mechanism and kinetics of the spontaneous thermal copolymerization of styrene/maleic anhydride....

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Mechanism and Kinetics of the SpontaneousThermal Copolymerization of Styrene/MaleicAnhydride. Experimental and SimulationStudies in the Presence of 4-oxo-TEMPOa

Josue D. Mota-Morales, Iraıs Quintero-Ortega, Enrique Saldıvar-Guerra,*Gabriel Luna-Barcenas, Martha Albores-Velasco, Judith Percino,Vıctor Chapela, Miguel A. Ocampo

J. D. Mota-Morales, I. Quintero-Ortega, G. Luna-BarcenasCinvestav Queretaro, Libramiento Norponiente No. 2000, Fracc,Real de Juriquilla, Queretaro, Qro. 76230, MexicoE. Saldıvar-GuerraCentro de Investigacion en Quımica Aplicada (CIQA), Blvd. EnriqueReyna No. 140, Saltillo Coah. 25253, MexicoE-mail: [email protected]. Albores-VelascoFacultad de Quımica, Universidad Nacional Autonoma de Mexico,CU Coyoacan 04510, Mexico DF, MexicoJ. Percino, V. ChapelaLaboratorio de Polımeros, Benemerita Universidad Autonoma dePuebla, Puebla, MexicoM. A. OcampoCentro de Fısica Aplicada y Tecnologıa Avanzada, UniversidadNacional Autonoma de Mexico, Queretaro, Qro 76230, MexicoaMost of this work was performed during a stay of J. Mota-Morales at CIQA.

The mechanism and kinetics of the spontaneous copolymerization of styrene (S) and maleicanhydride (MA) in the presence of 4-oxo-TEMPO nitroxide (N) were studied. Experiments wereperformed at 125 8C varying the S/MA and the N/S ratios and the evolution of conversion wasmeasured by dilatometry up to 20% conversion.Clean induction periods or severe retardation inthe initial stage of the reaction were observed.From a proposed kinetic mechanism amathemat-ical model was built, which was used for fittingthe relevant kinetic constants for the self-initiation steps, and the ratio kp=k

1=2

t . The modelperforms well in certain concentration regimes,but it remains a challenge to completely under-stand this complex system in other concentrationregimes.

Macromol. React. Eng. 2010, 4, 222–234

� 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Introduction

The commercial production of styrene (S)/maleic anhydride

(MA) copolymers is based in a mature technology; however

and despite its commercial importance, it is remarkable

that the corresponding reaction mechanism and kinetics,

especially those of spontaneous initiation, are poorly

understood and have not been studied in detail yet.

Copolymers of S and MA are produced by bulk

polymerization in a process similar to that used for the

production of crystal and impact grade polystyrene. The MA

content of these polymers typically ranges from 7 to 15%.

From public information made available by commercial

companies, we estimate that the annual world consumption

DOI: 10.1002/mren.200900061

Mechanism and Kinetics of the Spontaneous Thermal . . .

of S/MA in the 2 000–2 010 decade is in the order of 50–70 kt

per year. On the other hand, several groups have recently

reported the commercial use of the nitroxide mediated

radical polymerization (NMRP) in industry, in applications

oriented to high added value specialties, such as dispersants

and compatibilizers, some of them involving the copoly-

merization of S/MA.[1–3] In the last cases the mechanism of

autoinitiation becomes even more complicated due to the

influence that the nitroxide radical has on the spontaneous

generation of radicals that can initiate reaction.

Various mechanisms have been proposed to explain the

initiation process of the spontaneous copolymerization of S

with electron acceptor monomers such as MA and

acrylonitrile. The copolymerization of S with electron

acceptor monomers has been the subject of extensive

mechanistic discussions.[4,5]

With regard to the autoinitiation process, these mechan-

isms are based on those proposed for the self-initiated S

homopolymerization. In the case of S itself, two competing

initiation mechanisms have been proposed: i.e., the Mayo

and Flory mechanisms. In the Mayo mechanism,[6] initial

Diels Alder reaction [p4sþ p2s] between two molecules of S

leads the semibenzene dimer to the so-called Mayo dimer

form. This dimerization is followed by a hydrogen atom

abstraction by another S molecule to form two initiating

monoradicals. Detection of an accompanying cycload-

duct,[7] and some mechanistic behavior when acid cata-

lysts[8] are present, supports the Mayo mechanism for S. In

an earlier mechanism proposed by Flory for S spontaneous

polymerization,[9] the two monomer molecules generate a

tetramethylene diradical intermediate by bond formation

between two b-carbons. This diradical may actually ring-

close to form either a Mayo dimer, which can then transfer

hydrogen and initiate free radical polymerization, or the

1,2-diphenylcyclobutane derivative, a species that is

inactive to polymerization.[9] Isolation of a small

amount of 1,2-diphenylcyclobutane-1-phenyltetralin and

1-phenyl-1,2-dihydronaphthalene supports the Flory

mechanism for S to a minor competing extent.[10–12]

Hall and Padias[4] propose that in a copolymerization

between electron-rich monomers and electron-poor mono-

mers, the tetramethylene diradical formed may initiate

spontaneous polymerizations, either by an anionic (via

zwitterion tetramethylene) or free radical mechanism (via

tetramethylene diradical). In addition, from radical-

trapping experiments, several authors have concluded that

the tetramethylene diradical plays and intermediating role

in alternating copolymerizations, including the S and MA

case, and is the key element to understand their experi-

mental results.[13–16]

Part of the problem in studying the mechanism and

kinetics of S/MA copolymerization lies in the difficulty of

separating the initiation and propagation steps. Kothe and

Fischer[17] first used induction period experiments in the



self-initiated S polymerization in the presence of TEMPO, in

order to estimate kinetic coefficients associated with the

self-initiation reactions. In this way they first estimated the

value of the kinetic coefficient for S dimerization (see

Scheme 1) which is the first step of the radical self-

generation mechanism. This concept was further extended

by Bonilla-Cruz et al.[18] who used nitroxide radicals in order

to separate the initiation and propagation steps in the self

initiated S/MA copolymerization, and managed to provide

a preliminary order of magnitude estimate of the rate

constant for the dimerization of S and MA, assuming the

existence in this system of a reaction homologous to the S

dimerization for the formation of the Mayo dimer. An

interesting feature of the autoinitiation mechanism in the

case of the S/MA copolymerization in the presence of a

nitroxide radical is that, even for small amounts of MA in

the system, the induction period is dramatically reduced by

about one order of magnitude in comparison with the

nitroxide mediated S autopolymerization at 120–125 8C.[18]

From the scientific and technological viewpoint the

understanding and confirmation of mechanisms present in

the traditional and controlled radical (e.g., nitroxide-

mediated) copolymerization of S/MA, and the estimation

of the associated kinetic constants, are important.

In this work we undertake an experimental and modeling

study of the initial stages of the S/MA copolymerization in

order to provide a better understanding of the mechanism

and kinetics of this system of industrial and scientific

relevance. To this end, we synthesized copolymers of S and

MA by thermal autoinitiation in the presence and absence of

a nitroxide radical in an industrially relevant wide range of

S/MA and S/nitroxide ratios at 125 8C. Conversion rates in the

initial reaction stages were measured up to 20% conversion.

From these experiments, clean induction periods or severe

retardation behavior of the initial polymerization stages

wereobtained and then analyzed and discussed with the aim

of extracting mechanistic and kinetic information. A

mathematical model was developed to facilitate a better

understanding of the kinetic mechanism for this polymer-

ization process. The analysis and simulation of the experi-

mental data indicate the convenience of separating the

study of this system in different regimes that depend upon

the nitroxide concentration. In this study, with the help of

the mathematical model and simulations, we evaluate the

rate constant values for some of the proposed reactions in an

intermediate concentration regime. The extension of the

model to other concentration regimes, which may require

the inclusion of additional reactions not fully understood yet,

remains a challenge.

Experimental Part

In order to obtain kinetic data we performed thermal polymeriza-

tion reactions for the system S/MA in the presence or absence of

www.mre-journal.de 223

J. D. Mota-Morales et al.

Scheme 1. Mechanism proposed for the copolymerization of S/MA in the presence of 4-oxo-TEMPO.

224

4-oxo-2,2,6,6-tetramethylpiperidine-1-oxyl (4-oxo-TEMPO) in a

capillary dilatometer. The volume of the capillary bulb used is

5 mL; the capillary tube has a 2.2 mm diameter and a length of

10 cm. Fresh distilled S, recently sublimated MA and N,N’-

dimethylformamide (DMF) were put in a capillary in the presence

of 4-oxo-TEMPO (N) or without it and heated at 125 8C, after oxygen

evacuation from the capillary by bubbling the solutions with

high purity argon gas and sealing. Measurements of the induction

period and the conversion versus time curve after the induction

period were done according to literature.[19] DMF was used in

order to achieve complete dissolution of the MA in the reaction

media; without the presence of DMF the solubility of MA in S is

limited to about 3–5 wt.-%. Since the amount of DMF used in

the experiments is very small, the experiments are in practical



terms very similar to bulk polymeriza-

tions and therefore in the following we

refer to the reactions as bulk experi-

ments. Different compositions of the

pair S/MA and of the nitroxide mixture

were tested. In each experiment

the mixture initially increased its

volume by thermal expansion until

thermal equilibrium was established,

and then the zero-time point was

marked and the volume contraction

of the reaction mixture with time was

recorded and correlated with conver-

sion via standard calculations that use

the density of the monomer mixture

and the polymer.

In the capillary, the conversion in a

time increment can be calculated as

follows:

1

Dt

D M½ �M½ � ¼

1

Dt

DV=V0

d2 � d1ð Þ=d2(1)

whereD[M] is the monomer concentra-

tion change in a time increment Dt, DV

is the corresponding change of volume,

and V0 is the initial volume; d1 and d2

are the monomer and polymer density,

respectively. The fractional volume

change at total conversion is (d2� d1)/

d2, and DV/V0 is the fractional volume

change at time t. The ratio of these two

quantities is equivalent to the mono-

mer conversion at time t. Most of the

dilatometric experiments were run in

triplicate.

The induction period is estimated by

linear extrapolation of the non-zero

conversion-time data until they cross

the time axis. In those cases where

some data points exist with very small

conversions just before a well-defined

change of slope marking the end of the

induction period, this is estimated as

the crossing point of the two lines with different slopes.

Modeling

Kinetic Mechanism

Scheme 1 includes the main reactions in a plausible

mechanism of nitroxide-mediated radical thermal poly-

merization of S/MA.[18] In the mechanism proposed, the

homopolymerization of S may in principle compete with

the alternating polymerization of S with MA. Also, the

autoinitiation may arise either from the dimerization

reaction between the S and MA, either in a concerted way or

DOI: 10.1002/mren.200900061


not, or between two S molecules (based on the Mayo

mechanism). The dimer 8 can further react with more

monomer to form initiating radicals in the absence of a

nitroxide radical (Scheme 1 path A), or undergo a faster

hydrogen abstraction by a 4-oxo-TEMPO molecule

(Scheme 1 path B), in the same way as dimer 3 (paths C

and D).

Paths A and B have been proposed by Bonilla et al.[18] by

analogy with the spontaneous initiation mechanism that

seems to be occurring in S thermal homopolymerization in

presence or absence of a nitroxide radical,[20] and provided

spectroscopic evidence of the formation of the S–MA dimer

8. Connolly and Scaiano[21] (see Scheme 2) proposed

the direct addition of nitroxide to an S molecule

generating another propagating radical in autothermal

homopolymerization at very large concentrations of

TEMPO (50:50 mol/mol S/TEMPO). The rest of the reactions:

propagation, reversible capping of growing radicals by 4-

oxo-TEMPO, and irreversible termination, are well estab-

lished for this system.

Reaction Kinetics and Mathematical Model

The mechanism described in detail in Scheme 1 and 2 is

written in a simpler way in Table 1. Based on this

representation and doing the material balances for a batch

reactor one ends up with a set of ordinary differential

equations (see Appendix) that describe the evolution of the

species in the system. In order to simplify the mathematical

model we lumped together the primary radicals and the

growing polymeric radicals of Scheme 1, independently of

their chain length. Although the kinetic scheme can in

principle describe the molecular weight distribution, the

study of this feature is out of the scope of the present work

and therefore we decided to omit the description of the

chain length of the growing radicals. However, the

mathematical model contains enough detail to simulate

the autoinitiation mechanisms in Scheme 1 and the

Scheme 2. Radical generation mechanism by the direct addition of4-oxo-TEMPO to the monomers in the system S/MA.



occurrence of an induction period in the presence of

the nitroxide radical. On the other hand, due to the

incomplete understanding of the propagation step, we

modeled this as a pseudo-homopolymerization using an

effective propagation rate constant kp and the total

concentration of monomer and radicals, independently of

their detailed chemical nature as follows:

Rp ¼ kp M½ � R½ � (2)

where Rp is the overall propagation rate (or polymerization

rate), [M] the total monomer concentration, and [P] is the

total polymeric radical concentration. Based on abundant

empirical evidence,[22] we assumed that in the presence of

MA in the system, the propagation occurs in an alternate

fashion consuming one molecule of each one of the

monomers in two consecutive propagation steps:

R�n þ 2M �!Kp

R�nþ2

We have also confirmed experimentally that the S/MA

system produces an alternate copolymer[18] in the presence

of TEMPO derivatives; in addition, we have previously

modeled this copolymerization by using the terminal

model with reactivity ratios (close to zero) available in

the literature;[23] therefore, we do not consider necessary to

model the system as a copolymerization. This would have

unnecessarily complicated the modeling and would

have introduced additional parameters which would make

the parameter estimation task more difficult.

The reaction of Scheme 2 was assumed to occur only for

nitroxide concentrations higher than 0.1%, by analogy with

the findings of Connolly and Scaiano. No quasi-steady state

(QSS) assumption was made for the radical species and the

set of differential equations was solved by the DDASSL

algorithm which can handle systems of stiff differential

equations as well as differential/algebraic systems.[24]

Results and Discussion

Table 2 shows the experimental design that was performed;

this is essentially a 32 factorial in the variables nitroxide and

MA concentration, with additional points to explore

specific effects. In order to verify the reproducibility of

the dilatometric technique we ran two sets of experiments

using this method and then compared the results with

another experiment in which the conversion was measured

by gravimetry at the same conditions. The comparison of

these techniques can be observed in Figure 1, which shows

excellent reproducibility for the dilatometric technique and

very good agreement with the gravimetric determination.

From the triplicate runs of the dilatometric technique, an

estimation of the standard deviation was made for every



Table 1. Kinetic mechanism for the copolymerization of S and MA (A) in the presence of nitroxide radicals.

Step Reaction Kinetics

initiation dimerizationSþ S �!

KdimDS

Sþ A �!Kdsma

DA

initiation via SDS þ S �!Ki

D�S þ S�

DA þ S �!Kisma

D�A þ S�

initiation via nitroxideDS þN �!

KhD�S þNH

DA þN �!Khsma

D�A þNH

contribution to initiation via direct addition to monomerSþN �!

KadS�

AþN �!Kadma

A�

propagation capping/decapping propagationa)

R� þ N !Kd

Ka

RN

D�S þM �!Kp

R�2

D�A þM �!Kp

R�2

S� þM �!Kp

R�2

termination irreversible terminationR�n þ R�m �!

KtPmþn

R� includes the radicals of all lengths n, R�n.a)M¼ SþA.

Table 2. Experimental design. All reactions were performed at125 8C.

Experiment [MA] [4-oxo-TEMPO] [DMF]

wt.-% wt.-% wt.-%

1 15 0.01 6.5

2 15 0.01 10

3 15 0.1 10

4 15 1.0 10

5 10 0.01 6.5

6 10 0.01 10

7 10 0.1 10

8 10 1.0 10

9 5 0.01 0.15

10 5 0.01 10

11 5 0.1 10

12 5 1.0 10

13 5 0 10

14 10 0 10

15 15 0 10

226Macromol. React. Eng. 2010, 4, 222–234


experiment. The average standard deviation was estimated

as 0.68% conversion.

All the experiments were run with 10 wt.-% of DMF,

except for experiments 1, 5, and 9, in which a lower

concentration was used. No significant effect other than a

slight rate change due to the increased monomer concen-

tration was observed for the experiments with the reduced

DMF concentration. This indicates that the presence of DMF

in the concentration used in the study does not influence

significantly the kinetics of the system.

Figure 1. Representation of the S/MA copolymerization at 125 8C.[MA]¼ 5.0 wt.-%, [4-oxo-TEMPO]¼0.01 wt.-% (run 10). The opensymbols are the experimental data by dilatometry: the filledsymbols are experimental data by gravimetry.

DOI: 10.1002/mren.200900061


Figure 2. Conversion/time curves for the thermal copolymeriza-tion of S/MA in bulk at 125 8C at various MA concentrations and inthe presence of 4-oxo-TEMPO (0.01 wt.-%) with 10 wt.-% DMF(runs 2, 6, and 10 for 5, 10, and 15% MA, respectively).

Figure 4. Conversion/time curves for the thermal copolymeriza-tion of S/MA in bulk at 125 8C in the presence of various MAconcentrations and 4-oxo-TEMPO (1.0 wt.-%) (runs 4, 8, and 12 for5, 10, and 15% MA, respectively).

Parameter Fitting for Kdsma, Kisma, and Khsma

One of the aims of this study is to advance in the

understanding of the mechanism of spontaneous copoly-

merization of S/MA and to estimate the values of most

of the kinetic constants. In particular, we want to assess the

values of the kinetic constants associated with the self

initiation step involving the S/MA dimer (8): Kdsma, Kisma,

and Khsma. The evaluation of the dimerization rate

coefficient Kdsma is addressed first; Kdsma is the kinetic

constant for dimerization between S and MA molecules.

Figure 2–4 summarize most of the experimental results

at 0.01, 0.1, and 1 wt.-% of nitroxide radicals, respectively. A

first general observation drawn from the plots is that,

depending on the nitroxide concentration used, a clear

induction period is present in the reaction, as in Figure 2, or a

severe retardation period is observed, as in Figure 3 and 4,

which mimics to some extent a clean induction period, but

in which some polymerization also takes place. Induction

periods of this sort have been explained before in similar

experiments of thermal autoinitiated S homopolymeriza-

tion in the presence of TEMPO.[19,22] During the induction

period the free radicals self-generated by S are initially

trapped by the excess of TEMPO preventing propagation

Figure 3. Conversion/time curves for the thermal copolymeriza-tion of S/MA in bulk at 125 8C in the presence of various MAconcentrations and 4-oxo-TEMPO (0.1 wt.-%) with 10 wt.-% DMF(runs 3, 7, and 11 for 5, 10, and 15% MA respectively).



until the total concentration of self-generated radicals

approximately balances out the initial concentration of

TEMPO. At this point the capping/decapping equilibrium of

TEMPO is established, defining the end of the induction

period. Afterward, the de-capped radicals can propagate

resulting in controlled polymerization. A similar situation

occurs in the case of S/MA spontaneous copolymerization

in the presence of 4-oxo-TEMPO in Figure 2. However, at

higher nitroxide concentrations, the induction period is no

longer a clean one, apparently because some limited

propagation simultaneously takes place competing

with the nitroxide capping reactions. In the presence of

clean induction periods it is possible to use simple

calculations in order to estimate some of the kinetic

parameters of the self-initiation step. We illustrate this in a

previous work by our group,[18] in which we estimate

the kinetic constant Kdsma using experimental results that

exhibit a clean induction period by assuming the QSS for

the dimer 8. The same method was applied in this work to

the data in Figure 2 and, as shown in Table 3, the values of

Kdsma obtained are comparable with those estimated by our

group before. This method, however, is not useful for the

experimental data shown in Figure 3 and 4, in which the

induction period is not a clean one. In these cases it is not

possible to completely separate the initiation and propaga-

tion steps and therefore both phenomena have to be

simultaneously considered in the analysis. This can be done

by parameter fitting using the global model presented here

together with the experimental conversion-time data. With

this model, the kinetics will reflect the effect of all the

included reactions.

Using the global model, we performed a parameter

sensitivity analysis in order to assess the qualitative effect

of each of the kinetic constants (Kdsma, Kisma, and Khsma) on

some of the features of the predicted conversion-time

curves. In this analysis and in the rest of the simulations we

used constant values reported by our group for the kinetic

coefficients Kdim, Ki, and Kh evaluated from S homopoly-

merization data in the same conditions.[20]



Table 3. Values of the kinetic constant Kdsma calculated at 125 8C in experiments with clean induction periods.

Reference [4-oxo-TEMPO] [MA] Induction

period

Kdsma

wt.-% wt.-% min L �mol�1 � s�1

[18] 1� 10�3 0.1 27 2.6� 10�6

[18] 1� 10�3 1 7 0.9� 10�6

[18] 1� 10�3 5 2.5 0.6� 10�6

this work 1� 10�2 5 5.0 2.3� 10�6

this work 1� 10�2 10 3.1 1.9� 10�6

this work 1� 10�2 15 2.6 1.6� 10�6

228

The best value found forKdsma was 9� 10�6 L �mol�1 � s�1

which differs somewhat from the values estimated in

Table 3, but this is expected since the estimations reported

in the table come from a simplified analysis with some

inherent error. The length of the induction period exhibits

some sensitivity to the value of Kdsma.

Kisma is the kinetic constant for the reaction of hydrogen

abstraction from the dimer 8 by a S molecule to render two

initiating radicals. The Kisma value was considered to be the

same value as that of its homologous Ki from S homo-

polymerization (10�8 L �mol�1 � s�1) for most of the calcula-

tions. This value was adopted mainly because it provided

good agreement with the experimental data but also

because, from the sensitivity analysis, this parameter did

not exhibit significant influence in the development of the

induction period, so there was not enough support to

propose a different value based only on the experimental

data in the presence of nitroxide.

The induction period, and to some extent the slope of the

full reaction stage (i.e., mainly defined by Kp), are both

sensitive to changes in the value of Khsma, which was fitted

at a value of 10 L �mol�1 � s�1. Khsma is the kinetic constant

for the reaction of hydrogen abstraction from the dimer8by

a nitroxide molecule to render one initiating radical and

hydroxylamine.

Notice that the values of Kdsma and Khsma are higher than

the corresponding ones for S, and this is in agreement with

the stronger electron-acceptor character of MA compared

with S.

Figure 5. Simulations of the effect of different values of Kadma onthe kinetics for the S/MA copolymerization at 125 8C. The exper-imental length of induction period is reproduced withKadma¼4� 10�3 L �mol�1 � s�1.

Parameter Fitting for Kadma

At relatively high concentrations of nitroxide, the duration

of the induction period is reduced to smaller values than

those expected if only those reactions present in Scheme 1

were considered. This phenomenon was identified before in

the case of the thermal homopolymerization of S in the

presence of TEMPO,[20] and it was attributed to the direct

addition of nitroxide to S with a kinetic constant of

Kad¼ 7� 10�7 L �mol�1 � s�1. This reaction becomes signifi-



cant only at relatively high concentrations of TEMPO and

increases the rate of radical self-generation.[20] A similar

reaction seems to be occurring in the case of the

copolymerization of S/MA, since in this system and for

relatively large concentrations of 4-oxo-TEMPO (0.1 and

1.0%), the induction periods are drastically reduced with

respect to those predicted with the reactions in Scheme 1

when reasonable values for the parameters fitted are used.

This led us to propose a reaction of direct attack of nitroxide

over MA that would produce additional initiating radicals,

just as the direct addition of nitroxide to S documented

before does (see both reactions in Scheme 2). In order to fit

the value for the corresponding kinetic coefficient, Kadma, a

parameter sensitivity analysis for this constant was

performed. The value for this parameter was varied in

the range 1 to 9� 10�3 L �mol�1 � s�1 and, by comparing the

simulations with the experimental length of the induction

period, a value of 4� 10�3 L �mol�1 � s�1 was found as the

best fit for this constant. The corresponding analysis is

displayed in Figure 5. Notice that the fitting of this

parameter does not guarantee that other features of the

kinetic curve (such as the concavity during the induction

period and the slope after the induction period) are well

described by the model; however, this value gives an order

of magnitude estimate of this parameter for which there is

no previous data in the literature.

DOI: 10.1002/mren.200900061


0

5

10

15

20

25

4035302520151050

Time (min)

% C

onve

rsio

n

5%AM

Model 5% MA

10%Am

Model 10% MA

15%AM

Model 15% MA

Figure 6. Experimental data (points) and model predictions (lines)for the induction period and conversion/time behavior as afunction of the initial MA concentration in the thermal copoly-

Period of Full Rate Polymerization

In the previous sections we have analyzed those parameters

which most influence the duration and characteristics of

the induction or retardation periods. These parameters are

mainly associated with the self-initiation reaction, which is

of great importance in this system. This has been possible

due to the partial or total isolation of the self-initiation and

propagation steps. By analyzing the experimental data for

the rest of the polymerization it is hoped that some

mechanistic and quantitative information for the other

relevant kinetic steps in this system, such as the values for

the propagation and termination constants, can be

extracted, and this is better done by dividing the analysis

in three regimes, depending on the concentration of

nitroxide used. The justification for this division is

contained in the discussion that follows for each regime.

merization of S/MA in bulk with 0.01 wt.-% of nitroxide at 125 8C.(runs 2, 6, and 10 for 5, 10, and 15% MA, respectively).

Regime of Low N Concentration (0.01%)

In their study of the self-initiation kinetics for S in the

presence of TEMPO, Kothe and Fischer[17] essentially

analyzed the S dimerization kinetics (see the mechanism

at the top of Scheme 1). They reported that, given simple QSS

considerations, the concentration of TEMPO follows the

kinetic law:

Macrom

� 2010

d N½ �dt¼ �2Kdim S½ �2 (3)

for TEMPO concentrations above [N]� 0.05 M (�0.9 wt.-%).

Although they do not explain what happens at other

regimes, this suggests that the kinetics in the S case

deviates from Scheme 1 at low TEMPO concentrations,

perhaps due to the presence of other unaccounted

reactions which may be relevant at these conditions. In

the present case for the S/MA system, we attempted the

fitting of the lumped kinetic parameters involved in the

expression:

Rp ¼ kp M½ � ri

kt

� �1=2

(4)

bFor comparison purposes only and assuming a constant value forthe termination rate coefficient of 2� 108 L �mol�1 � s�1.

where ri is the initiation rate and kt is an effective

termination constant. Equation (4) represents a more

detailed version of Equation (2) and is based on the classic

QSSA for the total radical population. One would expect

the ratio kp=k1=2

t to be dependent of the S/MA composition,

but independent of other reaction conditions, in particular

of the nitroxide concentration, so we had hoped to fit a

unique set of values of that ratio independently of the

nitroxide concentration regime. An important underlying

assumption was that, given our previous analysis, the

initiation rate at this point was known or at least

ol. React. Eng. 2010, 4, 222–234

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

estimated with some accuracy. However, as we will see

in the rest of the paper, it was not possible to fit a unique

set of values for these parameters in all the regimes.

For the low concentration regime we show in Figure 6 the

results of the model fitting using the values of 2.8� 10�2,

7.1� 10�2, and 8.5� 10�2 L1/2 �mol�1/2 � s�1/2 for the ratio

kp=k1=2

t orb 400, 1 000, and 1 200 L �mol�1 � s�1 for the

propagation rate constant kp at 5, 10, and 15 wt.-% of MA

in the copolymerization, respectively. The agreement of the

model with the experimental data is good for the 5 and 15%

concentrations, but the behavior of the system is rather

nonlinear at the intermediate 10% MA concentration,

making more difficult the data fitting at this condition. Also,

as indicated for the S homopolymerization case, at this low

concentration of nitroxide some other unaccounted reac-

tions may become relevant and complicate further the

understanding of the kinetics. It is important to mention

that, although we could have modeled this system using the

terminal model for the copolymerization, this could not

have explained the observed non-linearity. We will return

to a discussion of these fittings in the next section.

Regime of Medium N Concentration (0.1%)

Figure 7 shows the results of the results of the model fitting

for the different S/MA compositions in this N concentration

regime. The values fitted for the parameter ratio kp=k1=2

t

were 2.8� 10�2, 3.2� 10�2, and 5.0� 10�2 L1/2 �mol�1/2 � s�1/2

or, expressed as propagation rate coefficient (assuming

again the same constant value as before for the termination



0

5

10

15

20

25

30

50454035302520151050

Time (min)

% C

onve

rsio

n

5%MA

5% MA Model

10%MA

10% MA Model

15%MA

15% MA Model

Figure 7. Experimental data (points) and model predictions (lines)for the induction period and conversion/time behavior as afunction of the initial MA concentration in the thermal copoly-merization of S/MA in bulk at 0.1 wt.-% of nitroxide at 125 8C (runs3, 7, and 11 for 5, 10, and 15% MA, respectively).

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

50403020100Time (min)

% C

onve

rsio

n

10% MA

5% MA

15% MA

5% MA Model

Figure 8. Experimental data (points) and model prediction (con-tinuous line) for the conversion/time as a function of the initialMA concentration in the thermal copolymerization of S/MA innitroxide-free reactions at 125 8C (runs 13, 14, and 15 for 5, 10, and15% MA, respectively).

230

rate coefficient), 400, 450, and 700 L �mol�1 � s�1, for kp

values at 5, 10, and 15 wt.-% of MA, respectively. As we see,

for the 10 and 15 wt.-% MA formulations, there is

discrepancy of these fitted values with those fitted at the

lower N concentration, although the fitting of the model

with the experimental data is better at the intermediate N

concentration and therefore these parameter values seem

more reliable. The discrepancy in the parameter values

fitted at the two N concentration regimes is probably a

consequence of the global error and uncertainty in our

estimations of the self-initiation kinetics. Another possible

reason for this discrepancy is that our simple lumped model

[Equation (4)] for the kinetics of propagation and termina-

tion in this system, together with the assumption of the sole

Table 4. Summary of kinetics constants used in the model simulatio

Kinetic constant V

Kdim[20] 1.325� 10�8

Kdsmaa) 9� 10�6

Kadmaa) 4� 10�3

Kad[20] 6� 10�7

Ki[20] 1� 10�8

Kismaa) 1� 10�8

Kh[20] 1

Khsmaa) 10

kp= k1=2

t at 5 wt.-% MAa) 2.8� 10�2 for all N

kp=k1=2

t at 10 wt.-% MAa) 7.1� 10�2/3.2� 10

kp=k1=2

t at 15 wt.-% MAa) 8.5� 10�2/5.0� 10

a)This work.



dependence of these parameters on the S/MA composition,

may not completely capture the complexity of the system,

perhaps due to additional unaccounted reactions which are

relevant at low N concentrations or more complex effects in

the propagation steps, which are discussed below. Table 4

summarizes the values of the parameters fitted at the

different conditions.

In order to gather additional information on the global

kinetics of the system, we ran three additional copolymer-

ization experiments varying the S/MA composition (5, 10,

and 15 wt.-% of MA) without nitroxide. The experimental

results are shown in Figure 8. It is instructive to estimate

lower bounds for the values of the ratiokp=k1=2

t directly from

the experimental data using Equation (4) in terms of total

monomer conversion x as kp=k1=2

t ¼ dxdt= 1� xð Þr1=2

i and

using in this equation an estimation of the upper bound

ns.

alue Unit

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

L �mol�1 � s�1

concentrations L1/2 �mol�1/2 � s�1/2

�2 for 0.01/0.1 wt.-% N L1/2 �mol�1/2 � s�1/2

�2 for 0.01/0.1 wt.-% N L1/2 �mol�1/2 � s�1/2

DOI: 10.1002/mren.200900061


Table 5. Calculation of an upper bound for the ratio kp

.k1=2

t from nitroxide-free experiments.

[MA] dx/dt Conversion

xrupi kp=k

1=2

tkp

a)

wt.-%

0 5.14� 10�5 0.180 8.06� 10�7 6.98� 10�2 984

5 5.50� 10�5 0.011 5.51� 10�5 7.49� 10�3 106

10 1.32� 10�4 0.015 1.09� 10�4 1.28� 10�2 181

15 3.90� 10�4 0.031 1.62� 10�4 3.16� 10�2 446

a)Assuming a constant value for kt of 2� 108 L �mol�1 � s�1.

for the initiation rate as:

cEven(0.01 w100 tim

Macrom

� 2010

rupi ¼ 2Kdim S½ � A½ � þ 2Kdsma A½ �2 (5)

where [A] is the concentration of MA. Notice that rupi is the

rate of S–MA dimer generation but, since there is no

guarantee that a QSS is reached for the dimer 8 in the

absence of nitroxide, this would be an upper bound for the

radical generation rate. The polymerization rates Rp were

directly estimated from the initial slope of the experi-

mental conversion/time curves. The results of these

calculations are shown in Table 5. Since the values of

the ratio kp=k1=2

t in Table 5 are lower bounds, they cannot

be used for simulations; however, it is encouraging that

they follow the same increasing trend with increase in MA

content, as the parameter ratio estimations in the presence

of nitroxide.

As an additional exercise we attempted to fit the data

with the complete model for the free-nitroxide copolymer-

ization for the lowest MA content (5 wt.-%). This is expected

to be the case with the lowest self-initiation rate and

therefore more likely to favor a QSS for the dimer 8

concentration. Using the value for kp=k1=2

t obtained for the

experiment with 5% MA in the presence of nitroxide

(2.8� 10–2 L1/2 �mol�1/2 � s�1/2), reasonable agreement of

the model prediction was obtained with the experimental

data for this MA concentration when the value of Kisma was

increased from 1� 10�8 L �mol�1 � s�1 (used in the simula-

tions in the presence of nitroxide radical) to

1� 10�5 L �mol�1 � s�1 (see Figure 8). As explained before,

this change in theKisma value should not affect the results of

the previous simulations (in the presence of a nitroxide

radical), because in those cases the dominant initiating

radical generation reaction is that of the dimer 8 with the

nitroxide radical (path B as opposed to path A in Scheme 1).c

Despite the last result, we decided not to pursue the data

for the case with the lowest nitroxide concentrationt.-%) the initiation via dimerþnitroxide (path B) is aboutes faster than that due to dimerþ styrene (path A).

ol. React. Eng. 2010, 4, 222–234

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

fitting for the other two MA concentrations since there is

high uncertainty for theKisma value and this could very well

depend on the MA concentration.

In summary, from the previous discussion it is clear that,

once the effect of the self-initiation rate is taken into

account, the ratio kp=k1=2

t increases with increase in the

concentration of MA, although the quantitative estima-

tions given for this and other parameters should be taken

with caution given the complexity of the system and the

difficulty of independently estimating the values of the

relevant unknown kinetic parameters.

Regime of High N Concentration (1%)

We attempted to fit the conversion-time experimental data

with the model for this N concentration regime by varying

the ratio kp=k1=2

t , but the qualitative behavior (shape and

concavity of the curves) predicted by the model was not

satisfactory. The shape of the experimental curves exhibit-

ing a pronounced and long retardation effect (Figure 4),

reflects a strong competition between the high rate of

radical self-generation, favored by the high N concentra-

tion, and the propagation rate. The behavior of the data

with 5 wt.-% MA was especially difficult to fit as the model

predicted a much longer retardation period than the

experimentally observed when the parameter values

previously obtained (at other conditions) were used.

Additional simulations not reported here for space reasons

are available elsewhere.[25] This suggests the presence of

unaccounted reactions in the model at this high N

concentration.

Mechanistic Considerations for the CopolymerizationPropagation Reactions

In Table 5 a nitroxide-free experiment of self initiation with

pure S was included. Taking this into account, the trend of

the lower bound values for the parameter ratio kp=k1=2

t as

the MA content increases from 0 to 15% seems to indicate

that after the addition of even a small amount of MA that



Scheme 4. Mechanism for the cross-propagation steps in the S/MA copolymerization.

