Pair potential models thermodynamic

M. Hemmati et al., in Comparison of Pair-Potential Models for the Simulation of Liquid Si02 Thermodynamic, Angular-Distribution, and Dijfusional Properties, in Physics Meets Mineralogy Condensed-Matter Physics in Geosciences, ed. by H. Aoki, Y. Syono, R.J. Hemley (Cambridge University Press, Cambridge, 2000), p. 325 M. Benoit et al., Europhys. Lett. 60(2), 269-275 (2002)... 

In principle, the expressions for pair potentials, osmotic pressure and second virial coefficients could be used as input parameters in computer simulations. The objective of performing such simulations is to clarify physical mechanisms and to provide a deeper insight into phenomena of interest, especially under those conditions where structural or thermodynamic parameters of the studied system cannot be accessed easily by experiment. The nature of the intermolecular forces responsible for protein self-assembly and phase behaviour under variation of solution conditions, including temperature, pH and ionic strength, has been explored using this kind of modelling approach (Dickinson and Krishna, 2001 Rosch and Errington, 2007 Blanch et al., 2002). 

Pair Potentials and Modelling of Spectroscopic, Collisional, and Thermodynamic Properties of Binary Complexes... 

Assume now that we are in the position to be able to calculate reliable pair potentials. The next task is to employ some statistical thermodynamic model which would permit us to pass from the pair complexes solvent-solute and solvent-solvent to a real liquid, A theoretical analysis of this problem is beyond the scope of this book, so that we restrict ourselves to stating that, in the conjucticn with ab initio calculations, the most sophisticated approach appears to be the statistical mechanics computer simulation of the finite system of N molecules in the volume V at the temperature T. The essence of the... 

The fundamental problem in classical equilibrium statistical mechanics is to evaluate the partition function. Once this is done, we can calculate all the thermodynamic quantities, as these are typically first and second partial derivatives of the partition function. Except for very simple model systems, this is an unsolved problem. In the theory of gases and liquids, the partition function is rarely mentioned. The reason for this is that the evaluation of the partition function can be replaced by the evaluation of the grand canonical correlation functions. Using this approach, and the assumption that the potential energy of the system can be written as a sum of pair potentials, the evaluation of the partition function is equivalent to the calculation of... 

Numerical experience accumulated so far indicates that the structure and energetics of liquid water are determined by a complex balance between various components of the interaction potential with nonadditive interactions playing a major role. This balance is certainly affected by thermodynamic conditions. Therefore, one cannot expect the empirical effective pair potentials, in which the nonadditive effects are included by distorting the parr interactions, to provide a universal model of water capable of correct predictions outside of the range of conditions which determined the potential parameters. 

The foremost thermodynamic property associated with any phase boundary is the location of its surface in the p-V-T phase diagram. Most laboratory experiments of glass formation are carried out in a particular V-T plane, usually for atmospheric pressure, and the temperature dependence of volume through the transition is determined. If the glass transition is indeed dictated by the repulsive part of the potential, we expect, at least for simple steeply repulsive systems, that it will occur at the same molecular-reduced volume for many real and model systems and that this will be largely insensitive to the strength of the attractive component of the pair potential relative to kT. 

In this section, we derive some general statistical mechanical expressions for the thermodynamic quantities of solvation which are independent of any assumptions about the model. We shall later examine special cases of these relations for either a molecular model for water (in terms of a model pair potential) or for a specific mixture-model view of liquid water. 

The second approach is to extend the simple two-parameter corresponding-states principle at its molecular origin. This is accomplished by making the intermolecular potential parameters functions of the additional characterization parameters /I, and the thermodynamic state, for example, the density p and temperature T. This can be justified theoretically on the basis of results obtained by performing angle averaging on a non-spherical model potential and by apparent three-body effects in the intermolecular pair potential. The net result of this substitution is a corresponding-states model that has the same mathematical form as the simple two-parameter model, but the definitions of the dimensionless volume and temperature are more complex. In particular the... 

Ramakrishnan and Zukoski (2000) extended the work of Rosenbaum et al. and tested the ability of different pair potentials to characterize the interactions and phase behavior of STA. The strength of interaction was controlled by dispersing STA in different salt concentrations. The experimental variables used in characterizing the interactions were the osmotic compressibility (dP/dp), the second virial coefficient(.82), relative solution viscosity and the solubility. Various techniques were then developed to extract the parameters ofthe square well, the adhesive hard sphere and the Yukawa pair potentials that best describe the experimental data. As mentioned before, the adhesive hard sphere potential describes the solution thermodynamics only where the system is weakly attractive but as would be expected fails when long range repulsions come into play at low salt concentrations. Model free representations were then presented which offer the opportunity to extract pair potential parameters (F/g. 19-8). 

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