Application of the Monomer Reactivity Ratios to the Kinetic-Model Discrimination and the Solvent-Effect Determination for the StyreneAcrylonitrile Monomer System

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Application of the Monomer Reactivity Ratios to the Kinetic-Model Discrimination and the Solvent-Effect Determinationfor the Styrene/Acrylonitrile Monomer System

ANDRZEJ KAIM

Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland

Received 10 March 1999; accepted 6 December 1999

ABSTRACT: The impact of reactivity ratios determined with the Nelder and Mead

simplex method on the kinetic-model discrimination and the solvent-effect determina-

tion for the styrene/acrylonitrile monomer system was investigated. For the monomer

system, the penultimate unit effect was inversely proportional to the polarity of the

solvent: acetonitrile N , N -dimethylformamide methyl ethyl ketone toluene.

Quantitatively, the penultimate unit effect could be correlated with an absolute value

of the difference between the standard deviation of the reactivity ratios determined for

the terminal and penultimate models. By application of the F test, the penultimate

model was justified for copolymerization in toluene. The conclusion was less certain for

polymerization in methyl ethyl ketone. With a scanning procedure based on the simplex

method, it was found that an equivalent representation of the copolymer-composition

data could be achieved with multiple sets of penultimate-model reactivity ratios.

However, the relationship between the triad-sequence distribution and copolymer

composition depended on the reactivity-ratio set chosen for the microstructure deter-

mination. The microstructure calculated with the penultimate-model reactivity ratios

determined with the simplex method from the initial guess (r11 r1, r21 1/ r2, r22 r2,

r12 1/ r1) did not obey the general “bootstrap effect” rule. This observation still

requires some theoretical interpretation. © 2000 John Wiley & Sons, Inc. J Polym Sci A:

Polym Chem 38: 846–854, 2000

Keywords: styrene; acrylonitrile; radical copolymerization; reactivity ratios; solvent

effects; microstructure

INTRODUCTION

The choice of the proper kinetic model for describ-ing the composition and microstructure of copol-

ymers produced by free-radical copolymerizationhas been the subject of many investigations. For

most monomer systems, the terminal1 model suc-ceeds in describing copolymer composition interms of the monomer-feed composition (eq 1). For

example, for the styrene/methyl methacrylate

(STY-MMA) monomer system, both the terminal

and penultimate2 models (eq 2) present almost

the same perfect fit to the composition data:3,4

n d M 1d M 2

M 1 M 2

M 1r1 M 1 M 2 M 2r2 M 2 M 1

(1)

n d M 1

d M 2

1 r21

M 1r11 M 1 M 2

M 2r21 M 1 M 2

1 r12

M 2r22 M 2 M 1

M 1r12 M 2 M 1

(2)Correspondence to: A. Kaim (E-mail: [email protected].

uw.edu.pl)

Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 38, 846–854 (2000)

© 2000 John Wiley & Sons, Inc.

846



where n represents the monomer ratio in the co-

polymer and [ M 1] and [ M 2] are the mole fractionsof monomer M 1 and M 2, respectively. Parameters

r1, r2, r11, r22, r21, and r12, defined in a conven-tional way, stand for the reactivity ratios of themonomers M 1 and M 2 in the terminal and penul-

timate models, respectively.Systems have been reported, however, in which

the introduction of the four-parameter penulti-mate model (also called the explicit penultimate

model2) gives an improved fit to the compositiondata over the two-parameter (terminal) model.For example, the styrene/acrylonitrile (STY-AN)

monomer system is better described5–7 with thepenultimate model than with the terminal model.