232

parameter ratio decreases with respect to the value

corresponding to the S homopolymerization case, and then

increases again as the MA concentration increases. This is

confirmed by comparing the values of the parameter ratio

kp=k1=2

t fitted for the experiments with 0.1 wt.-% N (see

Table 4) with the value known for S homopolymerization.

For this last system the ratio kp=k1=2

t at 125 8C can be

calculated as 0.125 L1/2 �mol�1/2 � s–1/2 using kinetic con-

stants taken from the literature and measured via pulsed

laser polymerization (PLP) experiments. When 5 wt.-% of

MA is used in the reaction, the value of the ratio kp=k1=2

t

drops to 2.8� 10�2 and then increases up to

5.0� 10�2 L1/2 �mol�1/2 � s�1/2 as the MA proportion is

increased up to 15%. These calculations seem to indicate

that after the addition of even a small amount of MA the

propagation mechanism drastically changes. The old

literature ascribed these mechanistic changes to the

intermediation of a charge transfer complex; more recent

studies[4,5] discard this hypothesis and explain related

experimental observations through the influence of a

tetramethylene diradical which is formed by the reaction of

S and MA molecules (see Scheme 3). According to these

authors this diradical acts as an intermediate in the

propagation reaction and is responsible for the alternating

character of the copolymer formed. Their theory has been

generalized for pairs or monomers having electron donor-

acceptor characteristics of which the S–MA system is an

example.

Radical stability considerations may also play a role in

the propagation reaction. The cross-propagation in the

S/MA system can be represented by the two reactions in

Scheme 4. Reaction 1 in Scheme 4 generates a more stable

radical than that produced in reaction 2 (the ionization

energy for obtaining the MA radical is around 414 kJ �mol�1

while the corresponding energy of the benzylic radical is

around 330 kJ �mol�1). Since the benzylic radical is more

stable it is also less reactive, therefore reaction 2 is slower,

the energy necessary to reach the transition state is larger

and as a consequence this reaction is the rate controlling

step in the propagation process. The former discussion

assumes that the propagation has alternating character and

Scheme 3. Mechanism for the formation of a diradical that mayinfluence the self-initiation and propagation steps in the S/MAcopolymerization.



that homo-propagation is negligible, which turns out to be

an experimental fact in the case of the S/MA system. Finally,

since the rate of a reaction depends on the concentration of

reactants, as the MA concentration increases the rate of

reaction 2 increases too, leading to an overall faster

polymerization.

With respect to the preference of this system for

alternating propagation over homopolymerization (at least

S homopolymerization), Fischer and Radom[26] conclude for

model systems that in general this behavior is due to the

difference in the energy barrier for the two reaction paths

with the path having the lower energy barrier being the

most favored one. This is due to a complex combination of

factors including the enthalpy of the reaction, charge

transfer during the reaction, steric effect contributions and,

finally, the electrophilic or nucleophilic character of the

substituents attached to the reacting group.

Conclusion

A detailed kinetic study of the NMR autopolymerization of

S/MA at 125 8C was performed in order to make an initial

assessment of the values of the kinetic parameters for the

self-initiation and propagation steps in this system. Care-

fully executed dilatometric experiments provided kinetic

data in the range of 5–15 wt.-% of MA at various

concentrations of the nitroxide radical (4-oxo-TEMPO).

Depending on the nitroxide concentration, two types of

induction period were observed: one that is a true induction

period and another one that is rather a severe retardation

rate period in which propagation and radical-capping

reactions compete.

A kinetic mechanism previously proposed by our group

was used as the basis for a kinetic model aimed at

describing the kinetics of NMR copolymerization of S/MA.

From the experimental data and simulations with the

model, estimates for the values of the relevant self-

initiation and propagation parameters, for which there is

very little information available in the literature, were

DOI: 10.1002/mren.200900061


provided. However, given the complexity of the system and

the uncertainty associated with the mechanism, the

numerical values should be taken with caution and as a

first approximation to the rate constant values for the

proposed reactions. The model based in the mechanism

proposed reproduces well the experimental data at

different MA contents at an intermediate nitroxide

concentration (0.1 wt.-%), but for other concentration

regimes, in general, some deviations of the model with

the experiment are present, which suggests that the

proposed kinetic mechanism may be overlooking some

reactions that become relevant in those concentration

regimes. Remarkably, however, the experimental data for

all the reactions with an MA concentration of 5 wt.-% are

reasonably well reproduced by the model at all the

nitroxide concentrations below or equal to 0.1 wt.-%,

including the nitroxide-free experiment, using a single

set of kinetic parameter values. The separation of initiation

and propagation steps by the use of radical trapping

experiments is promissory for mechanistic studies of this

system, but it is recommendable to try other families of

radical trapping species as a way to improve the separation

of the kinetic steps. A similar method can be followed to

study the mechanism and kinetics of other relevant self-

initiating copolymerizations involving an electron-donor

and an electron-acceptor monomer, such as the system S/

acrylonitrile.

To our knowledge this is the first attempt at measuring

the relevant self-initiation and propagation/termination

kinetic coefficients for the S/MA system. More experi-

mental work is required to get a better understanding of the

mechanisms and kinetics of the copolymerization of S/MA.

