • 1 ....
00 0 0 0 (\1 0.50 •
B-0.40 0 __,
~ (I) ..... 0.30 0
(.) ..... - 020 -(I) ' 0 0.10 ' ' (.) ' ' '
0.00 0 2 3 4 5
s {cm)
Figure 2.5. The coefficient <p2 as a function of the stroke length of pulsarion (Data
of Spaay et al {11).
(0) dr = 12 mm and de= JO cm; (T) dr =JO mm and de= 5 cm; (Jit.) dr = 8 mm and de
= 5 cm; (+) dr 25 mm and de = 22 cm; (D) dr = 25 mm and de JO cm.
Neither a mathematica! expression nor a physical interpretation of this function bas
been presented. The results of Spaay et al [ 11 also indicated that the column
diameter had no influence on the axial dispersion.
The different interpretations of <pl' <p2 and ~ by Göebel et al [31 on the one hand
and Spaay et al [ J 1 on the other hand makes a closer examination of these parameters
necessary. Göebel et al [31 considered <pl' <p2 and ~ as independent parameters.
However, this may not be the case. Equation (2.11) should also be valid in the
absence of pulsation, and changes into equation (2.8), which shows that ~ and <p1 are interdependent. From experiments with pulsation ~ can be determined by tak:ing
the minimum of E/(u.dr) as a function of (s.t)/u, according to equation (2.14), <pl
can then be determined from equation (2.8).
Examination of the parameter <p2 requires a consideration of the mtxmg caused by
pulsation. The axial dispersion can be supposed to consist of contributions of a
random movement of the liquid, reflected by the local convection coefficient D, and
a contribution of the radial velocity profile, represented by the Taylor diffusion
term. The local conveelion coefficient is determined on the one hand by the diameter
24
of the packing particles. This diameter is a measure for the displacement of liquid
elements (in an other direction than the original direction) at the moment of the
passage of the packing particles. On the other hand D is determined by the velocity
of the liquid elements that pass the packing particles. This is a measure for the
intensity of mixing of liquid elements in the separate streamlines. The column can
be regarded as a gathering of small channels between packing particles. Let us
suppose, that mixing of the liquid elements mainly occurs at locations where liquid
elements of separate streamlines can encounter, i.e. the beginning or the end of
each channel. In such a consideration the dependenee of the local convection
coefficient on both velocity and displacement is still valid, since the intensity of
mixing of the streamlines is determined by the velocity at which the streamlines
encounter. The length of the channels then determines the distance over which the
separate liquid elements cannot mix. Por a pulsed packed column it may be proposed
that part of the liquid will flow out of a channel, while the other part of the
liquid remains segregated in the channel (figure 2.6).
column
__l d,
Raschig nngs
Figure 2.6. Schematic drawing of a Raschig rings packing.
Let us suppose, that the pulsator is in the lowest position and can go only a
distance s in the upper direction. In figure 2.6 it can be seen that the liquid
25
elemtmts in the shaded part cannot flow out of the packing ring and can therefore
not mix with other liquid elements. This means that the parameter q>2 of equation
(2.9) should he represented as follows:
q>2 a + b.cl:> (2.17)
where cl:> stands for the fraction of the liquid that can flow out of a channel during
a pulsation cycle. This fraction cl:> is a function of the stroke length s. Por the
case that s < d , cl:> can he given by: r
s a;: (2.18)
Por s ~ dr no liquid elements remain segregated in the channels of the packing
particles, and cl:> adopts the value one.
2.3. Experimental
The axial mixing in a pulsed packed column was investigated by measuring the
response curves of pulse injections of a tracer solution. The tracer was an aqueous
sodium chloride solution (concentration: 1 kglm3). About 2 cm3 liquid was injected
per measurement.
Three different packing types were investigated: two random packings (glass Raschig
rings: d 6 mm and d 10 mm) and one structured packing (stainless steel Sulzer r r
SMV8-DN50 intemals). The pulsed packed column had a height of 5 m. The intemal
diameter of the column was about 5 cm. Göebel et al [3] recommended a maximum d!dc
ratio of 0.2 to avoid an irregular stacked packing in the column. The bottorn and top
section of the column are shown in tigure 2.7.
The pulsation is transmitted to the column by means of a plunger, which is situated
2 cm below the packed section of the column. Injection of the tracer occurred 2 cm
above the plunger, exactly at the beginning of the packed section of the column. The
feed also entered the column at this height. At the end of the packed section of the
column the sodium chloride concentration was measured conductometrically. The
measured conductance at the top of the column was proportional to the concentration
of the sodium chloride for the experimental conditions investigated ( < 50* w-3
kg/m\
26
packing
injection
dateetion cell
sieve plate
sieve plate
Figure 2.7. Bottom and top section of the pulsed packed column used for tracer
injections.
2.3.1. Solution of the dispersion equation
Solution of the dispersion equation (2.4) depends on the boundary values that are
chosen. These boundary values are determined by the methods of injection and
detection as pointed out by Kreft and Zuber (8].
Detection was carried out by means of the measurement of the electrical conductivity
from which the tracer concentration can be calculated. Because the volume of the
conductivity cell is open for backmixing the detection point may be considered as an
open boundary. The open boundary at the end of the column can be expressed by:
lim c 0 (2.19) x~oo
27
Characterization of the injection is not easy. In a simplified consideration an
infinitesimally small electrolyte layer at the height of injection can be assumed.
Such a situation can be described mathematically with a Dirac S function. However,
the injection point is located some distance above the plunger, and combined with
pulsation it is not clear whether the boundary is open or closed. An open boundary
allows backmixing at the lower side of the injection point. So part of the
electrolyte layer will diffuse upstream immediately after injection. A closed
boundary does not allow backmixing. A closed boundary can be considered as an
impenetrable wall. In the case of a pulsed packed column the plunger may be such a
wall. Such a problem can be described mathematically with a Dirac S function in time
for a closed boundary and a Dirac function in place for an open boundary [8]:
c(O,t) = ~.ö(t)
c(x,O) = e~.A.S(x)
where:
( closed boundary)
(open boundary)
Q = amount of injected tracer
F feed rate
A = cross-sectional area of the column
eb = bed porosity
(2.20)
(2.21)
lt is not clear a priori which boundary condition has to be chosen. It appeared that
the open boundary corresponded best to our experimental results. Solution of this
Equation (2.22), however, represents a skewed response curve. For such a skewed
31
curvè one can still use tmax and w 0
.607
to determine the mean and the deviation. The
relation between the modus, t (maximum), and the median, 't (mean), can be ma x calculated by differentiation of equation (2.22) with respect to time and setting
the first derivative to zero. This results in:
~~[------,..------2 L 2_ /I L - 2.E.tmax
* t 2 l ma x (2.27)
where L stands for the length of the packed section of the column. The factor y
represents the skewness of the curve with regard to a Gauss curve, since we can
write:
(2.28)
Analogous to the tirst moment of time, which is determined from tmax by using a
factor y, it is supposed that the second moment of time can be determined from
w by using a factor 1'. The function representing the dimensionless response 0.607
curve can be given by rewriting equation (2.22):
c' ;1 t • { 2 [ ~ax J . exp Ó. (2.29)
where c' = c(t)/c(tmax)
A relation between 0' and w is difficult to give, because a numerical 0.607
calculation is necessary for the solution of equation (2.29). Therefore an empirica!
relation between 0' and w bas been developed. With chosen values for E, L and u 0.607
the residence time distribution can be completely detined. The mean residence time
follows from L.~.NF (by detinition). The skewness factor y is then given by
equation (2.28) and 0' by equation (2.23). Using equation (2.29) a numerical
calculation leads to w . Now a wel! detined relation between 0', y and w is 0.607 . 2 0.607
obtained. In tigure 2.11 the empirica! relation between y w and 0' is shown. 0.607
From this tigure it follows that:
2cr = 1.031-w 0.607
(2.30)
32
4400r-------------------------~
l'-0
3520
~ 2640 0
1760
880
f.
,/i
I I
,I. I
,t,.'
I I
I
,Á/
I I
I I
I
,Á
I I
I lb.
I
/ I
I
I I
I
~~ I
/
0&---~~--~----~----~--~
0 440 880 1320 1760 2200
u (sec)
Figure 2.11. Empirica/relation between o and Iw . 0.607
2.4. Results and discussion
The results presented bere are those of two pack.ing types: glass Raschig rings and
stainless steel Sulzer SMV8-DN50 internals. First the Raschig rings will be
examined, since this packing type is lhe only one described in detail in lhe
literature. Then a comparison will be given between lhe results found with the
Raschig rings and the Sulzer packing.
2.4.1. Raschig rings
The mixing behaviour in a pulsed packed column can be visualized when E/(u.dr) is
plotted as a function of (s.f)/u. The course of the experimentally observed
relationship between E/(u.d) and (s.f)/u as presented in figure 2.12 agrees with
that predicted by equation (2.11). Figure 2.12 shows that for a 10 mm Raschig rings
packing E/(u.dr) passes through a minimum on increasing the value of (s.f)/u. For
(s.f)/u > 5 a linear relationship exists between E/(u.d) and (s.f)/u when the
stroke length is kept constant. The slope of the resulting lines is strongly
33
20.------------------------,
• 15
30
s.f/u Figure 2.12. Axial dispersion coefficient as a function of the pulsation velocity
for Raschig rings (dr = JO mm).
Stroke length of pulsation: s = 0-14.0 mm; Frequency of pulsation: f = 0-35 s-I;
lnterstitial velocity: u = 1.3-4.6 mm/s.
Experimental data: (e) s = 14 mm; (0) s 10.5 mm; (Ji..) s = 7 mm; ('V) s = 5.6 mm;
( .6) s = 3.5 mm; (Y) s = 0 mm.
Values according to equation (2.11) calculated with fitted parameters <p1. <f>z and K2:
(---} s = 14 mm; (-----) s = 10.5 mm; ( ..... .; s = 7 mm; (-·-·-) s 3.5 mm.
dependent on the stroke length of pulsation, which was varled from 3.5 - 14 mm.
Figure 2.13 shows that for the 6 mm Raschig rings the slope of the lines
representing the variation of E/(u.dr> as a function of (s.f)/u is independent of
the stroke length for s > 7 mm.
The results of the figures 2.12 and 2.13 are used to delermine values of the
parameters <p1, <p2 and ~· In figure 2.14 the experimental determined axial
dü;persion coefficient E in the absence of pulsation (s.f 0) is plotted as a
function of u.dr. Linear regression of the experimental values of E to equation
Figure 2.13. Axia/ dispersion coefficient as a function of the pulsation velocity
for Raschig rings (d = 6 mm). r Symbols and /ines represent the conditions mentioned in figure 2.12.
2.00 r---------------,
.......... 1.50 Cl)
.............. N
8 -... 1.00 0 ......
* ~ • 0.50 0
0 • 0
• 0.00
0.00 0.50 1.00
u*dp * 104 (m 2/s)
Figure 2.14. The axia/ dispersion coefficient as a function of u.d in the absence r
of pu/sation. Raschig rings: (0) d = JO mm; (111.) d = 6 mm. r r
35
The value of ~ can be determined by takjng the minimum of E/(u.d~ as a function of
(s.f)/u, according to equation (2.14). The value of q>1 is obtained from equation
(2.31). Both calculated values for <p1 and ~ are presenled in table 2.1 together
with results of Göebel et al (3}. A significant dependenee of <p1 on q>2, as supposed
by Spaay et al f 11 could not be observed. As stated earlier, the mutual dependenee
of the parameters <p1 and q>2 reported by these authors may have been caused by
neglecting the Taylor diffusion term. Our experiments showed that q>1 and ~ may be
regarded as constants within the experimental error.
Table 2.1. Values of the parameters K2 and q> r
•
our experiment s Göebel et al (31
parameter d = 6 mm dr = 10 mm dr 10 mm r
<p1 0.40 ± 0 . 05 0.24 ± 0. 05 0.57
)(2 0.64 ± 0. 05 0.42 ± 0. 05 0.27
Figure 2.15 shows that the experimentally determined coefficient <p2 depends on the
stroke length of pulsation, as was shown earlier by Spaay et al (11. For low values
of the stroke length there is a linear relationship between <p2 and s. For rather
high values of s, <p2 remains constant at a value q>2,max' This maximum va1ue of q>2 is
attained when the stroke length of pu1sation approaches the diameter of a packing
particle.
Our own measurements and the (recalculated) data of Spaay et al f 11 show a sirnilar
relationship between <p2 and s/dr. Two ranges of s can be observed: s < dr and s > dr. The first range is characterized by a coefficient q>2 which linearly depends on
s/dr. Measurements with Raschig rings of size 6 and 10 mm obeyed the empirica)
relation:
<p2. = 0.2 + 0.32.<f- (2.32) r
The recalculated results of Spaay et al (11 for Raschig ringsof size 8 - 12 mm gave
about the same relation. The second range is characterized by a constant value of
q>2. For this range our measurements showed:
q>2 = 0.60 ,max (2.33)
36
1.00 r---------------,
- 0.80 I -
....., $:; Q) ·-() ·---Q) 0 ()
0.60
0.40
0.20 ' ' ' '
' ' ' '
' ' ' ' '
• " ;-----=.:-- •
'
' ' ' '
,-------
0.00 '-----..L.-----'------'
0 2 3
s/dp (-)
Figure 2.15. The coefficient q>2 of the pulsation term ( equation (2.1 1)) as a
function of the ratio sldr. Experimental data of Raschig rings compared with results
from the fiterafure (Spaay et al [1]).
Experimental data: ('!f) dr = JO mm; (•) dr ::: 6 mm.
Lirerature values: (--) dr 8-12 mm; (-----) dr = 25 mm.
which value agrees well with the value of Spaay et al [ 1] for Raschig rings of size
8 - 12 nun. A further increase of the stroke length of pulsation showed to have no
significant influence on q>2, not even in the case s > n.dp where n :::: 1,2,3, ...
2.4.2. Sulzer SMV8-DNSO packing
The Raschig rings can be considered as a (completely) randomly orientated packing.
Therefore, the distribution of the channels in and between the packing rings is also
random. Contrary to these random packings also structured packing types are
available. In such a packing type the liquid is forced to flow through equal
geometrie channels. The Sulzer SMV8-DN50 is such a structured packing type (figure
2.16).
37
Figure 2.16. The Sulzer SMV8-DN50 column internal. (a) side view of packing element.
(b) top view of packing element. (c) complete stacking of internals in the column.
Figure 2.17. Schematic view of the mixing behaviour in a Sulzer SMV packing
(commercial information of Sulzer, Winterthur).
From the left to the right: stacking of the internals; sectionol view of the flow
pattern; plan view of the flow pattern.
38
The Sulzer SMV8-DN50 static mixer packing is built up of a limited number of
stainless steel elements (intemals) that are placed on top of each other. Each
element consists of a number of corrugated sheets of stainless steel. The waves of
the separate sheets make angles of 45° with the axis of the column. The sheets are
attached to each other in such a way that the waves interseet crosswise. Figure 2.17
shows the orientation of the internals in the column. The elements are placed in the
column in such a manner that the corrugated sheets of each element are perpendicular
to those in the nearest neighbour intemals. This way of stacking causes a flow
pattem represented in tigure 2.17. The mixing behaviour of a structured packing is
a result of the flow pattem. Because the liquid is forced to flow in radial
direction by zigzag channels, an intensive radial mixing will be achieved. Contrary,
in axial direction the mixing will be rather low, since all channels have equal
angles of 45° with the axis of the column and of 90° with the channels of the
neighbouring sheets.
6
2
0'------'-----'-----'------l 0 10 20 30 40
s.f/u Figure 2.18. Axial dispersion coefficient as a function of the pulsation velocity
for Sulzer SMV8-DN50 internals.
Stroke length of pulsation: s = 0-9.6 mm; Frequency of pulsation: f = 0-3.5 s·1;
lnterstitial velocity: u = 1.3-4.6 mmls.
Experimental data: (e) s = 9.6 mm; (0) s = 7.2 mm; (ltt.) s = 4.8 mm; (V') s = 3.8
mm; (!:::.) s = 2.4 mm; (?) s = 0 mm.
Values according to equation (2 .11) calculated with fitted parameters f.PJ, (.{)2 and K2:
(--) s = 9.6 mm; (-----) s = 7.2 mm; (··· .. ) s = 4.8 mm; (-·-·-) s = 2.4 mm.
39
In figure 2.18 the resuhs of axial m1xmg experiments in a pulsed packed column
with Sulzer SMV8-DN50 internals are collected. In this figure the width of a wave in
a corrugated sheet has been chosen as the characteristic diameter dr of the packing
elements (dr = 10 mm, figure 2.19). Just as for Raschig rings a minimum E-value can
I :"' .... ------1 I
d r -----~--"'
Figure 2.19. Characterislic diameter of the Sulzer SMV8-DN50 packing.
20 20 a
• 15 15
- -c.. c.. "0 "0
z 10 :I 10 -......... ......... l'tl l'tl
5 5
0 0 5 10 15 20 25 30 5 10 15 20 25 30
s.f/u s.f/u
Figure 2.20. Axial dispersion coefficient as a function of the pulsation
for the Sulzer SMV8-DN50 packing and for the Raschig rings packing ( dr
(a) Sulzer SMV8-DN50 packing. (b) Raschig rings: dr = JO mm.
All lines and symbols are according to the figures 2.12 and 2.J8.
40
velocity
JO mm).
be observed at low pulsation velocities. For (s.f)/u > 5 also a significant
influence of the stroke length of pulsation on the axial dispersion coefficient can
be seen.
Comparison of the results of the Raschig rings and the structured packing
(figure 2.20) leads to the conclusion that the axial mixing coefficients E in
the Sulzer SMV8-DN50 packing are much lower than those for the randomly
orientated packing (under the same experimental conditions).
The absolute values of the axial dispersion coefficient for the Raschig rings and
the Sulzer packing are given also for comparison in table 2.2. The minimum value of
the dispersion coefficient is determined from the minimum of the E/(u.dr) vs.
(s.f)/u - curve. The maximum measured value of E is taken at a pulsation frequency
of 3.5 s- 1, a pulsation stroke length of 9 mm and an interstitial velocity of 1.3
mm/s. The values of table 2.2 show that the axial dispersion coefficient for the
Sulzer internals is roughly a factor 3 lower than that for the Raschig rings.
Table 2.2. Minimum and maximum measured axial dispersion coe.fficients
for the Raschig rings and the Sulzer SMV8-DN50 înternals.
packing t ype E . mm * 104 (m2/s) Emax * 104
(m2/s)
Sul zer SMV8-DN50 0.04 0.57
Raschig r i ngs
d = 10 r mm 0.17 1. 73
dr = 6 mm 0.12 1.24
E1nax determined at: f = 3.5 s-1; s = 9 mm; u = 1.3 mmls.
Emin determined from the minimum of the El(u.d,J vs. (s.j)lu curve.
If the width of a wave (figure 2.19) is taken as a characteristic length
corresponding to dr in equation (2.11) the following values for K2 and <p1 can be
obtained for dr 10 mm:
K2 ::: 0.71
<pl = 0.80
41
For ep2 relation (2.34) can be derived:
<p2 = 0.1 + 0.04.s/dr (2.34)
Although the dispersion coefficient can be described well with above parameters for
(s.f)/u > 5, a deviation between the theoretica! predictions by equation (2.11) and
the experimental data is observed for (s.f)/u < 5 (see figure 2.18). The
disagreement between physical predictions and experimental data at pulsation
veloeities for (s.f)/u < 5 is possibly caused by the way of stacking of the packing
internals in the column. It appeared that because of the rigid structure of the
Sulzer packing four large 'holes' near the wa11 of the column remained unoccupied
with packing (see figure 2.21). The liquid elements flowing through these 'holes'
will not properly mix up with other liquid elements at low pulsation velocity, and
wiJl leave the column by this shorter route thus increasing the axial dispersion.
column wall
internal empty hole
Figure 2.21. Cross-sectionat view of a Sulzer internal, placed in the column.
