A method for determining reactivity ratios whenn copolymerizations are influenced by penultimate group effects

Eur. Polym. Y. Vol. 23, No. 11, pp. 833-834, 1987 Printed in Great Britain. All rights reserved

0014-3057/87 $3.00 + 0.00 Copyright © 1987 Pergamon Journals Ltd

A METHOD FOR DETERMINING REACTIVITY RATIOS WHEN COPOLYMERIZATIONS ARE INFLUENCED BY PENULTIMATE GROUP EFFECTS C. A. BARSON and D. R. F E N N * Department of Chemistry, The University of Birmingham, P.O. Box 363, Birmingham B 15 2TT, England

(Received 5 February 1987) Abstract--A novel kinetic treatment is proposed for the copolymerization of two monomers M t and M2 when terminal M 2. groups are susceptible to penultimate group effects. If [Md>>[M2], as is possible experimentally when M 2 is radioactively labelled, a value of the reactivity ratio r~ which is independent of penultimate group effects can be obtained. This value is then used to find values for the other reactivity ratios. The method involves a solution for reactivity ratios by means of intersecting curves, each curve representing a given monomer feed ratio and copolymer composition ratio.

INTRODUCTION

Copolymerizations are sometimes found to be influenced by the nature of the penultimate group in the growing copolymer radical. This was shown to be the case in copolymerizations involving s-methylstyrene [1]. It has already been shown that it is possible to circumvent penultimate group effects in copolymerization by using the greatly simplified copolymer composition equation which results when [Md>>[M2] [2]. This is because, under such conditions, terminal diads - M 2 M 2- and triads -M2M2M2. are extremely unlikely. Analysis of m o n o m e r feeds and of copolymers formed under these conditions can be readily achieved when M 2 is radioactively labelled. It is then possible to determine a realistic value of the reactivity ratio r~, despite penultimate group effects being important when normal molar ratios of comonomers are used. If all penultimate groups are taken into account, the total n u m b e r of different propagating steps is eight [3]. It is possible that one of the comonomers (for example M2), because of its more bulky structure, causes much greater steric hindrance than the other comonomer M~. The latter might be able to propagate quite freely. Under these circumstances, penultimate group effects may be negligible when MI is the ultimate group. In such a case, there are only four propagation steps which must take account of penultimate groups, i.e. steps involving an ultimate M 2 group. A novel way of determining all the reactivity ratios in such circumstances is now proposed. Although the mechanism considered involves a radical process, the kinetic treatment which follows is equally applicable to ionic copolymerizations.

group effect are as follows. -MI" + Ml ~ - M l "

kl2

-M1M2" + M1 --* -MI"

kl21

- M I M 2" + Mz --. - M 2 M 2.

k122

- M 2 M 2• + M 2 -o - M 2 M 2•

k222

- M 2 M 2. + M I -o -Ml"

k221

The rates of change of [M 1] and [M2] can be expressed as follows. ~l[Ml]/dt = k,1[-M~ "][M1] + kI21[-MjM2"][M d +k22j[-M2M2'][Md

(1)

and -d[M2]/dt = kl2[-Mt.][M2] + kI22[-MIM2.][M2] ÷ k222[-M2ME.][M2]

(2)

The rates of change of the concentrations of the growing radicals - M ~., - M ~M2' and -M2 M2" can also be expressed as follows. d[-M1 .]/dt = kI21[-MIM2.][MI] + k221[-M2M2'][Ml]- k12[-M l.][M2]

(3)

d[-MiM2']/dt = k12[-Ml'][M2] - k122[-MIM2"][M2]- k,2~[-M~M2"][Ml]

(4)

d[-M2M2-]/dt = k122[-MlM2"][M2] -

k22j[-M:M2'][M,]

(5)

Assuming stationary concentrations for the radicals -M2M2 • and either -M~- or - M I M 2. leads to

THE METHOD

The propagating steps which prevail when the ultimate group M~ is not susceptible to a penultimate

kll

-M~. + M 2 ~ - M 2.