However, an examination of the rate constantof propagation and termination in the copolymer-

ization of numerous monomer systems, including the STY-MMA monomer system, as a function of

monomer composition in a feed results in the con-clusion that the terminal model fails to describethe absolute rate of the propagation for the sys-

tem.8 Despite this, the model still is used often fordescribing the composition and microstructure of

most copolymers produced by free-radical copoly-merization. As summarized recently,9 to justifythe continued use of the terminal-model composi-

tion and triad/pentad fraction equations in suchsystems, the implicit penultimate model8 has

been proposed.It is well-recognized that the perfect fit of one

or another kinetic model can be considered when

it provides simultaneously a satisfactory fit to thecomposition and the overall propagation-rate da-

ta.9 However, a question can be raised: how pow-erful are composition data in discriminating be-

tween the terminal and penultimate model forbinary copolymerization? An interesting study on

the subject was dome some time ago by Moad etal.10

Some new aspects of the present state of theart justify in my opinion a further exploration of the problem. One of them is the successful appli-

cation of the nonlinear least-squares (nlls) ap-proach based on the Nelder and Mead11 simplex

method to fit both the terminal and the penulti-mate models to the copolymer-composition data.

This method enables to estimate reactivity ratiosand related standard deviations with optionalprecision. With a scanning procedure based on

the simplex method, it has been demonstrated4,12

that the equivalent representation of the copoly-

mer composition in terms of the monomer-feed

composition can be achieved with multiple penul-

timate-model reactivity ratios. These multiplepenultimate-model reactivity ratios belong to two

different sets of parameters, Set I and Set II,resulting from two different initial guesses for r11,

r22, r21, and r12 (Guess I: r11 r21 r1, r22 r12

r22; Guess II: r11 r1, r21 1/ r2, r22 r2, r12 1/ r1) used for the nlls approach. Moreover, the

most accurate reactivity ratios were surroundedwith sets of reactivity-ratio values of equal accu-

racy. In other words, multiple sets of penulti-mate-model reactivity ratios can describe thecomposition data with the same minimal stan-

dard deviation ( ). Similar results were obtainedfor both the STY-MMA and STY-AN monomer

systems.3,4,12 Contrary to the STY-MMA system,for which the penultimate model did not yield any

significant improvement in the fit to experimentaldata when compared to the terminal model, im-

plications of the nonuniqueness in determining the penultimate-model reactivity ratios can bequite different for the system displaying a pro-

nounced penultimate unit effect (e.g., the STY- AN system). This is quite obvious, because for

examining solvent effects formulated in terms of the relation between the copolymer compositionand the monomer-feed composition (the so-called

“bootstrap effect” by Harwood13), an adequate ki-netic model and well-fitted reactivity ratios are

required.14 When one considers the nonunique-ness in determining the penultimate-model reac-

tivity ratios, the choice of the penultimate-model

reactivity ratios used for this purpose can be evenmore complicated because, by analogy with the

copolymer of STY with MMA in bulk,15 the micro-structure of the STY-AN copolymer may depend

on the choice of the r-parameter set (Set I or SetII) used for calculation.

The multiple solutions of the copolymerizationequation originate from the nonlinear calculation

methods applied in determination of the reactiv-ity ratios. If this approach is assumed to be usedwidely today, the problem of the reactivity-ratio

selection used for the description of copolymeriza-tion systems can acquire in the future an even

greater importance. There is good reason for thisexpectation because determination methods for

the terminal-model reactivity ratios based on thelinearization of the Mayo–Lewis equation1 (eq 1)have been criticized for a long time,16,17 besides

being useless for the penultimate model (eq 2). Inrecent case studies and a comprehensive litera-

ture review18–20 on the estimation of copolymer-

APPLICATION OF THE MONOMER REACTIVITY RATIOS 847



T a b l e

I .

T e r m i n a l - a n d P e n u l t i m a t e - M o d e l P a r a m e t e r s f o

r t h e S t y r e n e ( M 1 ) / A c r y l o n i t r i l e ( M 2

) F r e e - R a d i c a l C o p o l y m e r i z a t i o n S y s t e m

i n T o l u e n e

( T ) , M e t h y l E t h y l K e t o n e ( M E K ) , N , N - D i m e t h y l f o r m a m i d e

