Microscopic theories of model macromolecular fluids and fullerenes: The role of thermodynamic consistency

Abstract

We investigate the accuracy of two well-known integral equation theories (IETs) of the fluid state, namely, the modified hypernetted chain (MHNC) approximation and the hybridized mean spherical approximation (HMSA), as applied to systems characterized by short-range interactions. The theoretical approaches are implemented by enforcing their thermodynamic consistency according to two different strategies: in one case the equality of the isothermal compressibility, as calculated via the virial and fluctuation routes from structure to thermodynamics, is imposed [“local” consistency (LC)]; in the other case the equality of the pressure as calculated either via the two previous routes, or via the virial and the energy routes, is imposed [“global” consistency (GC)]. We show that for the class of potentials at issue the GC is in general considerably more accurate than the LC. We document this result by investigating the performances of the MHNC and the HMSA, as applied to the calculation of the thermodynamic and structural properties of the hard-core Yukawa (HCY) potential, the Derjaguin–Landau–Vervey–Overbeek (DLVO) potential and the Girifalco potential for fullerenes. The obtained results are then compared with Monte Carlo simulation data, that we also produce for the same model systems. As far as the HCY potential is concerned, the investigation covers a range of the Yukawa inverse decay length, z, spanning from z=1.8 when the interaction mimics the Lennard-Jones 12-6 potential, to z=7 when the potential mimics the “effective” short range interaction between globular proteins in a highly charge-screened aqueous solution. IETs are then applied to the DLVO potential with charge and Hamaker constant values which fit the dynamical interaction factor of lysozyme in a solution of high ionic strength, and to the Girifalco potential with parameters appropriate to model C60 and C70. It emerges from the present study that the GC is able to provide Helmholtz free energies and chemical potentials which compare quite favorably with the simulation data. As a consequence, we are able to show that the GC estimates of the phase coexistence densities for the HCY and Girifalco potential agree almost quantitatively with the Monte Carlo ones, by thus definitely improving upon previous results obtained within the LC. We also comment on the relevance of confident phase diagram determinations from IETs, in connection with the prediction of protein crystallization. Possible extensions of the present thermodynamic consistency strategies to more sophisticated theories and realistic models of protein solutions and fullerenes are finally suggested.