Energy surfaces, model equations Subject

Equation (3.21) shows that the potential of the mean force is an effective potential energy surface created by the solute-solvent interaction. The PMF may be calculated by an explicit treatment of the entire solute-solvent system by molecular dynamics or Monte Carlo methods, or it may be calculated by an implicit treatment of the solvent, such as by a continuum model, which is the subject of this book. A third possibility (discussed at length in Section 3.3.3) is that some solvent molecules are explicit or discrete and others are implicit and represented as a continuous medium. Such a mixed discrete-continuum model may be considered as a special case of a continuum model in which the solute and explicit solvent molecules form a supermolecule or cluster that is embedded in a continuum. In this contribution we will emphasize continuum models (including cluster-continuum models). 

Chan (Chapter 6) presents a simple graphical method for estimating the free energy of EDL formation at the oxide-water interface with an amphoteric model for the acidity of surface groups. Subject to the assumptions of the EDL model, the graphical method allows a comparison of the magnitudes of the chemical and coulombic components of surface reactions. The analysis also illustrates the relationship between model parameter values and the deviation of surface potential from the Nernst equation. 

Numerical models have been relatively successful in describing the physical conditions in the solar interior. The models generally assume that the Sun consists of mass fractions of hydrogen, X, helium, T, and heavier elements, Z. The fraction Z lumps together all elements from lithium to uranium Z is often taken to be 0.02 in the models. Since X + Y + Z = I only one free parameter is left to characterize solar bulk composition. The models also assume spherical symmetry and hydrostatic equilibrium. Except for a small zone near the visible surface, temperatures inside the Sun are so high that atoms are fully ionized. The equation of state, the radiative opacity, and the energy production rates, all needed in the models as functions of temperature and density, can then be found from stellar interior and nuclear theories. Of course, matters are more complicated readers interested in stellar models may wish to consult books on that subject, for example, the one by Clayton (1968). 

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