Viscoelasticity of fluids with steeply repulsive potentials

Abstract

We consider the infinite frequency moduli and time correlation functions of fluids composed of particles that interact through a steeply repulsive potential of the general analytic form, φ(r)=kBT exp[−αf(r)], where α is a measure of the steepness or stiffness of the potential. Although these potentials have different analytical forms, in the steeply repulsive limit of α→∞, the derived properties become almost identical and are only dependent on the value of α and other basic variables. All the infinite frequency moduli which we study are proportional to α and the interaction part of the pressure is only weakly dependent on α. For the force and other configurational property time functions C(t), time t can be replaced by αt, i.e., C(t)=1−T*(αt*)2+O[(αt*)4], where T*=kBT/ε, is the reduced temperature, kB is Boltzmann’s constant, where ε is a characteristic energy for the potential, and t* is a reduced time. We proved this in earlier publications for an inverse power, r−n potential (where α≡n), and show here this more general relationship. The effective hard-sphere diameter by the Barker–Henderson equation, and an alternative prescription derived here, give to first order in α−1 the same formula for the effective hard-sphere diameter for these potentials. We have carried out molecular-dynamics simulations that confirm the equivalence in the steeply repulsive limit of both the static and dynamical properties of two such potentials, which have an inverse power r−n and exponential potential exp(−κr) form. We consider that the theory for the infinite frequency shear rigidity modulus presented here could be usefully applied to predict the infinite frequency storage modulus of colloidal liquids.