Persulphate Mechanism

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2160

M ac r om ol e c u l e s 1991 , 24 ,

2160-2171

Mechanism and Kinetics

of

the Persulfate-Initiated

Polymerization of Acrylamide

D. Hunkeler

D e par t m e nt

o

Chemical Engineer ing, Va nderbi l t U nivers i t y , Nashvi l l e , Tennessee

37235

Received Apri l 12, 1990;Revised Manu scr ip t Received August 29 , 1990

ABSTRACT: Acrylamide was polymerized at high monomer concentrations

(25-50

w t 5 ) at temperatures

between 40 and 60

"C

with potassium persulfate as the initiator. The rate of polymerization was found to

be proportional to the monomer concentration to the 5/&h power, a dependence extensively reported a t

low

and m oderate levels, suggesting that the rate order is invariant to the acrylamide concentration up

to

its

solubility limit in water. Limiting conversions have also been observed and are reciprocally related to the

initial monomer concentration. Both the high ra te orders and limiting conversion are found to be manifestations

of the same phenomena: the monomer-enhanced decomposition of potassium persulfate. A "hybrid cage-

complex" mechanism,

in

which hydrogen bonding between the monomer and initiator lead to association,

has been derived. This postulates that the m onomer-initiator associate leads to donor-acceptor interactions

between the amide and the persulfate . The decomposition of this charge-transfercomplex leads to a secondary

initiation reaction , which proceeds in competition with and often in preference

to

the thermal bond rup ture

of

the peroxide. It will be shown to give good quan titative prediction of the polymerization rate order,

monomer and initiator consumption, and molecular weight. Furthermore, the mechanism avoids the free-

energy inconsistencies characteristic of prior theories and is generalizable to o ther nonionic and ionogenic

acrylic water-soluble monomers

in

polar solvents.

Introduction

Polyacrylamide homopolym ers derive their utility from

their long chain lengths and expanded configuration in

aqueous solutions.

As

such they ar e used primarily for

water modification purposes. For example, drag reduction

agents function by transferring energy from the eddies to

provide a laminar flow regime and decrease t he hydro lytic

resistance. Polyacrylamides are also applied as thickening

agents,' cuttin g fluids,2an d soil stabilizers3 nd to a lesser

exte nt in gel electrophoresis,4 soaps,5 an d tex tile appli-

cations.6 They are also used in emulsion or microemul-

sion form as cleaners and in enhanced oil recovery.7

Recently, hydrophobic modifications have expanded the

m ark et for polyacrylamides. For commercial applications

polyacrylamide quality is derived from its moisture

insensitivity,oxidative stability,*and rapid dissolution in

water.

Review of Kinetics

In 1967, Riggs and R odriguezgobserved an unusual rate

dependen ce for aqueous acrylamide polymerizations ini-

tiated with potassium persulfate:

R , = k[M]'.25[I]0.5 (1)

Over the past two decades,

22

investigations have con-

firmed a m onomer depend ency exceeding first order while

maintaining that termination occurs predominantly

thro ugh a bimolecular macroradical reaction.1 Riggs and

Rodriguez'' inte rpre ted th e high rat e order as evidence of

monomeric influences on the rate of initiation. Th is had

previously been postulated by Jenkins12 to a ccount for

similar observations m ade while polymerizing styren e in

toluene with benzoyl peroxide

as

an initiator. Morgan'3

had taken the inference a st ep furth er, suggesting his ses-

quimolecular order was attrib utab le o seconda ry initiation

caused by the mon omer-e nhanced decomposition of per-

oxide. Th e credibility of this hypothesis has been en-

hanced thro ugh experimental work performed by Dainton

and c o - ~ o r k e r s . ~ ~ - ~ ~hey observed the rate dependence

0024-9297/91/2224-2160$02.50/0

to revert to unity in the absence

of

chemical initiators.

(Polymerizations were initiated with W o -rays, which

generated

H

and

OH

radicals, but left propagation,

termination, and transfer reactions unchanged.) Fu rther

experimental evidence of th e monom er-enhanced decom-

position phenomena will be presented in a subsequent

section of th is paper.

T o account for high ra te orders with respect to monom er,

thre e mechanisms have been proposed: the cage-effect

theory (Mathes on, 1946),18 he complex theory (Gee and

Rideal, 1936, 1939),19120

nd

the solvent-transfer theory

(B ur ne tt, 1955; Allen, 1955).21122Th e lat ter assumes that

the solvent acts a s a unimolecular term inating agent. A

necessary consequence is tha t th e corresponding transfe r

radical is unreactive. However, in aqueous media th e

solvent- ransfer mechanism is not a viable explanation

for the high rate order phenomena since the hydroxy-

transfer radical is very unstable an d is capable of initiating

olefinic m onomers (Noyes, 1955).23

The complex theory assumes a reversible association

complex is formed between th e m onomer and initiator.

Th is decomposes to produce a primary radical and

a

mac-

roradical of length one:

KC

1. I + M + I - M

ki

2.

I-M R,'

+

Rin'

Matheson's alternative explanation for th e initiation mech-

anism assumes that as two fragments of a dissociated

molecule ar e produced t he y are contain ed in a *cage'' of

solvent molecules. T hi s radical pair may combine several

times before diffusing ou t of th e cage. Th is hypothesis is

based on Eyring's (1940)observationz4 or benzene

at

room

tem per atur e, where a molecule ma de 10'0 movem ents in

its equilibrium p osition per second bu t underw ent 1013-14

collisions in th e same period. Fo r th e persulfate-initiated

polymerization of acrylamide th e cage-effect theory can

be written as

1991

American Chemical Society


2/12

Macromolecules,

Vol. 24,

No. 9

1991

1.

2.

3.

4.

kr

2Rin*-

khn

(Rin* Rin)

+

M

-

,

+

Rin*

Although, based on very different premises, both these

mechanisms reduce to a n identical rate equation

where

ki

is the com plex/initiator decomposition constant

for the com plex and cage theories, respectively, and

K

is

th e complex association con stant (K,)r the ratio kMI/k,,

which represents th e relative ra te a t which a caged radical

undergoes propagation and recombination.

These predict an increase in the ra te order from 1.0 to

1.5 as th e conversion increases.

While either mechanism

can satisfactorily pre dict t he conversion-time development

for acrylam ide

polymerization^,^^

there has been no direct

verification that the order is changing with monomer

concentration. Th is has caused concern tha t neither mech-

anism is representative of actual physical phenomena.

Furthermo re, since both theories reduce to th e same rdte

equatio n, kinetics cann ot be used to discriminate between

th e mechanisms. In th e following section, we will therefore

evaluate t he cage and complex mechanisms on th e basis

of thermodynamic consistency and nonkinetic experi-

mental observations.

Evaluation of the Cage-Effect

and

Complex The-

ories.

Flory (1953) has shown th at for typical values of

radical diffusivities (10-5 cmz/s) the monomer cannot

appreciably influence th e events in t he cage.z6 T ha t is,

the enhanced decomposition of caged radicals is insig-

nificant relative to diffusion out of the cage, unless, as

Jenk ins showed,l2 th e cage has enormous dimensions

(104-A adius), which seems improbable. T he theory does,

however, predict low efficiencies of in it ia ti ~ n ,~ ?nd these

have been reported for aqueous acrylamide polymeriza-

tions

(f

= 0.024).28

Noyesz3broadened th e scope of th e cage-effect theory

by developing a hierarchal cage structur e. He defined the

following: primary recombination, between two molec-

ular fragments that are separated by less than one mo-

lecular diameter; secondary recombination, between two

fragments of th e same molecule tha t have diffused greater

tha n one molecular diameter ap art , ertiary recombination,

between two fragments from diff erent initiator molecules.

Primary and secondary recombinations occur in =lO-3

and

lo4 s,

respectively. Since th e time between diffusive

displacements is approximately

lo-

s, monomer-en-

hanced decomposition cannot compete with primary

recom bination. However, if th e scavenger (mon omer)

concentration is high, Noyes calculated t ha t the fraction

of radicals reacting with scavenger tha t would otherwise

have undergone secondary recombination is, to th e first

approximation, proportional to Th at is

R , : [MI1/ (3)

which accounts for the observed rate behavior for acry-

lamide polymerizations, i.e.,

Rp

:

iW.25.

Noyes calculations suggest that although monomer-

cage interactions are insignificant for cages with s hort

Persulfa te-Initiated Po lymerization of Acrylamide 2161

lifetimes, for the fraction of cages where radicals are

significantly separated, the enhanced decomposition re-

actions are competitive.

Furthermore, the long cage

lifetimes necessary for enhanced decomposition suggest

th at if the cage theory is true, Flory and J enk ins have

overestimated the macroradical diffusion coefficient.

Noyes theoretical calculation is equivalent to th e kinetic

app roa ch we will develop in this paper. Specifically, we

will define the existence of two cage entities: com pact,

where the radicals are separated by less than one molec-

ular diameter and diffuse where they have diffused

furth er apart. It is postulated th at only the latter are

susceptible to monomer attack. Thi s is an oversimplifi-

cation, as physically there is a continuous d istribution of

cage sizes (radical separations). However, from a mech-

anistic viewpoint, there is a critical radical separation,

which, if achieved, allows th e monom er to co mpete with

radical fragment recombination. Therefore, the popula-

tion can be divided into two regimes according to their

reactivity.

Complex Theory.

The complex theory has been

historically criticized an d rejected because ex perimental

dat a indicate th at the association constant rises with tem -

peratu re. Th is is inconsistent with energetic predictions,

which indicate the com plex is less favorable a t higher tem-

peratures. Fu rth er indirec t evidence against amide-per-

sulfate complexability was presented by Riggs and Ro-

driguez who showe d th e overall activa tion energy for

aqueous acrylam ide polymerization (16 900 cal/mol) was

almost exclusively composed of the contribu tion from th e

thermal decomposition of potassium persulfate ( d/Z =

16

800

cal/mol; complex formulation should reduce th e

activation energy). However, more recent experimentsz9

indicate th at th e overall activation energy is appreciably

lowered, o below 10 kcal/mol in the presence of monomer.

In the same investigation ultraviolet spectrometry was

used to identify new complexes produced w hen acryloni-

trile and N-vinylpyrrolidone, two nitrogen containing

monom ers, were mixed with potassium persulfate. Fur-

thermore, the optical intensity of th e new bands reached

a maximum a t a time coincident with th e induction period

of the reaction. T he authors concluded a donor-acceptor

complex was produced between the nitrogen-containing

monomer an d th e persulfate (Trubitsyna, 1966).30 These

authors

also

attributed the color change, noticeable

imm ediately after mixing nitrogen-containing monomers

and persulfates, to th e formation of

a

molecular complex.

Fur ther evidence to this end came from polymerizations

withmonomers t ha t are stronger proton donors tha n acry-

lonitrile an d N-vinylpyrrolidone: styren e, methyl me th-

acrylate, isoprene, and m ethyl acrylate. When these are

added to persulfate, no polymerization occurs although

iodometrically th e concentration of potassium p ersulfate

decreases by 70% in the first hour. These monomers are

preferentially forming a complex with potassium persul-

fate a nd blocking out th e nitrogen-containing monomers.

Th is is significant in thr ee respects: first,

it

shows tha t

the new bands in the UV spectrum cannot be at tributable

to nonmonomeric species, such as oxygen; second, it

demon strates that proton donation from the monomer to

the persulfate is a prerequisite for enhanced decomposi-

tion; third,

it

implies that the complex

is

initiating po-

lymerization, since potassium persulfate alone at 20

C

s

incapable of initiating th e reaction.

Other peroxide initiators (benzoylperoxide: T rubitsyna,

1965I3lhave also been shown to decompose at faster rates

in th e presence of nitrogen-containing additives. In this

case the enhance d decom position was also accompanied


3/12

2162

Hunkeler

Macromolecules, Vol. 24, No. 9, 1991

2 ) The electrical environment of the monomer is the

primary factor in its interaction with peroxide.

(3)

Monomer-enhanced decomposition is limited to

initiator m olecules where th e radical pair has achieved a

minimum "critical" separation.

(4)

Th e enhanced decom position of complexed persul-

fate is caused by hindered recombination a nd not a greater

frequency of fragmen t dissociations. When the initiator

is bound to the monomer, the dissociated radical pair

cannot regene rate potassium persulfate by recombination.

Eith er radicals or an inert recom bination product of th e

form O0-SO3M03SO'- are produced. Therefore, in the

presence of donor-acceptor interactions, each radical

separation or "transient dissociation" results in the con-

sum ption of one initiator molecule. In th e absence of

bound monomer, an initiator transiently decomposes and

recombines

102 3

imes for each "pe rmanent decomposi-

tion".

by a decrease in the overall activation energy. Th is

was

observed by the same authors several years later for

reactions between benzoyl peroxide and aminated poly-

styrene,32 ndicating tha t t he donor-acceptor interactions

are no t dependent on molecular architecture.

In 1978,T r ~ b i t s y n a ~ ~sed conductivity to monitor th e

charged particles produced from the interaction of acry-

lamide and potassium persulfate. These experiments

found the onset of charged particle generation corre-

sponded to the induction period of th e reaction and th e

onset of radical generation,

as

determined by ESR.

Furthermore, they were performed below

20

"C, where

the thermal decomposition of potassium persulfate is

negligible, ind icating a secondary decomposition reaction

was occurring. On the basis of these observations, T ru -

b i t ~ y n a ~ ~roposed an electron donor m echanism, with

concurrent radical an d charge generation.

