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Register a new userThermal motions in complex liquids: the 2D Lennard-Jones liquid
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Added by
Alexander Patashinski
Publication date
2017
fields
Physics
and research's language is
English
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Thermal motions in the 2D Lennard-Jones liquid near solidification are studied at equilibrium and under shear flow conditions. At the temperatures of the study, the liquid is significantly aggregated. On times of few to few tens of particles vibration periods, the dominant features are particles in-cage vibrations and the highest frequency longitudinal and transverse Hypersound. On time-scales of hundreds to thousands of vibration periods, the liquid appears spatially heterogeneous. On these times, slow non-oscillatory fluctuating currents persist for surprisingly long times; the hierarchical dynamics of the heterogeneous liquid results in changing temperature, density, and velocity profiles across the system. Heterogeneity fades, and a crossover to non-fluctuational Hydrodynamics is observed for smoothing times of many tens of thousands vibration periods. On these asymptotically-large times, the liquid is spatially homogeneous except for thin layers near the boundaries where the degree of crystallinity increases and the mobility decreases due to liquid-boundary interactions.
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The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets is found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well defined core or surface. The environment of the nucleating droplets form randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. We also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.
In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulations of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph at all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant. A similar invariance is not seen along the isotherm or the isochore. Using a spatially non-local hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorph invariant on all length scales studied. This analysis implies the existence of a novel length scale which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast, the reduced-unit dynamics of the mass density is not invariant at length scales longer than the inter-particle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units at long length scales can be eliminated by scaling with $gamma$, a fundamental quantity in the isomorph theory framework, an empirical observation that remains to be explained theoretically.
Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, {it J. Chem. Phys.} {bf 152}, 011102 (2020)] with isomorph theory, from a single simulation, the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature range where the vant Hoffs assumption that energetic and entropic forces are temperature independent is valid. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the vant Hoffs assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from only a single simulation.
We numerically investigated the connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile is the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.
Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the ``exact values obtained from their relations to excess energy and pressure. Some consequences, in particular, in the context of the Lindemanns melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.
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