Interfaces, Monte Carlo study

I. Bitsanis, G. ten Brinke. A lattice Monte Carlo study of long chain conformations at a solid polymer-melt interface. J Chem Phys 99 3100-3111, 1993. 

A. Werner, F. Schmid, M. Muller, and K. Binder (1999) Intrinsic profiles and capillary waves at homopolymer interfaces A Monte Carlo study. Phys. Rev. E 59, pp. 728-738... 

Yang, J., Winnik, M. A., The Orientation Parameter for Energy Transfer in Restricted Geometries Including Block Copolymer Interfaces a Monte Carlo Study, J. Phys. Chem. B 2005, 109, 18408 18417. 

Binder K, Landau DP, Muller M (2003) Monte Carlo studies of wetting, interface localization and capillary condensation. J StatPhys 110 1411-1514... 

This picture of chains near the surface adopting rather flattened configurations has been confirmed by computer simulations. This is clearly illustrated in figure 2.26, in which the ratio of the chain end-to-end distances normal to the interface and in the bulk is plotted as a fimction of the position of the chain (Bitsanis and ten Brinke 1993). This lattice Monte Carlo study was carried out not for a free surface, but for a hard wall however, in another study, already mentioned above, a lattice model was extended to allow for a variable density by combination with a lattice fluid equation of state theory. This explicitly... 

Lamperski, S., and A. Zydor. 2007. Monte Carlo study of the electrode solvent primitive model electrolyte interface. Electrochimica Acta 52, no. 7 (February 1) 2429-2436. doi 10.1016. electacta.2006.08.045. 

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

In this situation computer simulation is useful, since the conditions of the simulation can be chosen such that full equihbrium is established, and one can test the theoretical concepts more stringently than by experiment. Also, it is possible to deal with ideal and perfectly flat surfaces, very suitable for testing the general mechanisms alluded to above, and to disregard in a first step all the complications that real substrate surfaces have (corrugation on the atomistic scale, roughness on the mesoscopic scale, surface steps, adsorbed impurities, etc.). Of course, it may be desirable to add such complications at a later stage, but this will not be considered here. In fact, computer simulations, i.e., molecular dynamics (MD) and Monte Carlo (MC) calculations, have been extensively used to study both static and dynamic properties [11] in particular, structural properties at interfaces have been considered in detail [12]. 

D. Y. Yoon, M. Vacatello, G. D. Smith. Simulation studies of polymer melts at interfaces. In K. Binder, ed. Monte Carlo and Molecular Dynamics Simulations in Polymer Science. New York Oxford University Press, 1995, pp. 422-A15. 

The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid-liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 10 to 10 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of infinite ensembles. 

Monte Carlo simulation shows [8] that at a given instance the interface is rough on a molecular scale (see Fig. 2) this agrees well with results from molecular-dynamics studies performed with more realistic models [2,3]. When the particle densities are averaged parallel to the interface, i.e., over n and m, and over time, one obtains one-dimensional particle profiles/](/) and/2(l) = 1 — /](/) for the two solvents Si and S2, which are conveniently normalized to unity for a lattice that is completely filled with one species. Figure 3 shows two examples for such profiles. Note that the two solvents are to some extent soluble in each other, so that there is always a finite concentration of solvent 1 in the phase... 

The use of molecular dynamics and Monte Carlo simulations to study electrochemical processes at the interface between two phases is only in its preliminary stages. The need to provide a molecular-level understanding of structure and dynamics at the interface to help in interpreting the new microscopic level of experimental data will increase. However, many important basic issues remain to be understood before these computational methods become routine research tools. 

The presence of bulky, (3-branched side chains can be helix promoting or destabilizing depending on the environment. 100 The role of hydrophobic residues in helix stabilization has been studied in Ala-based peptides 106 as well as through Monte Carlo calculations. 107 The positioning of hydrophobic residues is also important. In amphiphilic helices, hydrophobic residues repeat approximately every three to four residues, such that one side of the helix is hydrophilic and one side hydrophobic. The amphiphilicity makes the peptide susceptible to helix formation in the presence of lipid-water interfaces. 108 109 ... 

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