From the experimenta1ly determined correlation for the <p2 values obtained with the
Sulzer packing, as given by relation (2.34), it appears that the stroke length of
pulsation has a very small influence on axial mixing. Probably the flow inside the
packing elements is strongly segregated. If the flow through the channels in the
axial direction is assumed to he completely segregated, the direct neighbourhood of
the column wall is the only location in the column where axial mixing of fluid
42
elements with different residence times can be expected. The length of a channel in
a Sulzer intemal can be given by de.~' where de stands for the column diameter
(= 54.0 mm). Reptacement of dr in equation (2.27) by de.~ gives:
s 'P2 = 0.1 + 0.29.--
dc.~ (2.35)
This correlation shows good agreement with the relation for the Raschig rings
pacldng (relation (2.32)). From these considerations it can be concluded that axial
mixing probably mainly occurs in the direct neighbourhood of the column wall,
because axial mixing of fluid elements with a different residence time can be
expected to take place only there. This would imply that in our case we could better
take de.~ as the characteristic lengthof the Sulzer SMV8-DN50 packing. However,
to prove this supposition it is necessary to do experiments with columns of
different diameters, which we have not done.
2.4.3. Possible influence or latex properties on axial mixing
Assuming that the monomer dropiets and the polymer particles behave like rigid
spheres, the viscosity can be calculated by Einsteins equation ( 10]:
TJr = 1 + 2.5 \jf
where:
TJr = relative viscosity (= TJ./TJc)
Tie = viscosity of the emulsion
Tic = viscosity of the continuous phase.
\jf = volume fraction disperse phase
(2.36)
According to Einsteins equation the viscosity for an emulsion is expected to be
higher than that of the continuous phase. At a volume fraction of the monomer of 30
% (a so-called low solid recipe) an increase in relative viscosity of a factor 1.8
can be expected. Einsteins equation, however, gives not very accurate predictions
above 25 % dispersed phase. A more exact relation for high disperse phase contents
is given by Krieger and Dougherty (11]:
(2.37)
43
where \jfmax stands for the maximum volume fraction possible for the disperse phase.
Using the relation of Krieger and Dougherty and assuming \jfmax = 0.74 (the limiting
volume fraction at which the viscosity becomes infinite for uniform spheres) the
viscosity becomes a factor 2.6 higher than that of pure water. In the literature no
dependenee has been reported of the axial dispersion on the viscosity for unpulsed
packed columns for viscosities between 0.95*10-3 and 28*10-3 kg/(m.s) (Ebach and
White [12]).
The monomer and polymer phase both flow cocurrent. Both phases are present as very
small spheres: the polymer particles being w-8 - w-7 m and the monomer droplets,
w-6 - w-5 m. The axial dispersion coefficient is of the order of magnitude of w-4
m2/s, and much larger than the Brownian diffusion coefficients of the monomer
dropJets and polymet particles, which are of order. w- 13 m2ts and w-Il m2ts
respectively, if calculated with the Stokes - Einstein relation:
(2.38)
with DBr is the Brownian diffusion coefficient, kb is the Boltzmann constant, T is
the absolute temperature, TJ is the dynamic viscosity and dp is the diameter of the
particles.
Because the axial dispersion coefficients are relatively large and the particles in
emulsion polymerization are relatively smal!, and there is no dependenee to be
expected of the dispersion coefficient on the viscosity for emulsions up to 30
volume % disperse phase, we can easily assume that the axial mixing behaviour during
'low solid' emulsion polymerization in the pulsed packed column is the same as for
the tracer experiments.
2.5. Conclusions
For single phase flow in a pulsed packed column it has been shown that the residence
time distribution can be described by a solution of the dispersion equation for open
boundaries:
44
_ L . { L2.(1 _ t/t)2} f(t) - j , . exp - 4 E t
t. 41tEt · ·
where:
= residence time
't = mean residence time
L = column height
E = axial dispersion coefficient
f(t) = residence time distribution
The axial dispersion coefficient E is determined by three separate effects:
an effect of the nett flow rate;
- a contribution of the pulsation;
- an effect caused by the radial velocity profile.
These contributions are discounted in the relation:
2 2 K2.u .dr
E = <Pt·u.d + <P2.s.f.d + <P d + <P f d r r l.u. r 2.s .. r
(2.39)
(2.40)
The parameters <Pt and "2. may be regarded as constants, where "2. is related to the
column diameter.
The parameter <P2 depends on the fraction of the liquid that is subject to mixing by
pulsation. This fraction depends on the stroke length of pulsation and on the
characteristic length of the packing. At large stroke lengtbs the fraction is equal
to 1 and <P2 adopts a constant (maximum) value <P2 : ,max
(2.41)
<P2,max "" 0·5 (2.42)
Experiments in a column packed with Raschig rings and a column packed with Sulzer
SMV8-DN50 internals agree well with this physical description. For the Raschig rings
the length of a packing ring can be taken as the characteristic length. It appeared
that the characteristic length for the Sulzer SMV8-DN50 packing is the length of a
channel of the packing, being equal to dc.vr.
The axial dispersion in the Sulzer packing was much lower than in the Raschig rings
packing, which could be attributed to the ordered structure of the Sulzer packing.
45
2.6. References
1. N.M.Spaay, A.J.F.Simons, G.P.ten Brink, ISEC 71, Proceedings of the International Solvent Extraction Conference, J.C.Gregory, B.Evans, P.C.Weston, eds., Society of Chemica! Industry (London), (1971), pp. 281-298
2. A.J.F.Simons, "Steady-state and Transient Behaviour of Systems in Pulsed Packed Columns for Liquid-liquid Extraction", Ph.D. Thesis, Geleen, The Netherlands, (1987)
3. J.C.Göebel, K.Booij, J.M.H.Fortuin, Chem. Eng. Sci., 41, 3197, (1986) 4. O.Levenspiel, "Chemica! Reaction Engineering", John Wiley, New York, (1972) 5. R.Aris, Proc. Royal Soc., A235, 67, (1956) 6. E.J.Caims, J.M.Prausnitz, Chem. Eng. Sci., 20, (1960) 7. G.L.Jacques, T.Vermeulen, cited in ref.6 8. A.Kreft, A.Zuber, Chem. Eng. Sci., 33, 1471, (1978) 9. O.Levenspiel, W.K.Smith, Chem. Eng. Sci., Q, 227, (1957)
Chapter 3. Mechanism and kinetics of emulsion polymerization
3.1. Introduetion
Emulsion polymerization is a commonly applied technique of free radical
polymerization. The following elementary steps are important: radical forrnation,
propagation and termination.
At the moment when the reaction starts the emulsion consists of two phases, a
continuous phase (mostly water) and a disperse monomer phase. It is typical of an
emulsion polymerization that the initiator and emulsifier (soap) are good soluble in
the continuous phase. Formation of radicals then takes place in the continuous
phase, while propagation occurs in a separate polymer phase. This polymer phase is
formed during the polymerization as a third phase consisting of very small
monomer-swollen polymer particles (50 - 200 nm). The kinetics and mechanism of
emulsion polymerization are essentially different from those of suspension, salution
and bulk polymerization.
3.2. Polymerization mechanism
The reaction mechanism of emulsion polymerization includes at least two steps:
nucleation of polymer particles and growth of the nucleated particles.
Considering partiele nucleation (interval I of the polymerization), three different
mechanisms of partiele nucleation can be distinguished. The first one is homogeneaus
nucleation. This mechanism is aften observed in soap-poor systems and for monomers
that are reasonably soluble in the continuous phase. Radicals generaled in the
continuous phase react with dissolved monomer molecules to form an oligomeric
radical which precipitates from the salution at a critica! chain length to form a
stabie latex partiele [ 1,21. When these primary particles are not stabie they wil!
coagulate with other primary particles until a stabie polymer partiele is forrned
[3 1. The latter mechanism is aften referred to as coagulative nucleation.
However, the most familiar mechanism is the micellar nucleation, being effective at
emulsifier concentrations above the çritical m.icelle çoncentration (CMC). Radicals
generated in the continuous phase enter monomer-swollen emulsifier micelles and
rapidly polymerize the solubilized monomer, forming a monomer-swollen polymer
partiele [4,51. The radicals entering the micelles may be initiator radicals [61 or
oligomeric radicals [71. It is generally accepted that partiele nucleation stops at
the moment of disappearance of the emulsifier micelles.
47
Under certain extreme circumstances it is possible that also the monomer dropiets
become effective in radical absorption: the third mechanism of nucleation [8,9 1. Such a mechanism, however, requires a large total surface area of the droplets,
corresponding to very small droplet sizes. The reason why at most circumstances the
monomer dropiets hardly absorb radicals can he explained by the fact that their
total surface area norrnally is a factor 104 to 105 smaller than the total surface
area of the micelles.
The growth process of the polymer particles is deterrnined by the propagation
reaction on the one hand, and by the swelling of the particles with monomer on the
other hand. Two stages can he distinguished during the growth of the polymer
particles [4 ,51. The fi.rst stage (interval II of the polymerization) is partiele
growth in the presence of a separate monomer phase (the monomee droplets). Because
the rate of diffusion of monomee from the dropiets to the growing particles is rapid
as compared with the rate of polymerization, a constant equilibrium concentration of
monomee in the polymer particles can he maintained. Therefore, the polymerization
rate in the particles will he constant during this stage (as long as there is no
significant radical desorption).
In the last stage (interval lil of the polymerization) the separate monomer phase
has disappeared and the monomer concentration in the polymer particles decreases,
which results in a decrease in the propagation rate. At high conversions the
viscosity of the particles increases drastically. The diffusion of radicals in the
particles becomes slower and therefore the rate of terrnination may decrease. The
rate of polymerization is then deterrnined by the relatively strong decrease of
terminalion with regard to propagation, and thus may effectively increase under
certain circumstances. This effect is called the Trommsdorff- or gel-effect.
3.3. Polymerization kinetics
In this section a brief review will he given of the emulsion polymerization kinetics
in a batch reactor. Because the polymerization kinetics in a batch reactor include
all elementary reaction steps, a description of the batch kinetics forrns a basis for
a description of the emulsion polymerization in any kind of continuous reactor
system. This review concentrales on the emulsion polymerization kinetics of styrene.
Two modelling studies will he treated: the classical Smith-Ewart theory [61 and the
more recent model presented by Nomura and Harada [13-151. Both models arebasedon
the qualitative description of Harkins [4.51. Harkins distinguishes three
"intervals" in the emulsion polymerization process:
48
- interval I : partiele nucleation
- interval II : partiele growth in the presence of monomer dropiets
- interval lil: partiele growth in the absence of monomer droplets
For the partiele nucleation Harkins assumed the mechanism of micellar nucleation.
3.3.1. Smith-Ewart model
The frrst significant study on the modeHing of the emulsion polymerization
kinetics, based on the mechanism of Harkins (4,5], was given by Smith and Ewart {6].
According to the Harkins mechanism the overall polymerization rate may be given by
the next equation:
R = [N}.R p pp
where:
Rp = overall polymerization rate per unit volume
[NJ = number of polymer particles per unit volume
Rpp = polymerization rate per partiele
3.3.1.1. Nucleation of polymer particles
(3.1)
Smith and Ewart calculated the number of formed polymer particles in two idealized
situations:
(1) all radicals generated in the aqueous phase enter a micelle to form a polymer
particle. This case prediets too many particles, because absorption of radicals
by polymer particles already formed is neglected;
(2) micelles and polymer particles both absorb radicals at rates proportional to
their respective surface areas. According to Smith and Ewart this case prediets
too few particles, because in practice the mass flux of radicals to the surface
area is inversely proportional to the radius of the particles as can be derived
from the classica} diffusion theory.
Both limiting cases lead to similar expressions for the number of formed particles,
49
only varying in the value of the factor x:
[NJ = x.(p.tJlP.4.(a .[SJ )0·6 1 s m (3.2)
where:
p. = rate of formation of initiator radicals 1
Jl = volume growth rate of a partiele
as surface area occupied by an emulsifier molecule
[S]m emulsifier concentration effective for micelle formation
In this equation pi is given by:
(3.3)
where ki stands for the rate constant of initiator decomposition, f for the
efficiency of the initiator decomposition, and [I] for the initiator concentration
in the aqueous phase.
For the value of X Smith and Ewart found 0.37 < X < 0.53.
3.3.1.2. Polymerization rate per partiele
The polymerization rate per partiele can be given by:
where:
Rpp rate of polymerization in a single partiele
k = propagation rate constant p
[M)p = monoroer concentration in polymer partiele
ii = time-average number of radicals per partiele
Na = Avogadros constant
(3.4)
With the equations (3.1) - (3.4) a quantitative description of the emulsion
polymerization kinetics is possible. The only unkown parameter is the time-average
number of radicals per particle. For the determination of the average number of
radicals per partiele Smith and Ewart assumed the number of reacting polymer
particles to be constant in time:
50
g~n = RI.n - Rd.n = 0
where:
Nn = concentration of particles with n radicals
=time
RI.n = rate of formation of particles with n radicals
Rd.n = rate of disappearance of particles with n radicals
Particles with n radicals can be formed by:
- radical absorption by particles with n-1 radicals
- radical desorption from particles with n+ 1 radicals
- termmation in particles with n+2 radicals,
as described by equation (3.6):
Pa kt RI.n = Nn-J.Jir + Nn+l.(n+l).kd + Nn+2.(n+2).(n+l).v
p absorptioo desorptloo
where:
Ni = number of particles with i radicals
pa radical absorption ra te
kd radical desorption rate constant
kt termination rate constant
v p volume of a partiele
terminalion
Particles with n radicals can dissappear as a result of:
radical absorption by particles with n radicals
- radical desorption from particles with n radicals
terminalion in particles with n radicals,
as reflected by:
a bsorpiion desorption tennination
(3.5)
(3.6)
(3.7)
The salution of equation (3.5) is mathematically complex. Smîth and Ewart [6]
avoided a rigorous mathematica! solution. They distinguished three sîmplified
51
situàtions for which a simple salution of the recursive equation is available:
Case 1. ii << 0.5
Such a case arises when the rate of radical absarption is small as compared with the
rate of radical desorption and the rate of termination. The salution for this case
is given by:
p. 1/2 n = ( 2.[NÎ-kd ) (3.8)
where pi is the rate of radical formation in the l!.queous phase.
Case 2. -n 0.5
This case arises when desarption of radicals from the particles may be neglected and
terminalion of the radicals immediately occurs after entrance of every second
radical in a particle. The average number of radicals per partiele is then
independent of recipe, conversion, number of particles and partiele size:
ii = 0.5 (3.9)
This situation is often encountered in the emulsion polymerization of styrene.
Case 3. ii >> 1
This case 1s characteristic of large particles, where desarption of radicals from
the particles is negligible and the intrinsic rate of terminalion is small as
compared with the intrinsic rate of radical absorption. The average number of
radicals per partiele is given by:
(3.10)
where vp is the volume of a monoroer-swollen polymer particle.
In recent publications {10-12] a more general solution of Smith and Ewarts recursive
52
relation is given. In appendix A.l the derivation of the equations (3.8) - (3.10) is
presented. In this appendix also a global review of more general solutions of the
recursive relation (3.5) bas heen presented.
3.3.2. Nomura and Harada model
The most simple reaction model for emulsion polymerization, ·based on the mechanism
of Harkins {4,5), is given by Nomura and Harada {13-15). These authors made the
following assumptions:
- the nucleation mechanism is micellar in character;
- desorption of radicals from the particles is negligible;
- the particles contain either 0 or 1 radical: i.e. termination immediately occurs
after the entry of every second radical.
These assumptions agree well with Smith-Ewarts case 2 situation (ii = 0.5).
The Nomura and Harada model includes the next five steps:
(1) formation of radicals from initiator molecules according to:
I -t 2 R.
The generation rate of initiator radicals pi is given by:
(3.11)
(2) nucleation of micelles by absorption of a radical into a micelle.
The rate of radical absorption into micelles is given by:
p = k 1.[R·].[m] a,m s (3.12)
where [R.] represents the radical concentration m the aqueous phase, [m)s the
numher of micelles per unit volume of the continuous phase, and k 1 a kind of
overall mass transfer coefficient for the absorption of radicals into micelles.
(3) initiation of non-reacting polymer particles by absorption of a radical into a
non-reacting particle.
The rate of radical absorption into non-reacting particles is given hy the
following equation:
Pa = k-.[R·J.[NtJ ,pl ·-z. (3.13)
53
where [Nt] stands for the number of non-reacting polymer particles per unit
volume of the continuous phase and k2 for a kind of overall mass transfer
coefficient for the absorption of radicals into the particles.
(4) terminalion of radicals in polymer particles by absorption of a radical into a
reacting polymer partiele foliowed by immediate termination of the radicals in
the particle.
The rate of radical absorption into reacting particles is given by the equation:
Pa,pl = k2.[R"].[N"] (3.14)
where [N"] is the number of reacting polymer particles per unit volume of the
continuous phase and k2 a kind of overall mass transfer coefficient for the
absorption of radicals into the particles. It is assumed that this coefficient
is equal to that for the non-reacting polymer particles.
(5) the propagation reaction of the growing polymer chains, represented by:
P.· + M ~ P. 1· 1 I+
where pi· and Pi+ 1· represent polymer ebains of length i and i+l respectively,
and M a monomer molecule.
The overall reaction rate for this propagation reaction can be given by:
(3.15)
where [M]p is the monomer concentration in a polymer particle, kp the
propagation rate constant and [P") the concentration of radical chains per unit
volume of the continuous phase.
The power of this model is the simplicity in predicting the number of formed polymer
particles and the rate of polymerization. The model has proven its validity already
at low conversions [I 3]. Ho wever, no allowance has been made for the Trommsdorff or
gel-effect This implies that at high conversions the model may deviate from
( ex:perimental) reality. Another disadvantage of the model is that partiele size
distributions cannot be predicted with the model, because only reacting and
non-reacting particles are distinguished. This problem can he avoided by the
introduetion of an additional relation, descrihing the growth of a single polymer
partiele (see section 3.3.3).
54
3.3.2.1. Nucleation and number of formed polymer particles
Combining the equations (3.11) - (3.14) and assuming a quasi steady-state for the
number of radicals R' the following equation for the concentration of initiator
radicals in the aqueous phase can be derived:
(3.16)
where Na stands for Avogadros constant and [N] for the total number of reacting and
non-reacting polymer particles in the continuous phase.
Combination of (3.12) and (3.16) leads to:
(3.17)
where Ri stands for the rate of formation of polymer particles and [S]m for the
emulsifier concentration available for micelle formation,
and Ç is given by:
lc_ .M Ç=--z m (3.18)
in which Mm is the aggregation number of a micelle.
