Kinetics of Living Radical Polymerization - ACS Symposium Series

Chapter 2

Kinetics of Living Radical Polymerization Takeshi Fukuda and Atsushi Goto

Downloaded by STANFORD UNIV GREEN LIBR on September 20, 2012 | http://pubs.acs.org Publication Date: August 15, 2000 | doi: 10.1021/bk-2000-0768.ch002

Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

Activation processes and polymerization rates of several variants of living radical polymerization (LRP) are discussed. Despite the presence of side reactions such as termination and initiation, the products from L R P can have a low polydispersity, provided that the number of terminated chains is small compared to the number of potentially active chains. A large rate constant of activation, k , is another fundamental requisite for low polydispersities. Experimental studies on k have clarified the exact mechanisms of activation in several L R P systems. The magnitudes of k have been found to largely differ from system to system. Because of bimolecular termination, which is inevitable in L R P as well as in conventional radical polymerization, the time-conversion curves of L R P have several characteristic features depending on experimental conditions, such as the presence or absence of conventional initiation and/or an extra amount of stable free radicals or the like. A new analytical rate equation applicable to such general cases is presented. act

act

act

Living (or controlled/"living") radical polymerization (LRP) has opened up a simple and versatile route to the synthesis of well-defined, low-polydispersity polymers with various architectures ( i - i i ) . The basic mechanism common to all the variants of L R P is the alternating activation-deactivation process depicted in Scheme 1: wherein a potentially active (dormant) species P - X is supposed to be activated to the polymer radical P* by thermal, photochemical, and/or chemical stimuli. In the presence of monomer M , P* will undergo propagation until it is deactivated to the dormant species P - X . This cycle is supposed to be repeated enough times to give every "living" chain an almost equal chance to grow. Here we define a "living" chain as either an active or a dormant chain with the quotation specifying the presence of the two states. In a practically useful system, it usually holds that [P*]/[P-X] -Χ] (= KA ) 0

(Κ = kjk ) c

(9)

holds. (Fischer has shown this to be the case excepting the very initial stage of polymerization and noted the importance of the time range where the quasiequilibrium holds (73).) The solution can be cast into the form ln{[(l+jc)/(l^)]-[(l^ )/(l+^o)]} - 2(χ-*ο) = at χ = (R^Wf^X] a = 2R /(k^ A ) 0

m

2

2

{

m

Q

(10) (H) (12)

and Jto is the value of χ at t = 0 (R\ is assumed to be constant. For hints to the derivation of equations 10-12, see reference ( i i ) ) . The P" concentration and hence R = £ [P*][M] follow from equations 10-12 with [Ρ*] = KAo/[X'] (equation 9). Two special cases have been treated elsewhere (72,75). One is the case in which Ri > 0, [X"]o = 0, and t is sufficiently large (a*t » 1). In this limit, equation 10 simply reduces to χ = 1 (the "stationary state") or equivalently p

P

m

[X*] = (KAo) /(RJk ) t

(stationary state)

(13)

(stationary state)

(14)

or m

[Ρ'] = (Ri/k ) t

Thus R is independent of the reversible activation reaction and identical with the stationary-state rate of polymerization of the nitroxide-free system. This has been experimentally observed (72,74). p

In Controlled/Living Radical Polymerization; Matyjaszewski, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 2000.

34


This stationary-state kinetics is expected to hold also for degenerative transfer-type systems (Scheme lb), since the radical concentration is basically unchanged by a transfer reaction unless it is a retarding or degradative one. Stationary-state kinetics was in fact observed for the styrene polymerizations with a PS-I (62) and a PSSCSMe degenerative transfer agent (65). The other case that has been discussed is the one with R\ = 0 (a = 0), where equation 10 simplifies to (11) [X*f-{XV

2

= 3k (KA ) t t

(15)

0

Equation 15 with [X*] = 0 is the case discussed firstly by Fischer (75) and subsequently by us (75), which gives the characteristic power-law behavior of the conversion index ln([M]o/[M]): 0

