Polymerisation processes with intrapolymer bonding. II. Stratified processes

Abstract

We consider a polymerisation process stratified in that space is divided into regions, between which migration occurs, but with bonding occurring only within a region. In the case of a process whose specification is spatially homogeneous, criticality (gelation) is then easily detectable as the point at which statistical equidistribution over regions becomes unstable. Stratification does import a new feature, however, in that the equipartition solution can become metastable below criticality; local fluctuations of density can induce ‘gelational collapse’ at a density below the critical value. We derive also detailed results for the inhomogeneous case, both below and above criticality. Statistics of polymer size and structure are also easily determined in the stratified case, although one can locate the critical point without recourse to these. Finally, one can to a large extent treat the case in which inter- and intrapolymer reaction rates differ, and show that such difference affects the onset of metastability rather than of instability.