The factor Ç can be considered as an effectiveness factor for radical absorption by
polymer particles as compared with that of micelles. The factor Ç easily permits a
choice of the mechanism of radical absorption. Nomura and Harada [15} proposed four
different mechanisms of radical absorption:
1. Radical absorption is independent of the size of micelles and particles. This can
only be true when the rate of radical absorption is not determined by transport
phenomena outside the particles. The mechanism of radical absorption can be
visualized by some kind of bimolecular reaction between the terminating radical
and the partiele as a whole. Such a representation of the absorption process is
of course only realistic for very small particles with sizes corresponding to
those of micelles. From a physical point of view this mechanism is nol very
55
likely. It is generally assumed that this situation leads to an upper limit for
the number of formed polymer particles.
k1 and k2 are regarded as constants. teading to the following expression for ~:
(3.19)
2. Radical absorption obeys Ficks diffusion theory {16]. This is the case when the
rate of radical absorption is determined by diffusion of the radicals through a
stagnant liquid layer around the particles. Assuming the radical concentration
[R.] at the partiele surface being zero, the radical flux per unit of surface
area of the particles is given by:
. d[R.ll 2.ow . J = -Dw·<rr r=d /2 = a---·[R]
p p (3.20)
and the rate of radical absorption into particles by:
2.Dw . 2 . Pap = P p + Pa p2 = ---:r--.[R ].[N].1t.d = 2.n.D .dp.[R ].[N] (3.21) , a, 1 , up p w
For micelles an identical expression can be derived:
(3.22)
So, the mass transfer coefficients k1 and ~ are given by: k1 = 2.1t.Dw.dm and k2 = 2.1t.D w·dp, which leads to:
(3.23)
3. Radical absorption according to the so-called collision model [2,16]: in this
case it is assumed that a given interfacial area always has the same
effectiveness in capturing free radicals, regardless of the sîze of the partiele
upon which it is situated. Physically this case corresponds to a situation with
an extremely high degree of intrapartiele diffusion limitation. As a result the
termmation of radicals only happens at the partiele surface. Also, there is no
diffusion limitation outside the particles. From a physical point of view this
situation is not very realistic, because it would lead to relatively high radical
concentrations at the surface of the polymer particles. It is generally assumed
56
that this mechanism gives a lower limit for the number of formed polymer
particles.
The rate of radical absorption is proportional to the surface area of the
micelles and the particles. This implies for k1 and k2: k1 - dm2 and k2 - ct/, and for Ç:
(3.24)
4. Radic al absorption according to Ficks diffusion theory with the extension of
electrostalie repulsion between the radicals and the particles/micelles [ 161. For
low degrees of oligomerization the rate of radical absorption is affected by
electrostatic interactions between the ionic radicals and the micelles or the
polymer particles. For various degrees of oligomerization of the radicals Hansen
and U gelstad [ 161 did some calculations of radical absorption rates based on the
film diffusion theory. According to their calculations high degrees of
oligomerization of the radicals lead to rates of radical absorption which can be
described well by the diffusion theory. However, for low degrees of
oligomerization the radical absorption rates will be proportional to the volume
of the micelles and the particles. For the coefficients k1 and ~ this implies:
k1 - dm3
and k2 - ct/ and for Ç:
Ç = (d 3td \M = Ç d 3 p m m 3' p (3.25)
The case Ç = ~ = 0 (radicals are only absorbed by micelles), and the case Ç ç2 .dp 2 (radical absorption proportional to the surface area of micelle and particle)
correspond to calculations of Smith and Ewart [6] for the upper and lower limit of
the number of formed polymer particles respectîvely (see equation (3.2)).
For the lower and upper limit they found X 0.37 and X = 0.53, respectively.
According to Harada and Nomura [ 131 these limits give about twice the number of
particles actually observed. This is caused by too low values for the effectiveness
factor Ç. For styrene emulsion polymerization Harada and Nomura found for Ç an
experimental value of Ç = ç0 = 1.28 * 105. For the upper limit of the Smith-Ewart
theory it follows that Ç = r- = 0. For the lower limit the relation Ç = (d 2td 2).M ~ 4 p m m
holds, which gives a value for Ç of about 10 , because M is usually of the order of
102 for most emulsifiers and (d/tdm 2) normally bas a v~ue of about 102 [13].
57
3.3.2~2. Rate of polymerization and partiele growth
Using equation (3 .15) the following relation for the ra te of polymerization can be
derived:
R = k .[M] _[N"] p p p~
where:
Rp = overall rate of polymerization
kp = propagation rate constant
(M]p = monomer concentration in polymer partiele
Na Avogadros constant
(3.26)
From the model assumptions it follows that the particles are active only half the
time. This implies that only half the number of particles is active at any moment
during the polymerization [6,13]:
[N)' = (N]/2 (3.27)
It is generally assumed that [M]p is almost constant during interval II of the
polymerization (the interval of partiele growth in the presence of monomer
droplets). The value of [M] strongly depends on the kind of monomer and may vary,
for example, from 1.4 kmJ'vm3 for vinyl chloride to 9.1 kmoVm3 for vinyl acetate.
For styrene the next concentrations are known: 5.48 kmoVm3 [14] and 5.13 kmoVm3
[17].
In interval lil (the interval of partiele growth in the absence of monomer droplets)
the monomer concentration in the polymer particles decreases, and follows from a
mass balance:
q> /M [M] = q> .p /M = mon w
P mon P w q>mon/Pmo n + q> pol7Ppol (3.28)
where:
Mw = molecular weight of monomer
q>mon'q>pol = weight fractions of monomer and polymer
Pp'Pmon•Ppol = densities of particle, monomer and polymer, respectively
58
For styrene the following relation of <p with conversion, X , has been derived mon m from experimental data (figure 3.1):
<~>mon = 0.57 <p =1-X mon m
1.00 ' ' ' ' ' ' ' ' '
' 0.60 ' ' ' ' - ' ' ' '
0
I - 0.60 •c. .....
"'~ "" ~
= 0
s -8- 0.40
0.20
0.00 0.00 0.20 0.40 0.60 0.60 1.00
Conversion Xm (-)
(3.29)
(3.30)
Figure 3.1. Weight fraction styrene in polystyrene particles as a function of
16. F.K.Hansen, J.Ugelstad, "Emulsion Polymerization", I. Piirma ed., Academie Press, New Y ork, ( 1982), chap. 2
17. H.Gerrens, J. Polym. Sci., C, 27, 77, (1969)
62
Chapter 4. Emulsion polymerization of styrene in a pulsed packed column
4.1. Introduetion
Continuous emulsion polymerization is mostly carried out in a continuous stirred
tank reactor (CSTR) or in a series of CSTRs. The performance of a single CSTR is
quite different from that of a batch reactor. The main reason for this different
behaviour is the large residence time distribution in a CSTR, leading to broad size
distributions of the latex particles [ 1-31. In contrast wilh a CSTR, in a batch
reactor all polymer particles are usually formed during the first stage of the
reaction, and as a consequence, the partiele size distribution of the product latex
is narrow.
A second important difference between a CSTR and a batch reactor is the course of
partiele nucleation. A CSTR has shown to produce a much lower number of polymer
particles than a batch reactor operated under the same conditions [2 ,4]. It was
found that this difference was also caused by the large residence time distribution
of the CSTR. Because of the strongly non-linear character of the nuclealion process,
operation of a CSTR may lead to serious oscillations (12-18].
The third difference between a CSTR and a batch reactor concerns the molecular
weight characteristics. According to Poehlein and Dougherty [ 11 two factors
contribute to the distribution of molecular weights in the latex product from a
CSTR. First, there is the stochastic process of free radical entry into the
particles. Secondly, the distribution of partiele sizes leads to differences in
average free radical absorption rates, because large particles absorb radicals at a
higher rate than small ones. In a batch reactor partiele size distributions are
usually much smaller than in a CSTR. So a CSTR generally produces latex produels
with larger molecular weight distributions than a batch reactor.
The large differences between the properties of products obtained in batch or in
continuous reactor systems can he avoided when using a plug flow type reactor
instead of a CSTR. One of the main advantages of a plug flow reactor is the absence
of any residence time distribution. As a consequence, the course of the emulsion
polymerization process in this reactor type is almost identical to that in a batch
reactor. However, a serious problem in the application of a plug flow type reactor
in emulsion polymerization is the requirement of turbulent flow in the reactor. This
serves three purposes: (1) the avoidanee of deemulsification, (2) the prevention of
reactor fouling, and (3) sufficient radial mixing to remove the heat of reaction.
A new reactor type, that fulfills these requirements and can he scaled up rather
easily is a pulsed packed column. Because of its unique property of maintaining
63
turbtilence irrespective of the feed rate, this reactor can be used for emulsion
polymerizations up to very high conversions. The pulsation creates some axial
mixing, but this effect can be limited.
In this chapter the performance of the fulsed ~acked ç;olumn (PPC) in styrene
emulsion polymerization is compared with that of the conventional reactor types: a
CSTR and a batch reactor. Special attention wil! be payed to the properties of the
latex products of the different reactor types, in terros of the number of formed
polymer particles, partiele size distributions and molecular weights.
4.2. Comparison of reactor types
The emulsion polymerization of styrene m batch reactors is wellknown. The
polymerization kinetics can be described well by the Smith-Ewart case 2 theory
(average number of radicals per partiele n = 0.5) {5,6].
One of the specific aspects in which styrene differs from other more water soluble
monomers such as vinyl acelate or methyl methacrylate is that in styrene emulsion
polymerization desorption of radicals from the particles is negligible. This is
especially important for the styrene emulsion polymerization in a CSTR. The emulsion
polymerization of monomers with high radical desorption rate constanis has shown to
give large oscillations in conversion and number of formed polymer particles in a
CSTR {7-13]. This is a consequence of the fact that these systems are characterized
by very high rates of partiele nucleation and relatively low partiele growth rates
[14]. Styrene, however, shows a very low rate of radical desorption and is therefore
relatively insensitive to oscillatory phenomena { 12,13,15]. That does not alter the
fact that there are still several differences between the emulsion polymerization of
styrene in a CSTR and in a batch reactor, some of them considerably affecting the
properties of the latex product.
4.2.1. Partiele formation
Because of the large residence time distribution the partiele formation in a CSTR is
different from the partiele formation in batch. In a batch reactor almost all
emulsifier is available for partiele nucleation. In a CSTR, however, larger mature
particles are mixed up with freshly added emulsifier. As a result a larger amount of
the emulsifier is used for the stabilization of these large particles. Therefore,
only part of the emulsifier is available for the generation of new particles
64
(nucleation).
Oersbberg and Longfield [ 1 9] were among the first authors who have reported a bout
the emulsion polymerization of styrene in a CSTR. The mathematica! model they
presenled for predicting the numbers of formed polymer particles and polymerization
rates was to a large extent based on the concepts developed for batch reactors by
Smith and Ewart [5} in their case 2 model. The workof Oersbberg and Longfield was
further refined by DeGraff and Poehlein [20].
DeOraff and Poehlein developed a model for predicting numbers of formed polymer
particles and polymerization rates, based on the use of partiele size distributions.
Their model was based on the assumption that the absorption of radicals into
micelles and particles is proportional to the surface area of micelle and particle.
For the number of formed polymer particles in a CSTR they derived the following
equation:
pi. i .Na
[N] t [
kp. [MJP. i ]2/3
1 - a 1 . (M]P
where:
pi :::: generation rate of initiator radicals
i :::: mean residence time in the reactor
Na = Avogadros constant
[N]t = total number of polymer particles
as = surface area occupied by an emulsifier molecule
[S]m emulsifier concentration effective for micelle formation
kp = propagation rate constant
[MJP == monomer concentration in polymer partiele
In this equation a0
and a 1 are constants:
a = 3 85 (M V )213 o · · w· p
-3 a 1 = 10 * M .V w m
where:
Mw = molecular weight of monomer
V p = specific volume of polymer
V :::: specific volume of monomer m
65
(4.1)
(4.2)
(4.3)
Because the second term on the right hand side is usually much greater than unity,
equation (4.1) can be reduced to:
(4.4)
The relation for the number of formed polymer particles in a batch reactor, given by
the Smith-Ewart case 2 model (ii = 0.5), is:
[N]t = x.(r./J.L)0.4.(a .[SJ )0.6 1 s m 0.37 < x < 0.53 (4.5)
where J! is the growth rate of a particle.
Comparison of equation (4.5) with equation (4.4) shows some important differences.
In table 4.1 the exponents on the main recipe parameters are given for both
equations. As can be seen from this table, there is a remarkable difference in the
dependenee of [N]t on the recipe parameters between both reactor types. This means
that production of a latex in a CSTR with the same number of particles as a batch
product requires a totally different procedure.
Secondly, an even. more important difference between a batch reactor and a CSTR is
the maximum number of polymer particles that can be formed in both reactor types.
For a CSTR this maximum is derived by equating the first derivative, d[N]/di,
obtained from equation ( 4.1), to zero and solving the resulting relation for [N].
The result of this computation is:
[N]CSTR,maximum = 0·577 [N]batch (4.6)
Table 4.1. Model equation exponents for Smith-Ewart 'case 2' mode/s.
I equation exponent s I
parameter batch reactor CSTR
r . I
0.4 0
[S] m 0.6 1. 0
i - -0.67
66
Thus fewer particles will he produced with the same recipe in a CSTR.
The same value for this maximum was obtained by Nomura and Harada {4] who developed
a simpte partiele model that ignores the partiele size distribution and considers
the particles to he indistinguishable from each other.
Styrene emulsion polymerization experimentsof Nomura and Harada [4,21] carried out
in a CSTR showed good agreement with predictions of their model. A maximum in the
number of particles could be detected and the value of this maximum was about the
same as the predieled value. Nomura and Harada also showed that application of a
plug flow reactor as a seeding reactor, preceeding the CSTR, increased the number of
particles up to the batch level. This is not surprising, because a plug flow reactor
has the same residence time distribution as a batch reactor, thus teading to equal
numbers of polymer particles in the product latexes.
4.2.2. Partiele size distributions
The partiele stze distribution can have a significant effect on the rheological
properties of the latex. Because latexes produced indifferent reactor processes
would be expected to have different partiele size distributions, it is important to
know which type of reactor will be used for latex production.
In a batch reactor a shon; nucleation period, foliowed by a long period of partiele
growth, during which flocculation of the particles is avoided, results in latexes
with very smal! partiele size distributions. Because of the short nucleation period
all formed particles are of about the same size and will therefore grow with the
same rate. Partiele size distributions of latexes produced in a CSTR wil! be much
broader as a result of the large age distribution in this reactor. Partiele size
distributions in tubular reactors will be smal! if plug flow conditions can be
realized. Axial dispersion increases the partiele size distribution as compared with
plug flow.
Considerable work has been done on the investigation of partiele size distributions
in CSTR systems. A review of the developments in this field is given by Poehlein,
Lee and Stubicar {22]. All CSTR models being developed use the residence time
distribution as the basic concept to predict partiele size distributions. The
distribution of residence times in a single CSTR is given by the probability density
function:
(4.7)
67
where:
t'} = dimensionless time (t/i)
t = actual time
i = mean residence time in the reactor
The residence time distribution for N equally sized reactors is given by:
(4.8)
When the contribution of coagulation to the partiele growth is negligible the
following relation between the distribution of the partiele diameters (HN(d')) and
the residence time distribution function (fN(Ö)), being identical to the partiele
age density function, can be given by:
f (ö) H (d') = _N __ _
N ld(d' )/dól (4.9)
where:
d' = dp"d0
dp = partiele diameter
d0
= diameter of a freshly nueleated partiele or a seed partiele
Equation (4.9) is only valid when d(d')/dö is the same for all tanks in the system.
Otherwise HN(d') should be evaluated for each individual tank.
Application of Smith-Ewart case 2 kinelics in d(d')/d't leads to:
~. (d')2 ·f~.[(d')3-1JN-1Lxp f~.[(d')3-tJ} (N-1)! r (4.10)
~ is given by:
(4.12)
where ~ is the partiele growth parameter, and k0
the partiele growth constant.
68
In figure 4.1 HN( d ') is gi ven for several numbers of tanks in, serie~. The red u eed
partiele diameter d' is given for unswollen partieles. Figure 4.1 shows that a
larger number of tanks in series results in a narrower partiele size dist,ribution.
lt is obvious that this is caused by the much narrower residence time distribution
in such a system.
9.00.--------------------,
7.20
5.40
N=l 3.60
1.80
,'
3.40 5.80 8.20 10.60 13.00
d' (dimensionless)
Figure 4.1. Prediered partiele size distributions of the tanks in series model (!)
0.1).
Experimental data of DeGraff and Poehlein {20]. for styrene emulsion polymerization
in one single CSTR with partiele diameters less than 150 nm could be excellently
fitted to equation (4.11). For larger partiele diameters the model was not able to
give accurate predictions of the partiele size distributions. The main reason for
this discrepancy between theory and experiments is the average number of radicals
per particle, which is assumed to have a constant va1ue of n 0.5 for the
Smith-Ewart case 2 situation. For large partieles, however, n increases with
increasing partiele diameter. Correction for this increase in n can be made by
introducing the theory of Stockmayer {23] into the partiele growth equation. The
Smith-Ewart case 2 situation is a special salution for the basic theory of Smith and
Ewart [5,6]. Stockmayer gave a more general solution in which the average number of
radicals per particle, n, is a function of the partiele volume and the terminalion
ra te.
DeGraff and Poehlein showed that application of the Stockl)1ayer theory in the growth
model . gave good agreement between theory and experiments for partiele s1ze
distributions of polystyrene latex particles with diameters up to 300 nm.
69
4.2.3". Molecular weight properties
Molecular weights are determined by the time elapsing between the moment of
initiation and the moment of termination, and by the propagation rate constant, kp.
When more time passes between the moment of initiation and termination, Jonger
polymer chains will be formed. This is only true when there is practically no chain
transfer, which appears to be the case for styrene emulsion polymerization [24 1. In batch emulsion polymerization, when the particles are almost monodisperse, the
distribution of molecular weights is only determined by the stochastic process of
the en try of free radicals into particles. Katz, Skinner and Saidel [25 1 considered
the distribution of molecular weights of the polymer being formed in monodisperse
particles. They found that the ratio }Çf~n varies from 2.0 for smal! particles
(Smith-Ewart case 2 kinetics) to 1.5 for large particles (bulk polymerization). In
their derivations these authors assumed that the mean free radical entry frequency
and the mean chain growth rate were independent of time.
In a CSTR the distribution of molecular weights is determined by two factors. Not
only the stochastic entrance of free radicals into the particles contributes to the
distribution of molecular weights, but there is also a contribution of the partiele
size distribution, leading to differences in free radical absorption rates. Por
large particles the rate of radical absorption is higher than for smal! ones, which
influences the obtained distribution of molecular weights of the product formed.
DeGraff and PoehJein [201 considered the distribution of molecular weights in a
CSTR. They distinguished two different mechanisms of radical entry into particles:
(A) t he ra te of radical absorption is proportional to the surface area of the
particles (equal flux model);
(B) the rate of radical absorption obeys Ficks diffusion theory [261. which prediets
diffusion flux proportional to 1/d , d being the diameter of a polymer p p
particle.
The values for M~n obtained by DeGraff and PoehJein forthese mechanisms are given
in table 4.2.
Nomura and Harada [41 distinguished four different mechanisms of radical absorption,
two of them being the same as those of DeGraff and Poehlein. The other two
mechanisms are:
(C) the rate of radical absorption is independent of the partiele diameter;
(D) the rate of radical absorption obyes Ficks diffusion theory with the extension
of electrostatic repulsion [26 1. The predicted values of Nomurá and Harada for the ratio }Çi~n are also given in
table 4.2.
70
Table 4.2. Prediered values of MjMn for Jour different
mechanisms of radical absorption {4,20].
mee han îsm c B A
I\4 /I\4 w n 2.0 2.4 4.8
C: rndical entry independent of partiele diameter [4]
B: diffusion model [20]
A: equal flux model [20]
D: diffusion with electrost.atic repulsion [4]
D
>4. 8
Ex perimental values of I\4 !Kil of DeGraff and Poehlein gave an average value of 3.07. w-·~ . . .
Nomura and Harada reported experimental values of K-1~0 between 2 and 3, mostly
rather close to 2. This îndicates that the entry of radicals into the particles
preferably takes place according to the diffusion model.