( D M F ) , a n d A c e t o n i t r i l e ( A C N ) E s t i m

a t e d w i t h t h e S i m p l e x M e t h o d

P a r a m e t e r

T e r m i n a l M o d e l a

P

e n u l t i m a t e M o d e l

S e t I b

S e t I I c

T d

T

c

M E K e

D M F e

A C N d

T d

T e

M E K e

D M F e

A C N d

T d

T e

M E K e

D M F e

A C N d

r 1

0 . 3 6 9

( 0 . 4 2 3 )

0 . 3 2 8

0 . 3 3 4

0 . 2 4 0

0 . 4 8 8

( 0 . 4 8 5 )

r 2

0 . 1 2 8

( 0 . 1 1 8 )

0 . 1 0 3

0 . 0 7 8

0 . 1 1 7

0 . 0 6 5

( 0 . 0 8 1 )

r 1 1

0 . 2 5 4

( 0 . 2 4 2 )

0 . 2 2 5

( 0 . 2 4 2 )

0 . 2 5 8

( 0 . 2 8 4 )

0 . 2 0 5

( 0 . 2 2 7 )

0 . 4 2 7

( 0 . 3 2 2 )

0 . 2 0 6

0 . 2 2 0

0 . 2 4 9

0 . 2 0 0

0 . 4 4 8

r 2 2

0 . 2 5 5

( 0 . 1 3 3 )

0 . 1 2 0

( 0 . 1 0 8

0 . 0 7 1

( 0 . 0 6 3 )

0 . 1 0 9

( 0 . 1 0 5 )

0 . 0 6 0

( 0 . 0 5 2 )

0 . 2 1 9

0 . 1 9 5

0 . 0 6 6

0 . 1 0 8

0 . 0 7 1

r 2 1

0 . 4 5 9

( 0 . 5 6 6 )

0 . 5 3 2

( 0 . 5 5 9 )

0 . 4 7 0

( 0 . 5 7 0 )

0 . 3 1 5

( 0 . 4 4 0 )

0 . 6 0 3

( 0 . 6 2 1 )

2 5 . 6 3 5

1 0 7 . 5 7 2

6 . 0 1 8

6 . 1 7 8

1 7 . 6 4 8

r 1 2

0 . 0 6 0

( 0 . 1 0 9 )

0 . 0 9 5

( 0 . 1 1 9 )

0 . 0 9 9

( 0 . 1 3 2 )

0 . 1 4 2

( 0 . 1 7 5 )

0 . 0 7 7

( 0 . 1 0 5 )

1 . 0 5 5

1 . 4 3 9

1 . 1 4 4

2 . 5 7 0

1 . 7 2 7

f

0 . 0 2 4 6 0

( 0 . 0 4 9 )

0 . 0 1 9 2 8

0 . 0 1 2 4 1

0 . 0 1 7 1 8

0 . 0 0 6 2 0

( 0 . 0 5 1 )

0 . 0 0 8 1 5

( 0 . 0 2 3 )

0 . 0 1 1 0 6

0 . 0 1 0 7 7

0 . 0 1 7 7 3

0 . 0 0 5 1 9

( 0 . 0 2 0 )

0 . 0 1 2 2 9

0 . 0 0 9 7 2

0 . 0 0 7 7 2

0 . 0 1 7 8 1

0 . 0 0 6 2 1

g

0 . 0 1 6 4 5

0 . 0 0 8 2 2

0 . 0 0 1 6 4

0 . 0 0 0 5 5

0 . 0 0 0 0 1

0 . 0 1 2 3 1

0 . 0 0 9 5 6

0 . 0 0 4 6 9

0 . 0 0 0 6 3

0 . 0 0 0 0 1

p h

2

2

2

2

2

4

4

4

4

4

4

4

4

4

4

n i

1 1

1 3

1 4

1 5

1 2

1 1

1 3

1 4

1 5

1 2

1 1

1 3

1 4

1 5

1 2

F ( 9 9 . 5

% )

j

3 . 6 8

3 . 1 0

2 . 9 1

2 . 7 8

3 . 3 5

3 . 6 8

3 . 1 0

2 . 9 1

2 . 7 8

3 . 3 5

F c a l c d

k

2 8 . 3 9

9 . 1 7

1 . 6 4

0 . 3 4

1 . 1 7

1 0 . 5 2

1 3 . 2 0

7 . 9 2

0 . 3 8

0 . 0 1

V a l u e s i n p a r e n t h e s e s

c o m e f r o m

o r i g i n a l w o r k s .

