Monte Carlo simulation of polymer adsorption
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Monte Carlo simulation of polymer adsorption Christopher J. Rasmussen · Aleksey Vishnyakov · Alexander V. Neimark
Received: 15 May 2010 / Accepted: 12 January 2011 / Published online: 26 January 2011 © Springer Science+Business Media, LLC 2011
Abstract We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation. Keywords Monte Carlo · Chemical potential · Flexible chains · Lennard-Jones · Gauge cell · Polymers 1 Introduction The ability to calculate the free energy of confined chain molecules is one of the key issues in modeling various processes that involve polymer adsorption, including polymer chromatography, membrane separation, petrochemical processing, and more. In molecular simulations, free energies are typically obtained via thermodynamic integration along a continuous path of equilibrium states connecting the system of interest to a system where the free energy is known, or using various techniques for obtaining C.J. Rasmussen · A. Vishnyakov · A.V. Neimark () Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, NJ 08854-8054, USA e-mail: [email protected]
the chemical potential in the system of interest that typically require insertions (or, in some cases, removals) of new molecules into the system, tracing back to the Widom particle insertion technique and the grand canonical MC method (Widom 1963; Norman and Filinov 1969). The efficiency of all insertion-based techniques diminishes swiftly as the density and the molecule size increase, due a high probability of inserted particles overlaping with exisiting ones. For polymer molecules, this problem is aggravated dramatically as the polymer length increases, and the confinement of the molecule within pores makes insertions even more difficult. Two general approaches to solving these problems have been developed. The first approach is based on “growing” the trial molecules into available (low energy) space with a configurational bias (Rosenbluth and Rosenbluth 1955; Frenkel et al. 1991; de Pablo et al. 1992); this is the so-called Rosenbluth insertion. This approach suffers from two drawbacks: first, as the fluid becomes denser, only short chains can “find” low energy configurations, and second, the trial chains are not generated according
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