uorlelusrunJlsur a^rlfadsoJd se prlualod roleru seq enbruq]el urlu ureoJ frdols-oJfrrrr eql pue suo4nlos lrlrqdrqdrue ur sJ.rnlfnJlsoueu luelfeJ-rns 3o aruasard
er{} roJ sJolefipur se J^]JS deur suoqeuiloJ {lEIq elqe}sun pa^resqo 3r{+ leq}
1sa33ns sllnser arII 'seleJrelur str uo pue urlu aqt Jo {lnq eq} ur qtoq sarlqrues-se luelleJrns Suqsrxe aqi Jo uorlrn4sep pue uoqezrue8roer rr{t {t1m (s1ods pue
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1e lsrxa sate8a,rSSe pelquesse3las Jo serres E ler-l] uortdurnsse eLIt Jo srseq eql
uo palardrelur eJe sluauruadxe eql 'a8uer uorleJlue)uof luelfeJ.rns ,^aoJJeu e ur-r{il1v\ a8ueq: dreqs e ,{eldsrp srul5 arll Jo sfr}srral)ereq) lqeuDl aql Jo pra.,r.as (7)
slFsar aq1 'srs,(pue aSeurr s^qn)3suof pue Surprorar oeph 8urpn1:ur ,,(q parrord-rur (lleuollppe sr dntas pluarur;adxe eql 'e,l\o.rexf pue o{pnleqls Jo 11a: 8ur-JnseJur aql qll.A salerado LIllr{rK 'por{+Jru frrleuroJaJJaluroJfrur e er^ pe}e8Esa,r-ur are sfrlst;apeJer{l urlg ar{J 'pJ^resqo eq o1 sr dlqurosse1lJs Jo lesuo Ier+ruruaqa saqquenb apqdrqdrue Surqrear go ,Qrpqrssod anbrun e sa.tr8 srql 'sa8ueqr
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f SS I S Surfactant Nanostructures in Foam FilmsI
8.1Background
The investigation of the self,assembly of amphiphilic molecules into micellaraggregates is one of the oldest topics in colloid chemistry 17,2]. Within the widediversity of nanophenomena in fluid media, of particular importance is the on-set of seliassembled nanostructures in aqueous solutions of surfactants [3-11].
For more than 40 years the microscopic foam fi1m technique has been a ma-jor instrumentation mode in the study of surface forces and stability of colloidsystems 112-77). One of the major advantages of this instrumentation is thepossibility of registering and following fine changes in these forces during thedrainage of the liquid fi1ms. The films have radii in the range 10-500 pm andare formed in the Scheludko-Exerowa measuring cell of the thin liquid fi1m mi-crointerferometric technique. This instrumentation allows the direct measure-ment of most parameters that determine the properties and the behavior offoam films. The microscopic foam film was the first simple model of two inter-acting fluid interfaces related to the study of the classical theory of Derjaguin,Landau, Verwey and Overbeek (DLVO theory) 172-231and also provided its firstexperimental verification [13-1 5, 23].
Recent investigations on foam films from aqueous amphiphilic solutions haveproved that the film drainage kinetics contain important information about thepresence and reorganization of self,assembled nanostructures 124-271. Thesestudies are related to some other surfactant solution properties and particularlyto the data obtained in surface tension measurements [28, 291. In earlier stud-ies, Exerowa and Scheludko [30] and iater Exerowa and coworkers 128,29,3I)reported precise results concerning the surface tension isotherms for amphi-philic solutions. The basic outcome was that the surface tension curves of aque-ous solutions of certain surfactants (alkyl sulfate homologues, etc.) in the pres-ence of added electrolyte run in an unexpected manner.
In Fig. 8.1 are reproduced the data [28, 291 for the case of solutions of sodiumdodecyl sulfate obtained by the spherotensiometric technique of Scheludko [32](accuracy+0.005-0.01 mN m-1;. The curves contain distinct kinks and plateausectors. These regions are situated within the range of amphiphilic quantitiesthat are orders of magnitude lower than both the bulk critical micellar concen-tration (CMC) and the close packing values of the adsorption layers on thewater/air interface. One plateau portion is distinctly observed when the quantityof the added electrolyte is high: C"r,.,:0.5 M (curve 1). For a iower quantity ofadded electrolyte, C"1,.,:0.1 M, there are two portions: a plateau at lower surfac-tant concentration and a kink at high surfactant concentration (curve 2). Exero-wa and coworkers 128, 291were the first to advance the idea that this odd behav-ior might be due to the presence of smaller selflassembled structures. Theycalled them premicelles and introduced the concept of critical premicellar concen-tration (CPC). If premicellar entities could exist, their presence should inevitablyshow up in the results from other types of experiments also, as is the case withthe usual micelles (at the CMC).