a U s i n g r 1

0 . 5 a n d r

2

0 . 1 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .

b U s i n g r 1 1

r 2 1 r 1

a n d r 2 2

r 1 2

r 2 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .

c U s i n g r 1 1

r 1 , r 2 1

1 / r 2 , r 2 2

r 2 , a n d r 1 2

1 / r 1 a s t h e i n i t i a l g u e s s f o r t h e ( n l l s ) fi t .

d C a l c u l a t e d w i t h d a t a

b y H i l l e t a l . 6

e C a l c u l a t e d w i t h d a t a

b y K l u m p e r m a n a n d K r a e g e r .

7

f S t a n d a r d d e v i a t i o n i s

d e fi n e d a s

i 1

n

F i e x p t l F i c a l c d

2 / n p w h e r e F

i

i s t h e m o l e f r a c t i o n o f t h e m o n o m e r M

i

e x p r e s s e d f o r t h e t e r m i n a l a n d p e n u l t i m a t e

m o d e l s i n t h e c o r r e s p o n d i

n g r e a c t i v i t y r a t i o s , n i s t h e n u m b e r o f e x p e r i m e n t a l p o i n t s , a n d p i s t h e n u m b e r

o f r p a r a m e t e r s .

g A b s o l u t e v a l u e o f t h e d i f f e r e n c e b e t w e e n t h e s t a n d a r d d e v i a t i o n o f t h e r e a c t i v i t y r a t i o s d e t e r m i n e d f o r t h e m o n o m e r s y s t e m

i n t h e s o l v e n t f o r t h e t e r m i n a l a n d

p e n u l t i m a t e m o d e l s ,

( t e r m i n a l m o d e l )

( p e n u l t i m a t e m

o d e l )

.

h N u m b e r o f r p a r a m e t e r s i n t h e k i n e t i c m o d e l .

i N u m b e r o f c o p o l y m e r

i z a t i o n e x p e r i m e n t s .

j C r i t i c a l v a l u e s o f F f o

r t h e p r o b a b i l i t y l e v e l

9 9 . 5 % ( t a k e n

f r o m

r e f . 2 8 ) .

k F

c a l c d c a l c u l a t e d a c c o r d i n g t o e q . 3 , 2

7 w h e r e M o d e l s B a n d A s

t a n d f o r t h e t e r m i n a l m o d e l a n d p e n u l t i m

a t e m o d e l , r e s p e c t i v e l y .

848 KAIM



ization reactivity ratios, a further extension of the

nonlinear approach is recommended and, becauseof advances in computing power, anticipated.

Therefore, the proper choice of monomer reac-tivity ratios for the kinetic-model discriminationand the solvent-effect determination in the free-

radical copolymerization of the monomer pairsdisplaying the penultimate effect can be relevant.

The aim of this article is to study the impact of reactivity ratios determined with the simplex

method on the kinetic-model discrimination andsolvent-effect determination for a monomer sys-tem, such as the STY-AN system, displaying a

penultimate effect.

EXPERIMENTAL

In this study, monomer-feed- and copolymer-com-

position data for the STY-AN system given by Hillet al.6 for toluene and acetonitrile and by Klump-erman and Kraeger7 for toluene, methyl ethyl

ketone (MEK), and N , N -dimethylformamide (DMF)were used.

