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Open AccessArticle

Statistical Mechanics of Discrete Multicomponent Fragmentation

Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USA
Condens. Matter 2020, 5(4), 64; https://doi.org/10.3390/condmat5040064
Received: 7 September 2020 / Revised: 13 October 2020 / Accepted: 15 October 2020 / Published: 18 October 2020
(This article belongs to the Section Condensed Matter Theory)
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.
Keywords: discrete fragmentation; multicomponent; partition function; multiplicity of distribution discrete fragmentation; multicomponent; partition function; multiplicity of distribution
MDPI and ACS Style

Matsoukas, T. Statistical Mechanics of Discrete Multicomponent Fragmentation. Condens. Matter 2020, 5, 64.

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