ON THE FUNDAMENTALS OF THE GRADIENT THEORY OF VAN-DER-WAALS

In this study a simple relation has been derived for the influence par ameter in the gradient theory of van der Waals in terms of simple acce ssible quantities like temperature, the equilibrium densities, and the equilibrium isothermal compressibilities, Application of this relatio n leads to a substantially better agreement between interfacial tensio ns computed from the gradient theory and tensions obtained from experi ment and simulation. The basis for this novel relation is an expressio n that connects the influence parameter to the second moment of the di rect correlation function of pure fluids at states within the binodal region. The direct correlation functions for this study have been obta ined from solving of the Ornstein-Zernike equation and the Percus-Yevi ck (PY) or hypernetted chain (HNC) closure relations for a Lennard-Jon es (LJ) fluid. Special attention was paid to the behavior of solutions in the vicinity of the nonsolution region. It was shown for the PY cl osure that at the low density side the isothermal compressibility rema ins finite at the boundary of the nonsolution region. Along the isothe rms and isochors the isothermal compressibility terminates at this bou ndary in so-called square root branch points. The isothermal compressi bility diverges on the high density side although the correct location of the spinodal locus could not be found because of numerical inaccur acies. Diverging compressibilities are never encountered as the soluti on boundary is reached using the HNC closure. In all cases the isother mal compressibility terminates in square root branch points along the isotherms and isochors. In addition, computations show that at this bo undary, the second moment of the direct correlation function seems to diverge for both the PY and the HNC closure. Comparison of the tension s obtained from the gradient theory with those obtained from a partial summation of the gradient expansion shows that at low temperatures th e former results are similar to 50% higher. Comparison of the results obtained from the latter model with experiments and simulations shows good agreement. (C) 1997 American Institute of Physics.