Enhancing tracer diffusivity by tuning interparticle interactions and coordination shell structure

Abstract

This study uses a combination of stochastic optimization, statistical mechanical theory, and molecular simulation to test the extent to which the long-time dynamics of a single tracer particle can be enhanced by rationally modifying its interactions-and hence static correlations-with the other particles of a dense fluid. Specifically, a simulated annealing strategy is introduced that, when coupled with test-particle calculations from an accurate density functional theory, finds interactions that maximize either the tracer's partial molar excess entropy or a related pair-correlation measure (i.e., two quantities known to correlate with tracer diffusivity in other contexts). The optimized interactions have soft, Yukawa-like repulsions, which extend beyond the hard-sphere interaction and disrupt the coordination-shell cage structure surrounding the tracer. Molecular and Brownian dynamics simulations find that tracers with these additional soft repulsions can diffuse more than three times faster than bare hard spheres in a moderately supercooled fluid, despite the fact that the former appear considerably larger than the latter by conventional definitions of particle size.62 ‡ These authors contributed equally to this work.

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

“…These interactions are known to be of a repulsive Yukawa form at large inter-particle separations and strongly believed, in accordance with predictions from approximate integral equation theories, to be of a simple repulsive ramp-like form near contact for the step-function HS iso-g process [21,24,25]. Interestingly, a ramp-like interparticle potential was also recently shown to remove the coordination-shell structure of a tracer solute in a HS solvent [14,40], and a ramp-like fluid-wall interaction is known to similarly 'flatten' the density profile of a confined HS fluid [41]. To clarify the above issues, we seek to address the general accuracy of integral equation theory predictions for an iso-g process, as tested by molecular dynamics (MD) simulations, and confirm the possibly generic ramp-like interparticle potential form that apparently emerges for iso-g processes that initiate from HS fluid reference states.…”

“…The core prevents particles from approaching closer than a particle diameter d; i.e., g(r) = 0 for r < d. In dense fluids, packing constraints provided by the cores also give rise to a decaying oscillatory structure in g(r) for r > d, signifying the coordination shells that naturally form around the particles. The coordination-shell structure quantified by the radial distribution function is critical for the thermodynamic properties (e.g., the equation of state) of the fluid, but it can influence transport properties as well [13,14]. * truskett@che.utexas.edu…”

Predicting the structure of fluids with piecewise constant interactions: Comparing the accuracy of five efficient integral equation theories

“…2, along with the corresponding cumulative squared errors as calculated via Eq. (8). For this interaction, the analytic solutions (FMSA and EFMSA) perform better at higher rather than at lower equilibrium fluid densities.…”

“…Excess entropy, its two-body approximation, and p 0 have been shown to correlate with various dynamic properties of equilibrium fluids, e.g. diffusivity or viscosity [8,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Mode-coupling theory also predicts that dynamic phenomena can be directly estimated from knowledge of the static structure factor [32].…”

“…Recent applications include designing materials that self-assemble into specific crystalline lattices [3][4][5][6], fluids that display optimized structural correlations and related transport properties [7][8][9], or solids that exhibit specific optical characteristics [10]. Inverse design problems are commonly addressed by stochastic optimization strategies like simulated annealing.…”