M ~ r s i ~ ~bserved that diphenylamine enhanced the

decomposition of benzoyl peroxide. He also attr ibu ted

this to a donor-acceptor interaction between the am ine

and the peroxide an d suggested the interaction was caused

by a modification of th e peroxide's dihedral angle. Furth er

evidence that acrylamide associates with potassium per-

s ulfa te com es from B e k t ~ r o v , ~ ~ho found

Sod2-

salted

ou t poly(vinylpyrro1idone) bu t could not p recipita te poly-

acrylamide, presumably because it was neutralized by a

reaction with th e amide side chains. T he reaction of

amides with persulfate is not surprising in light of NM R

evidenceM tha t shows th at t he carbonyl groups are

hydrogen bonded to water b ut t he am ides are relatively

free. Coleman3' has confirmed t ha t the carbonyl and

amide subs tituen ts behave complementarily in tha t the

binding of one functional group is concurrent with the

reactivity of the second.

Chapiro3*conducted an extensive investigation of the

solvent effecta on acrylamide polymerization and reported:

Rp,water > Rp,acetic acid > Rp,methanol > Rp,DMF ZZ Rp,dioxane ZZ

Rp,toluene

>

Rp,acstonitrile

(4)

The se strong effects have been shown to be due t o the

polarity an d hydrogen-bonding affinity of acrylamide. Gro-

mo+9 stud ied acrylamide polymerization in water, DMSO,

and T H F and concluded t hat as the polarity of the solvent

rises its ability to donate protons to t he carbonyl rises.

This results in a positive charge on the amide and an

increased electron localization on the a-carbon. The se

observations will be shown to be c onsistent with a kinetic

model developed in a subsequent section of this paper.

Bune et al.40have confirmed, by 'H and I3C NMR, tha t

hydrogen bonding occurs predominantly through t he car-

bonyl group

(6c-o

shifts t o weaker field positions while

~ N H *

s essentially unchanged). Th ey also correlated th e

electron-accepting ability of th e carbonyl with a n increased

electron density on the conjugated double bond.

Manickam41 has a lso developed a m echanism w here

monom er-enhanced decom position is included outside the

framework of cage or complex theories, but this also

assumes a

100

efficiency for monomer-enhanced de-

composition, limiting its utility.

The following conclusions ensue from the preceding

discussion and serve

as

a basis for the derivation of a

synthesis m echanism an d kinetic model:

(1)

Monomers containing highly electronegative sub-

stit ue nts can form "associates" with peroxide-containing

initiators. Th is enhances the decomposition of, for

example, potassium persulfate, at low temperatures,

reducing the activation energy and extending t he useful

range of the initiator.

Elucidation of an Initiation Mechanism

Complex4age Equivalence.

We have shown in the

preceding section tha t th e formation of an intermediate

"associate" is a necessary precursor to m onomer-enhanced

decomposition. Th is allows th e electron-donating group

sufficient time

to

attac k the peroxide to be competitive

with the rapid radical fragmentation and recombination

reactions. Th is monom er-initiator associate can result

from either th e diffusive displacement of a m onomer to

the volume element of the peroxide (cage approach) or

th e formation of a molecular complex. Both of these

phenomena can be represented by a general reaction th at

is nonspecific to the forces drawing the monomer and

initiator into close proximity. (T his modification must

also be applied to Manickam's mechanism t o successfully

apply it.)

That is, the "associate" is a broadly defined concept

encompassing both covalent and weak-bonding interac-

t ions . However , s ince experimenta l m e a s ~ r e m e n ts ~ ~ave

found the associate to be irreversibly and nonspontane-

ously formed, uncharacteristic of covalently bonded mol-

ecules, a weak-bonding interaction must be responsible

for monom er-initiator association. Th is "associate" can

therefore be represe nted as a ''weak complex", form ed

presum ably due to hydrogen bonding, or equivalently, as

a "diffuse monomer swollen cage", the difference being

entirely semantic since in both models the monomer is

physically contained within th e three-dimen sional volume

elemen t of a diffuse radical pair. In other words, th e

complex an d cage treatm ents are nondiscriminating mod-

els of the same physical phenomena as far as am id ep er -

sulfate interactions are concerned. T he forces responsible

for th e formation of th e associate will be discussed in a

subs eque nt section of th e paper following a presenta tion

of the reaction mechanism.

The ambiguity in defining cage or complex structures

allows us to com bine th e positive fe atures of bot h mech-

anisms. Specifically, Noyes' hierarchical cage str uc tur e

will be used as a precursor to association and charge-

transf er reactions. Th is will allow th e implementation of

a monome r-enhanced decomposition mechanism without

th e inconsistency of association phenomena increasing with

tem peratu re, th e main drawback of existing mechanisms.

For obvious reasons, th e new mechanism w ill be referred

to as the "hybrid cage-complex" or "hybrid" mechanism

an d is developed below.


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Macromolecules,

Vol.24 No. 9,

1991

Proposed Mechanism.

Th e apparent increase in the

aasociation constan t (k,J with tempe rature can be ratio-

nalized if we consider associa tion,and the donor-acceptor

reactions, to.proceed within the framework of a caged

mechanism. Reactions of the sulfate radical th at generate

nonreactive products mu st

also be

included

to

accou nt for

low efficien cies of initiati on

(f =

0.06-0.4).

Initiator Reactions (Formation of a Caged Hier-

archy).

kd*

3.

{SO,'--'O,S) -

50, -

Paren theses indicate a "compact cage" and brace s signify

a "diffuee cage".

Swollen Cage Formation ( Association ) nd De-

composition.

5.

association

6.

dissociation through a donor-acceptor intermediate

7.

(SO,

M

'04S) f

Q inert products)

Step 7 epresents th e consu mption of m onomer-initiator

associates through a reaction tha t generates nonreactive

products. This initiator deactivation is necessary

to

avoid

nonu nit efficiencies of initiatio n.

Chain Initiation.

kii

8.

SO,'- M

-

,'

has shown th at sulfate rad icals can also react with

water

to

prod uce hydrox y radica ls, which are capa ble of

initiation.*

9.

SO,'-

H 2 0

SO; 'OH

ku

10.

'OH M

-

,'

Propagation.

11.

R; + M

f

Transfer to Monomer.

k h

12.

R,' M- , + R,'

Termination.

ku

13.

Kinetic Model

A t any

ime t, the persu lfate is comprised of undisso-

ciated ini t iator (S20e2-), "compact caged fragments"

R,' + Rae+ P,

+ P,

Per sulfa te-Initia ted Polym erization of Acrylamide

2163

(SO4*-

*04S),

and "diffuse cage fragments" (s04 -

*O&

The total persulfate in the system

It)

s

Zt =

[S20,2-]

+ (SO,'-*O,S) (SO,'-*O,S) (6)

where

(SO,'--'O,S)

=

O,Zt

and 00

+

91

02 = 1.0.

