Exactly soluble addition and condensation models in coagulation kinetics

Abstract

The kinetics of clustering through addition ( a k + a 1 → a k+1 ) and condensation ( a j + a k → a j+ k , j ≠ 1, k ≠ 1) for a model of cylindrically shaped monomeric units a 1 are studied, using Smoluchowski's coagulation equation, and analytic solutions for several limiting cases (flat disks and needles) with and without condensation reactions, were given. The condensation models of flat disks and needles include, respectively, the linear polymer model RA 2 and the branched polymer model A 2RB ∞ (with a gelation transition). If condensation reactions are inhibited, we obtain exactly soluble addition models with a monomer-cluster rate constant independent of or proportional to the cluster size. The monomers are (i) supplied in a given amount at the initial time; (ii) generated by a steady source; or (iii) supplied by an infinite reservoir that keeps the concentration of monomers, c 1( t), constant in time.