?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F594%2F&rft.title=How+to+Mix+Molecules+with+Mathematics&rft.creator=van%E2%80%99t+Hof%2C+B&rft.creator=Molenaar%2C+J&rft.creator=Ros%2C+L&rft.creator=Zaal%2C+M&rft.subject=Discrete&rft.subject=Materials&rft.subject=None%2FOther&rft.description=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%2C+the+individual+molecules+are+represented+by+their+geometrical+shape+with+an+electrical+charge+density+on+their+surfaces.+Next%2C+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%0D%0Aequations%2C+which+comprise+the+optimization+of+the+entropy+and+conservation+of+internal+energy%2C+can+efficiently+be+solved+in+general%2C+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.&rft.date=2009&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F594%2F1%2FWag3.pdf&rft.identifier=++van%E2%80%99t+Hof%2C+B+and+Molenaar%2C+J+and+Ros%2C+L+and+Zaal%2C+M++(2009)+How+to+Mix+Molecules+with+Mathematics.++%5BStudy+Group+Report%5D+++++