Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

Abstract

We employ Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and Modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions that the system is strongly over-compressed or supercooled, respectively. The theoretical results are compared to new crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation-of-state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MVbased virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good.The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our new crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

“…However, assessment of the core dynamical ideas of ECNLE theory for structurally complex viscous liquids involves two uncertainties: 1) the accuracy of the required pair structure information as computed using approximate integral equation theory, and 2) validity of the mapping. This recently motivated our combined theoretical and simulation analysis (42,44) which established specific links between dynamics, pair structure, and S 0 predicted by ECNLE theory for the metastable hard sphere fluid for which 1) is minimized and 2) is eliminated. A key prediction (42) is that the total barrier (logarithm of the alpha time in units of a short elementary time τ 0 ) scales inversely with S 0 to an integer power equal to unity in the noncooperative regime (log τ α = ( τ 0 ) ∝ βF B ∝ S −1 0 ) in which collective elasticity effects are negligible and three in the deeply supercooled cooperative regime, log τ α = ( τ 0 ) ∝ β F B + F el ( )∝ S −3 0 (Fig.…”

Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids

“…Similar results have been obtained for the case of hard-disk fluids and their mixtures 26 . More recently, the MV closure relation has been used in overcompressed and supercooled metastable hard-sphere fluids 27 , as well as in the study of correleations and nonuniversal effects in glass-forming liquids 28 , with good results overall.…”

“…In this work, we follow the original proposal by Verlet 13 , and rely on the particular formulation of the modified Ver-let (MV) approximation, which has proven to be an excellent approximation in several applications of the hard-sphere fluid [24][25][26][27][28] . Through the enforcement of compressibility consistency, the free parameters of the closure relation are found.…”

Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States

“…One may empirically deem a system to be nearly or effectively hyperuniform if H is roughly less than about 10 −4 [32]. The H index has been profitably used to quantify the effective hyperuniformity of polymer systems [49,50], amorphous ices [51], states along the metastable extension of the hard-sphere systems away from jamming [52] and low-temperature states of "quantizer" systems [53,54].…”

“…This formula is obtained by using exact results at low and high packing fractions and assuming that B is a cubic polynomial in φ (without a constant term). Specifically, the linear and quadratic terms are determined by the exact expansion of S(k) − S 0 in powers of φ through second order in φ, as determined from the the exact formula (52). The remaining cubic term is found by using the fact that B is exactly equal to 1/12 for the integer lattice at φ = 1 [1].…”