40€ZE; 3 0
20
Fig. 8.1 Surface ten:at dif ferent electroly
One specific fer
tions is their labil
and to the innate
as a result of weal
ing forces" [8, 10
do not maintain iwith each other llsusceptible to eve
lution, temperatt
fects the overall c
the amphiphilic :
identification of I
proaches that cou
struction of surfa
instrumentation
Generally, the
for the formatior
distribution com
bling principles :
demands for the
ing surfactant ag
potentially contai
factant selfassen
the specific adsor
tion demands "n
faces. The waterT
option'that migt
'areJrelul sII{} Jeeu ssaro-rd Surlqurasse1les Jr{} ur e.raJrelur }q8rur leql ,,uor1dorrqoqdo-rp,{q,, e,rrleula}le uB seJnsua reprrged ur e)eJJelur .rre/ralervl JrIf 'seleJ
-Jelur p1ng {q papr,tord are }eq} suor}rpuo) pluauruadxe ,,.replnu,, spueurep uoq-rurlsrp srr{f 'eueuouaqd Surlqurasse1les aqt pue s}telJa uoqd.rospe :grtads aq}uaa^qeq uollellueJaJJlp alernffe ar-11 sr enssr luegodun uy ,{lqurasse1lJs luelleJ-Jns Jo ursruerlreur aql ]noqe uoqeurJoJur le.rntrnJls alqenpl ureluof ,{1p4ua1odserlrlrqrssod uorlezrue8roa; esrql 'ISS] ,qlrulxo;d s1r ur sate8arSSe luepeg.rns 8ur-3.rarua rql Jo uorlnqrrtsrp azrs eql pue sa1e8a;88e er{} Jo urroJ ai{} roJ spueuep:gnads sefnpul ereJ-ralul ue Jo ,firurxo;d eql 'Jlrlerado ,(1pg are saldrturrd 3ur1q-uesse1lrs llere^o aqt q8noqllv 'uorlnlos
{1nc[ rr{t q}r1v\ pa.redulo: uoqnqrlsrpJZrs rrer{} ur sa8ueqf safnpur pue seJnpnrls pJlquesse1les Jo uor}EurroJ Jql roJsuortrpuot tgrtads eql seruangur .Lrepunoq aseqd e Jo afuasard aqt dlerauaS
'ltZ-tZ] puDi srq+ go uoqdo .Aaeu e paloutord seq uorlelueurn.rtsur)IrleruoraJJelulo.rflur urlg prnbrl uF{l Sursn seJn}fnJlsoueu }uelfeJJns Jo uorllnJ}s-ep pue uoqezrue?roar er{}Jo,(pn1s er{f 'sruets,{s qrns sserppe ppo) }eq} saq:eo,rd-de as,raa,tp aJolrr JoJ pueuap luelsuol B sr aJer{I 'sar:ads aseql Jo uor}Elgliuepraq] uI seqFlIJJIp snoIJJS lnoqe s8urrq taa,a,lrr,oq 'sarnlrnrlsoueu trpqdrqdure aLIl
Jo retrlerel{r ellqel rql'sarn}rm}s rrlrqdrqdure eq}Jo uoqnqrr}srp ilera^o ai{} s}leJ
Je e^oqe Jr{l Jo ,(ue 3o uo4erJe^ 't1a 'sa:e;ralur Jo ,Qru[xord 'aln1e-radurJl 'uoqnl
d1}:exa aJe suorlr-lulu e ,{eldsrp Id11er:ads '(SCS)
'suorlnlos luellr-rr ar-Il roJ Ioo] a
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pue elep Fluelur
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rueoJ go Suruurql
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3:o a8eure.rp uodn-Jr aq lq8rur a-rn
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Itstl su.r1t1 wool ctdocsotcllltl lo aSourotg 7'g
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lJ/2l 8 Surfactant Nanostructures in Foam FilmsI
(2) specific drainage characteristics (evolution of fi1m thickness values, film
drainage times).
8 .2 .1Black Patterns
The observed black patterns may formally be classified as of two types. The first
type (spots, black films) is characteristic of higher concentration ranges of the am-
phiphile used and are precursors of the classical black films [common black films
(CBFs) and Newton black films (NBFs)l [13-15, 38, 39]. These patterns generally
evolve into films that survive within longer time intervals (minutes, hours). They
are very well described and have been related to the lifetimes and the stability of
liquid films [13-15]. The common feature of the surfactant systems where these
precursors of black fi1ms are observed is that the adsorption surfactant coverage
on the liquid/air interface of the initial solutions is almost ciose packed. From this
point of view these black formations mark a specific stage of the evolution of black
(plane-para11e1) fiims, namely the transition to a new thickness of relatively stable
configuration: CBF or NBF. This thickness transition has been denoted the critical
thickness h., and the surfactant concentration at which the onset of this type of
black patterns is observed is C61 [74, 15,39].
