Density, thermodynamic Terms Links

Such a form of quasi-equilibrium distribution takes place due to the fact of the availability of two invariants of motion. In Equation 25 parameters a and p linked to the operators Hz and Hss are thermodynamically conjugative parameters for the Zeeman energy and the energy of spin-spin interactions respectively. We can expand the exponent in Equation 25 in jxjwers of xT-Lz and f Hss and keep only the linear terms. As we shall see later such a linearization corresponds to the high temperature approximation. In the linear approximation in x Hz and Hss, the density matrix is reduced to... 

While linking structure and thermodynamics based on the virial expression is not straightforward, this link can in fact be established using an alternative desciiptiOTi based on Kirkwood-Buff (KB) theory [76], Whereas the virial route requires information on the effective potential, the KB description does not make any assumption on the nature of the potentials, is exact, and its central quantities can be interpreted in terms of local solution structure. To this end, we consider the derivatives of the salt activity with respect to the density at constant pressure p and temperature T. For the systems shown in Fig. 5 these derivatives show the same order as the osmotic coefficients/salt activities for the different ions [70]. Hence, the microscopic mechanism explaining the order among the derivatives of the salt activity for the different ions also explains the Hofmeister series for the activities obtained by integration of the derivatives. Based on this, the relation between... 

Solubility. Solubihty of a polymer will reflect the compatibility with the solvent. For a polymer to be dissolved there is a requirement for the forces between the solvent to match those between the elements of the polymer itself If the match is close, then it is possible to create a situation in which the dissolved polymer is in a collapsed state corresponding to the thermodynamic requirements of the theta condition. At this point the forces between the segments balance the forces between the segments and the solvent. If the strength of the interaction is increased, the quality of the solvent is improved and the effective size of the polymer increases it swells. Thermoplastic polymers can be completely dissolved in a good solvent, whereas thermoset materials are only able to swell to a size that reflects the cross-link density of the matrix. It is possible for two nonsolvents to combine to form a solvating mixture, and this phenomenon is termed co-solvency (see Miscibility). 

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