Consequences of minimising pair correlations in fluids for dynamics, thermodynamics and structure

ABSTRACT

Liquid-state theory, computer simulation and numerical optimisation are used to investigate the extent to which positional correlations of a hard-sphere fluid – as characterised by the radial distribution function and the two-particle excess entropy – can be suppressed via the introduction of auxiliary pair interactions. The corresponding effects of such interactions on total excess entropy, density fluctuations and single-particle dynamics are explored. Iso-g processes, whereby hard-sphere-fluid pair structure at a given density is preserved at higher densities via the introduction of a density-dependent, soft repulsive contribution to the pair potential, are considered. Such processes eventually terminate at a singular density, resulting in a state that – while incompressible and hyperuniform – remains unjammed and exhibits fluid-like dynamic properties. The extent to which static pair correlations can be suppressed to maximise pair disorder in a fluid with hard cores, determined via direct functional maximisation of two-body excess entropy, is also considered. Systems approaching a state of maximised two-body entropy display a progressively growing bandwidth of suppressed density fluctuations, pointing to a relation between ‘stealthiness’ and maximal pair disorder in materials.

KEYWORDS:

• Hyperuniformity
• density fluctuations
• pair correlations
• entropy
• liquid structure

Acknowledgments

This work was partially supported by the National Science Foundation (1247945) and the Welch Foundation (F-1696). We acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The packing fraction of D-dimensional spherical particles of diameter d is given by φ = v_D(d)ρ, where v_D(d) = π^D/2(d/2)^D/Γ(1 + D/2).

2. Positive definiteness of S(k) is a practical and strong, necessary [19] condition for realisability of a given radial distribution function at given φ. More constraints are likely required to guarantee realisability of a packing, though understanding the nature and importance of these constraints remains an active area of research [20].

3. Hyperuniformity is characteristic of close-packed crystalline states, though disordered isotropic materials (i.e. maximally randomly jammed packings and the systems studied in this work) can also meet this criterion. [21,22]

4. The singular density is a direct consequence of halting pair structure evolution and can be understood as follows. Holding g(r) constant is equivalent to fixing , a quantity that exhibits a global negative minimum at k = 0 for hard spheres (typical of any purely repulsive system). Thus, there always exists a singular density, ρ_s, at which .

5. ‘Stealthy’ packings can be either ordered or disordered structurally. For the former, perfect crystals (no lattice displacements due to thermal motion or otherwise) are ‘stealthy’ at all wavevectors not associated with Bragg scattering. For the latter, special disordered point patterns have been constructed that specifically suppress a span of low k structure  [39,40].

6. One solves for , rather than , in order to avoid numerical error induced by ringing about the core discontinuity upon transforming back to r-space.

7. The full pair potentials βu(r) obtained in the inverse IET framework are defined by literal HS potentials (βu_HS = ∞ for r < d and βu_HS = 0 otherwise) combined with βu_{F, IET}(r) potentials that are non-zero only for r ≥ d. To approximate βu(r) with continuous potentials, we superimpose βu_WCA(r) and βu_F(r), where βu_F(r) is the potential βu_{F, IET}(r) extended linearly for r ≤ d according to the derivative d[βu_{F, IET}(r)]/dr at r → d⁺. This ensures smoothness of the superimposed potential at all r.

8. This reflects the squeezing out of vibrational motion (entropy) in locally trapped configurations or ‘basins of attraction’. It is in these configurational basins that a hard sphere system would become dynamically trapped upon compression [1,10] (neglecting so called ‘rattler’ particles).

9. This mixture ratio is based on preliminary simulations, where we observe that potentials from the HNC and PY closures over- and under-suppress structural correlations, respectively. RPA and MS closures yield very similar results to that of the HNC and PY closures, respectively.

10. This is presumably a result of the structural over-prediction of the underlying HS fluid within the HNC approximation.

Additional information

Funding

National Science Foundation [grant number 1247945] and the Welch Foundation [grant number F-1696].