Calculation procedures for the reactivity-ratiodetermination and scanning were based on the

Nelder and Mead11 simplex concept and wereused as described previously.4,12,21

RESULTS AND DISCUSSION

Penultimate Unit Effect in the Investigated Systems

Terminal- and penultimate-model reactivity ra-tios for the STY ( M 1)/AN ( M 2) monomer system in

toluene, MEK, DMF, and acetonitrile as esti-mated with the simplex method are presented in

Table I. For the penultimate model, two differentinitial guesses for the reactivity ratios (Guess I:

r11 r21 r1, r22 r12 r22; Guess II: r11 r1,r21 1/ r2, r22 r2, r12 1/ r1) led to two differentpenultimate reactivity-ratio sets, Set I and Set II.

More precisely, for all investigated systems, wideranges of penultimate-model reactivity ratios

with the same minimal standard deviation ( )were found. Multiple penultimate-model reactiv-

ity ratios in the STY-AN free-radical copolymer-ization system in bulk were the subject of myprevious article.12 Results obtained for a solution

copolymerization in acetonitrile, DMF, MEK, andtoluene were qualitatively very similar. Two-di-

mensional projections ( against rij; i, j 1,2; i

j) of the five-dimensional space (r11, r21, r22, r12, ) that resulted from the scanning experiments22

over wide ranges of the value had approxi-

mately the same shape for all the solvents, asshown schematically in Figure 1. The differences

for the investigated solvents consisted of the rel-ative position of the global and local minima (seeSet I and Set II in Table I). In addition, the

two-dimensional projections ( against rij; i, j

1,2; i j) resulted in a similar curve with one

minimum only (not shown). A comparison of the copolymerization-system

descriptions accomplished via the terminal- and

penultimate-model reactivity ratios (Table I) ispresented in Figure 2. The composition data for

all the investigated copolymerizations could bedescribed equally well with quite different sets of

the penultimate-model r parameters with veryclose standard deviations. An inspection of the

coincidence of the composition curves for the dif-ferent solvent systems revealed differences in thesignificance of the penultimate unit effect in the

solvent systems. The penultimate unit effect ap-peared to increase approximately in the following

order: acetonitrile DMF MEK toluene.Therefore, it was inversely proportional to the

polarity (expressed in Debye unit) of the solventused (3.92,23 3.82,24 2.77,25 and 0.36,26 respec-

tively). These findings led to the conclusion thatthe stronger interactions between the solvent andmonomers were less when the penultimate unit

effect was pronounced. Generally, it seems thatthe scale of the observed penultimate unit effect

depends on the solvent.

Figure 1. General picture of two-dimensional projec-

tions ( against rij; i, j 1,2; i j) of the five-dimen-

sional space (r11, r21, r22, r12, ) that resulted from the

scanning experiments22 for the STY-AN free-radical

copolymerization in toluene, MEK, DMF, and acetoni-

trile. values correspond to those for the penultimate

model given in Table I.




Figure 2. Copolymerization diagrams for the STY/AN free-radical copolymerization

systems at 60 °C with the reactivity ratios calculated by the simplex method presented

in Table I: (a) calculated for toluene with data by Hill et al.,6 (b) calculated for toluene

with data by Klumperman and Kraeger,7 (c) calculated for MEK with data by Klump-

erman and Kraeger,7 (d) calculated for DMF with data by Klumperman and Kraeger7

[points (Œ) were generated with the penultimate-model reactivity ratios given by these

authors (r11 0.227, r22 0.105, r21 0.440, r12 0.175, 0.02163)], and (e)calculated for acetonitrile with data by Hill et al.6 } experimental points; points

generated according to eq 1 with the reactivity ratios for the terminal model; E points

generated according to eq 2 with the reactivity ratios estimated for the penultimate

model with r11 r21 r1 and r22 r12 r2 as the initial guess for the (nlls) fit (Set I);

points generated according to eq 2 with the reactivity ratios estimated for the

penultimate model with r11 r1, r21 1/ r2, r22 r2, and r12 1/ r1 as the initial guess

for the (nlls) fit (Set II).

