How to mix molecules with mathematics

J. Molenaar, B. van 't Hof, L. Ros, M. Zaal

Research output: Chapter in Book/Report/Conference proceedingConference paperAcademicpeer-review

Abstract

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general.
Original languageEnglish
Title of host publicationProceedings of the Sixty-Seventh European Study Group Mathematics with Industry, 26-30 January 2009, Wageningen, The Netherlands
Pages47-65
Publication statusPublished - 2009
EventProceedings of the Sixty-Seventh European Study Group Mathematics with Industry, Wageningen, The Netherland -
Duration: 26 Jan 200930 Jan 2009

Conference

ConferenceProceedings of the Sixty-Seventh European Study Group Mathematics with Industry, Wageningen, The Netherland
Period26/01/0930/01/09

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