4.3. Experimental
Materials: The monomer used was industrial grade styrene. The inhibitor para
t-butylcatechol was removed by extraction with an aqueous 5 weight % sodium
hydroxide solution. Sodium dodecylsulfate was used as emulsifier, and sodium
persulfate as initiator. In aqueous solutions the persulfate ion decomposes
according to:
s 0 2-2 8
2 so .-4
Beside this reaction the following reaelions can take place:
HSO- + OH· 4
The formation of HS04- lowers the pH. At pH< 3 the next decomposition reaction of
E = 1.6*10-4 m2ts; <•J PPC (Sulzer internals): E 5.0*10-5 m2ts.
85
expected that this limit corresponds to the number of polymer particles formed in a
CSTR operaled at the same mean residence time. The figures 4.16 and 4.17 indicate
that the Peclet-number, PeL, may be a good criterion of the performance of a PPC.
Figure 4.18, however, shows that the expected unique relationship is not obtained by
use of PeL; the effect of E on the partiele formation is overestimated as compared
with the effect of u.
The above considerations mean that PeL is probably nol the correct parameter to
describe the performance of the PPC. The length L corresponds to the total column
length in which the emulsion is subject to axial mixing. Partiele nucleation in a
PPC, however, takes place in just a small section of the column (figure 4.19). It
can easily be seen that the number of polymer particles forrned is affected only by
the axial mixing in this section of the PPC.
Therefore, a better choice seems to be a Peclet-number (Pe1)
of the PPC in which the polymer particles are formed:
related to the section
(4.11)
where l is the length of the section of the PPC in which the partiele nucleation
takes place.
rr•••ct•
I l L
111
11 PeL
UL " x•l
Pel 1 I
• • I reactaat•
Figure 4.19. Polymerization intervals of the emulsion polymerization of styrene in a
pulsed packed column and the related peclet-numbers. I = partiele nucleation; /1
partiele growth in the presence of monomer droplets; /// = partiele growth in the
absence of monomer droplets.
86
Because partiele nucleation strongly depends on the physical conditions in the PPC,
the length of the partiele formation section will be a function of these conditions.
For Pe 1 we can write:
* 2 P _ u .I _ u.( 't .u) _ ". * u
el - c - E - ' ·--y- (4.12)
* where 't is the rnean residence time in the partiele nueleation section.
* 't depends on the polyrnerization kinetics, which are in turn affected by the axial
* mixing. In figure 4.20 experirnentally deterrnined values of 't are given for various * axial mixing conditions (as expressed by PeL). For the calculation of 't it was
assurned that the partiele nucleation ends at a conversion at which no ernulsifier is
available for rnicelle formation and all polyrner particles forrned are cornpletely
covered with a rnonornolecular layer of ernulsifier molecules. The principle of the * * calculation of 't is described in appendix A.S. The ernpirical relation between 't
and PeL that is obtained can be given by:
't * - Pe -0.5 L
Combination of (4.12) and (4.13) gives:
100
PeL (-}
(4.13)
1000
* Figure 4.20. Experimentally determined values of 't (see text) as a function of PeL.
('lf!f) PPC (Raschig rings): E 3.0*10"4 m2ts; (.lt.) PPC (Raschig rings): E 1.6*10-lf
m2ts; (e) PPC (Raschig rings): E == 6.4* 10·5 m2ts; (•) PPC (Sulzer internals): E =
5 0*1 -5 2 . 0 mIs.
87
(4.14)
Relation (4.14) clearly shows the different influence of E and u on the effect of
axial mixing during the period of partiele nucleation.
In figure 4.21 the number of polymer particles formed, [N]w, is plotted as a
function of Pel' It is obvious that one unigue relationship is obtained between [N]w
and Pet Again we can distinguish two separate regions. In the first region (Pe1 <
10) Nw depends on Pel' while in the secend region (Pe1 > 15) no significant
difference between a PPC and a batch reactor is observed. The transition between
both regions is located somewhere between Pe1 = 10 and Pe1 15.
At Pe1 = 0, (N]w corresponds to a number of particles formed at infmite residence
time. An infinitely large residence time means a conversion of 100 % at the entrance
of the PPC. At that conversion level the number of polymer particles forrned is about
[N]w = 0.8 * 1020 m-3 for equally sized particles.
20
- 16 M
8 ..........
' - -.-... " 12 ~ ' ," 0
'f 8 * "'' • 1:1: ,• z 4 "'' "' ' '
0 0 8 16 24 32 40
Pel (-)
Figure 4.21. W eight average number of polymer particles formed in a pulsed packed
column as a function of Pe1 for styrene emulsion polymerization. Recipe see figure
New York, (1982), chap. 2 27. I.M.Kolthoff, I.K.Miller, J. Am. Chem. Soc., 73, 3055, (1951)
95
96
Chapter 5. Reactor model for the emulsion polymerization of styrene in a
pulsed packed column
5.1. Introduetion
In literature only a few rnadelling studies have been publisbed aimed at predicting
polymer latex properties and reaction rates of styrene emulsion polymerization in
continuous reactor systems. For continuous emulsion polymerization the studies on
reactor modeHing were mostly limited to CSTRs.
The frrst theoretica! study of a CSTR was made by Gershberg and Longfield [ 1 }. These
authors developed a mathematical model that was based on the classical theory of
Smith and Ewart [2} assuming an average number of radicals per polymer partiele
being equal to 0.5. DeGraff and Poehlein [3} extended the model to predict partiele
size distributions. A comparison of theory and experimental results showed that
their modified model could be used to give accurate predictions of reaction rates
and partiele size distributions.
A different route in the rnadelling of a CSTR was foliowed by Nomura and Harada
[4-6]. These investigators developed a simpte model that ignores the partiele size
distribution and considers the particles to be indistinguishable. The model was
adapted to a CSTR [5} as well as to a batch reactor [4}. The advantage of this model
is the simplicity by which the number of polymer particles and the reaction rate can
be predicted. One of the .limitations of the model is the fact that the model does
not account for the Trommsdorff- or gel-effect that may occur at high conversions. A
second limitation is that partiele size distributions · cannot be predicted, for the
simpte reason that the model uses an average partiele size to describe the
polymerization process. Nomura and Harada showed that when conversions are not too
high and partiele sizes are not too large the model can safety be used to sünulate
the steady-state behaviour of styrene emulsion polymerization.
In this chapter a model is presented for predicting numbers of formed polymer
particles, partiele size distributions and conversions of the emulsion
polymerization of styrene in a ~lsed facked Çolumn (PPC). The model camprises a
reactor model and a kinetic model. The reactor model can be either a plug flow with
axial dispersion model or a tanks in series model. In the kinetic model assumptions
should be made conceming the mechanism of radical absorption into the polymer
particles and whether or not partiele size distributions are incorporated in the
model. In the following sections two models are discussed:
- a pi u g flow with axial dispersion model being based on average partiele sizes
(section 5.2);
97
a tanks in series model in which partiele size distributions are incorporated
(section 5.3).
5.2. Plug flow with axial dispersion model
5.2.1. Mass balances
When a fluid flows through a PPC, dispersion of the fluid occurs as a result of the
combined effect of molecular diffusion and turbulent mixing (see chapter · 2).
Generally there are two different ways of modelling an emulsion polymerization
reaction in a PPC. The PPC can be described as a number of ideally mixed tanks in
series. However, this is only allowed when the number of mixing stages in series j
exceeds a value of 10. For low values of j this model is not reliable. The only
alternative to describe an emulsion polymerization reaction in a PPC is the use of
the so-called plug flow with axial dispersion model. This model deals with smal!
deviations from plug flow, which are accounted for by the axial dispersion
coefficient, E (chapter 2).
Assuming that there are no radial concentration gradients and ·a steady state, a
balance for the number of formed polymer particles over a cylindrical element of the
column with a length ,1z leads to:
R. 1
where:
Ri = rate of partiele formation at height z
u = interstitial liquid velocity
E = axial dispersion coefficient
[N]t = total number of polymer particles per unit volume aqueous phase
z = column height
(5.1)
In the same way a mass balance for the monomer over an element of the column between
z and ,1z leads to:
R p
dX d2X m m u.[M]0 . a-z-- + E.[M]0 . -;-z-
z dz
98
(5.2)
where Rp stands for the overall polymerization rate, Xm for the monomer conversion
and [M]0 for the monomer concentration in the feed.
The third differential equation is related to the free (micellar) emulsifier
concentration in the emulsion:
(5.3)
where:
Ap total surface area of all polymer particles
as == surface area occupied by an emulsifier molecule
[S]m == number of emulsifier molecules (per m3) effective for micelle formation
In this equation the first term stands for a change in the amount of emulsifier (per
unit volume of continuous phase) that is present on the partiele surface. Because
the emulsifier does not really disappear (all emulsifier remains in the emulsion)
equation (5.3) can be replaced by:
(5.4)
where [S] is the feed stream concentration of emulsifier effective for micelle m,o formation (== [S]f - [S]cMd· [S]f the emulsifier concentration in the feed stream,
and [S]CMC the critica! micelle concentration of emulsifier.
So only two second order differential equations remain. With a few additional
relations derived from the Nomura and Harada theory {4-6] and four boundary
conditions these differential equations can be solved numerically.
5.2.2. Kinetic equations
According to Nomura and Harada {4] the partiele nucleation rate can be equated as:
(5.5)
where [N]tis the total number of polymer particles per unit volume aqueous phase, Ç
99
an effectiveness factor in absorption of radicals for particles relative to
micelles, p. the rate of formation of initiator radicals, and N Avogadros constant. 1 a
The overall polymerization rate is given by:
(5.6)
where kp stands for the propagation rate constant, [M]p for the monomer
concentration in the polymer particles, and [N'] for the number of reacting polymer
particles.
For the number of reacting polymer particles m styrene emulsion polymerization
Nomura and Harada proposed [4-6]:
[N'] = [N]/2 (5.7)
The total surface area of the particles was calculated by assuming an average
diameter for all polymer particles:
A = (36.n) 113 .v 213.[N] p p
where v p is the average volume of a polymer particle.
The average volume of a polymer partiele is related to the conversion by:
V = p
where:
[M]0
.Xm.( 1 +y)
[N]. pp.Mw
[M] = monomer concentration in feed stream 0
Xm = monomer conversion
y = monomer weight fraction in polymer particles
pp = density of monomer-swollen polymer particles
M = molecular weight of monomer w
(5.8)
(5.9)
The parameter Ç (equation (5.5)) is a factor descrihing the effectiveness of
absorbing radicals for particles relative to micelles. This parameter easily permits
a choice of the proper mechanism of radical entry into micelles and particles.
100
Nomura and Harada [6} distinguished four different mechanisms for radica1 absorption
(see also chapter 3 and 4):
Ç = ~ = constant (5.10)
ç = Çl.dp (5.11)
ç = ~.dp 2 (5.12)
ç = Ç3.dp 3 (5.13)
Nomura and Harada [4} assumed a radical absorption mechanism for which Ç may be
regarded as a constant (Ç = ~· Experimentally they obtained a value of: 'o = 1.28
* 105. We calculated Ç from our own batch experiments (carried out under conditions
as shown in tab1e 5.2) and we found: ~ = 1.32 * 105. This value is in good
agreement with that of Nomura and Harada. The presented value of 'o was determined
by repeated1y estimating a va1ue for Ç until the number of formed po1ymer particles,
predieled by the model, agreed well with the experimentally determined
weight-average number of polymer particles. The use of partiele numbers based on
weight-average diameters was allowed, because the partiele size distributions of the
batch products examined were very small (degree of dispersion of the distributions
a.;an == 1.07).
The calculated value of 'o is presented in table 5.1, together with values of the
constants based on other radical absorption mechanisms.
Table 5.1. Ç-values for different radical absorption mechanisms.
mechanism
* this work
* Ç-values
~ = 1.32 * 105
çl = 3.55 * 1010
~ = 1.04 * 1016
ç3 = 3.25 * 1021
** Nomura and Harada [4}
101
li terature values **
5.2.3. Solutions of the differential equations
Four houndary conditions are necessary for a solution of the differential equations
(5.1) and (5.2). The first two can he o)Jtained hy taking a halance over a
cylindrical element at z ::::: 0 (the entrance of the reactor):
x m(z=O)
E [dXm] U • <:fZ z=O
(5.14)
(5.15)
Both other houndary conditions are obtained hy a prediction of the axial pos1hon * (z ) in the reactor, where all micelles just have disappeared ([S] = 0). After the . m
moment of disappearance of the micelles the total numher of polymer particles wil!
remain constant during the remaining part of the polymerization process (figure
5.1). Therefore the. third boundary condition will he:
[d [N]1] ·
• - 0 · --uz-- z=z -
-0
2r-------------------------------~--~
diN]
dx • 0
oL-------------------~--------------~ 0 ~ w
length coordinate x
(5.16)
Figure 5.1. Assumed number of jorn1ed polymer particles in a pulsed packed column as
a function of the axial position in the column.
During interval IJ of the polymerization process the overall polymerization rate R , p
and therefore dXm/dz, will also remain constant (figure 5.2). So the fourth boundary
102
value will be:
2000~------------------------------------.
E ><
!:::: 0 ïii ""' \U. > c 0 u
l cl Xm
l dx
length coordinate x
• 0
40
(5.17)
Figure 5.2. Assumed conversion in a pulsed packed column as a function of the axial
position in the column.
Since we have the two differential equations (5.1) and (5.2) and the four boundary
conditions (5.14) - (5.17), the steady-state solution for the total number of formed
polymer particles and the monomer conversion during interval I of the polymerization
can be obtained. An analytica! solution of the differential equations is not * possible, because z is a dependent variabie and is a rather complex functîon of
[N]1
and Xm. Therefore, numerical methods have to be used to solve the differential
equations. For a straight-forward numerical solution of the problem it is necessary
to transforrn the two boundary conditions (5.16) and (5.17) into an initia! value
problem: [N]1, X , d[N] /dz and dX /dz have to be known at z :;: 0. However, the *m r m
definition of z makes it impossible to calculate the four initia! values. Therefore
a trial and error method was chosen for solving the differential equations. [N]t and
X were estimated at z = 0. (d[N] /dz) and (dX /dz) were calculated now using m r z=O m z=()
the equations (5.14) and (5.15). The four initia! values obtained in this way were * used to calculate the steady-state solution from z = 0 to z = z with a fourth order
* 2 2 Runge-Kutta method. At z z , d[N1(dz and d Xrrfdz were evaluated, after which
[N]1and Xmat z = 0 were recalculated. This process was repeated until d2Xm/dz2 and
103
* d[N]/dz at z = z were close enough to zero.
Our experiences when using this method showed, that especially at low values of E a x and high values of u (i.e. at very small residence time distributions) the numerical
method was very unstable. Both [N]1
and Xm at z = 0 had to be predicted very
accurately in order to be able to calculate monomer conversion and number of polymer * particles at z = z with an acceptable accuracy.
5.2.5. Comparison of theory with experiments for a PPC
In this section theoretica! predictions of the model are compared with results of
polymerization experiments in a PPC. Table 5.2 shows the experimental conditions.
The parameters used in the calculations are given in appendix AA.
Table 5.2, Experimental conditions of styrene emulsion
polymerization in the pulsed packed column.
Component Concentrat ion
styrene [M]f = 4.0 kmo11m3 H
20
sodium dode c yl sulfate 3 [ S] f = 0.048 kmol/m H20
s o di urn persulfate [ I ] f 0.011 kmo11m3 H
20
sodium hydroxide [ B] f 0.010 kmo11m3 H
2o
po lymerizat ion temperature: 50°C
pH of the emulsion: 12
Figure 5.3 shows the experimentally determined and the theoretically calculated
number of polymer particles as a function of the mean residence time in a pulsed
packed column packed with 10 mm Raschig rings. The calculations were carried out for
four different radical absorption mechanisms corresponding to the equations (5.10)
(5.13). The figure shows that a larger dependenee of the radical absorption
mechanism on the partiele size results in a lower number of formed polymer
particles. For smal! mean residence times (t < 60 min) the calculated values of [N]w
agree reasonably well with those derived from experimental results. However, at
larger mean residence times a large discrepancy between the theory and the
experimental results exists.
104
20
- 16 .. s ' - 12 2 ' 0 .....
8 ... .. z 4
0 0 60 12(1 180 240 300
Residence time (min)
Figure 5.3 .. Experimentally determined and theoretically prediered numbers of polymer
particles for styrene emulsion polymerization in a pulsed column packed with JO mm
Raschig rings at 50"'C.
Recipe: table 5.2; stroke length of pulsation: s = 9 mm; pulsarion frequency: f
3.5 s-1. Theoretica/ calculations: plug flow with a.xial dispersion model with
application of different radical absorption mechanisms (table 5.2).
( •) experimental data; ( -----) model predictions.
In these equations a and a are defined by:
(5.48)
where:
120
k. == rate constant of formation of initiator radicals 1
~ = rate constant of terminalion
[I] = initiator concentration
[N] = number of polymer particles
dp = diameter of a polymer partiele
N3
= Avogadros constant
The figures 5.7 and 5.8 show that no deviations between experimental data and model
predictions can he observed for the higher partiele diameters. This difference
between our results and those of DeGraff and Poeblein can probably he explained by
the difference in the initiator concentration, being 0.011 kmoVm3 and 0.075 kmoVm3
for our experiments and those of Degraff et' al, respectively. The effect of a lower
initiator concentration can easily he demonstrated: for small a (5.3*10-9 < a < 1.1*10-8 nm3 for the experiments of the figures 5.7 and 5.8) and not ton large
partiele diameters equation (5.47) can he rewritten to:
(5.49)
Combination of (5.48) and (5.49) leads to:
n - [IJ.dP3 (5.50)
This means that when the initiator concentration [I] is lowered by a factor of 8,
deviations in n from 0.5 will he noticeable only if the partiele diameter. d is
increased by a factor of more than 2. For the recipe used in the experiments ol the
figures 5.7 and 5.8 this means that deviations in n from 0.5 can be expected only at
partiele diameters above about 180 nm. However, such large particles are scarcely
present in the distributions.
5.3.3.3. Conversion
Equation (5.31) shows that the rate of polymerization is proportional to the number
of polymer partieles. In the foregoing sections it was demonstrated that for short
mean residence times the number of polymer particles fonned could be predicted well
by the nueleation theory of Nomura and Harada {5,6}. It was also shown that for
longer mean residence times this theory overestimates the number of particles. These
findings can also be seen in figure 5.10, where conversions calculated with the
(1981) 7. W.H.Stockmayer, J. Polym. Sci., 24, 314, (1957) 8. J.L.Gardon, J. Polym. Sci., A-1, Q, 623, (1968) 9. F.K.Hansen, J.Ugelstad, "Emulsion Polymerization", I.Piirma ed., Academie Press,
New York, (1982), chap. 2 10. J.P.Feeney, R.Gilbert, D.Napper, Macromolecules,l7, 2520, (1984)
126
Chapter 6. Coagulation effects during the emulsion polymerization of styrene
emulsified with a rosin acid soap
6.1. Introduetion
Rosin acid soaps became important as emulsifier for commercial styrene-butadiene
emulsion polymerization processes since 1946 [ 11. Later they were also used in
emulsion polymerizations of other dienes such as chloroprene or isoprene. One of the
main reasoos why rosin acid soaps are used instead of other soaps (for example fatty
acid soaps) is, that rubbers produced with rosin acid soaps show higher tackiness
[21. Rosin acid soaps are prepared from rosin, a resinous substance, that is
obtained from pine trees, either by wounding the living pine tree and collecting the
exudate (gum rosin) or by extracting wood stumps of the pine tree (wood rosin).
Rosin consists for about 90% of resin acids and for 10% of non-acidic materials.
Pigure 6.1 shows the structure of the resin acids that are present in rosin [3,41.
