Critical behavior of the particle mass spectra in a family of gelling systems.
The critical and post-critical behavior of coagulating systems, where the coagulation efficiency grows with the masses of colliding particles g and l as K(g,l)=0.5(g(alpha)(l)(beta)+g(beta)(l)(alpha), lambda=alpha+beta>1, mu=/alpha - beta/ <1 is studied. The instantaneous sink that removes the particles with masses exceeding G is introduced which allows one to describe the coagulation kinetics by a finite set of equations and define the gel as the deposit of particles with masses between G+1 and 2G . This system displays the critical behavior (the sol-gel transition) in the limit G-->infinity if lambda=alpha+beta>1. The exact post-critical particle mass spectrum is shown to be an algebraic function of g times a growing exponent. All critical parameters of the systems are determined as the functions of alpha and beta .
Lushnikov
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Department of Physical Sciences, University of Helsinki, P.O. Box 64, FI-00014, Helsinki, Finland.