GENERAL MATRIX FORMULA FOR THE WEIGHT-AVERAGE MOLECULAR-WEIGHTS OF CROSS-LINKED POLYMER SYSTEMS

On the basis of the first-order Markovian statistics, we propose a gen eral matrix formula for the weight-average molecular weight of crossli nked polymer systems, explicitly given by (M) over bar(w) = ($) over b ar(w,0) + WX0 (I - X)(-1) S-f. This equation is valid for both step an d chain-growth polymerizations, including those in a nonequilibrium st ate irrespective of the reactor types used. In the context of the pres ent 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 variou s types of gelling systems. (C) 1998 John Wiley & Sons, Inc.