Th e balances on

a l l

reactiv e species follow:

k,(SO, -- O,S)

(7)

~H [SO ,'-][H~ O] kjl[SO,'-][M]

O (11)

d['OH]

d t

- -

kH[SO,'-][H2O] -kiJOH][M]

m

0 (12)

From eq

10

Assuming

k ,

is independent of chain length (kil

= ka =

kp), eqs lo ,

11,

and

12

can be substituted into eq

13 to

yield

[R'] =

where

2fck,*{ SO,'--'O,S) [

M I ) 1'2

ktd

(so;--o,s) = a2(S,O,2-)

and

1

+ kc /kb

f

=

where can be defined equivalently

as

cage destruction

of com plex-decom position efficiency.


5/12

2164 Hunkeler

Macromolecules, Vol.

24, No.

9,

991

The long chain approximation subsequently yields

R , =

k , [ M ]

X

Discussion

of

the Derived Rate Equation. The

decomposition constant (kd) has been determined from

measurements of the concentration of undecomposed

initiator:44

d [ S

' '-

= - k

S O -

d t

d l 2 8 1

(15)

However, since only diffuse cage fragm ents can dissociate

to produce unpaired free radicals, eq 15 can more

appropriately be written as

(16)

Expressing th e concentration of these diffuse cages as a

fraction of th e overall initiator level, eqs 15 and 16 can be

combined to yield

which provides the iden tity kd

=

@2kd*. By an analogous

procedure it can be shown th at

k , = @2k,*,

where

ka

is the

appa rent (overall)association constant an d k,* is th e actual

(specific) association cons tant.

As the thermal energy of the system increases, the

frequency of equilibrium displace ment of sm all molecules

rises and the probability of recombination decreases. If

we interp ret this in te rm s of initiator reactions, the radical

pairs formed through the transient dissociation of the

initiator molecules will achieve greater molecular sepa-

ration and have longer lifetimes prior to recombination.

In th e context of the hierarchical cage mechanism devel-

oped herein, this is represented as an increase in the

fraction of diffuse cages

(@2)

a t the expense of a reduced

concentration of compact cages

( @ I ) .

Th e utility of the

hybrid mechanism is therefore immediately obvious.

A t

increased temperatures th e appa rent association constant

(k , )

has been observed to rise. Th is is

ot

due to a n actual

increase in association phenomena

(k,*),.

which is ener-

getically unfavorable, but rather to an increase in the

fraction of radical species with sufficient separation to

participate in association reactions (% increases). Such

thermodynamic consistency in the kinetic model is not

possible without hybridizing th e cage-effect and complex

theories, specifically using a caged precursor to association

and donor-acceptor interactions. This represents the

major improvement of the hybrid mechanism over the

existing theories.

Th e hybrid mechanism is furthe r characterized by two

competing initiation processes: therm al bond r uptu re and

mono mer-en hanced decomposition. The se yield th e fol-

lowing rate equations.

thermal decomposition dominates:

monomer-enhanced decomposition dominates:

Table

I

Equivalence

of

Two Kinetic Processes Which Provide '/4th

Power Rate Dependencies

monomer concn [MI R.

=

kl[M]l.=a R.

=

kl([M] [M]1.6)/2

0.5

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.42

1.0

2.38

3.95

5.66

7.48

9.39

11.39

kl

is assigned

an

arbitrary value

of

1.0.

0.43

1.0

2.41

4.10

6.00

8.09

10.34

12.76

The overall polymerization rate order with respect to

monomer concentration is therefore governed by the

relative rates of therm al decomp osition

(kd)

and association

(k,)

and their respective initiation efficiencies

(f,

f c ) .

Indeed the hybrid mechanism predicts a direct corre-

spondence exists between th e str eng th of th e monomer-

initiator association an d the rat e order, which lies between

1.0 and 1.5. If the mechanism is correct, it implies tha t

the observed 6 /4th power for acrylamide polymerizations

is actually an "apparent" order, with the true kinetic

process being a relatively e qual balance between unimo-

lecular and sesquimolecular reaction mechanisms (thermal

an d monom er-enhanced decomposition). Tab le I shows

rate da ta generated from th e hybrid mechanism (eq 14)

with arbitrary param eter values. These are virtually

indistinguishable from kinetics generated with a single

5/4th order term. Therefore , on th e basis of kinetic

observations, it cannot be ascertained whether t he unique

1.25

rat e order for acrylam ide is due to a single initiation

mechanism or comp etition between m ultiple processes of

unit and sesquimolecular order. Th e hybrid mechanism

cannot be refuted on kinetic bases an d mu st be evaluated

using nonkinetic criteria, such a s the free-energy analysis

in the preceding paragraph.

Generalizationof the Initiation Mechanism to

Other Water-Soluble Monomers

Th e charge-transfer complexes tha t form between per-

sulfate- and nitrogen-containing monomers require free

electrons on the donor (m onomer) and a polar medium.

For acrylamide polymerizations in dimethyl sulfoxide-

water mixtures, the rate order with respect to monomer

increases as the fraction of DMSO in th e solvent mixture

rise^.^^^^^

Th is is caused by the apro tic nature of dimethyl

sulfoxide and its inability to hydrogen bond to t he acry-

lamide carbonyl group. Th is less solvated monom er is

therefore more readily complexed with the peroxide an d

undergoes enhanced decomposition at an accelerated rate.

Th e rate therefore approaches sesquimolecular order, the

limit if monomer an d initiator form 1:l complexes, as the

fraction of DM SO rises, in agreement with exp erimental

observations.

This effect is also observed in other monomers with

electronegative atom s, for example, in acrylic acid (oxy-

gen)-persulfate systems.41 T he polarity and hydrogen-

bonding affinity of the hydroxy group exceed tha t of th e

corresponding amide, and t he rate order again approaches

the sesquimolecular limit. Indee d, th e monom er's ability

to form hydrogen bonds, through th e side-chain functional

group, appears to be the principal cause of association

with peroxide-containing initiators.

For N,N-dimethylacrylamide, which cannot hydrogen

bond to either the peroxide or persulfate oxygens, due

perhaps t o steric interference of t he bulky m ethyl sub-

stituents, association phenomena a nd monom er-enhanced


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Macromolecules, Vol. 24,

No .

9,

1991

Persulfate- Initiated Polym erization of A crylamide

2165

Generalization to Cationic Monomers.

