Equilibrium and kinetic analysis of the condensation of multifunctional units in the limit of high functionality

Abstract
Experimental data' has recently been obtained on the cluster size distributions for antigen-coated microspheres crosslinked by antibody molecules. A theoretical analysis of this system, assuming that thermo-dynamic equilibrium has been achieved, and using the appropriate bonding rules for this antigen-antibody system, results in a prediction that the cluster size distribution has the following form where Xm is the mole fraction of clusters containing m microspheres, Xo is the mole fraction of the total number of microspheres originally put into solution, and b is the mean number of bonds per microsphere. This distribution is identical to the Flory-Stockmayer distribution for the self-condensation of multi-functional units in the limit of high functionality. For such a distribution the sol-gel transition occurs at b=0.5.