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Register a new userHomogeneous and heterogeneous nucleation of Lennard-Jones liquids
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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.
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The phase diagram of the prototypical two-dimensional Lennard-Jones system, while extensively investigated, is still debated. In particular, there are controversial results in the literature as concern the existence of the hexatic phase and the melting scenario. Here, we study the phase behaviour of 2D LJ particles via large-scale numerical simulations. We demonstrate that at high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. As the temperature decreases, the density range where the hexatic phase occurs shrinks so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.
The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, $langle K rangle$, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that $langle K rangle$ increases exponentially with $beta = 1/k_BT$ and with pressure, $P$ in agreement with previous results in the literature. A method is illustrated for using $langle K rangle (beta, P)$ to generate a phase diagram for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
Efficient implementations of the classical molecular dynamics (MD) method for Lennard-Jones particle systems are considered. Not only general algorithms but also techniques that are efficient for some specific CPU architectures are also explained. A simple spatial-decomposition-based strategy is adopted for parallelization. By utilizing the developed code, benchmark simulations are performed on a HITACHI SR16000/J2 system consisting of IBM POWER6 processors which are 4.7 GHz at the National Institute for Fusion Science (NIFS) and an SGI Altix ICE 8400EX system consisting of Intel Xeon processors which are 2.93 GHz at the Institute for Solid State Physics (ISSP), the University of Tokyo. The parallelization efficiency of the largest run, consisting of 4.1 billion particles with 8192 MPI processes, is about 73% relative to that of the smallest run with 128 MPI processes at NIFS, and it is about 66% relative to that of the smallest run with 4 MPI processes at ISSP. The factors causing the parallel overhead are investigated. It is found that fluctuations of the execution time of each process degrade the parallel efficiency. These fluctuations may be due to the interference of the operating system, which is known as OS Jitter.
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.
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.
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