arXiv subjects

Peter H. Poole

Publications and source records attributed to Peter H. Poole.

34 records · Page 2Linked to original sources

arXiv2009

Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics

In simulations of supercooled, high-density liquid silica we study a range of temperature T in which we find both crystal nucleation, as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower T, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization limit on the liquid state in this case. We also explore the relation of the HNL to the Kauzmann temperature, and test for spinodal-like effects near the HNL.

cond-mat.mtrl-sci↗

arXiv2009

Spectral statistics of the quenched normal modes of a network-forming molecular liquid

We evaluate the density of states of the quenched normal modes of ST2 water, and their statistical fluctuations, for a range of densities spanning three regimes of behavior of a hydrogen bonded liquid: a lower-density regime of random tetrahedral network formation; in the vicinity of a liquid-liquid critical point; and in a higher-density regime of fragile glass-forming behavior. For all cases we find that the fluctuations around the mean spectral densities obey the predictions of the Gaussian orthogonal ensemble of random matrix theory. We also measure the participation ratio of the normal modes across the entire frequency range, and find behavior consistent with the majority of modes being of an extended nature, rather than localized.

cond-mat.soft↗

arXiv2006

Granular circulation in a cylindrical pan: simulations of reversing radial and tangential flows

Granular flows due to simultaneous vertical and horizontal excitations of a flat-bottomed cylindrical pan are investigated using event-driven molecular dynamics simulations. In agreement with recent experimental results, we observe a transition from a solid-like state, to a fluidized state in which circulatory flow occurs simultaneously in the radial and tangential directions. By going beyond the range of conditions explored experimentally, we find that each of these circulations reverse their direction as a function of the control parameters of the motion. We numerically evaluate the dynamical phase diagram for this system and show, using a simple model, that the solid-fluid transition can be understood in terms of a critical value of the radial acceleration of the pan bottom; and that the circulation reversals are controlled by the phase shift relating the horizontal and vertical components of the vibrations. We also discuss the crucial role played by the geometry of the boundary conditions, and point out a relationship of the circulation observed here and the flows generated in vibratory conveyors.

cond-mat.mtrl-sci↗

arXiv2006

Structural and dynamical heterogeneity in a glass forming liquid

We use the ``isoconfigurational ensemble'' [Phys. Rev. Lett. {\bf 93}, 135701 (2004)] to analyze both dynamical and structural properties in simulations of a glass forming molecular liquid. We show that spatially correlated clusters of low potential energy molecules are observable on the time scale of structural relaxation, despite the absence of spatial correlations of potential energy in the instantaneous structure of the system. We find that these structural heterogeneities correlate with dynamical heterogeneities in the form of clusters of low molecular mobility.

cond-mat.mtrl-sci↗

arXiv2006

Fractional Stokes-Einstein and Debye-Stokes-Einstein relations in a network forming liquid

We study the breakdown of the Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) relations for translational and rotational motion in a prototypical model of a network-forming liquid, the ST2 model of water. We find that the emergence of ``fractional'' SE and DSE relations at low temperature is ubiquitous in this system, with exponents that vary little over a range of distinct physical regimes. We also show that the same fractional SE relation is obeyed by both mobile and immobile dynamical heterogeneities of the liquid.

cond-mat.soft↗

arXiv2006

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modelled by the BKS potential. We find that at density $ρ=4.38$~g/cm$^3$, spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events. We then use parallel, constrained Monte Carlo simulations to evaluate $ΔG(n)$, the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200 and 3300 K. We find that the prediction of CNT for the n-dependence of $ΔG(n)$ fits reasonably well to the data at all T studied, and at 3300 K yields a chemical potential difference between liquid and stishovite that matches independent calculation. We find that $n^*$, the size of the critical nucleus, is approximately 10 silicon atoms at T=3300 K. At 3000 K, $n^*$ decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of $ΔG(n)$ when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of $ΔG(n)$ at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g. the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude.

cond-mat.soft↗

arXiv2005

Density minimum and liquid-liquid phase transition

We present a high-resolution computer simulation study of the equation of state of ST2 water, evaluating the liquid-state properties at 2718 state points, and precisely locating the liquid-liquid critical point (LLCP) occurring in this model. We are thereby able to reveal the interconnected set of density anomalies, spinodal instabilities and response function extrema that occur in the vicinity of a LLCP for the case of a realistic, off-lattice model of a liquid with local tetrahedral order. In particular, we unambiguously identify a density minimum in the liquid state, define its relationship to other anomalies, and show that it arises due to the approach of the liquid structure to a defect-free random tetrahedral network of hydrogen bonds.

cond-mat.stat-mech↗

arXiv2004

Phase diagram of silica from computer simulation

We evaluate the phase diagram of the ``BKS'' potential [Van Beest, Kramer and van Santen, Phys. Rev. Lett. 64, 1955 (1990)], a model of silica widely used in molecular dynamics (MD) simulations. We conduct MD simulations of the liquid, and three crystals (beta-quartz, coesite and stishovite) over wide ranges of temperature and density, and evaluate the total Gibbs free energy of each phase. The phase boundaries are determined by the intersection of these free energy surfaces. Not unexpectedly for a classical pair potential, our results reveal quantitative discrepancies between the locations of the BKS and real silica phase boundaries. At the same time, we find that the topology of the real phase diagram is reproduced, confirming that the BKS model provides a satisfactory qualitative description of a silica-like material. We also compare the phase boundaries with the locations of liquid-state thermodynamic anomalies identified in previous studies of the BKS model.

cond-mat.mtrl-sci↗

arXiv2003

Free energy and configurational entropy of liquid silica: fragile-to-strong crossover and polyamorphism