Appendix: Mathematical Model

d S½ �dt¼ Kdim S½ �2�Kdsma S½ � A½ � � Ki DS½ � S½ � � Kisma DA½ � S½ �

� Kp G�½ � S½ � þ A½ �ð Þ

d A½ �dt¼ Kdsma S½ � A½ � � Kp G�½ � S½ � þ A½ �ð Þ

d DS½ �dt¼ Kdim S½ �2�Ki DS½ � S½ � � Kh DS½ � N½ �

d DA½ �dt¼ Kdsma S½ � A½ � � Kisma DA½ � S½ � � Khsma DA½ � N½ �

d N½ �dt¼ Kh DS½ � N½ � � Khsma DA½ � N½ � � Kd R�½ � N½ � þ Ka RN½ �



d RN½ � �
dt¼ Ka RN½ � þ Kd R½ � N½ �
d R�½ �þ G�½ �ð Þdt

¼2Ki DS½ � S½ �þ 2Kisma DA½ � S½ �þ Khsma DA½ � N½ �

þKh DS½ � N½ � þ Ka RN½ � � Kd½ � R�½ � N½ � � Kt R�½ �2

For 1% N:

d S½ �dt¼ Kad S½ � N½ �

� Kdim S½ �2�Kdsma S½ � A½ � � Ki DS½ � S½ � � Kisma DA½ � S½ �

� Kp G�½ � S½ � þ A½ �ð Þ

d A½ �dt¼ �Kadma A½ � N½ � � Kdsma S½ � A½ � � Kp G�½ � S½ � þ A½ �ð Þ

d G�½ �dt¼ �Kad S½ � N½ � � Kadma A½ � N½ � þ 2Ki DS½ � S½ � þ 2Kisma DA½ �

� S½ � þ Khsma DA½ � N½ � þ Kh DS½ � N½ � � Kp G�½ �M½ �

d R½ � þ G½ �ð Þdt

¼ �Kad S½ � N½ � � Kadma A½ � N½ � þ 2Ki DS½ � S½ �

þ 2Kisma DA½ � S½ � þ Khsma DA½ � N½ � þ Kh DS½ � N½ �

þ Ka RN½ � � Kd R�½ � N½ � � Kt R�½ �2

Acknowledgements: Financial support from the National Councilfor Science and Technology of Mexico (CONACyT) through grant2004-46048 is gratefully acknowledged. Josue Mota acknowledgesthe M. Sci. scholarship and his present scholarship for PhD studiesfrom CONACyT. One of us (GLB) acknowledges support fromCONACyT grants 58239 & 78798.

Received: October 2, 2009; Revised: December 22, 2009;DOI: 10.1002/mren.200900061

Keywords: copolymerization; kinetics; 4-oxo-TEMPO; sponta-neous polymerization; styrene/maleic anhydride

[1] A. Gonzalez, E. Saldıvar, E. Fernandez, G. Zacahua, ‘‘A NovelStyrene-Maleic Anhydride Block-Copolymer Compatibilizer’’,in: Additives 2004 Conference, Tampa, Florida 2004.

[2] US 7 323 528 B2 (2008), invs.: E. Saldıvar-Guerra, A. Gonzalez-Montiel.

[3] F. O. H. Pirrung, C. Aushra, Polym. Prepr. 2005, 46, 316.[4] H. K. Hall, Jr., A. B. Padias, J. Polym. Sci., Part A: Polym. Chem.

2001, 39, 2069.[5] H. K. Hall, Jr., A. B. Padias, Helv. Chim. Acta 2005, 88, 1553.[6] F. R. Mayo, J. Am. Chem. Soc. 1953, 75, 6133.[7] W. Choi, X. Han, H. K. Hall, Jr., Polym. Bull. 2005, 54, 179.



234

[8] W. C. Buzanowsky, J. D. Graham, D. B. Priddy, E. Shero,Polymer 1992, 33, 3055.

[9] P. J. Flory, J. Am. Chem. Soc. 1937, 59, 241.[10] V. J. Kurze, D. J. Stein, K. P. Syima, R. Kaiser, Angew. Makromol.

Chem. 1970, 12, 25.[11] W. G. Brown, Makromol. Chem. 1969, 128, 130.[12] G. Moad, E. Rizzardo, D. H. Solomon, Polym. Bull. 1982, 6, 589.[13] L. Eberson, O. Persson, Acta Chem. Scand. 1999, 53, 680.[14] L. Eberson, O. Persson, Macromolecules 2000, 33, 2021.[15] R. Huisgen, Acc. Chem. Res. 1977, 10, 199.[16] T. Sato, M. Abe, T. Otsu, J. Macromol. Sci. Chem. 1981, A15, 367.[17] T. Kothe, H. Fischer, J. Polym. Sci., Part A: Polym. Chem. 2001,

39, 4009.[18] J. Bonilla-Cruz, L. Caballero, M. Albores-Velasco, E. Saldıvar-

Guerra, J. Percino, V. Chapela, Macromol. Symp. 2007, 248,132.

[19] M. J. Percino, V. M. Chapela, A. Jimenez, J. Appl. Polym. Sci.2004, 94, 1662.



[20] E. Saldıvar-Guerra, J. Bonilla, G. Zacahua, M. Albores-Velasco,J. Polym. Sci., Part A: Polym. Chem. 2006, 44, 6962.

[21] T. J. Connolly, J. C. Scaiano, Tetrahedron Lett. 1997, 38, 1133.[22] [22a] E. Tsuchida, T. Tomono, Die Makromol. Chem. 1971, 141,

265; [22b] W. Zeng, Y. Shirota, Macromolecules 1989, 22, 11;[22c] M.-Q. Zhu, L.-H. Wei, F.-S. Du, Z.-C. Li, F.-M. Li, M. Li, L.Jiang, Chem. Commun. 2001, 4, 365; [22d] J.-F. Lutz, B. Kirci, K.Matyjaszewski, Macromolecules 2003, 36, 3136; [22e] D. Brau,F. Hu, Prog. Polym. Sci. 2006, 31, 239.

[23] C. Guerrero-Sanchez, E. Saldıvar, M. Hernandez, A. Jimenez,Polym. React. Eng. 2003, 11, 457.

[24] K. E. Brennan, S. L. Campbell, L. R. Petzold, ‘‘Numerical Solutionof Initial-Value Problems in Differential-Algebraic Equations’’,Elsevier Science Publishing Company, New York 1989.

[25] J. Mota-Morales, M. Sc. Thesis, Centro de Investigacion yEstudios Avanzados (CINVESTAV) Queretaro, Mexico 2009.

[26] H. Fischer, L. Radom, Angew. Chem., Int. Ed. 2001, 40,1340.

DOI: 10.1002/mren.200900061

mechanism and kinetics of the spontaneous thermal copolymerization of styrene/maleic anhydride....

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