Because the abietic type acids and small amounts of phenolic materials present in
rosin act as inhibitors, unmodified rosin is not suitable for use as emulsifier
[3,51. The phenolic matenals can be removed by a refining process, while the
a bietic type acids have to be converted into other resin acids [5 1. This conversion
of abietic type acids can be performed by both hydrogenation and dehydrogenation or
by disproportionation. In a disproportionation reaction the abietic type acids are
completely converted into dihydro or tetrahydro acids and dehydroabietic acid [5 1. Por the use as an emulsifier in the production of a synthetic rubber a
disproportionated rosin is usually converted into a potassium or a sodium soap. Prom
the character of the carboxylic group of the soap it follows that the activity of
the soap is strongly pH dependent. Pryling and Pollett [61 showed with a cold
styrene-butadiene emulsion polymerization that the pH has a large influence on the
reaction rate when a rosin acid soap is used. Their experimental results showed that
the rate of conversion has a maximum at a pH of 10.5. This corresponds to a complete
ionisation of the carboxylic groups. in the rosin acid soap used. It is easy to
understand that the decrease in reaction rate at lower pH is caused by hydrolysis of
the soap with consequent loss of activity. Por the decrease in reaction rate at
higher pH a reasonable explanation could not be given.
In order to rnaintaio a high pH during the emulsion polymerization an alkali
metalhydroxide should be added to the emulsion. In many cases electrolytes such as
dipotassium carbonale or tripotassium fosfate are used to buffer the emulsion.
Addition of such a polycharged electrolyte has then also a function of increasing
the ion concentration. High ion concentrations cause a destabilization of the
127
Figure 6.1. Structures of the resin acids present in rosin [3,4}. (A) abietic acid;
In figure 6.2a the attraction energy, the repulsion energy and the total energy of
interaction of two spherical particles are given as a function of the distance H
between the particles. The figure shows that the total energy of interaction has a
maximum, V , at a distance H=H . The value of this maximum is of major max max importance for the stability of the particles. A high maximum is characteristic for
a stabie system. At H=H the repulsive forces are predominant. The particles ma x cannot coagulate in the primary minimum unless they collide with enough energy to
surmount the potential energy maximum. On the other hand a low maximum is an
indication of an unstable system. Particles approaching each other only need a low
kinetic energy to overcome the energy maximum and reach the state of primary
coagulation. Outside the energy maximum a secondary less deep minimum is situated.
Particles at a distance corresponding to the secondary minimum are bound hy weak
forces, and can he separated easily.
The height of the energy maximum is strongly dependent of the concentration of
electrolyte in the dispersion medium. Increasing the electrolyte concentratien leads
to a decrease in the thickness of the double layer of the particles, 1/JC. As a
result the repulsion forces also decrease and the energy maximum, V max' will become
lower. When the kinetic energy of the approaching particles is larger than V ma x every collision hetween particles will lead to primary coagulation (see also figure
6.2b). The electrolyte concentratien for which the value of V max is equal to the
kinetic energy of the particles is called the Çritical Çoagulation Çoncentration
(CCC). Increasing the electrolyte concentration beyond the CCC does not lead to a
further increase in coagulation rate.
6.2.2. Mechanisms of coagulation
The coagulation of particles in a colloidal suspension can be considered as a
process that is determined by two steps [29]:
- the mutual approach of the particles to such a distance that a permanent contact
can be formed (collision);
- the actual formation of the contact (coagulation).
According to Lowry [30] there are three basic mechanisms by which collisions and, as
a >consequence, coagulation can take place:
- coagulation caused hy the Brownian motion of the partiele (Brownian coagulatión);
- coagulation due to the motion of the surrounding fluid (shear coagulation);
- coagulation at the air-liquid interface of the suspension (surface coagulation).
133
6.2.2.1. Brownian coagulation
Von Smoluchowski [31} derived an expression for the Brownian coagulation of equally
sized spherical particles:
where:
[ 4.kb . T l 2 3.!L W br .[N]t
kb the Boltzmann constant
T the absolute temperature
1.1 = the dynamic viscosity
Wbr = the stability factor for Brownian coagulation (a function of Vt)
the time
[N]t = the total number of particles per unit volume
(6.8)
The stability factor Wbr accounts for collisions which do not end in a permanent
contact. For stabie systems W br is large. Lower values of W br result in an increased
tendency for coagulation. For W br = 1 every collision leads to coagulation. Reerink
and Overbeek [32} derived the following expression for W br:
00
wbr = 2.a. J exp 0
[ vt J 1 ~ . (H+2.a)2 .dH
(6.9)
The ra te of Brownian coagulation can be controlled by increasing V t. Increasing V t
can be accomplished either by the actdition of a surfactant or by the addition of
steric stabilizers. In the first case the repulsion energy is increased by a better
electrostatic stabilization of the particles. In the latter case the increase in the
stability of the particles is accomplished by steric effects.
Spielman [33} and Honig et al [34} have shown that hydrodynamic forces are also
important in deterrnining W br· When two particles approach each other, the amount of
the continuons phase between them has to be pusbed away, resulting in an additional
resistance against coagulation and should therefore be considered in deterrnining the
stability factor.
134
6.2.2.2. Shear coagulation
The first expression descrihing the rate of coagulation of particles in a fluid in
motion was reported by V on Smoluchowski [31}. A rather complex equation was derived
by which coagulation of spherical particles in simple laminar flow could be
descri bed:
(6.10)
where:
a = partiele radius
y = shear rate
W == stability factor
N number of particles per unit volume
=time
i,j,k = particles of size "i", "j" and "k"
If the particles are assumed to have the same sizes equation ( 6.10) can be
simplified to:
16 y 3 . 2 :,.- . w- .a .[N]t s
where W s stands for the stability factor for shear coagulation.
(6.11)
Although this expression was developed for laminar flow it can also be used for
turbulent flow, as long as the coagulation process only takes place within the
smallest eddies of turbulence. Coagulation experiments of De Boer et al [29} with
0.74 J.liD polystyrene particles have shown that equation (6.11) can heusedas a good
approximation for the initia! stages of coagulation in a stirred tank. Por the shear
rate De Boer et al used the average rate of shear as derived by Taylor [35} for
isotropie turbulence:
(6.12)
where:
135
y the average shear rate
e == the energy dissipation per unit mass of fluid
v = the kinematic viscosity
An even better approximation can be obtained if the effects of hydrodynarnic
interaction between the particles and the flow and the electrostalie interaction
between the particles are also taken into account for the calculation of the
stability factor [29].
6.2.2.3. Brownian coagulation versus shear coagulation
Combination of the equations for shear coagulation and Brownian coagulation results
in {30]:
3 -Js 4.J.l.a .y wbr -r- == kb.T . w-s .. br
where:
J s = shear coagulation rate
Jbr = Brownian coagulation rate
(6.13)
lf Wbr=Ws equation (6.13) indicates that Brownian coagulation is becoming more
important when the particles are small. The assumption of equal W br and W s may only
be used for colloidal systems in which the repulsion between the particles is very
low. In systems where repulsion between the particles may not be neglected, W s is a
decreasing function of the shear rate, whereas W br is independent of the shear rate.
W accounts for ·the increase in collision energy due to the fluid motion. Increasing s the shear rate increases the force of collisions, so the fraction of effective
collisions will raise. Therefore the contribution of shear coagulation to the
overall coagulation process is larger than that predicted from the assumption W br =
ws.
6.2.2.4. Surface coagulation
Surface coagulation is the third important mechanism by which a coagulation process
can take place. Heller et al {36] proposed the following reasons why particles being
136
stabie in the bulk can coagulate at the gas-liquid interface:
- a higher electrolyte concentration at the interface;
- a lower dielectric constant af or near the surface;
- asymmetry of the partiele double layer at the interface.
Lowry [30} proposed another reason:
- a higher concentration of particles at the surface.
This latter phenomenon is caused by relative interfacial tension. It can be
described in terrus of a Langmuir adsorption isotherm. The relation between the
number of particles adsorbed at the gas-liquid phase boundary (N ) and the maximum ps number of particles that can he adsorbed (Nmax) is then given by:
where:
Nt = the number of particles per unit volume. in the bulk
K = the Langmuir adsorption equilibrium constant
(6.14)
The rate of surface coagulation can he described with second order kinetics [36}:
(6.15)
where:
K0
= the surface coagulation rate constant
N1
the concentration of colloidal particles in the bulk
A/V= gas-liquid area per unit of volume of the bulk liquid
Surface renewal is accomplished by agitation of the system. When there is no
agitation a film of coagulum will he formed and the coagulation stops once the film
is formed.
Both Heller et al [37} and Lowry [30} have observed zerotb-order kinetics for the
surface coagulation rate of several latexes with different solid contents. A zeroth
order rate law will he found when:
(6.16)
This means that the gas-liquid interface is almost completely covered with a
137
monolayer of particles (9 "' 1), so that the partiele concentration at the phase
boundary is significantly higher than in the bulk liquid.
6.3. Experimental
Batch emulsion polymerizations were carried out in two types of stirred tank
reactors. Both reactors were cylindrical stainless steel vessels, equipped with an
eight-bladed turbine impeller. The dimensions of the reactors are shown in figure
6.3. In most experiments reactor I was used as the batch reactor. In case reactor Il
was used, this will be indicated.
The reactor systems used for the continuous emulsion polymerization experiments were
a f'ulsed f'acked Çolurnn (PPC) and a series of three Çontinuous ~tirred Tank Reactors
(CSTR). The dimensions of the CSTR's are the same as those of reactor II (figure
6.3). The dimensions of the PPC are given in figure 6.4. The column reactor was
packed with l 0 mm glass Raschig rings. A detailed description of both reactor
systems has been given in chapter 4.
i Ht
l -E---Dt-
Reactor I
t Hi ~
Impeli er
i Ht
1 Reactor 11 +--Dt-
t Hi t
Figure 6.3. Dimensions of stirred tank reactors. Reactor I: H1
180 mm; Dt = 90
mm; VT = 1.1 dm3; H. = 90 mm; D. = 70 mm; 8-bladed impeller: q = 14 mm; r = 17.5 I I 3
(dr = JO mm); Column height: H = 5 m (5 segmentsof 1 m each); inner diameter: D = 50 mm; Pulsarion velocity: frequency range 0 - 3.5 s-l; stroke length 0 - 14 mm.
The monomer used was styrene inhibited with para t-butyl catechol. The styrene was
kindly supplied by DSM Research. Before use the styrene was washed with an aqueous 5
weight % sodium hydroxide solution to remove the inhibitor. Double distilled water
was used as the dispersion medium. The initiator used was potassium persulfate. As
emulsifier Dresinate 214 was used, that is the potassium soap of a certain rosin
acid. The composition was measured by Maron et al [38]. The product was supplied to
us by DSM Research. Some experiments were carried out with sodium dodecyl sulfate as
emulsifier. In these experiments the initiator was sodium persulfate. The
electrolytes that were used as a pH-buffer for the emulsions and for adjustment of
the ionic strength of the emulsions were dipotassium carbonate, disodium carbonate,
potassium hydroxide and sodium hydroxide.
Before the polymerization was started water, emulsifier, buffer and monomer were
added to the reactor. The dissolved oxygen in these materials was removed by vacuum
139
degassing and bubbling argon through the mixture. Then the initiator solution was
added to the reactor and the polymerization was started. The reaction temperature
was maintained at 50.0 ± 0.5°C with a thermostalie bath. The impeller speed was kept
constant at 500 rpm.
Monoroer conversion was determined gravimetrically. The volume average diameters of
the polymer particles were measured by dynamic light scattering with a Malvem
autosizer type He (see appendix A.2). The volume average diameters measured with
the dynamic lightscattering technique agreed wel! with volume average diameters
obtained from measurements of the same samples with a Iransmission glectron
Microscope (TEM). The number of polymer particles was determined from the monoroer
conversion and the volume average diameters of the latex particles. Molecular
weights are measured by Qel fermeation Qhromatography (GPC).
6.4. Results and discussion
6.4.1. Preliminary experiments
Figure 6.5a shows the experimentally observed relation between the monoroer
conversion (Xm) and the time (t) for a batch emulsion polymerization of styrene
with Dresinate 214 as emulsifier and polassium persulfate as the initiator. In one
experiment the optimum pH was obtained by adding potassium hydroxide to the reaction
mixture, in the other experiment this pH was established by using dipotassium
carbonale as a buffer.
From figure 6.5a a remarkable difference between the increase of the conversion with
time can be observed for both experiments. The conversion rate for the experiment
with KOH agrees with the simple kinetic models developed by Harkins {39,40] and
Smith and Ewart [41]: an almost constant reaction rate in interval 11 of the
polymerization process (< 43% conversion [20]). For the experiment with K2co3 as a
pH-buffer such a constant reaction rate in interval IJ is not observed. The reaction
rate, being proportional to the slope of the tangent of the Xm vs. t curve,
decreases gradually with time.
The differences described above can be explained by consirlering the number of
particles as a function of conversion. These data are colleeled in figure 6.5b. For
the experiment with KOH the number of particles increases first as a result of
partiele formation in interval I and remains constant in the intervals II and liL
For the other experiment however, the number of particles decreases after an
increase resulting from partiele formation. At a conversion above about 50 % the
140
100 0 ... ... ... ... ... ...
... 80 ...
... ...
60 ...
= 0 ... ·;; ... ... A A A ..,
40 ... A > A = A 0 ... "" u "" 20 "" A
At> 6 ••
0 0 32 64 96 128 160
Residence time (min)
20 ~
6 ... ...... 16
A - ... ...... ... ... "e " ... ...
... ... ... ::::;.
12
~ " - 8
~ ... 6
z 4 A
" 61>. A I> A l>a,. 6 " A 6
0 0 20 40 60 60 100
Conversion (%)
}'igure 6.5. Typical course of emulsion polymerization of styrene emulsified with
As can be seen in the figures 6.6a and 6.6b the differences in polymerization rate
at the different emulsifier levels are considerable. Except for the highest
emulsifier concentration, all experiments show a decrease in polymerization rate in
interval II of the polymerization ( < 43 % conversion) The degree of conversion where
R decreases goes up with higher emulsifier concentration. Figure 6.6c shows that p
there is also a strong decrease in the number of polymer particles as a function of
conversion, except for the experiment with the highest emulsifier concentration. The
results indicate that below a certain emulsifier concentration, the polymer
particles can coagulate and coalesce owing to the electrostatic destabilization of
the particles. The coagulation of the particles is more striking at the lower
emulsifier concentrations, which is a direct consequence of a lower degree of
electrostatic stabilization of the latex particles at such emulsifier levels.
Information about the lowest soap concentration at which just no coagulation occurs
at a given cation concentration can be estimated from the minimum degree of
occupation of the surface of the latex particles with emulsifier molecules necessary
for a complete electrostalie stabilization of the emulsion. The fraction of the
surface area of the latex particles occupied with emulsifier molecules can be
calculated with:
e = as.Na.( [ S]-[S]CMC)
p (6.17)
where Ap stands for the partiele surface area per unit volume of continuous phase,
a for the surface area covered by one emulsifier molecule, [S] for the emulsifier s concentration in the recipe and Na for Avogadros constant.
For equally sized particles A can be obtained from: p
(6.18)
The number of particles per unit volume of the continuous phase ([N]) can be
obtained from the paniele diameter of the product according to:
[Nl
with:
6. [Mlo- Mw
1t.pp.dp
[Mlo= recipe monomer concentration
M = molecular weight of the monomer w
pp = density of the polymer particles
144
(6.19)
In table 6.1 the fraction of the surface area of the. particles occupied by
emulsifier molecules, e, is calculated for four different emulsifier concentrations.
Weight average diameters (d ) measured at low conversion were used to calculate e. p,w
Table 6.1. The calculated fraction 8 of the surface area of
the polymer particles occupied by emulsifier molecules.
[S] d [N]w * 10-20 e p,w
kmo11m3 nm m 3 %
0 .165 58 42 95
0.082 83 12 7 I
0 .041 17 5 1.4 70
0.020 413 0.1 75
The results of table 6.1 lead to some important conclusions. First, the degree of
surface accupation by emulsifier molecules seems to be independent of the emulsifier
concentration in systems that partly coagulated. Obviously a surface accupation of
about 0.7 is enough to stabilize each system at the given electrolyte concentration
of 0.30 kmo11m3 . No significant dependenee of e on the partiele diameter has H20
been observed.
A second important condusion that for the experiment with the high emulsifier
concentration ([S] = 0.165 kmo11m3 ) the surface accupation of the particles by H20
emulsifier molecules is as high as 0.95. A complete occupation of the partiele
surfaces with soap logether with the absence of a decrease of the partiele number
during the polymerization process indicates that the electrostatic stabiliztion is
strong enough to prevent any coagulation.
lt is interesting to see how the number of polymer particles, [N] , in the final w
latex depends on the emulsifier concentration when coagulation occurs. According to
the 'case 2' theory of Smith and Ewart {41] the dependenee of [N] on the micellar
emulsifier concentration ([S)m = [S] - [S]CMd can be given by:
[N] - [S] 0.6 m
(6.20)
In chapter 3 it was mentioned that relation (6.20) gives a reliable prediction of
the kinetics of the emulsion polymerization of styrene when sodium dodecylsulfate is
used as emulsifier. It can be expected that relation (6.20) will not be valid for
145
; 0 -*
0.02 .___ __ _;_ _ __;__;___;__..;.__c__;_..:._j
0.01 0.1
Figure 6.7. Number of polymer particles in ftnal latex as a function of the micellar
emulsifter concentration. Reaction conditions equal to those of ftgure 6.6.
the styrene emulsion polymerization with rosin acid soap as emulsifier. It may be
possible, that the partiele formation follows relation (6.20), but the proceeding
coagulation of the particles causes a drop in the number of polymer particles. In
figure 6.7 the measured values of [N]w are plotted as a function of the micellar
emulsifier concentration ([S]m). From the data collected in this figure the
following proportionality between [N]w and [S]m can be derived:
[N] _ [S] 2.9 w m (6.21)
which is notably different from the predictions of Smith and Ewart.
If we assume that the particles have the same diameter it is possible to predict
theoretically the dependenee of [N] on [S]m. For a final latex with equally sized
particles and 8 independent of [S]m combination of the equations (6.17) - (6.19)
leads to:
[N] _ [S] 3.0 m
(6.22)
which is very close to the actually observed dependenee as given in relation (6.21).
A good understanding of the conneetion between number of polymer particles and
conversion asks for knowledge about the rate of coagulation. Coagulation experiments
of De Boer et al [29} in a stirred tank with 0.74 Jlm polystyrene particles showed
146
that the time scale of coagulation (i.e. the time scale over whiëh a small change in
the partiele size distribution occurs) is of order 103 s, for the volume fraction of
solids being a bout w-5. For the initia! stages of coagulaüon De Boer et al found,
in close agreement with predictions of Von Smoluchowski [31], that the rate of
coagulation was proportional to the square of the volume fraction of solids. In our
polymerization experiments we have a volume fraction of polymer particles of about
0.30, being about 4 - 5 orders of magnitude Iarger than in De Boers experiments. It
is therefore probable that the time scale of coagulation during the polymerization
is much smaller than that of the polymerization reaction, being . of order 102 s for
the reaction conditions investigated. In addition to shear coagulation also Brownian
motion of the particles promotes coagulation. Therefore it may be assumed that at
any conversion during the polymerization the degree of surface accupation of the
particles by emulsifier molecules will be very close to the value for particles that
are just stabilized. For the system examined in this section this implies that the
degree of surface accupation of the particles, e, is about 0.7 at any time of the
polymerization. In this case it is possible to predict the number of polym~r
particles and the polymerization rate throughout the polymerization. If e is
constant throughout the polymerization it can be reasoned that the number of polym~r
particles, [N], is about constant during interval III of the polymerization. For
interval 11 of the polymerization it can be deduced that the total partiele surface
area is the following function of conversion and number of polymer particles:
_ [6. [M] 0.Mw.Xm]2/3 . 113 A - 1t. 1t . p . X .[N]
P p me (6.23)
where X is the critica! conversion at the end of interval 11 (X 0.43). me me Combination of the equations (6.23) and (6.17) gives the next relation between the
number of polymer particles and the conversion:
[N] (6.24)
In figure 6.8 the experimentally observed number of polymer particles are compared
with theoretica! predictions, assuming momentaneous coagulation and coalescence of
the particles, and a constant degree of surface accupation of 0.75. The good
agreement between theoretica! and experimental values indicates that the emulsion is
in physical equilibrium at any time, which means that the rate of coagulation and
coalescence is indeed very high in comparison with the growth rate of the particles
by polymerization.
