연쇄이동제에 의한 리빙 중합의 단일한 분자량분포와 제어성

김진욱, 이기준, 이홍희

서울대학교 화학공학과

Monomodal Distribution and Controllability in Living Polymerization with Chain-Transfer Agents

Jin Wuk Kim, Ki-Jun Lee and Hong H.Lee

Department of Chemical Engineering , Seoul National University

Introduction

Living polymerization is one in which the average molecular weight can easily be controlled. No termination is involved in the usual sense in the polymerization but rather the termination is controlled by a chain-transfer agent and/or a catalyst, thereby leading to the controllability of the average molecular weight. More transfer agent (catalyst) is needed for lower average molecular weight. In general, the chain-transfer agent is more effective than the catalyst.

Theoretical analysis of such living polymerization with chain-transfer agents has been made1,6 to examine the nature of the resulting molecular weight distribution. The results are, however, for the polymerization in a batch reactor. Characteristic of the molecular weight distribution resulting from a batch reactor is the existence of a bimodal molecular weight distribution4,5, i.e., a combination of two distinct molecular weight distribution. One is due to living polymer and the other due to dead polymer or end-capped polymer.

Although batch reactors are typically used in experiments, continuous reactors are also used in practice such as continuous stirred tank reactors (CSTR).

In this paper, it is shown that the use of a CSTR always leads to a monomodal molecualr weight distribution and thus to a monomodal polydispersity index (PDI).

It is desirable in any polymerization including the living polymerization with chain-transfer agents that the desired average molecular weight be obtained, that the PDI be minimized, and that the conversion of monomer and thus the yield be maximized. It has been revealed (Benedicto et al. 1995) that such objectives can be realized only for a narrow range of the kinetic parameters for the living polymerization in batch reactors.

In this paper, it is shown theoretically that the average molecular weight and the yield can be completely controlled when the living polymerization is carried out in CSTRs.

Monomodal Average Molecular Weight And PDI

The polymerization scheme1 can be represented as follows ;

[eqn: rm W_0 + M~ Buildrel rarrowk_i ~ W_1]

[eqn: rm W_n + M~ Buildrel rarrow k_p ~W_n+1, ~~~~~~~~n≥1]

[eqn: rm W_n + T_0~ Buildrel rarrow k_ct ~ W_0 + T_n, ~~~~~~~~~~~n≥1]

where W0 is the initiating species (catalyst), Wn is the living polymer of chain length n, T0 is the chain-transfer agent, Tn is the end-capped, dead polymer of chain length n, ki is the initiating rate constant, kp is the rate constant for the propagation, and kct is the same for the chain transfer.

At steady state, the mass balances around a CSTR can be written as follows :

[eqn: Q_c (W_0 )_i -QW_0 -V(k_i MW_0 -k_ct T_0 □_0 ) =0]	(1)      [eqn: Q_m M_i - QM -V(k_i MW_0 +k_p M□_0 ) =0]	(2)

[eqn: Q_t (T_0 )_i -QT_0 -Vk_ct T_0 □_0 =0]	(3)

where Q's (s=c,m,t) are the volumetric flow rates of the catalyst (c), the monomer (m), and the chain transfer agent (t), Q is the total volumetric flow rate such that Q=Qc+Qm+Qt , V is the volume of the reactor occupied by all the species, and the subscript i is for the reactor inlet. Note that the species nomenclature has been used interchangeably for the concentration. The quantities needed for the number-averaged molecular weight and the PDI are defined as follows :

[eqn: □_j ≡ SUM from n=1 to inf n^j W_n]             (j=0,1,2)	(4)

[eqn: □_j^d ≡ SUM from n=1 to inf n^j T_n]             (j=0,1,2)	(5)

where the superscript d is for the dead polymer. The mass balances for these defined quantities follow from eqs 1 through 3 and the definitions :

[eqn: -Q□_0 +V(k_i W_0 M-k_ct T_0 □_0 )=0]	(6)

[eqn: -Q□_0^d +Vk_ct T_0 □_0 =0]	(7)

[eqn: -Q□_1 +V(k_i MW_0 +k_p M□_0 -k_ct T_0 □_1 )=0]	(8)

[eqn: -Q□_1^d +Vk_ct T_0 □_1 =0]	(9)

[eqn: -Q□_2 +V(k_i MW_0 +k_p M(2□_1 +□_0 ))-Vk_ct T_0 □_2 =0]	(10)

[eqn: -Q□_2^d +Vk_ct T_0 □_2 =0]	(11)

It then follows from the definitions that

[eqn: {bar X}_n,d = □_1^d over □_0^d ~~~,~~~~~~ {bar X}_n,a = □_1 over □_0]	(12)

[eqn: PDI_d = {□_0^d □_2^d } over {(□_1^d )^2}~~~ ,~~~~~PDI_a = {□_0 □_2 } over {(□_1 )^2}]	(13)

where the subscript as well as the superscript d denotes dead polymer and the subscript a represents active (living) polymer. Here,[eqn: {bar X}_n] is the number-average degree of polymerization.

To show that the number-average molecular weight is the same for both the dead and the living polymer, it is sufficient that

[eqn: □_0 □_1^d =□_1 □_0^d]	(14)

which follows from the definitions in eq 12. Use of eqs 7 and 9 in eq 14 should reveal that [eqn: □_0 □_1^d] is equal to [eqn: □_1 □_0^d] , that is[eqn: {bar X}_n,d = {bar X}_n,a]. Thus, the average moleular weight is monomodal.

Likewise, it is sufficient to show for the monomodal PDI that

[eqn: □_0^d □_2^d (□_1 )^2 = □_0 □_2 (□_1^d )^2]	(15)

which follows from eq 13. Again, use of eqs 7, 9 and 11 for[eqn: □_0^d],[eqn: □_1^d] and[eqn: □_2^d] , respectively, in eq 15 should show that[eqn: □_0^d □_2^d (□_1 )^2] is equal to[eqn: □_0 □_2 (□_1^d )^2]. Thus, the PDI is also monomodal.

The fact that both the number-average molecular weight and the PDI are monomodal implies that the molecular weight distribution is also monomodal.     Shown in Figure 1 are the number-average degrees of polymerization resulting from a batch system (Figure 1a) and from a CSTR (Figure 1b) for the identical living polymerization. The[eqn: {bar X}_n] in Figure 1a is that obtained by Benedicto et al.1 and it is indeed bimodal.

Figure1-a. Variation of the number-   Figure1-b. Variation of the number-

average degreeof polymerization       average degree of polymerization

with conversion. ki:kp:kct=1:1:0.1.       with conversion. ki:kp:kct=1:1:0.1.

Concentration of catalyst:monomer:    Concentration of catalyst:monomer:

chain-transfer agent=1:100:10. The	chain-transfer agent=1:100:10. The

reactor is batch system.               reactor is CSTR system.

(Qc:Qm:Qt=1:3:3)

References

1.Benedicto, A.D.;Claverie, J.P.;Grubbs, R.H. Macromolecules, 28, 500 (1995)

2.France, M.B.;Grubbs, R.H.;McGrath, D.V. Macromolecules, 26, 4742 (1993)

3.Kouzai, H.;Masuda, T.;Higashimura, T. Macromolecules, 25, 7096 (1992)

4.Yuan, C.;Yan, D. Makromol. Chem., 187, 2629 (1986)

5.Yuan, C.;Yan, D. Makromol. Chem., 187, 2641 (1986)

6.Largo-Cabrerizo, J.;Guzman, J. Macromolecules, 12, 526 (1979)