With certain amphiphilic solutions, however, black patterns of a second typ",
dots and unstable biack spots, are observed [2a-291. The unstable black forma-
tions appear when there is some deficiency of the surfactant in the adsorption
coverage on the interfaces for miscellaneous reasons. These formations have
lifetimes of no more than several seconds. The respective foam films drain
quickly and survive for at most a minute or two. Their onset is also closely re-
lated to the specific structure of the surfactant. There are no systematic data in
this sense, but it seems that, as a rule, the stabiliztng arnphiphile should have a
long hydrophobic tail as opposed to a comparatively sma1l hydrophilic head [40,a1]. This surfactant structure ensures the formation of foam films at lower sur-
factant concentrations, which, although of shorter lifetime, still live long enough
for it to be possible to investigate them.
The black dots (Fig. 8.3) appear at the lowest surfactant concentrations [atabout (2-3)x10-6 M SDSI. They live for 3-10 s and do not grow in size. It
should be noted that the minimum concentration for the first onset of these
black patterns does not depend on the electrolyte concentration. V/ithin the
range of electrolyte concentrations added here, the "criticaL' value is at about
(2.0-2.5\x10-6 M SDS 1271. The spots (Fig. 8.a) are characteristic of higher am-
phiphile concentrations. They live for less than 1 s but quickly grow in size.
Upon increase of the amphiphile concentration both their number and the
probability of their onset rise (Figs. 8.5 and 8.6).
In Figs. 8.3 and 8.4 are presented typical pictures of the foam fi1ms and re-
sults from the respective image analysis. The morphological difference between
the two biack formations is well distinguished. The "b1ack dots" (Fig.8.3b) are
shallow local thinnings with irregular thickness. The "spots" are thinner black
a)
?
P z ox
a-o r nc
; 5xiI
0
b) Pi
patterns and ma'
background foam
Although the
nuances in their
higher electrolyte
and are well obsr
a more subtle dil
first observed wh
teau portions of 1
rise in the surfac
accompanied by
change in size, br
The basic resul
of the onset and
in the draining f<
sion isotherms. T
-elrpur ue se pereprsuor aq tq8rur s+op {lelq Jo efuereJdde aq1 'srureq}osr uors-url efeJrns aql ur suor8a.r nealeld pue {uDI eql pue surlu ureoJ Sururerp eqt ur(slods pue slop {relq) sura}ted {relq elqe}sun er{l Jo sargadord pue tresuo ar{+ Jo,{uorqru,{s uor}eJluefuol eq} sr suor}elrrsqo a^rletglenb er{t Jo }lnsel rrseq aql
's1ods alqelsun ta8rel uroJ pue ,tnor8 ueql lnq 'ezrs ur a8ueq:
lnoqlr.^a spuofes le-re^as roJ e^rl r{llr{A\ 's1op zvrau Jo }asuo aqt ,(q parueduro::eseurqauros sr Jequrnu lods ur eseeJfur aql 'uorleJluafuof ]uetleJJns ar{l ur JSrJ
e qlt,/n '(t'S'3lg ur ]esur er{r aes) rurer{losr uorsua} eleJrns ar{}Jo suor}rod neal-e1d aq+;o a8uer Jq] uro! eJE suorleJluefuof ]uelfeJ.rns eql urr{,^a pa^resqo tsrusr lop e Jo tasuo aq1 's1ods ar{t pue s}op aq} uea^\}aq eruerelJrp ei}qns erotu esr eraqt '(lf"N
I I I'0) uorlerluatuor aldlortrale rr^\ol }V 'pauasqo IIa./!\ ere pue
auq ra8uol e roJ a^rl slop eql '(lfeN IAI S'0) uorlerlueruor a1d1o.rpa1a ,raq8rq
1e '.(1arue51 '.Qr1uenb tFS pappe aqt o1 ]radsa; Lllyv\ saturleJll rleql ur seruenuauros eJe ereq] 'aures Jr{l sr a8ue; uor}eJ}uafuof }ue}feJ.rns aqt q8noqtly
'(qt'g'3tg) urru ureoJ punorS4:ec1ar{} ulqll^\ (surlgor:nu) suorpod 1a11ered-aue1d se peaar^ aq deru pue suralled
uorlrsod loxrd001
&-,o o''''..,--.,-,.._r. r..i 4
>llelq Jeuurr{} Jrr
a.re (qg'g'3rg) ,,s.uea^\lJq elueralJ-aJ pue s[ulu urr
aql pue raqrunu'azrs ur mo.r8 dp-ure raq8rr{ Jo rrl
Fig.8.4 (a) Example for the evolut ion of unstableb lack pa t te rns : b lack spo t ; (b ) image ana lys i s o fb lack spo t .