/3 m

ln([M]o/[M]) = (3/2yc (KAo/3k Y t p

(16)

t

This behavior has been observed in part by experiments (75-77). Equation 10 is applicable to more general cases in which, for example, R is nonzero but so small that the stationary state is reached only after a long time or never reached at all in the duration of a typical experiment. It also describes the case in which, for example, R is nonzero, and [X"] is considerably larger than the stationary concentration given by equation 13. What happens in this case would be that the polymer radicals produced by the conventional initiation combine with the extra X " radicals to produce extra adducts P - X until [X*] decreases down to the stationary concentration (equation 13 with A so modified as to include the extra adducts produced from the extra X \ ) Correspondingly, the R in such a system would be small or virtually zero when t is small because of the extra X", and gradually increase up to the stationary value given by equation 14. Such intermediate behaviors are clearly different from those for the two special (limiting) cases discussed above. The behavior that one would experimentally observe depends basically on the magnitudes of the two parameters x and a, as equation 10 shows. There are several causes that can introduce deviations from equation 10. One may be the inadequacy of the assumptions on which equation 10 is based, in particular, the approximation of [P-X] = A (= constant). When R\ = 0, [X*] increases and [P-X] necessarily decreases with time because of termination (cf. equation 15). The magnitude of error introduced by this cause would be on the same order as that involved in the approximation [P-X] =A . For example, if [P-X] is smaller than^4 by 10 % at time t, the [X*] (hence R ) estimated from equation 15 would be in error by about 10 %. The second cause may be side reactions other than initiation and termination. For example, alkoxyamines are known to undergo thermal degradation (78,79). We also note that the conventional initiation can be accelerated by the presence of a nitroxide (80). The third possible cause of deviations may be the dependence of the kinetic parameters on chain length and/or polymer concentration. In the analysis of their A T R P experiments (81), Shipp and Matyjaszewski (82) have in fact noted the importance of taking the chain length dependence of k into account. x

Y

0

0

p

0

0

0

0

p

t


35 Remember that in a living polymerization, chain length and conversion or polymer concentration are directly related to each other. Also note that the above equations for nitroxide systems are basically applicable to A T R P systems by the reinterpretations of X " = A X , k = k [A], and k = k (K = k [A]/k ), as suggested previously (11,77). With these discussions in mind, the simple analytical equations given here will be hopefully useful in understanding the fundamental features, and enable consideration of the more sophisticated aspects, of LRP.


d

A

c

OA

A

OA

Abbreviations a A C r κ

reduced rate of initiation (equation 11) initial concentration of dormant species (A = [Po-X] = [P-X]o) monomer conversion degenerative transfer constant (equation 5) equilibrium constant (equation 9) activation rate constant in A T R P (Scheme 1) pseudo-first-order activation rate constant (Scheme 1) combination rate constant (Scheme 1) dissociation rate constant (Scheme 1) deactivation rate constant in A T R P (Scheme 1) deactivation rate constant (Scheme 1) degenerative transfer rate constant (Scheme 1) propagation rate constant termination rate constant number-average molecular weight weight-average molecular weight polymer radical dormant species initiating dormant species (conventional) initiation rate propagation rate weight fraction of the subchain Κ (K= A or B ) (equation 1) reduced stable radical concentration (equation 10) stable free radical polydispersity factor (Y = MJM - 1 ) average number of activation deactivation cycles that a chain experiences during polymerization time t (y = k t) number-average degree of polymerization 0

0

^act Κ h kOA kdeucl k ex

k

p

k

x

M M P" P-X Po-X Ri R w X X' Y n

w

P

K

yn

n

n

act

Acknowledgments We thank Professor K . Matyjaszewski, Dr. G . Moad, Dr. E . Rizzardo, Professor Β. B . Wayland, and Professor H . Fischer for collaboration and/or valuable discussions.


36

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Kinetics of Living Radical Polymerization - ACS Symposium Series

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