850 KAIM



Klumperman and Kraeger7 also related the co-incidence of the copolymer-composition curves for

the discussed systems with the polarity of thesolvent. However, they found qualitatively, con-

trary to our results, that the copolymer-composi-tion curve for polymerization in DMF was not inagreement with the proposition. They tried to ex-

plain this exception with subtle differences in theinteractions between the electron-donor and elec-

tron-acceptor molecules present in the polymer-

ization system. In my opinion, a different expla-nation is also possible. Quantitatively, the signif-icance of the penultimate unit effect for themonomer system in the discussed solvents can be

(rigorously under certain statistical conditions)correlated with an absolute value of the difference

between the standard deviation ( ) of the reactiv-ity ratios determined for the terminal and penul-

timate models ( in Table I). According to TableI, increased in the same order as the penulti-mate unit effect (acetonitrile DMF MEK

toluene) regardless of the penultimate reactiv-ity-ratio set (Set I or Set II) taken for comparison.

Differences between the numerical values of appeared to be meaningless, but a case with the

solvent effect of DMF proved the contrary. For thereactivity ratios given by Klumperman and Krae-ger7 (r11 0.227, r22 0.105, r21 0.440, r12 0.175), the calculated standard deviation ( )was 0.02163. However, for the reactivity ratios

estimated with the simplex method from the

same experimental data (r11 0.205, r22 0.109,

r21 0.315, r12 0.142) was 0.01773 (Table I).Because the difference between the two values

was 0.0049, it is easy to distinguish on thegraphic scale [Œ in Fig. 2(d)]. This example showsagain how high the level of accuracy in the deter-

mination of reactivity ratios must be to concludefrom composition data the correct kinetic-model

discrimination.Hill et al.27 proposed the application of the

statistical F test28 to prove if the use of the four-parameter (penultimate) model is justifiable forfitting the composition data. In other words, with

this test a justness of the use of a higher ordermodel can be verified. According to the proposal,

the test is based on the ratio F of the residualsums of the squares ( 2) of Models A and B, where

Model B (terminal) is a special case of Model A (penultimate) (eq 3):

F B

2 A

2 / p A p B

A2 / n p A

(3)

Figure 3. STY ( M 1) -centered triad fractions for the

STY/AN free-radical copolymerization estimated withthe reactivity ratios for the terminal model (full points)

and penultimate model (blank points) with r11 r21 r1 and r22 r12 r2 as the initial guess for the (nlls)

fit (Set I). , ƒ toluene with data by Hill et al.;6 F, E)

toluene with data by Klumperman and Kraeger;7 ‹,

MEK with data by Klumperman and Kraeger;7 },

DMF with data by Klumperman and Kraeger;7 Œ,

‚ acetonitrile with data by Hill et al.6

Figure 2. (Continued from the previous page)




where p A and pB are the numbers of the param-

eters for each model and n is the number of copo-lymerization experiments. Calculated F calcd ratios

and critical values of F for the probability level (

99.5%) are shown in Table I. Results showed

that from a statistical point of view, the applica-

tion of the penultimate model for the description

of STY-AN copolymerization in toluene ( F calcd F (99.5%)) is justified. For copolymerization in

MEK, the result of the test was not certain anddepended on the penultimate reactivity-ratio set

(Set I or Set II) taken for consideration. However,

Figure 4. STY ( M 1) -centered triad fractions for the STY/AN free-radical copolymer-

ization estimated with the reactivity ratios for the penultimate model with r11 r1, r21 1/ r2, r22 r2, and r12 1/ r1 as the initial guess for the (nlls) fit (Set II): (a) f M 1 M 1 M 1

triad fraction, (b) f M 2 M 1 M 2 triad fraction, and (c) f M 2 M 1 M 1 triad fraction. ƒ toluene

with data by Hill et al.;6 E toluene with data by Klumperman and Kraeger;7 ‹

MEK with data by Klumperman and Kraeger;7 } DMF with data by Klumperman

and Kraeger;7 Œ acetonitrile with data by Hill et al.6

852 KAIM



for copolymerization in DMF and acetonitrile so-

lutions, the penultimate model should be rejectedbecause it does nor provide a better fit to experi-

mental data in comparison with the terminaldata. Note that the F test results were in generalagreement with the conclusion that the penulti-

mate unit effect can be correlated with an abso-lute value of the difference between the standard

deviation of the reactivity ratios determined forthe terminal and penultimate models. Other con-

sequences of treating the same experimental databy different models with a different number of parameters have been discussed previously.4,21