Recent molecular dynamics (MD) simulations of liquid silica, using the ``BKS'' model [Van Beest, Kramer and van Santen, Phys. Rev. Lett. {\bf 64}, 1955 (1990)], have demonstrated that the liquid undergoes a dynamical crossover from super-Arrhenius, or ``fragile'' behavior, to Arrhenius, or ``strong'' behavior, as temperature $T$ is decreased. From extensive MD simulations, we show that this fragile-to-strong crossover (FSC) can be connected to changes in the properties of the potential energy landscape, or surface (PES), of the liquid. To achieve this, we use thermodynamic integration to evaluate the absolute free energy of the liquid over a wide range of density and $T$. We use this free energy data, along with the concept of ``inherent structures'' of the PES, to evaluate the absolute configurational entropy $S_c$ of the liquid. We find that the temperature dependence of the diffusion coefficient and of $S_c$ are consistent with the prediction of Adam and Gibbs, including in the region where we observe the FSC to occur. We find that the FSC is related to a change in the properties of the PES explored by the liquid, specifically an inflection in the $T$ dependence of the average inherent structure energy. In addition, we find that the high $T$ behavior of $S_c$ suggests that the liquid entropy might approach zero at finite $T$, behavior associated with the so-called Kauzmann paradox. However, we find that the change in the PES that underlies the FSC is associated with a change in the $T$ dependence of $S_c$ that elucidates how the Kauzmann paradox is avoided in this system. Finally, we also explore the relation of the observed PES changes to the recently discussed possibility that BKS silica exhibits a liquid-liquid phase transition, a behavior that has been proposed to underlie the observed polyamorphism of amorphous solid silica.

cond-mat.mtrl-sci↗

arXiv2002

Bulk motion of granular matter in an agitated cylindrical bed

Experimental results are reported for the bulk motion induced in a bed of granular matter contained in a cylindrical pan with a flat bottom subjected to simultaneous vertical and horizontal vibrations. The motion in space of the moving pan is quantified. A number of distinct bulk dynamical modes are observed in which the particle bed adopts different shapes and motions. At the lowest pan excitation frequency $ω$, the bed forms a ``heap,'' and rotates about the cylinder axis. As $ω$ is increased, a more complex ``toroidal'' mode appears in which the bed takes the shape of a torus; in this mode, circulation occurs both about the cylinder axis, and also radially, with particles moving from the outer edge of the pan to the centre on the top surface of the bed, and back to the outer edge along the pan bottom. At the highest $ω$, surface modulations (``surface waves'' and ``sectors'') of the toroidal mode occur. The origin of this family of behavior in terms of the pan motion is discussed.

cond-mat.mtrl-sci↗

arXiv2001

Influence of mass polydispersity on dynamics of simple liquids and colloids

We conduct molecular dynamics computer simulations of a system of Lennard-Jones particles, polydisperse in both size and mass, at a fixed density and temperature. We test for and quantify systematic changes in dynamical properties that result from polydispersity, by measuring the pair distribution function, diffusion coefficient, velocity autocorrelation function, and non-Gaussian parameter, as a function of the degree of polydispersity. Our results elucidate the interpretation of experimental studies of collective particle motion in colloids, and we discuss the implications of polydispersity for observations of dynamical heterogeneity, in both simulations of simple liquids and colloid experiments.

cond-mat.stat-mech↗

arXiv2001

Fragile-to-strong transition and polyamorphism in the energy landscape of liquid silica

We study the static and dynamic properties of liquid silica over a wide range of temperature T and density using computer simulations. The results reveal a change in the potential energy landscape as T decreases that underlies a transition from a fragile liquid at high T to a strong liquid at low T. We also show that a specific heat anomaly is associated with this fragile-to-strong transition, and suggest that this anomaly is related to the polyamorphic behaviour of amorphous solid silica.

cond-mat.mtrl-sci↗

arXiv2000

Computer simulations of liquid silica: equation of state and liquid-liquid phase transition

We conduct extensive molecular dynamics computer simulations of two models for liquid silica [the model of Woodcock, Angell and Cheeseman, J. Phys. Chem. 65, 1565 (1976); and that of van Beest, Kramer and van Santen, Phys. Rev. Lett. 64, 1955, (1990)] to determine their thermodynamic properties at low temperature T across a wide density range. We find for both models a wide range of states in which isochores of the potential energy U are a linear function of T^(3/5), as recently proposed for simple liquids [Rosenfeld and P. Tarazona, Mol. Phys. 95, 141 (1998)]. We exploit this behavior to fit an accurate equation of state to our thermodynamic data. Extrapolation of this equation of state to low T predicts the occurrence of a liquid-liquid phase transition for both models. We conduct simulations in the region of the predicted phase transition, and confirm its existence by direct observation of phase separating droplets of atoms with distinct local density and coordination environments.

cond-mat.stat-mech↗

arXiv1998

Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature.

cond-mat.soft↗

arXiv1997

String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid

A large-scale molecular dynamics simulation is performed on a glass-forming Lennard-Jones mixture to determine the nature of dynamical heterogeneities which arise in this model fragile liquid. We observe that the most mobile particles exhibit a cooperative motion in the form of string-like paths (``strings'') whose mean length and radius of gyration increase as the liquid is cooled. The length distribution of the strings is found to be similar to that expected for the equilibrium polymerization of linear polymer chains.

cond-mat.dis-nn↗

arXiv1997

Dynamical heterogeneities in a supercooled Lennard-Jones liquid

We present the results of a large scale molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify ``mobile'' particles. We find that these particles form clusters whose size grows with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the bulk, and that this difference increases with decreasing temperature.

cond-mat.dis-nn↗