Collective modes in simple melts: Transition from soft spheres to the hard sphere limit

Abstract

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for . Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.

Unified description of sound velocities in strongly coupled Yukawa systems of different spatial dimensionality

“…The sound velocities of strongly coupled Yukawa systems can also be obtained from infinite-frequency (instantaneous) elastic moduli, directly related to the instantaneous normal modes. [57][58][59] This approach is applicable to fluids and solids and allows to calculate both the longitudinal and transverse sound velocities in a universal manner and hence is adopted here.…”

“…The elastic waves modes (instantaneous normal modes) in the strongly coupled plasma-related fluids are rather well described by the quasilocalized charge approximation (QLCA), 8,9,60 also known as the quasicrystalline approximation (QCA). 58,61,62 This approximation relates wave dispersion relations to the interparticle interaction potential φ(r) and the equilibrium radial distribution function (RDF) g(r), characterizing structural properties of the system. It can be considered as either a generalization of the random phase approximation or as a generalization of the phonon theory of solids.…”

Elastic properties of dense hard-sphere fluids

“…Based on our previous experience with strongly coupled fluids with isotropic purely repulsive interactions, an approximate equality K K S can be expected [29][30][31]. In particular, in a recent study of fluids with IPL potentials (∝ r − ), this approximate relation has been verified in the entire region where the conventional expressions for the elastic moduli are applicable ( 25) [11]. Figure 1 compares the elastic moduli defined by Eqs.…”

“…In our previous study of collective motion in IPL melts [11], it was observed that the conventional expressions for the elastic moduli are apparently applicable down to −1 ∼ 0.04. The question of how the HS limit is approached for 0 −1 0.04 remains unsolved and we hope to address it in future work.…”

Self-diffusion in single-component Yukawa fluids

“…This value has been obtained using the fitting formula by Daligault [34], adopting Γ m ;172 at the fluid-solid phase transition [17]. The hard-sphere result for the self-diffusion near freezing is somewhat smaller D R ;0.02 [49], possibly signaling the crossover between soft sphere and hard sphere regimes of collective motion and transport [50]. All this implies that certain tendencies identified in this work are unlikely specific to the Yukawa interaction potential, but can be applicable to other model and real systems, provided the interactions are soft enough.…”