Microstructure of the Copolymers

A comparison of the STY ( M 1) -centered triad

fractions f M 1 M 1 M 1, f M 2 M 1 M 1, and f M 2 M 1 M 2 for theSTY-AN free-radical copolymers estimated with

reactivity ratios for the terminal and penultimatemodels (Set I in Table I) is presented in Figure 3.In the curves for the STY-AN free-radical copoly-

merization in acetonitrile, DMF, MEK, and tolu-ene, the bootstrap effect is observed; that is, the

relationship between the triad-sequence distribu-tion and copolymer composition did not depend onthe solvent employed. Without a detailed study, it

can be concluded, however, that points relating tothe terminal model (full points) were displaced

slightly (especially for the f M 2 M 1 M 1 and f M 2 M 1 M 2

triads) when compared to those corresponding to

the penultimate model (blank points). This can be

regarded as an additional proof for the presence of the penultimate unit effect in the discussed mono-

mer systems. This observation is not new. Thetriad distribution versus the copolymer composi-

tion presented by Klumperman and O’Driscoll14

for the copolymerization of STY with maleic an-

hydride in bulk, MEK, and toluene showed com-paratively poor agreement with the terminal

model when compared to the penultimate model.The situation changed dramatically when Set

II of the penultimate-model reactivity ratios (Ta-

ble I) was used for the triad-sequence calculation(Fig. 4). An examination of the discussed copoly-

mers shows that the triad distribution dependedon the solvent used for the copolymerization. The

sequence distribution in the copolymers synthe-sized in toluene was especially different, al-though, as we remember from the previous sec-

tion and Figure 2(a,b), the copolymer-compositioncurves for toluene calculated for both reactivity-

ratio sets (Set I and Set II) overlap precisely.

Note, however, that there is a difference in fitting

the particular triad fractions ( f M 1 M 1 M 1, f M 2 M 1 M 1,

f M 2 M 1 M 2) to the general bootstrap effect rule: tri-

ads involving both monomers M 1 and M 2 lessaccurately fulfill the expectation in terms of thebootstrap effect symptoms.

The results are difficult to interpret from atheoretical point of view. However, the STY-AN

monomer systems in toluene indicated the mostsignificant penultimate unit effect among all the

discussed solvents. The question arises whetherthe observed convergence was coincidental and,therefore, without any physical meaning, or could

be interpreted in terms of the copolymerizationkinetics.

CONCLUSIONS

From this study, it can be concluded that on thebasis of the composition data alone, it is possible

to discriminate between the terminal and penul-timate models for the STY-AN monomer system

under the condition of a very accurate reactivity-ratio determination. The nonlinear approach tothe estimation of reactivity ratios based on the

Nelder and Mead simplex method seems to be a very useful tool for the purpose. The results indi-

cate that the significance of the penultimate uniteffect for a given monomer system can be corre-

lated with an absolute value of the differencebetween the standard deviation of the terminal-

and penultimate-model reactivity ratios. The pen-ultimate unit effect depends on the solvent andseems to be inversely proportional to its polarity.

Contrary to the full equivalence in the represen-tation of the copolymer-composition data with dif-

ferent but numerically equivalent penultimate-model reactivity ratios, the relationship between

the triad-sequence distribution and copolymercomposition does depend on the set of penulti-mate-model reactivity ratios chosen for micro-

structure determination. This observation stillneeds some theoretical interpretation.

This study was supported with 120-501/68-BW-1418/ 18/98 from the Faculty of Chemistry, University of

Warsaw.

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854 KAIM

Documents

Application of the Monomer Reactivity Ratios to the Kinetic-Model Discrimination and the Solvent-Effect Determination for the StyreneAcrylonitrile Monomer System