tor for the presence of amphiphilic structures in the initial surfactant solutionsfrom which the respective foam films are formed 137), while the onset and evo-
lution of the black spots mark the crucial change in the interrelation betweenthe bulk-film drainage properties and the change in the adsorption layers on
the interfaces [25, 271. The persistent emergence of, although unstable, clearlydistinguished black patterns (dots and spots) influences the drainage behaviorof the foam films.
8 .2 .2Drai nage Characteristics
The video recording and the image analysis permit closer examination of the
drainage evolution of the foam films within the entire concentration interval
that is investigated. The foam fi1ms studied do not reach equilibrium thickness
[25, 26]. Provided that the investigated foam films originate from surfactant so-
Fig.8 .7 Exper imenta l th inn ing ve loc i ty resu l ts versus actua l f i lm th icknessfor cer ta in sur factant concent ra t ions.C. r : (a) 0 . . l and (b) 0 .5 M NaCl .
*: im"r.: : : : the calculated values for the Reynolds drainage in the
lutions of concentrations that are lower than both the close packing value andthe CMC values, they drain quickly and rupture within 1min. The film drain-age itself is performed in a regime of increased tangential mobility of the filminterfaces, as can be seen from the representative results for the drainage veloc-ity against the fi1m thickness shown in Fig.8.7.
Particularly informative are the following drainage characteristics of the stud-ied fi1ms: (1) the evolution of fi1m thickness with time and (21 film drainagetimes asainst the surfactant concentration of the initial solutions.
10
a)
Fig. 8.8 Mean thickn
The evolution ,
pending on the s
characteristic "br<
disjoining pressul
lou'er thickness v
be expected, the
out wide. These b
the concentration
served. Thus, in
consists of three
plateau and the I
trolyte concentrat
surface tension is
The film drain
thin film until thr
dependence ofthr
u.^aor{s a;e urd 00I Jo rrper rul5 rog (-z) seruq a8eure.rp ueeur aq} Jo aruapuadap
er{} roJ s}lnsrr a^rteinunl aril. 'a,rn1dn,r ,ro }ods {lelq Jo }asuo aql Flun rul5 ulrll
e Jo uorleurroJ Jo luJurour JI{} uro4 pagr:ads ale saurl} a8eurerp ur15 eql'(qS'g'8tg) o^l lsnI a.re sar{runq arrrlradsar eql'surrar{}osl uolsual r]eJrns
eql ur uorSar nealeld +lurlsrp auo dluo sr erer{} sE reJosul 'suorJe.r}ue:uor ap(1o.t1-ra1a .raq8lq roJ pe^-resqo sr aures aril'(eS'S'3lg) suor8ar >lul>l rr{t pue nealeld
er{} Jo s}asuo Jqt e}elrpul ot se os padnor8 'seq)unq }lul}slp aarql Jo s}slsuof
Jo r{lunel aqtr se}elrpur }eqt de'l e qlns uI padnor8 aJe ser{funq asrql 'epl^\ }noLIllJJtrs ]eq} 'seqrunq lluqslp preles olul seleredas ,.urooJq,, eq] 'papadxa aq
o1 sr JJnssard Sururofsrp aqt 3o lredurr elqelou e ueq.AA 'sanlel ssau>l]Ii{l rJ,llol
1y raqraSol qlunq e ur urrT salJn) eql 'alrleJado 1qs ]ou sr a.rnssard Surutolsrp
eq] uJi{.l senlel ssau{rrql q8rq lV 'peurJoJ sr selrnf Jo ,,urooJq,, frJSrJJ}feJeI{l
e 1eq1 .{errr e qfns ur unJ selJnl aql 'uoqeJ}uefuol }ue}feJJns aq} uo Surpuad-aCI '8'8'8tC ul paluasard sr eurrl qlu!\ sseu{llt{} urlg eq} Jo uoqnlo^a el{f
'lfeN y\ S'0 (q) pue ['0 (e):1": roJ eurl r]11/v\ uoltnlo^e ssaulrrql ueay\ 8'g'3ll
(q [sl r (ea7,0t0Ew0tw0I
bt
a8eurerp uru (Z)-pnls Jrl] Jo sfrlsl
-lolel a8eurerp arrulu rr{};o .Qrpqr-urErp ruru eql'pue enle^ 3ur4:e
***F**n*I{"OIX{I'E:J
si L-01\02:J o
$01x0 f=J :jl
tr^r1.r0lxg.Z=) Es
tr{',t}l}:0'Z= 3 o
0l\l't:3 ItceN w f'0 :sos
09
08
H
H
001E
08
00[*
t4{.-0lxE:'J
hl.-0lxl=J
t&"0IxFJ
hl,,()lxS=)
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Irctl sut1t1 u.loo1 ttdotsotc11111{o a?outotq 7'g
f 93 | S Surfactant Nanostructures in Foam FilmsI
4.(l
tr
tr
3 0 b
C 5 0e
P
SDS: 0. lM NaCl: t :22"C
Aa"
N/t
/' ./'n-t -x/ /'''
L ^r"- ,//// ^ '/' / n - '/ /'-
N"/ j-'
l\ r-,/nA I n - t i
n--41 o.=tr
--.1-.l
a- -n-E--a- t r /Lr
8.3Understanding th
The major result
First, all the film
a remarkable cor
sion currres. Seco
and the probabil
the other rise in r
rnarrze, the "irrel
in the state of th
the surfactant co
the drainage cha
tervals, where th
In an attempt
of the possible
was first abandc
ness of the filmr
shown in F ig .8 .
