Cross-linking of Identical Particles by Multiple Ligand-Types

This paper uses branching processes to model the cross-linking of identical particles by multiple ligand-types. We derive gel points and mole- and weight-average cluster sizes for Binomial and Poisson bonding.In Immunology, this model might apply to cross-linking by antibodies specific to different antigenic sites. It represents a refinement of the Goldberg-Watson theory of immune complex formation and makes predictions readily tested by experiment.The model makes the undesirable assumption that no intramolecular bonding occurs. Relaxation of this assumption is mathematically challenging and is of interest to polymer chemists.