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Register a new userCoupling of sedimentation and liquid structure: influence on hard sphere nucleation
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The discrepancy in nucleation rate densities between simulated and experimental hard spheres remains staggering and unexplained. Suggestively, more strongly sedimenting colloidal suspensions of hard spheres nucleate much faster than weakly sedimenting systems. In this work we consider firstly the effect of sedimentation on the structure of colloidal hard spheres, by tuning the density mismatch between solvent and colloidal particles. In particular we investigate the effect on the degree of five fold symmetry present. Secondly we study the size of density fluctuations in these experimental systems in comparison to simulations. The density fluctuations are measured by assigning each particle a local density, which is related to the number of particles within a distance of 3.25 particle diameters. The standard deviation of these local densities gives an indication of the fluctuations present in the system. Five fold symmetry is suppressed by a factor of two when sedimentation is induced in our system. Density fluctuations are also increased by a factor of two in experiments compared to simulations. The change in five fold symmetry makes a difference to the expected nucleation rates, but we demonstrate that it is ultimately too small to resolve the discrepancy between experiment and simulation, while the fluctuations are shown to be an artefact of 3d particle tracking.
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Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius $delta_c$, for four different models: maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, and inherent structures of the quantizer energy. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. Often, $delta_c$ is used as the key characteristic length scale that determines the fluid permeability $k$. A recent study [Torquato. Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of $k$ based on the second moment of the pore size $langledelta^2rangle$. Here, we confirm that, for all porosities and all models considered, $delta_c^2$ is to a good approximation proportional to $langledelta^2rangle$. However, unlike $langledelta^2rangle$, the permeability estimate based on $delta_c^2$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $langledelta^2rangle$ to be a promising candidate for convenient and reliable estimates of $k$ for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the $tau$ order metric. We find that (effectively) hyperuniform models tend to have lower values of $k$ than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
High strength-to-weight ratio materials can be constructed by either maximizing strength or minimizing weight. Tensegrity structures and aerogels take very different paths to achieving high strength-to-weight ratios but both rely on internal tensile forces. In the absence of tensile forces, removing material eventually destabilizes a structure. Attempts to maximize the strength-to-weight ratio with purely repulsive spheres have proceeded by removing spheres from already stable crystalline structures. This results in a modestly low density and a strength-to-weight ratio much worse than can be achieved with tensile materials. Here, we demonstrate the existence of a packing of hard spheres that has asymptotically zero density and yet maintains finite strength, thus achieving an unbounded strength-to-weight ratio. This construction, which we term Dionysian, is the diametric opposite to the Apollonian sphere packing which completely and stably fills space. We create tools to evaluate the stability and strength of compressive sphere packings. Using these we find that our structures have asymptotically finite bulk and shear moduli and are linearly resistant to every applied deformation, both internal and external. By demonstrating that there is no lower bound on the density of stable structures, this work allows for the construction of arbitrarily lightweight high-strength materials.
Polyvalent metal melts (gallium, tin, bismuth, etc.) have microscopic structural features, which are detected by neutron and X-ray diffraction and which are absent in simple liquids. Based on neutron and X-ray diffraction data and results of textit{ab initio} molecular dynamics simulations for liquid gallium, we examine the structure of this liquid metal at atomistic level. Time-resolved cluster analysis allows one to reveal that the short-range structural order in liquid gallium is determined by a range of the correlation lengths. This analysis performed over set of independent samples corresponding to equilibrium liquid phase discloses that there are no stable crystalline domains as well as molecule-like Ga$_2$ dimers typical for crystal phases of gallium. Structure of liquid gallium can be reproduced by the simplified model of the close-packed system of soft quasi-spheres. The results can be applied to analyze the fine structure of other polyvalent liquid metals.
We study the thermodynamics of binary mixtures wherein the volume fraction of the minority component is less than the amount required to form a flat interface. Based on an explicit microscopic mean field theory, we show that the surface tension dominated equilibrium phase of a polymer mixture forms a single macroscopic droplet. A combination of elastic interactions that renormalize the surface tension, and arrests phase separation for a gel-polymer mixture, stabilize a micro-droplet phase. We compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the importance of the rheological properties of the solvent in dictating the thermodynamic phase behavior of biopolymers undergoing liquid-liquid phase separation.
We demonstrate that the time evolution of the van Hove dynamical pair correlation function is governed by adiabatic forces that arise from the free energy and by superadiabatic forces that are induced by the flow of the van Hove function. The superadiabatic forces consist of drag, viscous, and structural contributions, as occur in active Brownian particles, in liquids under shear and in lane forming mixtures. For hard sphere liquids we present a power functional theory that predicts these universal force fields in quantitative agreement with our Brownian dynamics simulation results.
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