A novel FastRSA algorithm: Statistical properties and evolution of microstructure

Abstract

While the Random Sequential Adsorption (RSA) process for the generation of 2D geometries containing discrete entities has been extensively studied, both in terms of numerical simulations and in terms of its statistical properties, all the mechanisms involved are not fully understood, especially in dense configurations of elongated particles. This is mainly due to the very slow asymptotic approach to high packing configurations, especially when highly elongated particles are involved, which makes the creation of such configurations a time consuming task. For the estimation of the statistical properties of such configurations we therefore have to resort to extrapolations that do not always give accurate results. In this work we reveal the interaction of the mechanisms that come into play in the RSA process. We specifically show that the overall result of an RSA process is the summary outcome of these interwoven mechanisms, namely those involving the formation and destruction of Particle Area, Overlap Area and Influence Area – terms which we introduce and define in this work – resulting in a behavior that often appears counter-intuitive. We also show the shift of their importance as the particle aspect ratio α varies and explain how nematic structures are created when high aspect ratio particles are involved as well as the mechanisms behind their appearance. Following this, we propose a new algorithm for the process of random sequential adsorption (named FastRSA) which is capable of creating very high count configurations through all the range of particle aspect ratios and which follows Feder’s law with a θ∼τ−1∕2 behavior instead of the θ∼τ−1∕3 of the classic approach, where τ is the number of attempts to place a particle and θ is the degree of packing. We show how the new algorithm can be coupled with the classic RSA approach and point out the benefits of such a coupling. Use of the FastRSA algorithm has enabled us to study the evolution of the extent of packing using actual geometries, without the need to resolve to extrapolations and assumptions. For the case of highly elongated particles, this is the first time in our knowledge that estimations of maximum packing from actual configurations near the jamming limit have been obtained.