Thermodynamic computer simulation

A presentation of molecular dynamics and Monte Carlo simulations as natural extensions of the theoretical treatment of statistical thermodynamics. I philosophically subscribe to the notion that computer simulations significantly augment our natural capacity to study and understand the natural world and that they are as useful and accurate as their underlying theory. Solidly founded on the theoretical concepts of statistical thermodynamics, computer simulations can become a potent instrument for assisting efforts to understand and engineer the microcosm. 

D. Nicholson, N. D. Parsonage. Computer Simulation and the Statistical Thermodynamics of Adsorption. New York Academic Press, 1983. 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

Computer simulation generates information at the microscopic level, and the conversion of this information into macroscopic terms is the province of statistical thermodynamics. An experimentally observable property A is just the time average of A(F) taken over a long time interval,... 

The use of computer simulations to study internal motions and thermodynamic properties is receiving increased attention. One important use of the method is to provide a more fundamental understanding of the molecular information contained in various kinds of experiments on these complex systems. In the first part of this paper we review recent work in our laboratory concerned with the use of computer simulations for the interpretation of experimental probes of molecular structure and dynamics of proteins and nucleic acids. The interplay between computer simulations and three experimental techniques is emphasized (1) nuclear magnetic resonance relaxation spectroscopy, (2) refinement of macro-molecular x-ray structures, and (3) vibrational spectroscopy. The treatment of solvent effects in biopolymer simulations is a difficult problem. It is not possible to study systematically the effect of solvent conditions, e.g. added salt concentration, on biopolymer properties by means of simulations alone. In the last part of the paper we review a more analytical approach we have developed to study polyelectrolyte properties of solvated biopolymers. The results are compared with computer simulations. 

The linkage of microscopic and macroscopic properties is not without challenges, both theoretical and experimental. Statistical mechanics and thermodynamics provide the connection between molecular properties and the behavior of macroscopic matter. Coupled with statistical mechanics, computer simulation of the structure, properties, and dynamics of mesoscale models is now feasible and can handle the increase in length and time scales. 

Molecular dynamics and Monte Carlo simulations have been extensively applied to molten salts since 1968 to study structure, thermodynamic properties, and dynamic properties from a microscopic viewpoint. Several review papers have been published on computer simulation of molten salts. " Since the Monte Carlo method cannot yield dynamic properties, MD methods have been used to calculate dynamic properties. 

The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3-6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11-18]. The picture that emerged from... 

Patapoff, T. W., Mrsny, R. J., and Lee, W. A., The application of size exclusion chromatography and computer simulation to study the thermodynamic and kinetic parameters for short-lived dissociable protein aggregates, Anal. Bio-chem., 212, 71, 1993. 

The determination of the character and location of phase transitions has been an active area of research from the early days of computer simulation, all the way back to the 1953 Metropolis et al. [59] MC paper. Within a two-phase coexistence region, small systems simulated under periodic boundary conditions show regions of apparent thermodynamic instability [60] simulations in the presence of an explicit interface eliminate this at some cost in system size and equilibration time. The determination of precise coexistence boundaries was usually done indirectly, through the... 

Our point of view is that the evaluation of the partition function (9.5) can be done by using any available tool, specifically including computer simulation. If that computer simulation evaluated the mechanical pressure, or if it simulated a system under conditions of specified pressure, then /C,x would have been determined at a known value of p. With temperature, composition, and volume also known, (9.2) and (9.1) permit the construction of the full thermodynamic potential. This establishes our first assertion that the potential distribution theorem provides a basis for the general theory of solutions. 

The first of these assumptions, generally accepted in macromolecular chemistry [1,3], is correct enough when considering the propagation reaction under copolymerization of the majority of monomers. Simple estimates reported in paper [74] support the correctness of the second assumption. As for the third one, it is true, strictly speaking, only under 0-conditions. The conformational statistics of macromolecules in a thermodynamically good solvent is known [30] to differ from the Gaussian one. Nevertheless, this distinction may hardly influence the qualitative conclusions of the simplest theory of interphase copolymerization. To which extent the account of the excluded volume of macromolecules will affect quantitative results of this theory, may be revealed exclusively by computer simulations. 

Whilst this Chapter is primarily concerned with the methods of determining the free energies of tautomeric or ionisation equilibria via computer simulation of free energy differences, many of the issues raised relate also to the determination of other molecular properties upon which behaviour of the molecule within the body may depend, such as the redox potential or the partition coefficient.6 In the next section, we shall give a brief explanation of the methods used to calculate these free energy differences -namely the use of a thermodynamic cycle in conjunction with ab initio and free energy perturbation (FEP) methods. This enables an explicit representation of the solvent environment to be used. In depth descriptions of the various simulation protocols, or the accuracy limiting factors of the simulations and methods of validation, have not been included. These are... 

A central issue in statistical thermodynamic modelling is to solve the best model possible for a system with many interacting molecules. If it is essential to include all excluded-volume correlations, i.e. to account for all the possible ways that the molecules in the system instantaneously interact with each other, it is necessary to do computer simulations as discussed above, because there are no exact (analytical) solutions to the many-body problems. The only analytical models that can be solved are of the mean-field type. 

To test these theoretical approaches in a computer simulation, one needs to proceed in several steps. In the first step, one determines the entropy per monomer in the simulation by measuring the energy per monomer e(p, T) and by calculating the free energy per monomer through thermodynamic integration of the excess chemical potential96... 

Given this background, we can now provide several examples of how free volumes have been related to thermodynamic and dynamic properties of liquids, and how their measurement has been employed in computer simulations to derive microscopic insights that are otherwise not accessible from experiment. We consider first how to compute thermodynamic values from free volumes and follow that with the relationship of free volumes to dynamics. 

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