Hard-particle fluid compressibility

Figure 7.12 Excess chemical potential of the hard-sphere fluid as a function of density. The open and filled circles correspond to the predictions of the primitive quasi-chemical theory and the self-consistent molecular field theory, respectively. The solid and dashed lines are the scaled-particle (Percus-Yevick compressibility) theory and the Carnahan-Starling equation of state, respectively (Pratt and Ashbaugh, 2003).

Despite the absence of capillary condensation, the one-dimensional hard-rod fluid is still so useful because we have an analytic expression for its partition function [see Eq. (3.12)] that permits us to derive closed expressions for any thormophysical property of interest. One such quantity that is closely related to the Isothermal compressibility discussed in the preceding section is the particle-number distribution P (N), whidi one may also employ to compute thermomechanical properties [see, for example, Eqs. (3.65) and (3.68)]. Moreover, in a three-dimensional system P ) is useful to investigate the sj stem-size dependence of density fluctuations as we shall demonstrate in Section 5.4.2 [see Eq. (5.80)]. 

This procedure is conceptually straightforward, as one utilizes the very definition of the isothermal compressibility and its connection to the number fluctuations. Furthermore, Eqs. (141) and (142) are very advantageous when studying quantum hard-sphere fluids, since the error bars of the pressure estimates are far more controllable than when using the virial pressure involving Fierz s term [96]. By extension, the same is expected to happen when studying quantum fluids in which very strong repulsions between the particles play a dominant role. 

Before concluding this discussion of surface tension let us make a more careful analysis of these intercorrelations of properties for which the scaled particle theory has been used. The approach assumes that the thermodynamic derivatives can be interrelated by the properties of a hard-sphere fluid. In particular, the compressibility, thermal expansion, and surface tension can be related to one another. The ability to relate the surface tension to the other properties is unique to the scaled particle theory and it is not possible to test the consistency of the approach to that relation. However, for the hard-sphere scaled particle solution to relate the thermal expansion coefficient and the compressibility we must have d UjdV )x T d SldV )rp, This requirement is obvious when the thermal expansion... 

Another option is to dissolve large particles of dmgs in aqueous or organic solution followed by wet granulation or fluid bed granulation. Compress the granules into tablets or fill into hard gelatin capsules. Nevertheless, solubilization... 

---