Friend and

Alexanders8 were the first t o observe a n interaction

between persulfate and quaternary ammonium com-

pounds. TrubitsynamJ3@an d Kurenkov54 later observed

complexes an d enhanced decom position of persulfate du e

to cationic ammonium additives. Fu rther , the mag nitude

of th e enhanced decom position was significantly grea ter

th an was observed for acrylamide. I t has been showns8

tha t charge-transfer interactions are responsible for the

formation of a 1:2 stoichiometric com plex of t he following

type:

Table I1

Rate Equations for Several Acrylic Water-Soluble

Monomers

0 in

monomer R,

0:

Ma ref

NjV-dimethylacryl-

1.0

Kurenkov, 1 9 8 W

methacrylamide

1.13

Gupta,

198751

acrylylglycinamide 1.22 Haas, 197060

acrylamide 1.25 Riggs and Rodriguez, 19679

acrylic acid

1.50

Manickam,

1979.

diallyldimethyl-

2.00

Jaeger,

198466

ammonium chloride Hahn, 198356*57

A

third-order dependence has been reported. However, he mon-

omeric salt influences propagation between charged radicals and

monomer molecules. This results in a first-order relationship between

the propagation rate constant and the monomer concentration.

amide

decomposition are

not

observed and t he rate order reverts

to

unity.47tG Ergozhin49 nves tigated th e kine tics of a serie s

of N-substituted amides and observed the rate o rder with

respect to monomer concentration to decrease as the

accessibility to the vinyl group was hindered. This

confirms Trubitsyna's postulate33 tha t th e amide is

responsible for the electron rearrangem ent leading to the

monom er-initiator association. Haasm has observed that

other amide-containing monomers, for example, acrylyl-

glycinamide, enhance t he d ecomposition of potassium per-

sulfate and have the same rate order with respect to

monomer concentration as acrylamide, which is again

consistent with a hydrogen -bonded associate. If meth-

acrylamide replaces acrylamide as the monomer in a per-

sulfate reaction, a greater th an first-order dependence is

again observed

R , a

W l3; upta, 1987).s1 Th e reduced

order from the 5/4th power may be an experimental

anomaly, as methacrylamide has not been extensively

investigated. However, it is more likely tha t the a-methyl

substitution is affecting the electron arrangem ent neces-

sary to produce a monom er-initiator complex.s2 (M eth-

acrylam ide radicals are present in a resonance-stabilized

stru cture where th e &carbon can more easily stabilize a

radical than th e a-methyl-substituted carbon.s3)

Ta ble I1 summ arizes the observed kinetic relationships

for several acrylic water-soluble monomers (acrylamide,

acrylylglycinamide,acrylic acid, NJV -dimethylacrylamide,

methacrylamide). Th ere is a direct correspondence be-

tween the m onomer's hydrogen-bonding affinity an d the

rate order with respect to monom er concentration. During

th e derivation of th e hybrid cage-complex initiation mech-

anism, it was shown that high rate orders occurred

concom itant with monomer-initiator association. If we

combine these two observations, then the hybrid mech-

anism infers tha t hydrogen bonding between th e monomer

an d persulfate is the cause of association phenomena. T his

seems intuitively reasonable and is quite probable.

Th e sum of a first- and sesquimolecular-order initiation

mec hanism, th e hybrid cage-complex model, is therefore

flexible enough to quantitatively describe a broad array

of kinetic observations for nonionic and anionic acrylic

water-soluble monomers. Th e stronger the hydrogen

bonding between th e monomer a nd persulfate, th e greater

the strength and extent of association and a larger

proportion of initiator decomposes through a monomer-

enhanced reaction (higher rate order). Contrarily, steric

interferences shield th e hydrogen bonding an d hinder th e

ability to form charge-transfer com plexes. Tn is results in

a larger fraction of the persulfate, which decomposes

through a thermal bond rupture mechanism (rate order

approaches unity).

&

n i l

-OSOOSO-

II II

&N*

These decom pose to produce two mac roradicals of length

1 when 1:l complexes are produced, one prim ary radical

is liberated). Such a mechanism reduces to a second-order

rate dependence on monomer concentration, in agreement

with experimental observations for diallyldimethylam-

monium chloride polymerization (Jae ger, 1984).ss Jaeger

also showed th at th e rate ord er was reduced by

1

when a

noncomplexing initiator [azobis(pentanoic acid)] was used

in place of potassium persulfate. Therefore, the high rate

orde rs observed for polym erization of acrylic water-so luble

monomers in aqueous media initiated by persulfate

are

almost certainly due to hydrogen-bonding and ionic

interactions between th e monom er-initiator pair. T he

stren gth in this interaction determines th e deviation in

order from unity. Table I1 summarizes the observed

kinetic relationships for several nonionic, anionic, and cat-

ionic acrylic water-soluble monom ers. A correlation

between th e rate order with respect to monomer and th e

str en gth of the monom er-initiator complex is again

observable.

On th e basis of th e preceding litera ture survey, we can

propose the following general initiation mechanism for

acrylic water-soluble monomers with persulfate:

3.

4.

{SO,'--'O,SJ

- SO,'-

5.

6.

7.

SO,- H,O

-

SO,

+

OH

SO, - M - ,'

*OH

+

M -

,'

8.

9.

10.

where x is the stoichiometric ratio of monomer in the

initiator complex. T ha t is, for anionic and nonionic

monomers,

x = 1

and

R, a

kM k M3I2,

and for cationic

monomers,

x = 2

and

R ,

a kM

k"M2.

An oppositely charged monom er-initiator pair is there-

fore able to form higher stoichiom etric complexes th an if

the initiator a nd m onomer are of the same charge, or if

one or both of the species are uncharged. Th is accounts

for the higher order in rate with respect to monomer


7/12

2166 Hunkeler

I .o I

t

- h r r = I

8 .

0,s

z -

0.6

u

w -

>

5 0.4

Table I11

Polymerization Conditions

8

-

8

-

- 8

temp,

C

50

50

50

50

50

50

40

60

[acrylamide],

mol/L

3.35

4.03

4.69

5.37

6.04

6.41

6.70

6.70

[KzSzOsl,

mmol/L

0.252

0.228

0.251

0.248

0.250

0.238

1.573

0.0609

mass

of

aqueous

phase, g

10oo.o

10oo.o

10oo.o

10oo.o

10oo.o

1Ooo.o

10oo.o

10oo.o

mass of

Isopar-K,

g

1Ooo.o

1000.3

999.9

1Ooo.o

1002.1

1000.3

1000.2

1000.6

mass of

SMS,O g

100.0

100.0

100.0

100.0

99.9

100.0

100.0

100.0

a Sorbitan monostearate.

Table

IV

Limiting Conversion versus Monomer and Initiator

Concentration

1

m

n

g

conversion

(Xl)

0.92

0.95

0.96

0.996

0.996

0.997

0.76

0.999

acrylamide

concn, mol/L

6.41

6.04

5.37

4.69

4.03

3.35

6.70

6.70

Table V

Parameter Estimates

potassium

persulfate concn,

mmol/L

0.238

0.250

0.248

0.251

0.228

0.252

0.0609

1.573

param value units

f

40 O C : 1.0

dimensionless

50

C:

0.372

60 "C: 0.065

40 O C : 3.17 X L/mol.min

60 C: 1.93 X

50

o c : 1.06 x

10-3

km 2.433 X

lo4

dm2/mol.min

Aob

8.01 dimensionless

Aib

2.0 x 10-2 K-1

(Kim and Hamielec, 1984)

k. = (+?k.*) = 8.77 X 10rl exp(-66500/RT) . A is a gel effect

parameter

in t h e

expression k d o / k u

=

exp(Awp) where A

=

A0

-

concentration for aqueous polymerizations of cationic

monomers with persulfate.

