Structural Relaxation of a Gel Modeled by Three Body Interactions

We report a molecular dynamics simulation study of a model gel whose interaction potential is obtained by modifying the three body Stillinger-Weber model potential for silicon. The modification reduces the average coordination number, and suppresses the liquid-gas phase coexistence curve. The low density, low temperature equilibrium gel that can thus form exhibits interesting dynamical behavior, including compressed exponential relaxation of density correlations. We show that motion responsible for such relaxation has ballistic character, and arises from the motion of chain segments in the gel without the restructuring of the gel network.Comment: 5 pages, 5 figure

Configurational temperature in active matter. II. Quantifying the deviation from thermal equilibrium

This paper suggests using the configurational temperature \Tc for quantifying how far an active-matter system is from thermal equilibrium. We measure this ``distance'' by the ratio of the systemic temperature \Ts to \Tc, where \Ts is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. \Tc is ``local'' in the sense that it is the average of a function, which only depends on how the potential energy varies in the vicinity of a given configuration; in contrast \Ts is a global quantity. The quantity \Ts/\Tc is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine \Ts/\Tc. We validate the suggestion that \Ts/\Tc quantifies the deviation from thermal equilibrium by data for the radial distribution function of 3d Kob-Andersen and 2d Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that \Ts/\Tc, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation (MIPS) boundary in the phase diagram of the 2d Yukawa model. The measure \Ts/\Tc is not limited to active matter; it can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium.Comment: Paper I is available at arXiv:2204.0681

Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model

This paper shows that the configurational temperature of liquid-state theory, \Tc, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's \Tc for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, demonstrating lines of approximate reduced-unit invariance of the radial distribution function and time-dependent mean-square displacement.Comment: Paper II is available at arXiv:2212.0904

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.</p

Computer Simulation Study of the Phase Behavior and Structural Relaxation in a Gel-Former Modeled by Three Body Interactions

We report a computer simulation study of a model gel-former obtained by modifying the three-body interactions of the Stillinger-Weber potential for silicon. This modification reduces the average coordination number and consequently shifts the liquid-gas phase coexistence curve to low densities, thus facilitating the formation of gels without phase separation. At low temperatures and densities, the structure of the system is characterized by the presence of long linear chains interconnected by a small number of three coordinated junctions at random locations. At small wave-vectors the static structure factor shows a non-monotonic dependence on temperature, a behavior which is due to the competition between the percolation transition of the particles and the stiffening of the formed chains. We compare in detail the relaxation dynamics of the system as obtained from molecular dynamics with the one obtained from Monte Carlo dynamics. We find that the bond correlation function displays stretched exponential behavior at moderately low temperatures and densities, but exponential relaxation at low temperatures. The bond lifetime shows an Arrhenius behavior, independent of the microscopic dynamics. For the molecular dynamics at low temperatures, the mean squared displacement and the (coherent and incoherent) intermediate scattering function display at intermediate times a dynamics with ballistic character and we show that this leads to compressed exponential relaxation. For the Monte Carlo dynamics we find always an exponential or stretched exponential relaxation. Thus we conclude that the compressed exponential relaxation observed in experiments is due to the out-of-equilibrium dynamics

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard–Jones Systems

In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF