Thermodynamic microscopic approach

Metallic Solutions, Thermodynamics of (Oriani) Microscopic Approach to Equilibrium and Non-Equilibrium Properties of Electrolytes (Resibois and Hasselle-Schuermans). ... 

This problem is analogous to describing the behavior of a gas using Newton s laws of motion for the individual molecules and keeping track of all their trajectories (i.e., a microscopic approach). It can be conceptualized, but in practice it is impossible. It is much more fruitful to characterize such a system in terms of the simple gas laws of thermodynamics (i.e., a macroscopic approach). The key issue is selection of an appropriate representation for the system. 

The two standard approaches in any treatment of kinetics [28] are to explain the system in terms of me thermodynamic driving forces (namely, VjJ.) or in terms of the fnndamental rate eqnations. The rate equations can be fnrther subdivided into an atomistic, or microscopic, approach that accounts for individual molecules as they go through the various processes (adsorption, desorption, diffusion, capture, and release) or a phenomenological, or macroscopic, explanation that looks for correlations and the so-called scaling laws over large distances (much larger than the lattice spacing). 

Linear response theory is an example of a microscopic approach to the foundations of non-equilibrium thermodynamics. It requires knowledge of the Hamiltonian for the underlying microscopic description. In principle, it produces explicit formulae for the relaxation parameters that make up the Onsager coefficients. In reality, these expressions are extremely difficult to evaluate and approximation methods are necessary. Nevertheless, they provide a deeper insight into the physics. 

The microscopic approach has been particularly successful in the treatment of the Hall effect in electrolytes, summarized in an earlier overview [5]. As in the case of Hall conductivity, the magnitude of the magnetic field effect on diffusion is very small [6,7] but not negligible in a rigorous sense. The Llelmezs-Musbally formula [6] based on the theory of irreversible thermodynamics for bi-lonic systems ... 

This volume is spht into two parts. In the first part, Chapter 1 is dedicated to phase modehng tools and covers the modeling of a phase constracting potential characteristic functions. Chapter 2 covers the microscopic approach and presents the characteristic matrices that group together thermodynamic coefficients, from different experimental data. Chapters 3,4 and 5 cover tools used in the microscopic modeling of phases through the use of statistics of molecular objects and microcanonical and canonical spaces. The calculation of state functions from molecular data allow the characteristic functions of a phase to be calculated. 

In Section 2 the formalism of the Master equation, our main tool in the microscopic approach developed in this chapter, is laid down. This formalism, which constitutes a convenient intermediate between purely microscopic and macroscopic theories, accounts for microscopic dynamics through the fluctuations of the macrovariables. We review the main assumptions at the basis of this description, the formal properties of its solutions, and some results established in the early literature on this subject in connection with bifurcations leading to steady-state solutions. We subsequently focus on dynamical bifurcation phenomena and discuss, successively, thermodynamic fluctuations near Hopf bifurcation (Section 3) and in the regime of deterministic chaos (Section 4). A summary and suggestions for further study are given in the final Section 5. 

To understand the basic experimental results, we will briefly examine the theoretical continuous (macroscopic) and molecular (microscopic) approaches and the physical concepts on which they are based. These two approaches supplement each other. The continuous theories use the laws of conservation which are valid for any continuous medium. The rheological and thermodynamic relations (equations of state) which complete them are derived from the general laws of mechanics and thermodynamics without the use of model concepts concerning the structure of LC and the molecular-kinetic mechanism of their flow. 

For what is probably the earliest microscopic calculations of thermodynamic cycles in proteins see Ref. 12, that reported a PDLD study of the pKtt s of some groups in lysozyme. The use of FEP approaches for studies of proteins is more recent and early studies of catalysis and binding were reported in Refs. 11, 12, and 13 of Chapter 4. 

The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface specific techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface specific experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid-liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electrified interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8-21]. 

The common disadvantage of both the free volume and configuration entropy models is their quasi-thermodynamic approach. The ion transport is better described on a microscopic level in terms of ion size, charge, and interactions with other ions and the host matrix. This makes a basis of the percolation theory, which describes formally the ion conductor as a random mixture of conductive islands (concentration c) interconnected by an essentially non-conductive matrix. (The mentioned formalism is applicable not only for ion conductors, but also for any insulator/conductor mixtures.)... 

Instead of the classical approaches, a molecular-based statistical thermodynamic theory can be applied to allow a model of adsorption to be related to the microscopic properties of the system in terms of fluid-fluid and fluid-solid interactions, pore size, pore geometry and temperature. Using such theories the whole range of pore sizes measured can be calculated using a single approach. Two simulation... 

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

Section 5.1 presents the fundamental method as the heart of the chapter— the statistical thermodynamics approach to hydrate phase equilibria. The basic statistical thermodynamic equations are developed, and relationships to measurable, macroscopic hydrate properties are given. The parameters for the method are determined from both macroscopic (e.g., temperature and pressure) and microscopic (spectroscopic, diffraction) measurements. A Gibbs free energy calculation algorithm is given for multicomponent, multiphase systems for comparison with the methods described in Chapter 4. Finally, Section 5.1 concludes with ab initio modifications to the method, along with an assessment of method accuracy. 

---