Proposed Experimental Investigation

The hybrid mechanism predicts

that

the rate order with

respect to

monomer

is exclusively a function of

the

chemical interactio nsbetween the monomer-initiator pair,

hydrogen bonding for

the

acrylamide/persulfate/water

system. This implies tha t the rate order is independent

of

reaction conditions, for example,

the

monomer con-

centration. (The cage-effect

and

complex theories predict

a decrease in the rate orde r with monomer concentration.)

This, however, cann ot be verified from existing experi-

ment al observations,1 which are limited t o acrylamide

levels below

30

w t 7 . A series of polymerizations are

therefo re planned between 25and 50 w t % monomer, the

latter delineated by t he solubility of acrylamide in water.

The

suitability of the hybri d mechanism to describe

the

kinetics

at

high conversion a nd th e molecular weight will

also be determined.

Experimental Section

Conversions were inferred from measurements of the residual

monomer concentration by high performance liquid chromatog-

raphy. This method has been described in detail@JS6l and is

AIT.

0 60.0 120.0

180.0

TIME (m inu tes)

Figure 1. Conversion-time data m) for an acrylamide polym-

erization. The experimental conditions were [monomer]

= 5.37

mol/L,, [KzSzOs]= 2.44 X l W m ol/ L, and temperature = 50

C.

A

limiting conversion of 0.97 is observed. Increasing the

temperature to

60 C

arrow) did not lead to consumption of

additional monomer.

I O 1

0 8

1

04

0

0 60.0 120.0 180.0 240.0

TIME

(minutes)

k t

o'20 0 2 0.4 0.6 0.8

1.0

CONVERSION

Figure 2. (a) Conversion-time data m) and kinetic model

predictions (-) for an acrylamide polymerization at 50 C:

[monomer]

=

3.35 mol/L2 and [KzSzOs]

=

0.252

X 10-3

mol/L.

(b) Weight-average molecular weight-conversion data m) and

kinetic model predictions (-) for the same experiment.

applicable below 1ppm with 95% confidence limits of k0.25 % .

A C N column (9% groups bonded toap-Porasil (silica)substrate,

Waters Associates) with a 8-mm i.d. and

4-pm

articles was used

as the stationary phase. The column was housed in a radial

compression system (RCM-100, Waters) and was operated at a

nominal pressure of 180 kg/cm*. The HPLC system consisted

of a degasser (ERC-3110, Erma Optical Works), a Waters U6K

injector, a stainless steel filter, and a CN precolumn (Waters).

An ultraviolet detector (Beckman 160) with a zinc lamp operating

at a wavelength of 214 nm was used to measure the monomer

absorption.

A

Spectra-Physics SP4200 integrator was used to

compute peak areas. The mobile phase was a mixture of 50 vol

% acetonitrile (Caledon, distilled in glass, UV grade) and 50 vol

% double-distilled deionized water, containing 0.005 mol/L of

dibutylamine phosphate. The flow rate was 2.0 mL/min. The


8/12

Macromolecules,

Vol. 24,

No.

, 1991

z

v

W

>

P

a

8

c

0

E

-

I o

0.8

0.6

0.4

60.0 120.0 180.0

TIME (minutes)

I .o I , I

0.8I

0.6

8 8

0

0 0.2

0.4

0.6

0.8 I o

CONVERSION

Figure

3.

(a) Conversion-time data

(D)

and kinetic model

predictions

(-)

for an acrylamide polymerization at

50

OC:

[monomer] = 4.03 mol/L, and [K$32Oe] = 0.228 X 10-9 mol /L .

(b) Weight-average molecular weight-conversion data

(D)

and


peak separation was optimized by varying the acetonitrile/water

ratio.

Molecular weights were measured by using a Chromatix

KMX-6 low-angle laser light scattering photometer, with a cell

length of 15 mm and a field stop of 0.2. This corresponded to

an averagescattering angle of 4.8O.

A

0.45-jtm cellulose/acetate/

nitrate filter (Millipore) was used for polymer solutions. A 0.22-

jtm filter of the sametypewas used to clarify the solvent. Distilled

deionized water with 0.02 M Na2SO. (BDH, analytical grade)

was used as a solvent. Weight-average molecular weights were

regressed from measurements of the Rayleigh factor using the

one-point method.B2 This has been observed to reduce the error

in light scattering 2-fold over the conventional dilution procedure.

The refractive index increment of t.he solvent was determined

by using a Chromatix KMX-16 laser differential refractometer

at 25 C and a wavelength of 632.8 nm. The dn/dc was found

to be 0.1869.

For polymerizations solid acrylamide monomer (Cyanamid

B.V., The Netherlands) was recrystallized from chloroform (Cale-

don, reagent grade) and washed with benzene (BDH, reagent

grade). Potassium persulfate (Fisher Certified, assay 99.5%)

was recrystallized from double-distilled deionized water. Both

reagents were dried in vacuo to constant weight and stored over

silica gel in desiccators.

Method

of

Polymerization. Polymerizationat high monomer

concentrations in solutions requires chain-transfer additives to

lower molecular weight, reduce viscosity, and provide more

efficient heat transfer. However, for this experimental set, chain-

transfer agents are undesirable since they can affect the initiation

mechanism through redox coupling with persulfate. Therefore,

a heterophase water-in-oil polymerization process (inverse mi-

crosuspension) was employed. This permitted high aqueous

phase monomer concentrations while maintaining a stable, in-

viscid reaction mixture, ideal for the generation of reliable kinetic

data.

A

prior investigation had demonstrated that inverse-mi-

crosuspension and solution polymerization are kinetically equiv-

alent if a water-soluble initiator is employed.10 In such instances,

Persulfate-Initiated Polymerization of Acrylamide 2167

o.2

tt

r,,,,,,l

0.0

120.0 180.0

OO

TIME

(minutes)

t o , , ,

I

I I I I

1

1 0.2

0

0.2

0.4

0.6 0.8 1.0

CONVERSION

0

Figure

4.


(D)

and kinetic model

predictions (-) for an acrylamide polymerization a t 50 OC:

[monomer]

=

4.69 mol/L, and [K2S2Oe]

=

0.251 X 10-9 mo l/ L.

(b) Weight-average molecular weight-conversion data

m)

and

kinetic model predictions

(-)

for the same experiment.

each isolated monomer droplet contains all reactive species and

behaves like a microbatch solution polymerization reactor.

