H. Tobita et M. Hayashi, Molecular weight development in free-radical polymerization with polyfunctional chain-transfer agents, 1 - Equal reactivity model, MACROMOL TH, 10(6), 2001, pp. 573-580
The analytic expression for the weight-average molecular weight development
in free-radical polymerization that involves a polyfunctional chain-transf
er agent is proposed. Free radical polymerization is kinetically controlled
; therefore, the probability of chain connection with a polyfunctional chai
n-transfer agent as well as the primary chain-length distribution changes d
uring the course of polymerization. We consider the primary chains, and the
heterochain branching model is used to obtain the weight-average chain len
gth at a given conversion level in a matrix formula, described as (P) over
bar (w) = W{D-w + (I + T)SP(I-TSP)D--1(f)}. Because the primary chains are
formed consecutively, the number of chain types N is extrapolated to infini
ty, but such extrapolation can be conducted with the calculated values for
only three different N values. The criterion for the onset of gelation is s
imply described as a point at which the largest eigenvalue of the produce o
f matrixes, TSP reaches unity, i.e., det(I-TSP)=0. The present model can re
adily be extended for the star-shaped polyfunctional initiators and the rel
ationships between the model parameters and kinetic rate expression for suc
h reaction systems are also shown.
[GRAPHICS]
Extrapolation method to obtain P-w at N --> infinity for C2 at x = 0.5. The
curve is a quadratic regression determined from the values at N = 50, 70 a
nd 100.