147
- 24 "e "'-
18
12 *
6
I I
\t; \
'
•
',ll '4 4~~,~~A~--A--A------A----------
0~--~--~~--~------~----~------~
0 20 40 60 80 100
Conversion (%)
Figure 6.8. Theoretically predicted and experimentally observed numbers of polymer
particles as a function of conversion. Reaction conditions equal to those of flgure
6.6. The lines correspond to theoretica/ predictions.
<•J and (--) [SJ 0.082 kmol!n:/H20
; (1:::.) and (-----){SJ = 0.041 kmo11m3 1120
;
(6.) and (·· .. ') {SJ = O.o20 kmol!m Hzo·
Until now the influence of the emulsifier concentration on the overall rate of the
polymerization has mainly been described in terms of the partiele number [N]w.
However, another factor of likely importance is the reaction rate per particle,
Rp/[N]w. In the following part this quantity will he discussed.
The results of the figures 6.6a and 6.6c can he used to calculate Rp/[N]w. In figure
6.9 the values of Rp/[N]w are given as a function of conversion. Hereafter the range
between 10 % and 43 % conversion (interval II of the polymerization) will he
examined.
Figure 6.9 shows a significant increase of RJ[N]w with conversion for the lower
emulsifier concentrations. The increase in R /[N] is possibly related to the large p w increase in partiele diameter. Especially at the low emulsifier concentrations
partiele diameters grow with a factor 4-8, due to the coagulation and coalescence of
the particles.
Figure 6.10 gives a view of the dependenee of Rp/[N]w on the partiele diameter. The
larger particles show a much higher polymerization rate than the smaller ones. The
differences in polymerization rate can he explained by considering the time-average
number of radicals per particle, which may he a function of partiele size. The
time-average number of radicals per partiele is determined by a number of processes:
radkal absorption and radical desorption, terminalion of radicals in the particles
148
0.30 .. ..
-en .. '-.. 0.24 .. ö E ..
0.18 .. .. 2 .. 0 A
~· ·~
.. * 0.12 A A
!I' .. A AA A A A
z A '-.. 0.06 AA Q.,
o"'~ • • 0:: ri' • • • A • ••
.a oA•c [J [J • • D D D o• D ~cfla.... 0.00
0 20 40 60 80 100
Conversion (%) Figure 6.9. Reaction rate per partiele as a function of conversion. Reaction
The results are presented in the figures 6.l3a-c. Figure 6.13a shows the relation
between the conversion and the reaction time for some K2s2o8-concentrations.
Contrary to results reported for sodium dodecylsulfate as emulsifier {20,23J the
course of the conversion with time is only slightly dependent on the initiator
concentration used. The small influence of the initiator concentration on the
overall reaction rate is also in line with the number of polymer particles as a
function of conversion as collected in figure 6.13c for some initiator
concentrations. Figure 6.13c shows that the number of polymer particles is
independent of the intiator concentration within experimental error. This is in
complete contradiction with the regular Smith-Ewart model which prediets the
following proportionality between the number of polymer particles ([N]) and the
initiator concentration ([1]):
(6.28)
This means that a tendency for a higher number of particles at higher initiator
levels is immediately counterbalanced by a coagulation and coalescence process.
A small positive effect of an increasing initiator concentration on the overall
polymerization rate can only he observed in figure 6.13a for smal! conversions. This
effect probably originates from a somewhat higher partiele formation rate at higher
K2s2o8 concentrations. Unfortunately it was not possible to measure numbers of
forrned polymer particles at those low conversions.
0.30
0.24 -fll ...........
ö 0.18 s ... -z 0.12
... 0 ........... ~~~1:1· 0 0. o@ a o a 0
P::: ••a"' q,~,. 0 ... ... 0
0.06 .pa lilo ...
~ "'l0
...
0
0.00 0 20 40 60 80 100
Conversion (%)
Figure 6.14. Reaction rate per partiele as a function of conversion. Reaction
conditions equal to those of figure 6.13. (D) [IJ 0.0125 kmo11m3 H
20; (y) [IJ =
0.0063 kmo11m3 H
20; ( o) [IJ = 0.0031 kmo11m3
H20
.
155
The 'more pronounced differences in the relations between conversion and time, for
the initiator concentrations investigated, at conversions above 0.6 can be explained
by the reaction rates per particle .. Figure 6.14 shows that for con versions above
about 60 % a slight increase in R /[N] for the higher initiator concentrations was found, p w whereas the lower initiator concentrations did not show this effect. The only
explanation that can be thought of is the gel-effect. A high initiator concentration
corresponds to a high rate of radical formation, r.. According to Stockmayers I
theory [43] an increase in r. leads to an increase in the time-average number of . I
radicals per particle, ii. This change in ii is only noticeable at high conversions,
when partiele sizes are large and diffusional transport of the radicals through · the
particles is relatively slow. Wilh the parameters given in appendix AA we have made
calculations of the time-average number of radicals per partiele for the three
initiator concentrations examined in this paragraph. The results are shown in figure
6.15. It is obvious that the gel-effect may be neglected at low conversions, but has
to be taken into account at conversions above about 60 %. It may also be noticed
that for low conversions n = 0.5 for all three initiator conèentrations.
10
8
6
Is:: 4
2
0 0 20 40 60 80 100
Conversion (%}
Figure 6.15. Calculated time-average manher of radicals per partiele as a function
of conversion according to Stockmayer [43 r Reaction conditions equal to those of 3 3 flgure 6.13. (--) [Ij
3 0.0125 kmollm H
20; (-----) [Ij 0.0063 kmollm H
20;
( .... ) {Ij 0.0031 kmollm , H20
6.4.4. Variation of monomer concentration
Results of batch emulsion polymerizations at different monomer/water ratios are
156
100 w 0 c 0 cc
80 c c N' c - c c 60 rP " 0 ;;; c " c
"" ... c <I> " " i> 40 c " " 0 c c
Cl ...... " 0 0 u c ...... 0 0 0 0 0
0
20
,~0 0
0 50 100 150 200 250
Residence time (min)
1.00 c b
0 c
0.80 8 c - 0
"! 00
Êl 0 0.60 c ........ .. .. c
0 0 " 0
1! 0
O.fA co 0
0.40 0 Q. a:y. " 0
0:: 0" ........ Cl
0.20 o 99oo o" " Cl 0 "<1/.""
"" " 0 " 0.00 0 20 40 60 80 100
Conversion (%)
25
c 0 - 20 0
"s 0 " c 0
........ " - 0 15
' 0 0
0 " 0
0 0 0 oo 0 'tPo - o• 0
10 0 0
0 ó> .... ~ z 0 ........
5 <Sf6 ......... J "" " ~00 0
0 0 20 40 60 80 100
Conversion (%)
Figure 6.16. Emu/sion polymerization of styrene at various monomerlwater ratios. [SJ
= 0.082 kmo11m3 H20; [Ij= O.Olf kmo11m3
H20
; [K+} 0.30 kmo~n/ H20
; T = 50°C; pH=
11. (Dj [M} = 4.0 kmol/m H20
; ( .& ) [M} = 6.4 kmol/m H20
; ( o) [M] = 9.6
kmofirn H20
157
depicted in the figures 6.16a-c. It appears from the figures 6.16a and b that the
monomer/water ratio strongly affects the polymerization rate and conversion.
Analogous to the findings in the sections 6.4.2. and 6.4.3. the observed decrease in
polymerization rate can he contributed to a decrease in numbers of polymer particles
(see figure 6.16c). It can he seen in figure 6.16c that the monomer/water ratio
influences the number of polymer particles in rhe final latex. This is in
contradiction with results reported for sodium dodecyl sulfate as emulsifier
{20,23], where it was shown that the kineties could he reasonably described by the
theory of Smith and Ewart {41]. According to Smith and Ewart the number of formed
polymer particles has to he independent of the monomer/water ratio.
The observed dependenee of [N]w on the monomer/water ratio (i.e. the recipe monomer
concentration) can he contributed to the coagulation and coalescence of the polymer
particles as is described in the foregoing sections. For larger weight fractions of
monomer in the recipe, the initially formed polymer particles can grow into
significantly larger partiele diameters. The total partiele surface area increases
therefore also considerably. On account of the lesser stabilization of the
particles, the rate of coagulation is larger and the number of polymer particles
decreases further. Therefore the partiele number in the final latex is a decreasing
function of the monomer/water ratio (figure 6.17). The experimentally observed
linear correlatîon between log [N] and log [M] can he expressed as: 10 w . 10
[N] - [Mf2.3 w
(6.29)
-s --...... 10 -.. .. ' 0
~ z
Figure 6.17. Number of polymer particles in final latex as a function of the recipe
monomer concentration. Reaction conditions equal to those of figure 6.16.
158
Values for e (the degree of occupation of the partiele surface area with emulsifier
molecules) are given in table 6.3. The results confrrm the expectation that e is
independent of the monomer/water ratio. Notice also that the obtained values of e are about equal to those obtained earlier for variabie emulsifier concentration (see
section 6.4.2.).
Table 6.3. Calculation of the fraction e of the surface area of
the polymer particles occupied by emulsifier molecules.
[M] dp( w) [N]w * 10-2o e
kmo 1tm3 nm m -3 %
4. 1 83 12 71
6.4 141 4.2 74
9.6 217 1.7 75
A theoretica! prediction of the exponent in relation (6.29) is very well possible.
Combination of the equations (6.18) and (6.19) gives the following relation for the
Again three different regions can he distinguished. At very low energy dissipation
rates (ei < 5*10"2 W/kg) this tigure shows that the degree of surface occupation of
the latex particles with emulsifier molecules (E>) is independent of the energy
dissipation rate. For the two lowest emulsifier concentrations the plots of E> as a
function of ei coincide within experimenta.l error. For the higher value of [SJ the
values of 0 are considerably higher for e. < 5*10-2 W/kg. For e. > 3*10-l W/kg the 1 1
values of 0 are also independent of [SJ and e. within experimental error.
In the region of low values of ei (ei < 5*10-2 W/kg) the flow in the major part of
the reactor is laminar. This becomes clear from the Reynolds number for stirred
tanks , Red, defined as:
2 R
_ p.N.D ed- Jl (6.42)
where p, N. D and l1 stand for the density of the liquid, the rotational impeller
speed, the impeller diameter and the dynamic viscosity of the liquid respectively.
The values of Red < 2000 forstirring speeds N below 1.5 s- 1 (ei< 5*10-2 W/kg for
the tank used) point to laminar flow. At very low liquid veloeities coagulation by
collisions originating from the Brownian motion of the particles has to he
168
considered. Using the equations (6.8) and (6.9) it was explained that the rate of
Brownian coagulation is mainly deterrnined by the height of the potential energy
harrier (Vt' figure 6.2) between the latex particles. The height of the potential
energy harrier resulting from the electrostatic repulsion caused by the emulsifier
molecules increases on increasing . the emulsifier concentration on the partiele
surface (the so-called surface emulsifier concentration). The critica.! value of V1
below which coagulation will occur is determined by a critica! surface occupation of * the latex particles with emulsifier molecules, 0 . When the emulsifier concentradon
* in the recipe ([S]) is so low that 0 < 0 coagulation and coalescence will occur * until the partiele surface has decreased to such an extent that 0 = 0 ([S] ::;; 0.041
kmo11m3 H
20). For low emulsifier concentrations the surface occupation of the
particles with emulsifier in the final latex is independent of S. This points to the * condusion that 0 = 0.45 for Brownian coagulation in laminar flow. For high
emulsifier concentrations ([S] ~ 0.082 kmo11m3 ) the values of 0 of the final * H20 latex are considerably higher than 0 . For these high emulsifier concentrations the
partiele number can be expected to be equal to the value predicted by the
Smith-Ewart theory. This has been shown in table 6.6 where the partiele numbers
calculated with the Smith-Ewart theory, modified by Nomura and Harada {20,41], are
collected together with the observed partiele numbers. For the highest emulsifier
concentration investigated ([S] = 0.082 kmo11m3 ) the predicted partiele number is H20
indeed equal to the experimentally observed value. For the two other emulsifier
concentrations investigated the experimentally found partiele numbers are
considerably lower than the calculated ones. Here coagulation and coalescence take
Table 6.6. Comparison of numbers of polymer particles and values of 0
in final latexes for the laminar flow region and in case of absence
of partiele coagzdation (calculated).
experimental calculated
I am i nar flow reg i on a b se nee of coagula t ion
[S] [N]w * 10-2o e [N]w * 10-2o e kmo11m3 -3 -3 m m
0.082 24 0.60 23 0. 61
0.041 5.2 0.46 14 0. 33 0.020 0.45 0. 45 8 0. 17
169
* place until e e !
In the considerations pre~nted above the influence of the sulfate endgroups of the
polymer molecules present at the partiele surface has not been taken into account.
In table 6.7 the surface concentration of the sulfate groups is given together with
that of the emulsifier molecules for the three emulsifier concentrations
investigated. In the calculations teading to table 6.7 the differences in sulfate
end group concentrations caused by differences in polymerization time are also taken
into account. The values for the sulfate endgroups are compared with calculated
concentrations of emulsifier molecules present at the partiele surface. Some care
has to be taken in comparing the sulfate endgroups of the polymer molecules with the
carboxyl groups of the emulsifier molecules, since their influence on the
stahilizing electrical double layer may be different. However, table 6.7 shows that
the surface concentrations of sulfate endgroups are much lower than the
concentrations of the carboxyl groups. From this difference between the surface
. concentrations it is probable that the sulfate end groups only play a minor role in
the electrostalie stabilization of the latex particles.
Table 6.7. Concentrations of emulsijier molecules and sulfate endgroups
of polymer molecules at the surface of the polymer particles.
[S] [S] surf ace [I] surf ace
kmo11m3 mol/m 2 mol/m 2
0.082 2.25 0.0 l
0.041 1.80 0.12
0.020 1. 12 0.33
In the region of energy dissipations between 5*10-2 and 3*10-1 W/kg corresponding
with 2000 < Red < 7500 a considerable increase of 9 9 .1
is observed when e. 3 en 3 1
increases for [SJ = 0.020 and 0.041 kmoVm mo· Por [SJ = 0.082 kmoVm mo figure
6.23 shows only a small increase of e at higher impeller speeds. An increase of
9 .1
is necessary for higher impeller speeds because the collision forces resulting en from the shear forces then also increases. Therefore higher electrostatic repulsion
forces are 1ikely to be necessary to prevent coagulation. As stated earlier the
electrostatic repulsion forces between the particles increase on increasing the
surface emulsifier concentration at a constant electrolyte concentration.
Figure 6.23 shows that in the region of highly turbulent flow (ei > 3*10-l m2ts3,
170
Red > 7500) E> = E>crit = 0.75 is equal for each of the three emulsifier
concentrations studied. This region is of main importance for emulsion
polymerization, since most commercial processes require a certain turbulence for
proper emulsification. In the upper region the expected dependenee of E> on the
energy dissipation can not be seen anymore although the shear rate is increased
drastically. The only acceptable explanation may be that for these high energy
dissipations coalescence of primary coagulated particles is prevented by the very
high local emulsifier concentrations at the point of contact. If the particles are
closely encountered hydrodynamic interactions have to be taken into account. In his
coagulation theory Von Smoluchowski [31} assumed that particles move along
rectalinear trajectories. Real collisions between colloidal particles, however, are
more complicated. According as the particles approach closer the remaining narrow
liquid film between the particles needs more effort to be displaced by diffusion
[60,61}. Therefore, the approaching particles move along trajectories that can
differ considerably from a rectalinear approach. In fact a lot of the colliding
particles do not coagulate at all. Van de Ven and Mason [62} have taken this extra
resistance against coagulation into account by defining a 'capture efficiency', a0,
being the ratio of the collisions that really take place to the collisions that
should take place on rectalinear approach. Van de Ven and Mason found that a0 decreases with increasing shear rate. They also showed that an increase in repulsion
forces between the particles could strongly decrease a0. At high shear rates and
high repulsion forces (which corresponds to high values of E> in our system) one can
even have a situation in which a0 0, i.e. no coagulation can take place at all.
In an emulsion in which the particles can coalesce the situation is more
complicated. In such a system one should also consicter the time necessary for the
particles to approach to such a distance that coalescence is possible. If this
'critica!' time is relatively long compared with the time that the particles are 'in
contact' they will be separated again by the shear forces before coalescence can
happen. The coalescence of dropiets in an emulsion was studied extensively by lvanov
[63} and by Zapryanov et al [64}. According to their theory the factors governing
the 'critica!' time are the rate of thinning of the liquid film between the
particles and the critica! thickness at which film ropture occurs. They proposed
that the rate of film thinning and the critica! film thickness are both strongly
affected by emulsifier present at the interface of the droplets. High emulsifier
concentrations retard the drainage of the film by the so-called Marangoni-Gibbs
effect: the moving liquid carries surfactant away, thus causing perturbation in the
equilibrium surfactant concentration at the interface. This results in interfacial
lension gradient and surfactant transport from the bulk liquids to the interface,
171
which has a decreasing effect on the rate of film thinning. A detailed description
of the rate of film thinning in emulsions is given in the work of Zapryanov et al
[ 64]. The effect of emulsifier concentra ti on on the critica) film thickness is
twofold. The rupiure of the film is believed to be affected by capillary waves
arising in the film at small film thickness (see Figure 6.24). The amplitude of
these waves delermines the critica) thickness at which film ropture occurs. At small
wave amplitudes the critica) thickness, h , will also be small. It has been shown er that high emulsifier concentrations have a decreasing effect on the amplitudes of
the capillary waves. A second effect of high emulsifier concentrations is, that the
interfacial tension decreases, which also has a decreasing effect on the critica}
film thickness. An extensive description of the critical film thickness in emulsions
is given in the work of lvanov [63].
Figure 6.24. Occurance of capillary waves in thin liquid films between two
approaching particles.
The above consideration of partiele coagulation and partiele coalescence makes elear
that prevention of partiele coalescence at high emulsifier concentrations and high
shear rates may very well be the actual cause of the constant 9-value observed in
our emulsions at high shear rates. However, an exact hydrodynamic analysis of the
observed phenomena is not possible at the present knowledge, because of the great
complexity of the different processes that are involved.
6.4.6.2. Influence of shear rate in pulsed packed columns
The flow in a PPC can be characterized as a quasi-homogeneous turbulent flow with
172
uniform shear rates all over the column. The energy dissipation in a pulsed packed
column is caused by resistance to flow. For the energy dissipation the following
equation can be written:
e _ 6P.1t.s. f - p.eb.H
where:
óP= pressure drop over the packed bed
s stroke length of pulsation
f = frequency of pulsation
p = density of the liquid
~ bed porosity
H = height of the packed bed
(6.43)
The pressure drop over the packed bed due to friction is the next function of the
pulsari on:
1 [1 ]2
2 óP = 4.fr.2.p.(Hidr>. 2.s .ro .cos(ro.t) (6.44)
with fr is the friction factor, dr is the characteristic diameter of the packing
particles and ro is the frequency (= 2.n.f).
From equation (6.44) it can be seen that the pressure drop due to friction, and
therefore also the energy dissipation, shows a cyclic behaviour. lt is expected that
the coagulation and coalescence of the polymer particles is mainly determined by the
maximum energy dissipation during this cycle. The corresponding maximum pressure
drop due to friction can be easily measured by differential pressure measurements.