mains virtually ,
va1. The run of t
respective surfac
There is alwal
the state of the
the quantity of t
of equilibrium f
and quickly witt
age due the Ma
[42, 431and one
mass transfer o
- t
1o- ' l o l
C, [mol/U
Fig. 8.9 Mean drainage t imes of foam f i lms against the surfactantconcentrat ion of in i t ia l sodium dodecvl sul fate solut ionsa t C"1 :0 .1 M NaCl .
l 0 - o ' - - - - - - - - - - - l
0 5 l 0 rC, lmoVll
F ig .8 .10 Mean d ra inage t imes o f foam f i lms aga ins t the su r fac tan tconcen t ra t i on o f i n i t i a l sod ium dodecy l su l fa te so lu t i ons a tC ' : 0 . 5 M N a C l .
in Figs. 8.9 and 8.10. The experimental results for the kinetics of foam film
drainage are juxtaposed on the concentration peculiarities of the surface tension
isotherms for the same surfactant systems. As one can see, there is a marked
concentration coincidence of the run of foam film drainage times and the kink
and plateaus in the respective surface tension isotherms.
1. amphiphilic na2. surface forces a3. the films are d
terfaces and thi
8 . 3 . 1Premicellar Concel
The starting poin
understanding thsurfactant solutio
at concentrations
what different frc
originating from
Generally, the orcipriori restrictions
the onset of self,ation of weaker "o
ist, the general sesibility for model
them as symmetr
An attempt to crbased on this ide;
8 .3 .2Surface Forces in t
Applied to the forits most importar
Foam films are rcontains self,asserfilm itself is modt
terfaces) 123,491.in all the phases
cal equilibrium.
The specific buJ
:1,t"" curve of tl
Xl : Yo'b;'rnt'bX
r 0 0
a)
a
P - . - "
SDS.0 lMNaCl : t -22"C
Iv/I
./tI,V-I
--r I/\+-silT'r - r _ [ - -- Eryennent
' N H
-d-_ 60t--
SDS: O.5MNaCl.t-22"C
t/5I
-'- E{rcd're't- - - v N t t
I +/ '
. . .
b)1 0 "
l 0 ' l 0 r 1 0 6 l 0 - 5C" frmlA]
F ig .8 .12 Exper imen ta l da ta and d ra inage t ime accord ing to conven t iona lf i lm hydrodynamics. (a) Inf luence of Marangoni ef fect (notat ions accordingto [a3 b]) : V-oulVn. : 1 +b+h, I h; b : - (3 a q I fq()os I Ac) ; hs:16ry (0 fs I Ac) II 's(doslA c) j ; Vn": (2h3 LPl3ryR') . (U) Inf luence of non-homogenei t ies inf i lm th i ckness ; Vp6 i s the ve loc i t y acco rd ing to the law in [47 ] .
C" [rnoVl]
would just back up the general tendency of the overall rise of the drainage timeagainst the surfactant concentration. It cannot explain the stepwise changes inthe foam film drainage experiments and their concentration coincidence withthe peculiarities of the surface tension results with increase in the overall am-phiphile quantity. The inadequacy of the common fi1m hydrodynamic approachis illustrated by an attempt to relate the drainage times to the known hydrody-namic factors that are fu1ly operative in our case also, namely the influence ofthe Marangoni effect [43] and the impact of thickness non-homogeneities onthe film hydrodynamics (Fig. 8.12) 147).
