Configurational space thermodynamics

In the standard (or Smoluchowski) theory, it is assumed that inertial effects due to the mass of a bead have all relaxed away, and that a stationary flow in configuration space occurs. This flow is maintained by balancing the above total force by a thermodynamic force,... 

Lattice Monte Carlo (LMC) simulations are another approach for the study of the principles of liquids thermodynamics. In these simulations it is assumed that molecule-like objects can occupy one or more sites of a predefined regular lattice. Mostly, only nearest-neighbor interactions of the objects are allowed, resulting in a kind of surface interaction, Ey, between objects, i and j, on neighboring lattice sites. Given certain mole fractions xt of the different objects, the configuration space of such a lattice... 

We shall begin (Section II) by assembling the basic equipment. Section II.A formulates the problem in the complementary languages of thermodynamics and statistical mechanics. The shift in perspective—from free energies in the former to probabilities in the latter—helps to show what the core problem of phase behavior really is a comparison of the a priori probabilities of two regions of configuration space. Section II.B outlines the standard portfolio of MC tools and explains why they are not equal to the challenge posed by this core problem. 

MD and MC simulations have provided data on layer spacings, thermodynamic properties, as well as interlayer water configurations, interlayer-species self-diffusion coefficients, and total radial distribution functions that are consistent with experimental data. Most of the clay surface is relatively... 

FIGURE 1.15.1 Illustration of a reversible path (solid curve) connecting states 1 and 2, and of an irreversible path (dashed curve) connecting states 2 and 1. The dashed curve is meant to convey the fact that the irreversible process involves many thermodynamic coordinates which fall outside the domain of the indicated configuration space. 

State space, configuration space, phase space. An abstract space spanned by coordinate axes, one for each thermodynamic coordinate, on which a given point represents the numerical value of that coordinate. A hyperspace is then formed by a mutually orthogonal disposition of these axes about a common origin. 

Another important issue are the potential functions or potential model that are suitable to describe the macroion solution under confinement. These potential functions further are employed in a Metropolis algorithm to explore the configurational space during MC procedure to reach the thermodynamic equilibria in the entire system as well as to collect the ensemble averages. Because of the large size asymmetry of the species comprising a real macroion solution, the most widely used potential model is based on the one-component... 

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