GELATION AND CLUSTER GROWTH WITH CLUSTER-WALL INTERACTIONS

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side rea ctions of metal atoms with the polymer matrix: [GRAPHICS] where lambda > 0 and where c(k) denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the poly mer matrix For reaction with metallic atoms. The initial conditions ar e required to be nonnegative and satisfy Sigma(j=1)(infinity) jc(j)(0) = 1 and p(0) = p(0). We assume that R-jk = [dj(alpha)k(alpha) + (j k)(j(alpha) + k(alpha))]/(d + j + k) for 0 less than or equal to alpha less than or equal to 1, which encompasses both bond linking kernels (R-jk = j(alpha)k(alpha)) and surface reaction kernels (R-jk = j(alpha ) + k(alpha)). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in ot hers. We provide numerical evidence that gelation occurs for the class ical coagulation equations (lambda = 0) with the bond linking kernel ( d --> infinity) for 1/2 < alpha less than or equal to 1. We examine th e relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on lambda(-1) in the limiting case R-jk = jk, p(0) = 1.