Hence the coupled peculiarities of the "static" surface-tension measurementsand of the "dynamic" foam film drainage characteristics cannot be understoodwithin the premise of the monomolecular state of the amphiphile inside thefilm bulk. Therefore, a different notion is needed to correlate these two types ofexperiments.
o,]xo'nixo,,#xq ffx - {x
{1,'q aLI} rog sar:ads rellarrur er{t Jo a^rnf ""lJ;e qlr.^a petouap are sarlrluenb >1pq rgnads eq1
rnr-rqrpnba p:-rurrrer{r pue Ielrueqletu
'Fu.req} ur e.re re}}el aqt '[Ot, 'L€ 'gt] saseqd eq] Ue uralqrssod sr dlqruasse1lrs apqdrqdure eq+ ]eqt prurnsa.rd sr 1I '[6t 'g7] (sategral-ur prnbrl/le) saseqd areJrns CZ o"^Al pue aseqd {1nq e se peleporu sr Jles+r urluaql 'suoqnqulsrp ezrs Jlruuap {q pezlreperer{l saqque pelqurasse3les sure}uofdle4rur leql uoqnlos lue]leJ.rns e uro4 pauretqo se papre8ar eJe surlu rueoC'[Ot 'Lt '9g] a.rnssa-rd Sututofsrp aqt dlarueu 'frlsrJal]eJerp ]ueuodurr lsour s1rroJ stunor:e dlqurasse1les lpqdrqdue go ,fuoaql eq] 'urlu ureoJ eql ot pallddy
:strlnser a8eurerp url5 ureoJ eqt Jo srs,(1euepue uollelardralur ar{l JoJ Ier}uassa ,(ltsoru aJe s}uaruour ,(a>1 eel{l 'ue1s of
I tOz I stlnsay lo\uautuadxl aqt Surpuolstapun t'8
(r)
paluasa;d aq .(eur urlg rqt Jo-lrlslp ezrs er{J 'q }dursradns
;o sadfi o,^ 1 eseql
aqtr epISuI eg{dlq
poolsJapun eq lorsluJrue.Inseeur uo
uo sarlreuaSouroq
Jo eruangur aq+ {-dporpdq u^\oDI r
q:eordde :rueu,(p-[ue IFre^o ar{} uI
r{}r.^a sruapllulol
ur sa8ueqr asvurd.
arurl a8eurerp eql
6L
[l,4oru] "J
2O2l 8 Surfactant Nanostructures in Foam FilmsI
where
v b N l y b : N l ,An
N* + I , r l ' A* -
Ng + | ,N|i i
and
Xlo- (x lb)"" . r ( * ; * ,
Xft'o : ""P \(*i '- , t) ' lkTVs
b T A "
In the above, { and *, "r" the mole fractions of the bulk solution aggregates
and the solvent, respectively. The details of the theoretical scheme and the first
two multipiiers in Eq. (1) are reported elsewhere 133, 34,36, 50, 51]. The most
important advantage of Eqs. (1) to (3) is that the bulk micelle formation and in-
teraction influence are effectively decoupled from the interface adsorption and
specific film effects. In the above expressions, trz?'o and 1tf;'b are the standard
chemical potentials of a monomer and an n-rner, respectively.
The size distribution curve of the 2D arnphiphilic structures is obtained in
complete analogy with the buik micellization [35, 36, 52, 53]. All quantities char-
acterizing the interfaces are denoted with a superscript s. The result is
rzs - rz0.s 17int .s 17J .s1\n - 1\n nn At.,
where
Xioo-*r (#)
XIo:*r{#eos(h)+rr(h)ht (,ffi ffi) }
x,?'-(xi)"*r(- ff#t)
l@"\,- ui,i)Nij
)(zr nt.s- ' n - nai' \-
zkrA? a-,
( 3 . )
(3 d )
(s)
(6 ")
Lo'"- na\- ai (6 b)
c l L aX i " : e x P l - ;
L l l ,
tI
x e x p l -
LAgain, the intersl
are effectively dec
of the interface n-
a monomer and a
formation about 1
phile on the inter
For thinning fc
very important (se
centration is high
fectively depresse
Waals constituent
disjoining pressul
seliassembled str
in thinner films
comparison with
as the film draina
8 . 3 . 3Foam Film Hydrod
The films drain q
of this is that thr
equilibrium film
is well known tha
and the mass tra
the monomolecul
source of amphip.