Deterrnination of the maximum energy dissipation during a pulsation cycle from
pressure drop measurements is described in detail in chapter 7.
Styrene emulsion polymerization experiments were performed in a pulsed packed column
(PPC) at various pulsation velocities. The column was packed with glass Raschig
rings (outer diameter: d = 10 mm). The dimensions of the column are shown in figure r
6.4. The recipes used are the same as of the experiments carried out in batch
(section 6.4.6.1). The mean residence time in the column was kept constant at 30
minutes for all experiments (interstitial velocity: u = 2.78 * 10-3 m/s). In chapter
3 it was shown that at such a high interstitial velocity the reactor performance of
the PPC in terms of conversion and partiele number is identical to that of a batch
173
50,-------------------------.
40
c 30 0
ïii ... :: 20 c 0 u
10
6 12 18 30
Residence time (min)
50.-----------. [!]
40
c 30 0 ïii ... :: 20 c 0 u
10
6 12 18 24 30
Residence time (min)
50.-------------------------,
c 30 0 ïii ... :: 20 c 0
u 10
6 12 18 24 30
Residence time (min)
Figure 6.25. Experimental conversion residence time curves of the emulsion
polymerization of styrene in a pulsed packed column at various emulsifier
concentrations and various pulsation velocities. [IJ 0.0125 kmol!m3 ; [K+ J = 3 ~ 3
In figure 6.28 numbers of polymer particles in the product latex are given for
several experiments at different electrolyte concentrations. lt is shown that a
decrease in electrolyte concentration with a factor 6 can increase the number of
polymer particles with a factor 10 at an emulsifier concentration of 0.041
kmoVm3 H
20• Potassium concentrations below 0.065 kmoVm3
H20
could not be achieved.
This lower limit is determined by the concentrations of emulsifier, · initiator and
alkali added to the reaction mixture. At potassium ion concentrations above 0.50
kmoVm3 H
20 massive coagulation and flocculation of the particles occurred.
The data collected in figure 6.28 can be used to calculate the degree of surface
occupation of the polymer particles with emulsifier molecules. The results of these
calculations are also presented in figure 6.28. It appears that for high electrolyte
concentrations the polymer particles have a 8-value of about 0.8. In view of the
errors introduced in the deterrnination of e, the degree of occupation of the
particles at these high electrolyte concentrations can be higher than 0.8, i.e.
close to unity. In such a case the maximum possible amount of emulsifier present at
the partiele surface is not enough to pre.vent the particles to coagulate. This can
be an explanation for the observed massive flocculation of the particles observed at
electrolyte concentrations above 0.50 kmoVm3 . H20 3 At the lowest possible electrolyte concentration of 0.065 kmoVm mo an inflection
in the curves can be noticed. This is an indication that at those low electrolyte
177
lil 0 -~ z
15 100
12 80
--Q--r· ----0
9 --- 60 -- 0
6 40
3 20
OL----~--~--'----'------0
0.00 0.08 0.16 0.24 0.32 0.40
[K+] (kmol/m3)
<D
~
Figure 6.28. Number of polymer particles in the final latex and the degree of
surface occupation of the polymer particles by emulsifier molecules as a function of
the cation concentration for rosin acid soap as emulsifier. [SJ = 0.041 kmo11m3 ; 3 a ~
[IJ 0.0125 kmollm H20
; 30 vol.% monomer; T 50 C; pH = 11; N = 500 rpm.
(e) number of polymer particles [NJw; (0) degree of surface accupation e.
concentrations ([K+] < 0.10 kmoVm3 H20) coagulation of the particles does not occur.
The electrostalie stahilization of the latex is sufficient . to prevent coagulation.
Partiele numbers are now solely determined hy partiele nucleation.
For an interpretation of the data of figure 6.28 it should he realized that all
experiments are performed at a rotational impeller speed of N = 500 rpm. This speed
was chosen for practical purpose, since most emulsion polymerization processes
require high impeller speeds to avoid deemulsification. From the results discussed
in section 6.4.6.1 it can he derived that at impeller speeds ahove N = 200 rpm (è = 5*10-2 m2ts3) coalescence is prevenled as a result of the hydrodynamic interaction.
This will prohahly influence the final size of the polymer particles. Viewed in that
light the results of figure 6.28 should also be explained by consictering the
hydrodynamic interaction. The prevention of coalescence of particles by hydrodynamic
interaction can occur if the time necessary for the particles to coalesce is
relatively large. This is the case when:
the emulsifier concentration in the liquid film between the particles is high thus
leading to very low rates of film thinning by diffusion and a small critica! film
thickness;
the height of the potential energy harrier and the kinetic energy of the
approaching particles are of the same order of magnitude.
178
When large amounts of electrolyte are added to the emulsion, the repulsion potential
between the particles is lowered. Van de Ven and Mason [61], consiclering the effect
of hydrodynamic interaction on partiele coagulation, showed that the capture
efficiency o.0
strongly increases at increasing electrolyte concentration, due to a
decrease in the repulsion forces between the particles. This implies that at
constant shear rate the value of e should be considerably higher than at lower
electrolyte concentrations to attain the situation corresponding to a negligible
capture efficiency. Figure 6.28 shows that the experimental results are in
qualilalive agreement with the above theory.
To compare the stahilizing effect of the two emulsifiers used in this study,
identical experiments are carried out with sodium dodecyl sulfate, a surfactant that
is extensively described in the literature. Sodium dodecyl sulfate can be
characterized as an emulsifier with a good stahilizing effect. The emulsification
properties of sodium dodecyl sulfate are rather insensitive to the pH, which means
that sodium dodecyl sulfate, in contrast with rosin acid soap, can also be used in
neutral environments. Figure 6.29 shows the experimentally determined values of [N]
and e for experiments with sodium dodecyl sulfate, performed at identical recipes as
the experiments with the rosin acid soap. It appears that the stahilizing effect of
sodium dodecyl sulfate is much larger than that of the rosin acid soap. The polymer
particles are stabie up to cation concentrations of 0.25 kmol!m3 mo· In figure 6.30
~ 0
11' z
15r-----------~.--~.------------, 100
• 12 80
.-er 9 -:f-"' 60
' ' ' ' -- -Q--- O--- -c--- -e- / 0
6 40
3 20
oL-----~----~----L-----L---~0
0.00 0.08 0.16 0.24 0.32 0.40
[Na+] {kmol/m3)
(])
-~
Figure 6.29. Number of polymer particles in the final latex and the degree of
surface accupation of the polymer particles by emulsifier molecules as a function of
the cation concentradon for sodium dodecylsulfate as emulsifier. [SJ == 0.041 3 3 0 kmol!m H
20; [1] = 0.0125 kmollm H
20; 30 vol.% monomer; T= 50 C; pH= 11; N = 500
rpm. ( •) number of polymer· particles [N] w; ( o) degree of surface accupation e.
179
the data of both emulsifiers are collected. There were also some experiments carried
out with sodium dodecylsulfate at lower emulsifier concentrations. These data are
also given in the same figure. In figure 6.30 only data are given of experiments
that showed a decrease in the number of particles during the course of the
polymerization, i.e. experiments in which the final number of particles is
determined by coagulation and coalescence of the particles and not exclusively by
partiele nucleation. Because both emulsifiers investigated have different a -values, s the use of 0 is not a good criterion for the comparison of both emulsifiers. It was
therefore chosen to use the (critica!) emulsifier concentration at the surface of
the polymer particles as the criterion to compare both surfactants.
In figure 6.30 it can be seen that in the range of practical cation concentrations
(0.1 kmoVm3 H
20 < [X+J < 0.3 kmoVm3
H2J the concentration of emulsifier at the
partiele surface is about 2-3 times higher for the rosin acid soap than for the
sodium dodecyl sulfate (at the same pH), thus indicating that the stahilizing effect
of sodium dodecyl sulfate is much larger than the stahilizing effect of the rosin
acid soap. The observed differences in stahilizing effect should be contributed to
different influences of both emulsifiers on the behaviour of the liquid films
between the particles, such as rate of film thinning and critica! fllm thickness,
and on the repulsion forces between the particles (i.e. the height of the energy
harrier between the particles). The latter contribution is probably the most
important one. There is experimental evidence that part of the rosin acid soap
present at a styrene/water interface is present in the protonated form of the anion.
This information was obtained from a very simple experiment of creating a flat
interface between a layer of a rosin acid soap solution and a styrene layer and
watching the phenomena taking place at the interface. After a short time ( < 1
minute) a white precipitate could be clearly observed at the liquidlliquid
interface, being the water-insoluble protonated form of the rosin acid soap. The
white precipitate remained at the interface and disappeared only when mixed up with
the bulk of the rosin acid soap solution. The precipitation of acid at the
styrene/water interface can be explained by supposing that the water phase is
buffered with an electrolyte, for example bicarbonate. At the styrene/water
interface the concentration of rosin acid soap is be rather high and probably much
higher than in the bulk of the water phase. So, the interface will be strongly
negatively charged. Tilis negative charge repels ions of the same charge, among them
the buffering carbonale ions. Therefore a pH-gradient between the bulk liquid and
the interface exists resulting in a partial protonation of the rosin acid soap
anions present at the interface. If such a behaviour is also valid for the
polymer/water interface during an emulsion polymerization, we may contribute the
180
24
18
12
6
I
I I .
I I
o~--~----~----~----~----
o.oo 0.08 0.!6 0.24 0.32 0.40
[X+] (kmol/m3)
Figure 6.30. Critica/ emulsifier concentration on the partiele surface as a function
of the cation concentration for rosïn acid soap and for sodium dodecyl sulfatè as
observed differences in stahilizing effect between sodium dodecyl sulfate and the
rosin acid soap for an important part to the above phenomenon. Some care should be
taken by the above consideration because the different characters of the ionic
carboxyl groups and sulfate groups and of the hydrophobic parts of the emulsifier
molecules may also influence the stability of the particles.
6.4.8. Influence of residence time distribution
In chapter 4 the kinetics of the emulsion polymerization of styrene (in the absence
coagulation phenomena) were examined in several continuous reactor systems that can
be characterized by a certain amount of residence time distribution. The
performances of a pulsed packed column (PPC) and of a series of CSTRs were
investigated for various residence time distributions. It was shown that the number
of formed polymer particles decreases with increasing residence time distribution.
The parameter that can be used for the PPC to account for the effect of residence
time distribution on the number of formed polymer particles is the Peclet-number,
related to the section of the column in which the partiele formation takes place
181
(Pe1): For the series of stirred tanks the mean residence time of the first tank can
be used as the parameter, provided that the partiele formation takes place only in
the first tank.
If an emulsion is electrostatically destabilized and partiele coagulation and
coalescence can occur, an estimation of the contribution of the influence of
residence time distribution on the number of particles in the final latex may be
difficult. Probably coagulation and coalescence of the particles decrease the number
of polymer particles so drastically that effects of residence time distribution
cannot be distinguished anymore.
To investigate the combined effects of coagulation/coalescence and residence time
distribution on the number of polymer particles, experiments were performed in a PPC
and in a series of three CSTRs. The reactor types that were used in the experiments
are shown in the figures 6.3 and 6.4 respectively. The impeller speeds of the CSTRs
were adjusted to 500 rpm. The pulsation velocity in the PPC was kept constant at f*s
48*10-3 m/s in all experiments. The mean residence time was varled by varying the
reactor throughput. In the case of the PPC this influences also the residence time
distribution. The emulsifier concentration in all experiments was kept constant at
0.082 kmoVm3
Hzo· Figure 6.31 shows the number of polymer particles in the outlet stream of PPC and
the tanks as a function of the mean residence time in the reactors. The number of
20
-"' 16 e
"--12
:a l> 0 " 0 - •
8 * l> IJ " ;J: • z 4 l> 0
0 0 40 60 120 160 200
Residence time (min)
Figure 6.31. Number of polymer particles as a function of the mean residence time 3 3 + for several r;actor types. [SJ = 0.082 kmol/m HZO; [IJ = 0.0125 kmollm H
Figure 6.33. Number of polymer particles in a pulsed packed column as a function of
Pet Reaction conditions equal to those of figure 6.31.
particles in the product latex of a batch reactor, which was determined by
coagulation and coalescence of the particles, is also shown in the figure. It can be
recognized that at the same mean residence time much more particles are formed in
the PPC than in the tanks. It can also be seen that partiele formation in the
CSTR-cascade only takes place in the first tank (the partiele number doesn't change
anymore in the other tanks). Although figure 6.31 gives some information about
183
partide formation in a PPC and in a CSTR-cascade it is not possible to separate the
contribution of the residence time distribution on the number of particles, [N]w,
from that of coagulation and coalescence. More information can be obtained when [N] w
is plotted as a function of the conversion in the outlet stream of the reactors
(figure 6.32). Comparison of the data of the continuous reactor systems with data of
a batch experiment shows, that in the series of tanks at all conditions exarnined
[N]w remains far below [N]w of the batch experiment, indicating that the number of
particles in the CSTR is determined by partiele formation only. The same result can
be observed for the PPC at longer mean residence times (high conversions). At
relatively short mean residence times (conversion X > 0.6) however, the [N]-values m
for the PPC are equal to those of the batch experiment, thus indicating that at
those circumstances the number of formed polymer particles is deterrnined by
coagulation and coalescence of the particles. The number of polymer particles., [N]w,
of the PPC can also be plotted as a function of Pe1, the Peclet-number related to
the section of the colunm in which the nucleation of the polymer particles takes
place (figure 6.33). If the number of polymer particles is only determined by
partiele formation, then [N]w would follow the dasbed line of figure 6.33. However,
the experimentally determined curve lies well below the dashed line. At Pe-numbers * below a 'critical' Pe-value, Pe1 , the number of particles in the product latex is
determined by the residence time distribution during the partiele formation period. . *
At Pe-numbers above Pe1 coagulation and coalescence of the particles deterrnines the
number of particles in the final latex. It is shown that for an emulsifier 3 * concentration of [S] = 0.082 kmoVm H
20 Pe1 has a value of about 5.
A somewhat different picture is obtained at a lower emulsifier concentration. The
results for an emulsifier concentration of 0.041 kmo11m3 H
20 are shown in the figures
6.34 - 6.36. Figure 6.34 shows the remarkable phenomenon that over a large range of
mean residence times the number of polymer particles produced in the colunm is
relatively low. lt follows from figure 6.35 that this is completely caused by
coagulation and coalescence of the particles during the course of the
polymerization. All data of the PPC and as much as half the number of data of the
CSTR-series show that besides partiele nucleation coagulation and coalescence of the
particles delermine the number of particles in the product latex. Only the data of
the CSTR-cascade, obtained at low conversions and short mean residence times show
that only partiele formation determines the number of polymer particles. In figure
6.36 the [N]w-values of the PPC are given as a function of Pef The dasbed line
again represents the hypothetic situation that the number of polymer particles is
completely determined by the residence time distribution during the partiele
formation period. It is shown that the discrepancy between prediction from partiele
184
20
- 16 ., E!
""-.. - 12 0 .. • 0 - l!. [J
8 t * a::
l!. [J
:z 4 V
oLi ------~----~------~----~----~ 0 40 80 120 160 200
Residence time (min)
Figure 6.34. Number of polymer particles as a function of the mean residence time . 3 3 +
for several reactor types. [SJ = 0.041 kmol!m H20; [IJ 0.0125 kmol!m H20
Chapter 7. Monomer droplet sizes in styrene emulsion polymerization
7.1. Introduetion
For quite some time it has generally been accepted that the only locus of initiation
in emulsion polymerization is the aqueous phase. Two mechanisms have been proposed
for the initiation:
1. micellar nucleation: a radical generaled in the "aqueous phase enters a
monomer-swollen emulsifier micelle. The solubilized monoroer in the initiated
micelle rapidly polymerizes, thus forming a monomer-swollen polymer partiele
[1,2];
2. homogeneous nucleation: radicals generated in the aqueous phase reaèt with solute
monomer molecules to form oligomeric radicals. At a critical chain length the
oligomeric radicals precipitate from the solution to form a colloidally unstable
precursor partiele (dp "' 2 nm). These precursors may either grow to form stabie
latex particles (d ~ 20 nm), or coagulate with other primary particles thus p . gaining stability ("coagulative nucleation"), or coagulate with a mature polymer
partÎcle {3-5 I. In both mechanisms the polymer particles formed are considered to be the locus of
further polymerization. The monoroer dropiets are considered to serve as monoroer
reservoirs only, that feed monomer to the polymerizing particles by diffusion
through the aqueous phase. It is assumed that the monomer dropiets hardly contribute
to initiation, because their overall surface area is much smaller than that of the
monomer-swollen micelles or the primary particles. This assumption is based on the
workof Stearns [6] who showed that in isoprene emulsion polymerization the monoroer
droplet phase, which was separated by centrifugation, contained less than I %
polyisoprene.
According to Harkins { 1 ,2] the emulsion dropiets are normally sized 2-5 IJ.m. At this
size the dropiets cannot compete effectively with the much smaller and much more
numerous monoroer-swollen micelles or primary particles in capturing radicals
generaled in the aqueous phase. However, Ugelstad et al {7j demonstraled that at
average emulsifier concentrations and droplet sizes below 2 IJ.m the monoroer dropiets
cannot be neglected as a locus of initiation. At droplet sizes smaller than 1 IJ.m the
dropiets are even a principal locus of initiation, since in such a situation almost
all available emulsifier will be present at the monomer-water interface. Only a
small fraction of the emulsifier is dissolved in the water phase at a concentration
that may be well below the critical micelle concentration. Therefore, it is
important to have an indicàtion of the size of the monomer dropiets in order to
191
obtain a proper description the emulsion polymerization kinetics.
The objective of this chapter is to show how monomer droplet sizes in styrene
emulsion polymerization depend on agitation conditions, emulsifier concentration and
possibly other parameters. Two reactor types were used to examine the droplet sizes:
a stirred tank and a pulsed packed column.
7.2. Liquid-liquid dispersions
In a liquid/liquid dispersion a process of continuous break-up and coalescence of
dropiets takes place. The size distribution of the dropiets is determined by a
dynamica} balance between break up and coaiescence of the droplets.
7.2.1. Break-up of droplets
The dropiets that are produced by agitation are subject to shear stress and
turbulent flow and pressure variations along their surfaces. These processes cause
the dropiets to deform. According to Hinze [8} break-up of dropiets may occur when
the kinetic energy of the droplet oscillations is suffïcient to provide the gain in
surface energy necessary for break-up. The kinetic energy of the oscillating
dropiets is assumed to be proportional to:
(7.1)
where:
u2(d) = mean square of the relative velocity fluctuations between two diametrically
opposite points on the surface of the droplet
pc = density of the continuous phase
d = droplet diameter
The minimum gain in surface energy is assumed to depend on:
(7.2)
where cr is the surface tension.
192
The break-up of dropiets can be described by the Weber number, which is defined as
the ratio of the kinetic energy to the surface energy:
~ We = pc.u (d).d
0" (7.3)
Break-up occurs as soon as a critica! value of the Weber number, Weer' is exceeded.
In most studies the break-up of dropiets is characterized by a so-called maximum
stable droplet diameter dmax' which is related to Weer according to equation (7.3).
The break-up of dropiets in an isotropie turbulent field can be described by two
mechanisms: break up by inertial forces (turbulent velocity and pressure
fluctuations across the surface of the droplets) [8], or break-up by viscous shear
forces [9]. What mechanism is responsible for the break-up of the dropiets depends
upon the droplet size. A generally accepted criterion is Kolmogoroffs microscale of
turbulence. Kolmogoroff [10,11] stated that in any turbulent flow at sufficiently
high Reynolds numbers the smali-scale components of the turbulent velocity
fluctuations are statistically independent of the main flow and of the
turbulence-generating mechanism. He defined a length scale (TJ) and a velocity scale
(v) by:
v = (v.e)1/4
where:
T] = Kolmogoroffs length scale for turbulence
v = Kolmogoroffs velocity scale for turbulence
e = nett energy dissipated per unit time and mass
V = kinematic viscosity
(7.4)
(7.5)
These parameters can be used to characterize the smallest energy-dissipating eddies.
