The Smoluchowski Ensemble—Statistical Mechanics of Aggregation

Entropy

Themis Matsoukas¹ 

[1] Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USA;

关键词: statistical thermodynamics;    irreversible aggregation;    Smoluchowski equation;    gelation;    phase transitions;   

DOI  :  10.3390/e22101181

来源: DOAJ

【 摘 要 】

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

【 授权许可】

Unknown