Further, the unr
neities in the cou
the onset of loca
and the amphiphi
patterns) is accorr
and by an increas
black formations
the background t
opportunities are
the film hydrodyn
Hence in thinn
retardation is the
(2 )
( 3 a )
(3 b )
(4)
- N :\,z5 11
n" Ni + )._ tNij
'i;'i4lI
:"to I
'ZVl k;g
'3tg) -tg Surure.rp lalpred-aue1d a8rel ur se rures aqt sr uoqeprelersrql Jo ursrueqleru eql 'papreleJ sr ./v\og Floi aql 'suor8eJ Jauurql ur afuaH
reJsuerl sseur tuepeJlns eql pue srrureu,tpo"rp,(q urg aqlgo Surldnor eql uI seruareTJlp Ielol Jo r{lunel eql roJ pe}eell ere serlrun+roddoe.rour 'surlu:or)nu eseqt ul 'urlu ureoJ lalpred-aue1d Suruulqt punorbpeq aqtult{lr,/lt (surlgonnu) sqtprm de8 raleurs go sareld eqt rzrlensrl suoqeurroJ >llelqalqetsun pa^resqo aqt '(Ot'g pue 6'g
's8lg) saurl+aJll rulrJ ul eseerrur ue dq pue,Qrto1a,t Suruurql urlu Ilera^o eqt Jo u.^ op 8ur.,vro1s e ,(q paruedruotre sr (sura11ed
{lelq) saqrauaSouoq-uou aseql Jo }esuo eqI 'raJsuerJ sseur apqdrqdure aq+ pues:rureu,(porp,(q u4g 3o Surldnor praua8 aql ur sa)uareJJrp le)ol Jo tesuo eql.ro3 uorldo eJlxe ue seleeJf srql 'a8eulerp uriu rueoJ or{l Jo asJnof eql ur ser}reu-aSoruoq-uou ssau{rlr{} Jo u8rs reep e ere surelled >pe1q elqelsun aq+ taqung
'sa11acrulatd arl] :sap)e1oru rrpqdrqdrue Jo ef.rnos
Fuolllppe uB sI alel{l erai{ ta^el\oq '}ue}feJrns eql Jo e}e}s Jelnlalououoru eq}
Jo eser ar{t a{rpn 'lr)t-Zt} }ue}leJrns Surzrpqels ar{} Jo .raJsuer} sseru aq+ puestrrueudporpdq utp;o Surldnor tgr:ads e ur stlnser lreJ sn{l leql u1\\ou>l IIa.^a sr
Jo ]asuo rql roJ lusrllJJnsur sr ,{14uenb aFqdrqdute lpra^o aqt }eql sr srr{} Joesnel ar-lJ. &l[qoru Fr]eJratur Fquetsqns 3o aun8a-r e ur ,(14trnb urelp surl5 rr{I
srrueu{po.rp{g ru;r1 ueol
t'€'8
'spaarord a8eure.rp url5 eqt sesesee.rfur sJeurouour aeu er{} Jo raqunu eq} pue surlu JeTlrql qlr^\ uosrreduro:ur pasee.r)ep sl se4r+uJ luepeJ.rns ra3re1 er{} Jo uorlfeu ar{} slulu rauurql urefurH 'safeJra+ur ulrJ er{l le pue {pct uIIU er{} ur q+oq sernpnlts palqluessejlesSutlsxa eql Jo uolpn4sap pe)uet{ue Jo uorlfaJrp ei{l ur slre arnssard Sururolsrpsleed\ rep ue^ eqt'lL€'9g] sraded snonard ur u1v\or{s sV *If }uanutsuo) sleed\rep ue^ eql sr sefroJ efEJrns aql Jo ru-ra1 Surpeel eql pue passerdap d1a,rr1raJ
Je sl arnsserd Sururofsrp eI{} Jo luauodurof )I]eJsor}lela ei{} 'r{8li{ sr uoqer}uar-uor a/ior+rala eql perpnls seser eql 11e uI'(]9 pue p€'sbt aas) luegodrur fualsr arnssrrd Sururolslp ar{} Jo t]aJJa er{i '[0+(11)ul slulu tueoJ Suruurql rog
'll uro;; paruroJ sl urlg urqt e eroJeq uorlnlos {1nq e Jo r)eJretur eql uo allqd-rqdrue er{} Jo sarlrado;d Surlqruesse1las efeJrns rrsurr}ur aq} lnoqe uoqeurroJ-uI eq] t{srct d",il flarrrpadsa.r 'saseqd-Cz eqi ur aleBer37e-u ue pue reurouour e
Jo slequatod pluaql prepuels eq] a-re ,,[/ pue ,,j/ pue s]eu-u e)eJulur ar{} Jouo4le]J elotu eleJrns eql sl TX suoqenba e^oqe aql uI 'paldnorap ,(la,upagga a.re>llnq rulg er{l Jo a)uangul rgnads aql pue suor}fe.re}ur sar:adsra}ur eq} 'ure8y
P,,=Y,o + lt '# l#l#v.(ru1 \= i{ = j[ - D' ̂ # - Utc d = t f - r { , c { = c ^ - c {
surface tensionisotherms
Fig.8 .13 F i lm hydrodynamics is coupled wi th the mass t ransfer o f thestabi l izing surfactant. Schematic diagram of the impact of surfactantnanostructures on the drainase of foam f i lm with unstable black oattern.