Inverse-microsuspension polymerizations were performed by

using Isopar-K

(Esso

Chemicals)

as

the continuous phase and

sorbitan monostearate (Alkaril Chemicals)as he emulsifier. The

aqueous phase consisted of recrystallized acrylamide monomer,

distilled deionized water, and recrystallized potassium persul-

fate. The ratio of aqueous to organic phases was 0.741.

Polymerizations were performed in a l -gal stainless steel reactor,

continuouslyagitated a t 323f 1 pm. This provided large particle

diameters ( = l o jtm), which minimized interfacial effects. The

reactor was purged with nitrogen (Canadian Liquid Air, UHP

grade, 99.999

%

purity) throughout the polymerization. A

complete description of the experimental procedures is given in

a prior publication.Bl

Exp erimen tal Conditions. Polymerizations were performed

isothermally at 40, 50, and 60 C at monomer concentrations

between 25 and 50 w t % of the aqueous phase. The latter cor-

responding to the solubility limit of acrylamide in water. Table

I11 summarizes the experimental conditions for all polymeriza-

tions. For all experiments reactor control was excellent, with

thermal deviations never exceeding

1

C.

Results and Discussion

Rate Order with Respect to Monomer Concen-

tration. The measured residual monomer concentrations

were used

to calculate

the

initial rates

of polymerization.

A series of six experim ents were performed at 50 O C with

monomer concentrations between 25

and

50

w t 5

of the

aqueousphase, varied in

5

% increments.

From

these data

the

following rate equatio n was estimated:

Th e 95 % confidence limi ts were determined from a non-

linear least-squares estimation routine

based

on Mar-

quardt's algorithm.

The 95

confidence interval

sur-


9/12

2168 Hunkeler

I

o

0.2

1

i

I

I I I I

60.0

120.0 180.0

TIME

(minutes)

t i

0: '

0.2

0.4

0.6 0 8 1.0

CONVERSION

Figure

5.


(m)

and kinetic model

predictions (-) for an acrylamide polymerization at 50 O C :

[monomer]

= 5.37

mol/L, and

[K 08] = 0.248 X 10-3 mol/L,.

(b)

Weight-average molecular weight-conversion data

m)

and


rounds

1.25,

and therefore the hypothesis that at high

monomer concentration t he ra te order deviates from the

5/4th power is rejected. In other words, th e rate order

with respect to monomer concentration is the same (1.25)

from th e dilute regime t o t he solubility limit of acryla-

mide in water. Th is has mechanistic implications as it

suggests that variable order r ate models; the

unmodified

cage-effect and complex theories are not applicable to

aqueous per sulfate-initiated polymerization of acrylamide.

However, the kinetic observations are consistent with the

hybrid mechanism, which predicts that the strength of

the m onomer-initiator association, and hence the rate

order , is strictly a function of th e chemical composition

of the monomer and initiator, independent of the con-

centration of the reactants. Th e reliability of the 1.34

order is furth er accentuated by Kurenkov's recent (1987)64

result:

R, = iW3'

for monom er levels between 0.85 and

4.93

mol/L, which has been published after this work

began.

Limiting Conversion.

During the se polymerizations,

limiting conversions were observed for several reactions

a t high monomer or low initiator levels (Tab le IV). (The

usual reciprocal relationship between the limiting con-

version and t he ra t e of p~ ly m er i za t i o n~ ~as been found

in this investigation.) Incomplete monomer consumption

is generally a ttribu ted t o either a depletion of th e initiator

or isolation of the macroradicals. The se phenom ena can

be distinguished by raising the temperature after the

limiting conversion is reached. If residual initiator is

prese nt b ut is physically hindered from reaching the acry-

lamide monomer, increasing the thermal energy to the

system will increase the diffusion of small molecules and

increase th e rate. Figure 1 shows such an experim ent for

this system. T he temperature rise did not increase the

conversion, indicating the initiator concentration had

z

v)

[L

w

>

2

P

c

1 J

0 0 2

04

0 6 0 8

10

CONVERSION

Figure

6.

(a)

Conversion-time data

(m)

and kinetic model

predictions (-) for an acrylamide polymerization

at 50

O C :

[monomer]

= 6.04

mol/& and

[K 208]= 0.250 X 10-3

mol /L .

(b)

Weight-average molecular weight-conversion data

(m)

nd

kinetic model predictions

(-)

for the same experiment.

previously been exhausted. Therefo re, the limiting con-

versions offer additional evidence of a second initiator

decomposition reaction. Indee d we can conclude th e

hybrid m echanism is not refuted by t he limiting conversion

observations. Furthermo re, th e simultaneous occurrence

of

limiting conversions in polymerizations with high rat e

orders with respect to monomer concentration suggests

that they are both m anifestations of th e same phenomena:

the formation of hydrogen-bonded associates between

acrylamide an d potassium persulfate, which leads to th e

monomer-enhanced decomposition of the initiator.

Parameter Estimation.

T he conversion-time da ta

were used t o estimate two grouped param eters:

@zk,

and

f

(= 1 / 1 + k, /kb , which ar e unique to the hybrid mech-

anism. Additionally, measu remen ts of weight-averagemo-

lecular weight were used to estimate the transfer to

interfacial emulsifier param eter. (Molecular weight de-

velopment in inverse-microsuspension polymerization has

been detailed previously.e1@) Th e differential equations

were solved with a variable-order Runge-K utta procedure

with a ste p size of

1

min.

A t each tem pera ture parameter es timates were obtained

from a nonlinear least-squares regression routine based

on Marquardt's procedure. The se estimates were obtained

utilizing residual monomer concentration and molecular

weight data for all polymerizations a t a given tempera-

ture. This

is

preferable to the common practice of

estimating param eters from individual experiments, which

is unable

to

identify interexperimental da ta inconsisten-

cies. Th is parameter overfitting leads to unreliable

estimates, which cannot be generalized to other reaction

conditions.

Table

V

shows the values of parameters determined in

thi s investigation. T he activation energy for transfe r to


10/12

I.O I

-

1 . n 8

0.8 -

Persulfate- Initiated Polym erization of A crylamide

2169

Pr

0 2

:

1

60.0 120.0 180.0

TIME (minutes)

i

8

I

8

8 8

0

-

0.4

0

0

0.2

0.4

0.6 0.8

1.0

CONVERSION

Figure

7. (a)

Conversion-time data

m)

and kinetic model

predictions

(-)

for an acrylamide polymerization at 50

O C :

[monomer]

= 6.41

mol/L, and [K ~S ~O B]

0.238 X 1 0 - 3

mol/L,.

(b)

Weight-average molecular weight-conversion

data m)

and

kinetic

model predictions

-) for

the same experiment.

emulsifier was found to be -141 J/mol, typical of a

term ination reaction. It was not, however, significantly

smaller than zero at the

95 %

confidence level, an d we can

conclude that unimolecular termination with interfacial

emulsifier is thermally invariant over the range investi-

gated.

