Matsoukas Themis
Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USA.
Entropy (Basel). 2020 Oct 20;22(10):1181. doi: 10.3390/e22101181.
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.
我们对不可逆二元聚集体进行了严格的热力学处理。我们将斯莫卢霍夫斯基系综构建为在固定数量的合并事件中达到的离散有限分布集，并在此系综上定义一个概率测度，使得平均场近似中的平均分布由斯莫卢霍夫斯基方程支配。在标度极限下，这个系综产生了一组与熟悉的统计热力学相同的关系。热力学处理的核心要素是选择泛函，它是可行分布的泛函，将分布的概率与聚集模型的细节联系起来。我们得到了一般核的标度表达式以及常数核、和核与积核特殊情况的封闭形式结果。我们研究了最概然分布的稳定性，给出了溶胶 - 凝胶转变的判据，并通过简单的热力学论证得到了凝胶后区域的分布。