43]: The flow sweeps the surfactant molecules outside the black pattern, creat-ing locally a surface tension gradient that causes the onset of a tangential forcethat acts in a direction opposite to the fluid outflow, resulting in effective immo-bilization of the black pattern interfaces. The existing nanostructures in the mi-crofilm bulk are already destroyed and it is depleted of surfactant molecules. Inthe neighboring regions, however, there are still selfassemblies. Upon thinningthey are further on destroyed, providing an additional amount of monomers.The latter could participate in the feed-up of the black pattern interfaces(Fig. 8.13). This extra surfactant flow gives a certain additional time to theemerged local surface tension gradient to be maintained for a while and the in-terface flow to be retarded. This results in retardation of the further thinningwithin the black pattern region. The increase in the overall concentration of theinitial solution leads to the onset of more of these black patterns (Fig.8.5). Thelarger their number, the sharper is the rise of the overall drainage time of thefilm.
The proposed slow-down mechanism couples the presence of amphiphilic na-nostructures with the specific film hydrodynamics and the mass transfer of thesurfactant molecules in thinning foam films. It allows a unified explanation ofthe film drainage behavior and the surface tension measurements (Fig. 8.14).The juxtaposition of the presented results, related to two Wpes of experiments(static and dynamic), shows a synchronized onset of specific peculiarities in therun of the surface tension isotherms and the drainage characteristics of foamfilms against the surfactant concentration. Therefore, it may be regarded as ex-perimental evidence of amphiphilic selfassembly at surfactant concentrationslower than the CMC values.
$films
hydrod-vnamics
8.4Conclusion
This chapter has
of the microinter
Exerowa measurir
that specific filmperiments with inCMC. These para
'wV '['uosuo{ 'S 'ede '41 'ureg:7,tr 'l z'9SZ (€16I) Zt
''Z plol1ox'uresr61 '{ r
suorle4ualuol lut-xe se papre8a.r aq
ureoJ Jo sfllslJellt
Jr{} uI seqlJellnlec
sluaunradxa Jo Sa'(t.f 'S'3rg) sluaur;
Jo uorleueldxa par
3r{} Jo reJsue4 sse-eu :rpqdrqdrue;c
aI{} Jo aruq a8eutt
aril '(S'S'3rg) sur;
eql Jo uoqelluefu
Suruurq] rarlunJ i-ur rr.ll pue elq,u
aql ol 3urll lBuorsereJrJlur uralled'sreurouour
Jo lulSuruurqt uodn 's;
uI 'saplelour luel-[u aq] uI seln]lr-oururr aA4laJJe ur
J)roJ lequa8ue] e-lean 'ura11ed >pt
)uaJejau
'erpetu plng q seJnlrn-rlsoueu ]uelfeJ-rns go dpnls ei{l ur IootSursnuord pue aleudordde l-ra,t e se elJas lq8rur uoqeluJurnrlsur urlg prnbrlurq]:rdo"""'i,L"Jiff
fffiiH j#";iJ,[]Iff :iildffi J;""TjjJj;:r, roJ eluaplla lelueturradxa se pareprsuol aq deur uoqerlualuof apqdrqdrue eLIl
lsure8e srllslrelfeJel{r urlu tueoJ lrteuDl er{} Jo unJ er{I 'sefeJJalur slr uo sra.,te1uoqdrospe eql ur pue urlu eql ur qloq serlquresse luelleJrns Suqsrxa Jo uorlez-rueS-roar rr{} pue strureudp url5 Jo Surldnor aq} +lelter s.ra}aurered asaql ')hl)
++ E. Mileva, B. Radoev, Colloids Surf. A, 74(1ee3) 2se.
45 E. Mileva, L. Nikolov, Colloids Surf. A, 74(1993\ 267.
a6 E. Mileva, B. Radoev, in En'tulsiorus: Strwc-ture, Stability and lnteractions (Yol. Ed.D.N. Petsev), Vol. 4 of Interfacial Scienceqnd Technology (Series Ed. A. Hubbard),Elsevier, London, 2004, Chapter 6,pp.215-256.
47 E. Manev R. Tsekov B. Radoev Dispers.Sci. Technol, 18 (1997) 769.
48 D. Langevin, A. Sonin, Adv. Colloid Inter-
face Sci., 51 (1,9941 7.49 A. Rusanov A, Phasengleichgewichte und