T he complex-cage efficiency

fc)

is observed to decrease

with te mp eratu re, implying the monomer-swollen cage

preferentially forms inert species rather than active

radicals. Th is is consistent with limiting conversion da ta,

which indicate tha t initiator deactivation is more favorable

a t higher temperatures.

Th e ap parent association parameter (k,= a&,*) is found

to increase with tem pera ture according to an Arrhenius

dependence. Th is has been reported previously for acry-

lamide polymerizations initiated by potassium p er ~ ul fa te .~

As was discussed in th e derivation of th e mechanism , thi s

is th e man ifestation of two indepe nden t phenomena: a

decrease in th e specific association co nstant (ha*),which

is entropically less favorable at elevated temperatures,

and an increase in th e fraction of potassium persulfate

present as diffuse cages

(W.

Th e lat ter, which is the only

form of potassium persulfate capable of participating in

monomer-enhanced decomposition reactions, are more

abun dant a t high temperatures due to a greater frequency

of radical diffusive displacem ents and a lower rate of radical

fragment recombination. T he ability of the hybrid mech-

anism t o qua ntitatively predict association phenom ena,

without th e thermodynam ic inconsistency of the specific

association parameter increasing with temperature, is a

second major adv antage over th e unm odified cage-effect

an d complex theories.

All other ra te parameters

(kp,ktd, krm

k d ) were obtained

from the literature a nd have been summ arized in a prior

publication.63

0.8 -

z -

0.6 -

CL

w -

>

0.4

-

8

8

I

I

1

I

I

0 60.0 120.0 180.0 240.0

TIME (minutes )

c 0

.8

' O B

8

=

0.6

8

8 8

-

j

0.4

8 8 .

Id

c

1

0.2

0

0

0.2 0.4 0.6

0.8

1.0

CONVERSION

Figure

8. (a)

Conversion-time data m) and kinetic model

predictions

(-)

for

an acrylamide polymerization at

60 O C :

[monomer]

= 6.70

mol/L,, and

[K&Oe] =

0.0609 X

l W 3

mol /L .

(b)

Weight-average molecular weight-conversion dat a

(a)

and

kinetic model predictions (-) for the

same

experiment.

Comparison of Kinetic Model to Experimental

Data.

Figures

2-9

show conversion-time and weight-

average molecular weight-conversion data and model

predictions for all experiments. Th e hybrid m echanism

is cgpable of predicting th e initial polymerization ra te an d

weight-average molecular weight well over a range

of

t em-

peratures, m onomer concentrations, and rates of initiation.

T he m olecular weight behavior with conversion is typical

of acrylamide polymerizations w here transfer t o monomer

dom inates. A slight decrease in molecular weight with

conversion (although statistically significant at the

905

confidence evel),and the increase with the initial monomer

concentration, is evidence tha t a fraction of th e chains are

terminated throu gh a bimolecular process. Th e limiting

conversion is also predicted well at low initiator levels and

mod erate m onomer concentrations bu t, however, is slightly

overpredicted when it occurs at very high conversions

(>go% ). Th is is due to the authors' personal preference

to obtain accurate kinetic parame ters a t the expense of

fitting limiting conversion da ta. Consequently, initial rate

data were given a greater weighting in the analysis to

compensate for the larger num ber of residual monomer

measurements

at

high conversions.

Figure 10 illustrates th e relative magn itudes of therma l

an d mon omer-e nhanced decomposition of potassium per-

sulfate.

A t

the onset of polymerization the majority of

chains are initiated through a donor-acceptor interaction

between the acrylamide an d persulfate. This effect is most

extreme a t elevated temper atures. As th e conversion rises,

both th e monomer and initiator have depleted (Figure 11

and thermal bond rupture of the peroxide becomes the

predom inant initiation reaction. Figure

11also

shows hat

th e rate of consumption of initiator is strongly dependent

on the initial monomer concentration. Furthermo re, for

th e conditions of th e simulation, the potassium persulfate


11/12

2170 Hunkeler

Macromolecules,

Vol.

24, No. 9, 1991

TIME (minutes)

0 .81 o/7

0

0

0.2

0.4 0.6 0 8 1.0

CONVERSION

Figure 9. (a) Conversion-time data m) and kinetic model

predictions (-) for an acrylamide polymerization at 40 O C :

[monomer] = 6.70mol/L, and

[K&Os]

= 1.573X lo4 mol/L,.

(b)

Weight-average molecular weight-conversion data (H) and


I

.o

I I I 1 I I I

t \

\-I

0.2

1

t

v

-0 0.2 0.4

0.6

0.8

1.0

CONVERSION X

1

Figure

10.

Fraction of polymer chains initia ted by monomer-

enhanced decomposition of potassium persulfate (@-) as a

function

of

conversion. Simulations were performed at

40 "C

(- -1

and 60 C (-) with [K 3208]

6.088

x

lP

mol/L,, [acry-

lamide] = 7.04mol/L,, and @,lo = 0.74.

is exhausted before t he reaction is completed for initial

acrylamide concentrations exceeding 25 w t 5 . For

example, at 50 w t 5 monomer, the radical generation

ceases

at 78%

conversion, in agreeme nt with experimental

observations (XL 0.76).

Conclusions

The persulfate-initiat ed polymerization of acrylamide

is characterized by the formation of hydrogen-bonded

associates between the amide and the persulfate, the

decomposition of which proceeds via a donor-acceptor

mechanism. Th e strengt h

and

stoichiometry of these

associates determine the relative rates of thermal and

monomer-enhanced initiation, the rate order of the

po-

0.2

-

0

1

I I

I

0 0.2 0.4 0.6 0.8 1.0

CONVERSION

( X

1

Figure 11. Concentration of potassium persulfate scaled with

respect to

ita

initial level (I/ ) as a function of conversion.

Simulations were performed at 60

C

with [K2S2Oa]

= 2.4 X 10-4

mol/L, and initial acrylamide concentrations of 1,5,10,25,nd

50

w t '?6

based on the aqueous phase.

lymerization

with

respect t o monomer concentration, and

th e limiting conversion.

This

association phenomena is

observable for any acrylic water-soluble monomer con-

taining electronegative side groups and peroxide-contain-

ing

initiators

and

hasbeen

included within

the

framework

of a

free-radical

polymerization mechanism.

The hybrid mecha nism offers a significant improve-

ment over existing models for initiatio n: th e cage-effect

and complex theories.

These

incorrectly predict a de-

pendence

of the rate order

on monomer

concentration

(found to

be

invariant

to

the acrylamide level up to

ita

solubility in water) and contain parameter

values

that

contrad ict free-energy expectations.

References and Notes

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Registry

No

K2S208, 7727-21-1; acrylamide, 79-06-1.

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