Monte-Carlo simulations of methane/carbon dioxide and ethane/carbon dioxide mixture adsorption in zeolites and comparison with matrix treatment of statistical mechanical lattice model Lawrence J. Dunne a , Akrem Furgani b , Sayed Jalili b , George Manos b, * a Department of Engineering Systems, London South Bank University, London SE1 0AA, UK b Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK article info Article history: Received 12 November 2008 Accepted 28 February 2009 Available online 6 March 2009 Keywords: Mixture adsorption Monte-Carlo simulation Lattice model abstract Adsorption isotherms have been computed by Monte-Carlo simulation for methane/carbon dioxide and ethane/carbon dioxide mixtures adsorbed in the zeolite silicalite. These isotherms show remarkable dif- ferences with the ethane/carbon dioxide mixtures displaying strong adsorption preference reversal at high coverage. To explain the differences in the Monte-Carlo mixture isotherms an exact matrix calcula- tion of the statistical mechanics of a lattice model of mixture adsorption in zeolites has been made. The lattice model reproduces the essential features of the Monte-Carlo isotherms, enabling us to understand the differing adsorption behaviour of methane/carbon dioxide and ethane/carbon dioxide mixtures in zeolites. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Mixtures of simple gases can be separated by adsorption in zeo- lites due to the special characteristics of zeolite channels which may be designed to allow adsorption to selectively occur on the ba- sis of molecular size and shape [1–4]. However, due to the diffi- culty of experiments, no adsorption isotherms have been published for methane/carbon dioxide and ethane/carbon dioxide mixtures at fixed gas phase composition. As an alternative to experiments, in this paper we present the results of Grand Canon- ical Monte-Carlo (GCMC) simulations for methane/carbon dioxide and ethane/carbon dioxide mixture adsorption in the zeolite silica- lite. These show remarkable differences with the ethane/carbon dioxide mixtures displaying adsorption preference reversal at high coverage. However, despite their predictive capacity Monte-Carlo calculations do not provide a simple interpretation of the isotherm structure. Thus to explain the differences in the Monte-Carlo mix- ture isotherms an exact calculation of the statistical mechanics of a lattice model of mixture adsorption in zeolites has been performed. The mixture Grand Partition function for methane/carbon dioxide and ethane/carbon dioxide mixtures adsorbed in a zeolite channel is calculated exactly using a previously described matrix method [5]. Approximate treatments, such as mean-field theory, are well known as being incorrect in one-dimensional systems [6,7] by erroneously predicting phase transitions which may show as artefactual steps in adsorption isotherms and hence to have confi- dence in our results an accurate statistical mechanical treatment of the one-dimensional adsorbed phase is required. A single lattice fluid model can by appropriate choice of param- eters represent molecules in the alkane/carbon dioxide mixture in various configurations in the silicalite nanochannel. Vacant sites or holes are also introduced to allow for incomplete filling of the lat- tice sites. For a wide range of interaction parameter free energies the lattice model gives unusual features in the shape of adsorption isotherms similar to those observed in Monte-Carlo simulations for ethane–carbon dioxide mixtures adsorption in silicalite thereby allowing us to interpret the results of the Monte-Carlo simulations. At higher pressures carbon dioxide molecules displace ethane molecules and we have named this phenomenon in a previous publication [8] as ‘Adsorption Preference Reversal’. 2. Monte-Carlo simulations of ethane/carbon dioxide and methane/carbon dioxide mixtures in silicalite Monte-Carlo simulations of small molecule adsorption in zeo- lites have been widely discussed and undertaken [9–11]. The method for the mixture was described in a previous publication [5] and uses united atoms. We have applied the same method to Monte-Carlo simulations of ethane/carbon dioxide and methane/ carbon dioxide mixtures in silicalite. All pseudo-atoms interact via Lennard-Jones type potentials. The silicalite cage (see Fig. 1) is regarded as rigid while methane and ethane are considered as one and two pseudo-atoms as discussed previously [11]. Ideally 0301-0104/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2009.02.013 * Corresponding author. Tel.: +44 20 7679 3810; fax: +44 20 7383 2348. E-mail address: g.manos@ucl.ac.uk (G. Manos). Chemical Physics 359 (2009) 27–30 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys