arXiv subjects

Peter H. Poole

Publications and source records attributed to Peter H. Poole.

At least 19 recordsLinked to original sources

arXiv2021

Liquid-liquid phase transition in simulations of ultrafast heating and decompression of amorphous ice

A recent experiment [K. H. Kim, et al., Science 370, 978 (2020)] showed that it may be possible to detect a liquid-liquid phase transition (LLPT) in supercooled water by subjecting high density amorphous ice (HDA) to ultrafast heating, after which the sample reportedly undergoes spontaneous decompression from a high density liquid (HDL) to a low density liquid (LDL) via a first-order phase transition. Here we conduct computer simulations of the ST2 water model, in which a LLPT is known to occur. We subject various HDA samples of this model to a heating and decompression protocol that follows a thermodynamic pathway similar to that of the recent experiments. Our results show that a signature of the underlying equilibrium LLPT can be observed in a strongly out-of-equilibrium process that follows this pathway despite the very high heating and decompression rates employed here. Our results are also consistent with the phase diagram of glassy ST2 water reported in previous studies.

cond-mat.stat-mech↗

arXiv2021

Free energy surface of two-step nucleation

We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] by comparing the predictions of the theory to numerical results for the FES recently reported from Monte Carlo simulations of TSN in a simple lattice system [James, et al., J. Chem. Phys. 150, 074501 (2019)]. No adjustable parameters are used to make this comparison. That is, all the parameters of the theory are evaluated directly for the model system, yielding a predicted FES which we then compare to the FES obtained from simulations. We find that the theoretical FES successfully predicts the numerically-evaluated FES over a range of thermodynamic conditions that spans distinct regimes of behavior associated with TSN. All the qualitative features of the FES are captured by the theory and the quantitative comparison is also very good. Our results demonstrate that Iwamatsu's extension of classical nucleation theory provides an excellent framework for understanding the thermodynamics of TSN.

cond-mat.stat-mech↗

arXiv2019

Surface tension of supercooled water nanodroplets from computer simulations

We estimate the liquid-vapour surface tension from simulations of TIP4P/2005 water nanodroplets of size $N$=100 to 2880 molecules over a temperature $T$ range of 180 K to 300 K. We compute the planar surface tension $γ_p$, the curvature-dependent surface tension $γ_s$, and the Tolman length $δ$, via two approaches, one based on the pressure tensor (the "mechanical route") and the other on the Laplace pressure (the "thermodynamic route"). We find that these two routes give different results for $γ_p$, $γ_s$ and $δ$, although in all cases we find that $δ\ge 0$ and is independent of $T$. Nonetheless, the $T$ dependence of $γ_p$ is consistent between the two routes and with that of Vega and de Miguel [J. Chem. Phys. 126, 154707 (2007)] down to the crossing of the Widom line at 230 K for ambient pressure. Below 230 K, $γ_p$ rises more rapidly on cooling than predicted from behavior for $T\ge 300$ K. We show that the increase in $γ_p$ at low $T$ is correlated to the emergence of a well-structured random tetrahedral network in our nanodroplet cores, and thus that the surface tension can be used as a probe to detect behavior associated with the proposed liquid-liquid phase transition in supercooled water.

cond-mat.soft↗

arXiv2019

The stability-limit conjecture revisited

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region, and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this reentrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si.

cond-mat.stat-mech↗

arXiv2018

Phase transitions in fluctuations and their role in two-step nucleation

We consider the thermodynamic behavior of local fluctuations occurring in a stable or metastable bulk phase. For a system with three or more phases, a simple analysis based on classical nucleation theory predicts that small fluctuations always resemble the phase having the lowest surface tension with the surrounding bulk phase, regardless of the relative chemical potentials of the phases. We also identify the conditions at which a fluctuation may convert to a different phase as its size increases, referred to here as a "fluctuation phase transition" (FPT). We demonstrate these phenonena in simulations of a two dimensional lattice model by evaluating the free energy surface that describes the thermodynamic properties of a fluctuation as a function of its size and phase composition. We show that a FPT can occur in the fluctuations of either a stable or metastable bulk phase and that the transition is first-order. We also find that the FPT is bracketed by well-defined spinodals, which place limits on the size of fluctuations of distinct phases. Furthermore, when the FPT occurs in a metastable bulk phase, we show that the superposition of the FPT on the nucleation process results in two-step nucleation (TSN). We identify distinct regimes of TSN based on the nucleation pathway in the free energy surface, and correlate these regimes to the phase diagram of the bulk system. Our results clarify the origin of TSN, and elucidate a wide variety of phenomena associated with TSN, including the Ostwald step rule.

cond-mat.stat-mech↗

arXiv2018

Evaluating the Laplace pressure of water nanodroplets from simulations

We calculate the components of the microscopic pressure tensor as a function of radial distance r from the centre of a spherical water droplet, modelled using the TIP4P/2005 potential. To do so, we modify a coarse-graining method for calculating the microscopic pressure [T. Ikeshoji, B. Hafskjold, and H. Furuholt, Mol. Simul. 29, 101 (2003)] in order to apply it to a rigid molecular model of water. As test cases, we study nanodroplets ranging in size from 776 to 2880 molecules at 220 K. Beneath a surface region comprising approximately two molecular layers, the pressure tensor becomes approximately isotropic and constant with r. We find that the dependence of the pressure on droplet radius is that expected from the Young-Laplace equation, despite the small size of the droplets.

cond-mat.soft↗

arXiv2017

"Swarm relaxation": Equilibrating a large ensemble of computer simulations

It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\barτ$, where $\barτ$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.

cond-mat.stat-mech↗

arXiv2017

Influence of sample preparation on the transformation of low-density to high-density amorphous ice: An explanation based on the Potential Energy Landscape

Experiments and computer simulations of the transformations of amorphous ices display different behavior depending on sample preparation methods, and on the rates of change of temperature and pressure to which samples are subjected. In addition to these factors, simulation results also depend strongly on the chosen water model. Using computer simulations of the ST2 water model, we study how the sharpness of the compression-induced transition from low-density amorphous ice (LDA) to high-density amorphous ice (HDA) is influenced by the preparation of LDA. By studying LDA samples prepared using widely different procedures, we find that the sharpness of the LDA-to- HDA transformation is correlated with the depth of the initial LDA sample in the potential energy landscape (PEL), as characterized by the inherent structure energy. Our results show that the complex phenomenology of the amorphous ices reported in experiments and computer simulations can be understood and predicted in a unified way from a knowledge of the PEL of the system.

cond-mat.stat-mech↗

arXiv2016

Potential Energy Landscape of the Apparent First-Order Phase Transition between Low-Density and High-Density Amorphous Ice

The potential energy landscape (PEL) formalism is a valuable approach within statistical mechanics for describing supercooled liquids and glasses. Here we use the PEL formalism and computer simulations to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) at different temperatures. We employ the ST2 water model for which the LDA-HDA transformations are remarkably sharp, similar to what is observed in experiments, and reminiscent of a first-order phase transition. Our results are consistent with the view that LDA and HDA configurations are associated with two distinct regions (megabasins) of the PEL that are separated by a potential energy barrier. At higher temperature, we find that low-density liquid (LDL) configurations are located in the same megabasin as LDA, and that high-density liquid (HDL) configurations are located in the same megabasin as HDA. We show that the pressure-induced LDL-HDL and LDA-HDA transformations occur along paths that interconnect these two megabasins, but that the path followed by the liquid is different than the path followed by the amorphous solid. At higher pressure, we also study the liquid-to-ice-VII first-order phase transition, and find that the behavior of the PEL properties across this transition are qualitatively similar to the changes found during the LDA-HDA transformation. This similarity supports the interpretation that the LDA-HDA transformation is a first-order-like phase transition between out-of-equilibrium states.

cond-mat.stat-mech↗

arXiv2015

Phase diagram of the ST2 model of water

We evaluate the free energy of the fluid and crystal phases for the ST2 potential [F.H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)] with reaction field corrections for the long-range interactions. We estimate the phase coexistence boundaries in the temperature-pressure plane, as well as the gas-liquid critical point and gas-liquid coexistence conditions. Our study frames the location of the previously identified liquid-liquid critical point relative to the crystalline phase boundaries, and opens the way for exploring crystal nucleation in a model where the metastable liquid-liquid critical point is computationally accessible.

cond-mat.stat-mech↗

arXiv2015

Free energy of formation of small ice nuclei near the Widom line in simulations of supercooled water

The ST2 interaction potential has been used in a large number of simulation studies to explore the possibility of a liquid-liquid phase transition (LLPT) in supercooled water. Using umbrella sampling Monte Carlo simulations of ST2 water, we evaluate the free energy of formation of small ice nuclei in the supercooled liquid in the vicinity of the Widom line, the region above the critical temperature of the LLPT where a number of thermodynamic anomalies occur. Our results show that in this region there is a substantial free energy cost for the formation of small ice nuclei, demonstrating that the thermodynamic anomalies associated with the Widom line in ST2 water occur in a well-defined metastable liquid phase. On passing through the Widom line, we identify changes in the free energy to form small ice nuclei that illustrate how the thermodynamic anomalies associated with the LLPT may influence the ice nucleation process.

cond-mat.stat-mech↗

arXiv2014

Two-state thermodynamics of the ST2 model for supercooled water

Thermodynamic properties of the ST2 model for supercooled liquid water exhibit anomalies similar to those observed in real water. A possible explanation of these anomalies is the existence of a metastable, liquid-liquid transition terminated by a critical point. This phenomenon, whose possible existence in real water is the subject of much current experimental work, has been unambiguously demonstrated for this particular model by most recent simulations. In this work, we reproduce the anomalies of two versions of the ST2 model with an equation of state describing water as a non-ideal "mixture" of two different types of local molecular order. We show that the liquid-liquid transition in the ST2 water is energy-driven. This is in contrast to another popular model, mW, in which non-ideality in mixing of two alternative local molecular orders is entropy-driven, and is not sufficiently strong to induce a liquid-liquid transition.

physics.chem-ph↗

arXiv2013

Heterogeneous Nucleation in the Low Barrier Regime

In simulations of the 2D Ising model, we examine heterogeneous nucleation induced by a small impurity consisting of a line of $l$ fixed spins. As $l$ increases, we identify a limit of stability beyond which the metastable phase is not defined. We evaluate the free energy barrier for nucleation of the stable phase, and show that contrary to expectation, the barrier does not vanish on approach to the limit of stability. We also demonstrate that our values for the height of the barrier yield predictions for the nucleation time (from transition state theory) and the size of the critical cluster (from the nucleation theorem) that are in excellent agreement with direct measurements, even near the limit of stability.

cond-mat.stat-mech↗

arXiv2012

Free energy surface of ST2 water near the liquid-liquid phase transition

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.

cond-mat.stat-mech↗

arXiv2011

Dynamical Behavior Near a Liquid-Liquid Phase Transition in Simulations of Supercooled Water

We examine the behavior of the diffusion coefficient of the ST2 model of water over a broad region of the phase diagram via molecular dynamics simulations. The ST2 model has an accessible liquid-liquid transition between low-density and high-density phases, making the model an ideal candidate to explore the impacts of the liquid-liquid transition on dynamics. We locate characteristic dynamical loci in the phase diagram and compare them with the previously investigated thermodynamic loci. The low-density liquid phase shows a crossover from non-Arrhenius to Arrhenius behavior, signaling the onset of a crossover from fragile-to-strong behavior. We explain this crossover in terms of the asymptotic approach of the low-density liquid to a random tetrahedral network, and show that the temperature dependence of the diffusion coefficient over a wide temperature range can be simply related to the concentration of defects in the network. Our findings thus confirm that the low-density phase of ST2 water is a well-defined metastable liquid.

cond-mat.stat-mech↗

arXiv2011

Mixture-like behavior near a liquid-liquid phase transition in simulations of supercooled water

In simulations of a water-like model (ST2) that exhibits a liquid-liquid phase transition, we test for the occurrence of a thermodynamic region in which the liquid can be modelled as a two-component mixture. We assign each molecule to one of two species based on the distance to its fifth-nearest neighbor, and evaluate the concentration of each species over a wide range of temperature and density. Our concentration data compare well with mixture-model predictions in a region between the liquid-liquid critical temperature and the temperature of maximum density. Fits of the model to the data in this region yield accurate estimates for the location of the critical point. We also show that the liquid outside the region of density anomalies is poorly modelled as a simple mixture.

cond-mat.stat-mech↗

arXiv2010

Spatial Correlation of the Dynamic Propensity in a Glass-Forming Liquid

We present computer simulation results on the dynamic propensity [as defined by Widmer- Cooper, Harrowell, and Fynewever, Phys. Rev. Lett. 93, 135701 (2004)] in a Kob-Andersen binary Lennard-Jones liquid system consisting of 8788 particles. We compute the spatial correlation function of the dynamic propensity as a function of both the reduced temperature T, and the time scale on which the particle displacements are measured. For T\leq0.6, we find that nonzero correlations occur at the largest length scale accessible in our system. We also show that a cluster-size analysis of particles with extremal values of the dynamic propensity, as well as 3D visualizations, reveal spatially correlated regions that approach the size of our system as T decreases, consistent with the behavior of the spatial correlation function. Next, we define and examine the "coordination propensity", the isoconfigurational average of the coordination number of the minority B particles around the majority A particles. We show that a significant correlation exists between the spatial fluctuations of the dynamic and coordination propensities. In addition, we find non-zero correlations of the coordination propensity occurring at the largest length scale accessible in our system for all T in the range 0.466<T<1.0. We discuss the implications of these results for understanding the length scales of dynamical heterogeneity in glass-forming liquids.

cond-mat.mtrl-sci↗

arXiv2010

Simulations of a lattice model of two-headed linear amphiphiles: influence of amphiphile asymmetry

Using a 2D lattice model, we conduct Monte Carlo simulations of micellar aggregation of linear-chain amphiphiles having two solvophilic head groups. In the context of this simple model, we quantify how the amphiphile architecture influences the critical micelle concentration (CMC), with a particular focus on the role of the asymmetry of the amphiphile structure. Accordingly, we study all possible arrangements of the head groups along amphiphile chains of fixed length $N=12$ and 16 molecular units. This set of idealized amphiphile architectures approximates many cases of symmetric and asymmetric gemini surfactants, double-headed surfactants and boloform surfactants. Consistent with earlier results, we find that the number of spacer units $s$ separating the heads has a significant influence on the CMC, with the CMC increasing with $s$ for $s<N/2$. In comparison, the influence of the asymmetry of the chain architecture on the CMC is much weaker, as is also found experimentally.

cond-mat.soft↗