[ - M I M 2 '] =

k~2[-M, '][M2] kl22[M2] + k121[Ml]

(6)

and

*Present address: Lucas Research Centre, Shirley, Solihull, West Midlands B90 4J J, England.

[-M2M 2.] 833

k~2k~22[-M ~.] [M2] 2 km[Ml](kl22[M2] + km[Ml])

(7)

834

C.A. BARSONand D. R. FENN

Combining Eqns (1) and (2) and substituting for [-M~M2"] and [-M2M2'] leads to d[M1] 1 + rI[MI]/[M:] -

-

=

(8)

diM2]

[M2](r2 + [MII/[Mz]) [M,](r~ + [M1]/[M2] )

1 +r~

where r I = kll/k12, r 2 : k222/k221 and r~ k122/k121. At low conversion, d[Md/d[M2] will also be identical to the copolymer composition ratio ml/m2. Equation (8) can then be rewritten by making the substitutions F = [MI]/[M2] and f = ml/m2. Thus F ( f - 1) F 2 r ~ r~(F + r2) =

-

-

-

- -

l

(9)

f

f (F + r~) The equation in this form corresponds to the simpler equation derived by Fineman and Ross [4] for copolymerizations where penultimate group effects can be ignored. In the Fineman and Ross equation F(ff

1) -

F2rl f

r2

(10)

it is possible to determine both reactivity ratios r~ and r 2 from a plot of F ( f - 1)/fagainst F2/f. In the case of Eqn (9), there are three reactivity ratios, rl, r2 and r~, and a direct plot of experimental data is not possible. But Eqn (8) can also be written in terms of F and f as follows. f-

1

+rlF

r~(r 2 + F) 14 F(r~ + F)

(11)

This can be rearranged to express r2 in terms of r~. Thus Fx F2x r2 = - ~ - + f~-2 - F

(12)

where x = 1 + r i F - f Therefore, if r~ can be determined independently, solutions for r 2 and r~ can be found. If rl is determined under conditions such that [MI]>>[M2], a value is obtained which is completely independent of any penultimate group effects [2]. According to Eqn (12), each experimental pair of values of F and f, together with the derived values of r~, describes a curve when r2 is plotted against r~. If all the data for F and f a r e plotted, a series of curves is obtained which, in theory, have a single point of intersection, defining the values of r2 and r~. With experimental data, the intersections of all pairs of curves will be scattered within an area of the graph. The location of this area defines r2 and r~ and its magnitude is a measure of the experimental errors. Such a plot is illustrated in Fig. 1.

r2 I

Fig. I. Diagram showing the intersections of four curves each representing a set of experimental data for F, f a n d r~. As an alternative solution, experimental values of F a n d f c a n be used to generate a set of simultaneous equations of the form F,xi F2ixi r2 = ~ + f r ~ -- Fi

(13)

where the subscript i refers to a particular set of values for F and f A set of n pairs of F and f wilt therefore generate n ( n - 1)/2 pairs of simultaneous equations, giving n ( n - 1)/2 estimates of both r 2 and r~. The best values for r2 and r~ are the arithmetic means of the individual estimates, with the distributions of individual values about these means giving the experimental uncertainties. As the success of the method depends upon an accurate determination of r 1 which is independent of penultimate group effects, the radiotracer method [2] is ideal for studying such copolymerizations. It is therefore possible to determine the values for all three reactivity ratios resulting from copolymerizations where one of the comonomers exhibits a penultimate group effect. Acknowledgement--The authors acknowledge the award by the Science and Engineering Research Council of a research studentship to D.R.F. REFERENCES

1. G. E. Ham. J. Polym. Sci. 45, 183 (1960). 2. C. A. Barson. Eur. Polym. J. 20, 125 (1984): 3. E. Merz, T. Alfrey and G. Goldfinger. J. Polym. Sci. 1, 75 (1946). 4. M. Fineman and S. D. Ross. J. Polym. Sci. 5, 259 (1950).