화학공학소재연구정보센터
Journal of Polymer Science Part B: Polymer Physics, Vol.36, No.13, 2423-2433, 1998
General matrix formula for the weight-average molecular weights of crosslinked polymer systems
On the basis of the first-order Markovian statistics, we propose a general matrix formula for the weight-average molecular weight of crosslinked polymer systems, explicitly given by (M) over bar(w) = ($) over bar(w,0) + WX0 (I - X)(-1) S-f. This equation is valid for both step and chain-growth polymerizations, including those in a nonequilibrium state irrespective of the reactor types used. In the context of the present theory, the onset of gelation is simply stated as a point at which the largest eigenvalue of the matrix X reaches unity (i.e., det(I - X) = 0). The present theory provides a unified point of view for various types of gelling systems.