For droplet sizes larger than the turbulent length scale T], droplet break-up is
caused by the inertial forces. For droplet sizes smaller than the turbulent length
scale T] the break-up occurs within the smallest turbulent eddies; in this region the
viscous forces are the main cause of droplet break-up [9]. For both regions a
relation can be given for the mean square of the relative velocity between two
points separated by a distance r [10-14}:
193
(r > 11) (7.6)
~ - 2 U (r) = C2.(e).r /V (r < 11) (7.7)
Ford > 11 the break-up is described by Hinze [8] and Vermeuten [15]. They derived
the next equations for Weer and dmax:
(7.8)
d = C .(o/p )0.6.(ëf0.4 max 3 c (7.9)
where a is the surface tension and Pc the density of continuous phase.
In emulsion polymerization droplet sizes are mostly in the range 1-10 J.1In [1,2],
which is smaller than Kolmogorovs microscale. Under common conditions of agitation
the viscous shear forces are the dominant forces. An expression for the maximum
stabie droplet diameter in the case of droplet break-up caused by the viscous shear
forces only, is given by [9.16]:
(7.10)
where:
<I>{J..I.iJ.I.c)= function dependent on the ratio J..l.illc
J..l.d = dynamic viscosity of the disperse phase
J.l.c = dynamic viscosity of the continuous phase
v c = kinematic viscosity of the continuous phase
7.2.2. Coalescence of dropiets
The rate of coalescence of dropiets in a dispersion can be increased or decreased by
turbulent motion, dependent on the physical properties of the components in the
system. Local velocity fluctuations increase the collision frequency of the
droplets, thus increasing the chance of coalescence. However, only a small fraction
of the collisions results in immediate coalescence of the droplets. This is caused
194
by a thin liquid film between the approaching dropiets that acts as a kind of
elastic cushion and may cause the dropiets to recoil. If two dropiets approach, the
thickness of the separating film wiJl gradually decrease by diffusion. When the film
is thin enough the dropiets can coalesce. lt may occur; however, that turbulent
velocity fluctuations meanwhile transmit so much energy to the dropiets that they
are re-separated before coalescence can take place. This effect is Jarger if the
time neerled for the thinning of the film is lengthened artificially; for example by
the addition of a stahilizing emulsifier. In some cases this may lead to total
prevention of coalescence in a turbulent flow. The effectiveness of prevention of
coalescence is a function of the individual droplet size, because the adhesion
forces and the inertial forces are both functions of the droplet diameter.
For small dropiets the turbulent energy supply is insufficient to surmount the
adhesion harrier. A minimum stabie droplet diameter, dmin' can be defined, which is
the diameter of the smallest dropiets for which coalescence can be prevented by the
turbulent motion. Droplets with diameters smaller than dmin will coalesce until they
have reached a diameter dmin· Fordropiets with diameters above dmin the chance of
coalescence is very small. d . depends on the. intensity of agitation and on the mm physical properties of the components. According to Shinnar [9] the adhesion energy
between dropiets can be given by:
E - d a (7.11)
In case d > rt. Shinnar derived the following relation for the minimum stabie droplet
diameter:
(7.12)
d C -3/8 (-)-1/4 min s·Pc · e (7.13)
When d < rt the force preventing coalescence is the viscous shear force. According to
Sprow [ 17.18] the minimum stabie drop diameter can than be given in this case by:
d . = c6.p -I12.(v .ërt/4 mm c c (7.14)
7.2.3. Simultaneous break-up and coalescence
In an agitated dispersion the size distribution of the dropiets is determined by
195
both · break-up and coalescence of the dropiets occurring simultaneously. The
diameters defined in the equations (7.9), (7.10), (7.13) and (7.14) are in reality
statistica! averages. In case of the equations (7.9) and (7.10) the diameters are
droplet sizes below which break-up probably wiJl not occur, and in case of the
equations (7.13) and (7.14) droplet sizes above which prevention of coalescence
becomes effective. In figure 7.1 minimum and maximum stabie droplet diameters are
given as a function of the mean energy dissipation. Four different zones can be
distinguished:
I. above both curves most dropiets will break up and only a few will coalesce;
11. below both curves most dropiets will coalesce and only a few will break up;
111. in the area where dmin > dmax the dropiets will rapidly coalesce and break up;
IV. in the area where dmax > dmin break-up and coalescence sporadically occurs.
In the steady state, the average diameter of the dropiets will be found in the areas
lil and IV. Whether the true d(ë) relation is closer to the A or the B line will be
determined by the rates of the dispersion and coalescence processes. Little is known
about these rates.
QO 0
log [;
Figure 7.1. Logarithmic plot of droplet diameter as a function of mean energy
dissipation. Line A: controlled by break-up only; Line B: controlled by coalescence
only.
In some dispersions prevention of coalescence is the determining factor for the
droplet sizes. Addition of a protective compound, such as a soap, will strongly
suppress the coalescence process. As a result, the minimum stabie droplet size,
d . , will be much smaller than in a system without soap. Shinnar [9] called such mm
196
systems turbulence-stabilized dispersions.
Nomura et al [19] derived an empirica} equation for average droplet sizes in a
styrene/water emulsion stabilized with sodium dodecyl sulfate:
(7.15)
where:
a = average diameter of the monomer dropiets
[S]. = initia! emulsifier concentratien I
N = rotational impeller speed
D = diameter of impeller
The term (0.15 + 1.4 si-3' 2) represents the effect of prevention of coalescence of
the monomer droplets.
7.2.4. Energy dissipation in an agitated vessel
The mean energy dissipation per unit of time and mass in an agitated vessel can be
calculated from the power input. According to Rushton et al [20,21] the power input
in an agitated vessel is a function of impeller size and impeller speed:
where:
P = power input
Np= power number
p = density of liquid
N = rotational impeller speed
D = impeller diameter
(7.16)
The power number Np of equation (7.16) depends on the geometry of impeller and
vessel, and on the impeller speed. For laminar flow Np is a function of the Reynolds
number Re [20,21]:
-1 Np= A.(Re)
197
(7.17)
where A is constant for a given vessel-impeller geometry. For Newtonian liquids Re
is defined as:
2 Re= p.N.D
Jl
where Jl is the dynamic viscosity.
(7.18)
Values of A for different geometries of vessel and impeller are given by Rushton et
al [20,21], Calderbank and Moo-Young [22], Ullrich [23], Bateset al [24] and other
workers.
For turbulent flow, in case of a baffled vessel, Np is independent of the Reynolds
number and only a function of the geometry of vessel and impeller. Rushton et al
[20 ,21] obtained for a standard tank configuration (figure 7 .2):
N = 6 p
I H
1
-"J-
(7 .19)
~ t --o- c J
T
Figure 7.2. Standard tank configuration according to Rushton [20,21]. D = 0.33 T; C
= D; H = T; 4 baj]le plates: J = 0.1 T; 6 impel/er blades: W 0.2 D; L = 0.25 D.
For 6-bladed turbine impellers of widely differing geometry and size the power
number can he given by relation (7.20), which reduces to relation (7.19) in case of
the Rushton configuration [20-22]:
N = l60.W.L. (D-W) p DJ
(7.20)
198
where D stands for the impeller diameter, W for the width of an impeller blade, and
L for the height of an impeller blade.
Recently, several investigators have obtained values of the Power number lower than
the value reported by Rushton for the turbulent range (relation (7.19)). Calderbank
{25] measured values in the range 4.2 5.5. Bates et al {24] reported values of 4.8
and 5.0.
The effect of the number of impeller blades, B, on the power number was also studied
by Rushton et al {20,21]. For impeliers having less than 6 blades they obtained:
N = B0.84 p
(7.21)
and for impeliers having more than 6 blades (up to a maximum of 12 blades):
N = B0.74 p (7 .22)
Other geometrical factors, such as the ratio of impeller to tank diameter (Dtr),
baffle width (J) and impeller distance to tank bottorn (C) have been studied
extensively by Bates et al {24] and cannot be given by simpte relationships.
For turbulent flow in an unbaffled vessel Rushton et al {20,21] showed that Np is
not constant anymore, but decreases at increasing Reynolds number, due to increased
vortexing. The Froude number, defined as:
Fr (7.23)
can be used to account for the decrease in Np for this case. Here g 1s the
acceleration of gravity.
The mean energy dissipation per unit time and mass in an agitated vessel is:
p
~ (7.24)
with V T is the volume of the vessel.
The energy dissipation in an agitated vessel is not homogeneously distributed over
the vessel content. The energy dissipation in the impeller stream will be several
times higher than in the bulk of the liquid, due to the much higher intensity of the
199
turbulence in the impeller zone. According to Cutter [26], who has measured the
turbulence in an agitated vessel, the appreciable differences in state of turbulence
at different positions within the vessel are expected to give rise to differences in
the dissipation rate at these positions of the order tens or hundreds of times. In
order to study processes like droplet break up and coalescence in agitated vessels
properly, these dissipation rate distributions should he taken into account. The
energy dissipation rate distribution in an agitated vessel was studied extensively
by Okamoto et al [27]. They divided the vessel into two regions: an impeller flow
region and a circulation region, which comprises the rest of the space within the
vessel. Por the energy dissipation they defined an Ei' representing the value of E
in the direct neighbourhood of the impeller, and an Ec, being the value of E for at
sufficient distance from the impeller. Measurements of Okamoto et al with a hot-film
current meter showed, that for a Rushton contiguration about 75 % of all energy was
dissipated in the impeller reg ion, while the volume V i of the impeller region was
only 5 % of the total volume of the vessel. Okamoto et al also gave values of Ei,
E c' V i and V c for different impeller to tank diameter ratios. Their results indicate
that the larger the ratio D(f, the more uniform the distribution of E within the
vessel became.
7.2.5. Energy dissipation in a pulsed packed column
The energy dissipation in a packed column is caused by resistance to flow. For the
steady state the pressure drop over the packed section of the column can he
expressed as:
where:
AP= pressure drop
f = friction factor r
H = height of the packed bed
dr = packing diameter
p = density of the liquid phase
v = liquid velocity
(7.25)
The pressure drop in a pulsed packed column is a function of the pulsation velocity
and consists of two contributions: a contribution resulting from friction and one
200
originating from the acceleration of the liquid. For the friction term the following
relation can be written:
(7.26)
where:
(J) = 2.1t.f
f = frequency of pulsation
s = stroke length of pulsation
The acceleration or impulse term can be given by:
(7.27)
with eb is the bed porosity and fi is a zigzag factor, which accounts for the fact
that the acceleration of the liquid is not exactly in vertical direction, but is
determined by the orientation of the packing particles.
Figure 7.3 shows the measured pressure drop in a pulsed packed column as a function
of time. The figure clearly shows two peaks in the pressure drop during one
pulsation cycle. The first peak is caused by the contribution of the acceleration
term to the pressure drop, the second one by the friction. However, only the
friction term of the pressure drop contributes to the energy dissipation in a pulsed
........ .. "' e
p., <J
-0.20 [__ ________________ __,
0.00 0.50 1.00 1.50 2.00
time (s)
Figure 7.3. Measured pressure drop in a pulsed column packed with Raschig rings (d r JO mm) as a Ju netion of time. f = 1.75 s-1; s = 14 mm, H = 2 m.
201
packed column. The maximum pressure drop resulting from friction during one
pulsation cycle is the second maximum of the 8P vs. time curve, because the friction
term attains its maximum, when the impulse term is zero. The maximum energy
dissipation during a pulsation cycle can then be calculated according to:
(7.28)
With equations (7.26) and (7.27) we found the following values for the friction
factor fr and the zigzag factor fi (table 7.1):
Table 7.1. Experimentally determined values for f and f. in pulsed r 1
columns packed with Raschig rings ( d r JO mm) and with Sulzer
SMV8-DN50 internals at various pulsarion velocities.
Packing type f (s- 1) I s (mm) f [. r 1
Ra s eh i g r i ngs 3.5 7.0 3.8 3.9
d r = 1 0 mm 3.5 10.5 3.6 5.5
3.5 14.0 3.2 6.9
S u I ze r in t ernals 3.5 4.5 2.0 1.6
SMV8-DN50 3.5 6.8 1.6 1.9
3.5 9.0 1.5 2.1
7.3. Experimental
Monomer droplet sizes were measured in several agitated vessels and pulsed packed
columns. Two types of vessels were used. The dimensions of the vesse1s are given in
table 7.2. Type I is a flat-bottomed vessel with a Rushton configuration (the
geometrical ratios of vessel and impeller are identical to the geometrical ratios of
the vessels and impeliers used by Rushton et al {20,21] in determining power
numbers). Type 11 is also a flat-bottomed vessel with a turbine impeller. However,
the impeller to tank diameter ratio D(f is much higher than of type I. Four
different turbine impellers were used in combination with type 11 (see table 7.2).
Two types of pulsed packed colums were used (see chapter 2). The fust column was
packed with glass Raschig rings of dr = 10 mm. The second column was packed with
202
structured stainless steel Sulzer SMV8-DN50 intemals. The experiments in the pulsed
packed columns as well as in the agitated vessels were all conducted batchwise.
Table 7.2. Dimensions of mixing vessels.
Type I vessel: T 200 mm; H T: c = 0.5 T
ba ffles: R 4; J = l/10 T
i mpeller; D 66.7 mrn; B 6
Type II vessel: T 90 mm; H = 2 T; c T
ba ffles: R 4; J = l/12 T
impellers: D 70 mm; B 8
D 60 mm; B 6
D 60 mm; B I 2
D = 30 mm; B 6
All vessels flat-bottomed cy l i ndrical
All impellersofdisk turbine type: W 0.2 D; L = 0.25 D
The monomer used was styrene, contammg some para t-butylcatechol to avoid
spontaneous polymerization during the experiments. The aqueous phase was a diluted
emulsifier solution. Two emulsifiers were used: Dresinate 214 (a rosin acid soap)
and sodium dodecyl sulfate. The rosin acid soap solutions were buffered wîth
potassium carbonale at pH == 11 for optimum emulsification properties. The sodium
dodecyl sulfate solutions were not buffered. No other chemieals were added to the
monomer phase or the aqueous phase. The emulsions that were prepared in the columns
and the vessels contained 30 volume % monoroer phase and 70 volume % aqueous phase.
Monoroer droplet sizes were analyzed by light scattering. The samples taken from the
vessels and columns were diluted immediately with a very concentraled stahilizing
rosin acid soap solution ([S] == 0.1 kmoVm3 ), after which the diluted samples H20
were analyzed with a Malvem 2600 HSLBD partiele sizer. The principle of the light
scattering method of the Malvem partiele sizer is given in appendix A.3. lt
appeared that the monoroer droplet sizes in the diluted samples did not change
significantly over a period of at least ten minutes, which was enough to obtain
reliable data from the Malvem partiele sizer. The energy dissipation in the pulsed
packed columns was determined by measuring the pressure drop with a Hottinger
Baldwin PD1 differential pressure gauge.
7.4. Results and discussion
Because the existing literature does not provide a uniform value of Np it was
203
decided to delermine the power number by measuring the power input with a
dynamometer. The vessel used was type I with the Rushton configuration. In order to
approximate the rheological conditions of liquid!liquid emulsions as close as
possible the power input was measured in a styrene/water emulsion (volume ratio
Figure 7.14. Mean droplet diameter (volume mean diameter) as a function of energy
dissipation in a pulsed packed colunm (PPC) and an agitated vessel.
(PPC: e ; agitated vessel: e.). Type I vessel; Emulsifier: rosin acid soap; max t 3 Emulsifier concentration: [SJ = 0.090 kmol/m H20; Monomer content: 30 vol %;
(e) Rushton type vessel; (D) pulsed column packed with Raschig ringsof dr JO
mm; (•) pulsed column packed with Sulzer SMV8-DN50 internals.
Figure 7.14 shows that when e is used to account for the effect of the energy max dissipation rate on the mean droplet diameter in a PPC, the column packed with the
Sulzer packing can be compared well with an agitated vessel. This seems to be
plausible, since this type of packing has a regular structure. Therefore, the flow
pattem in the packing wîll be uniform and, as a consequence, the energy dissipation
ra te distri bution in the column must be narrow.
The data from the Raschig rings column fall below the line connecting the data from
the Sulzer column and the stirred tank. A possible explanation might be found
consictering the broader distribution of local energy dissipation rates in the
Raschig rings column, as compared to the Sulzer column. This would mean that if the
maximum energy dissipation rate is characteristic, a higher value of e would have to
be used in the graph.
215
7 .S. Conclusions
Monomer droplet sizes of styrene emulsions were studied in agitated vessels and
pulsed packed columns (PPC). From the experiments and discussion the following
conclusions can be derived:
- The mean droplet diameter in an emulsion is only determined by break up of the
droplets. Coalescence of the dropiets does not occur because of a preventive
action of the emulsifier. The dropiets are smaller than the smallest turbulent
eddies, so the forces causing the break up of the dropiets are the viscous shear
forces.
- The mean droplet diameter was shown to be a function of the energy dissipation
rate in the region with the highest turbulence: a - e-0.5. For an agitated vessel
the energy dissipation rate in the impeller region should be used. For a PPC the
maximum energy dissipation rate in the column during one pulsation cycle can be
used. A PPC packed with a structured Sulzer SMV8-DN50 packing can be compared very
well with an agitated vessel by taking this maximum energy dissipation rate. For a
column packed with Raschig rings also the maximum energy dissipation rate during
one pulsation cycle can be used. However, for thîs packing type the measured
droplet sizes are somewhat smaller than in an agitated vessel at the same energy
dissipation rate. This can be attributed to the irregular structure of the
packing, which causes a distribution in the energy dissipation.
- The emulsifier type and emulsifier concentration have shown to influence the mean
droplet size by affecting the viscosity of the continuous phase (emulsifier type
mainly) and the surface · tension of the styrene/water interface (emulsifier
concentration mainly).
- For the mixing conditions normally used in emulsion polymerization almost all
measured droplet sizes are within the range 2-10 J.lm. These sizes indicate that the
monomer dropiets cannot compete effectively with the much smallerand much more
numerous monomer-swollen micelles or primary polymer particles in capturing
initiator radicals, which makes it unlikely that polymerization occurs in the
monomer droplets, to any significant extent.
216
7 .6. References
1. W.D.Harkins, J. Am. Chem. Soc., 69, 1428, (1947) 2. W.D.Harkins, J. Polym. Sci., j_, 217, (1950) 3. R.M.Fitch, Off. Dig., J. Paint Tech. Eng., 37, 32, (1965) 4. C.P.Roe, Ind. Eng. Chem., 60, 20, ( 1968) 5. R.M.Fitch, "Polymer Colloids", R.M. Fitch ed., Plenum Press, New York, (1971),
p.73 6. R.S.Steams, cited in references 1 and 2 7. J.Uge1stad, M.S.El-Aasser, J.W.Vanderhoff, J. Poly. Sci., Poly. Lett. Ed., U.
10. A.M.Kolmogoroff, C. R. Acad. Sci. URSS, 30, 301, (1941) 11. A.M.Kolmogoroff, C. R. Acad. Sci. URSS, 32, 16, (1941) 12. G.K.Batchelor, Proc. Camb. Phil. Soc., 43, 533, (1947) 13. G.K.Batche1or, Proc. Camb. Phil. Soc., 47, 359, (1947) 14. G.K.Batche1or, "The Theory of Homogeneous Turbu1ence", Cambridge University
