arXiv subjects

Brian B. Laird

Publications and source records attributed to Brian B. Laird.

At least 19 recordsLinked to original sources

arXiv2025

A quantitative theory and atomistic simulation study on the soft-sphere crystal-melt interfacial properties: II. Interfacial free energies

This study proposes a new method for predicting the crystal-melt interfacial free energy ($\gamma$) using the Ginzburg-Landau (GL) model, enhanced by atomistic simulation data for more accurate density wave profiles. The analysis focuses on the soft-sphere system governed by an inverse power potential that stabilizes both BCC and FCC phases. Equilibrium molecular dynamics (MD) simulations are used to obtain density wave amplitude distributions, which serve as inputs for the GL model to predict $\gamma$ and its anisotropy. The predicted $\gamma$ values exhibit strong agreement with prior benchmark simulation experimental studies, particularly for FCC crystal-melt interfaces (CMIs). The GL models for the CMI $\gamma$ are proved to be both computationally efficient and reasonably valid, offering quantitative predictions of $\gamma$ while providing insights into the factors controlling its magnitude and anisotropy. Key improvement is suggested for the variational procedure used in the two-mode CMI free energy functionals, and potential upgrades to the GL model are also proposed to further enhance predictive accuracy.

cond-mat.mtrl-sci↗

arXiv2024

Solid-liquid interfacial free energy from computer simulations: Challenges and recent advances

The theory of interfacial properties in liquid-liquid or liquid-vapour systems is nearly 200 years old. The advent of computational tools has greatly advanced the field, mainly through the use of Molecular Dynamics simulations. Despite the successes and advances in the theory of interfacial phenomena for liquid-liquid systems, the study of solid-liquid interfaces remains a challenge both theoretically and experimentally. The main reason why the treatment of solid-liquid systems has fallen behind that of liquid-liquid systems is that there are complications that arise whenever an interface involving solid systems is considered involving both theory of the solid-liquid interface and the calculations using MD simulations. An example of the former is that, contrary to the liquid-liquid case, the interfacial properties of solids depend on the lattice orientation. The main complications in these calculations arise from the fact that for solids the ``mechanical route'' cannot be used. To overcome this problem, several numerical approaches were proposed. The main purpose of this review is to provide an overview of these different methodologies and to discuss their strengths and weaknesses. We classify these methodologies into two main groups: direct and indirect methods. Direct methods are those that can calculate directly the properties of interfaces, while in indirect approaches the properties of the interface are not the primary result of the simulations. We also included a discussion on the origin of the difficulties in considering solid interfaces from a thermodynamic point of view. In the second part of the review, we discuss two key related topics: nucleation theory and curved interfaces. They both represent an important problem in the study of interfaces and in the context of solid-liquid ones for which the research is still extremely active.

cond-mat.soft↗

arXiv2023

Coexistence of multiple interfacial states at heterogeneous solid/liquid interface

The growing trend towards engineering interfacial complexion (or phase) transitions has been seen in the grain boundary and solid surface systems.Meanwhile, little attention has been paid to the chemically heterogeneous solid/liquid interfaces. In this work, novel in-plane multi-interfacial states coexist within the Cu(111)/Pb(l) interface at a temperature just above the Pb freezing point is uncovered using atomistic simulations.Four monolayer interfacial states, i.e., two CuPb alloy liquids and two pre-freezing Pb solids, are observed coexisting within two interfacial layers sandwiched between the bulk solid Cu and bulk liquid Pb. Through computing the spatial variations of various properties along the direction normal to the in-plane solid-liquid boundary lines for both interfacial layers, a rich and varied picture depicting the inhomogeneity and anisotropy in the mechanical, thermodynamical, and dynamical properties is presented. The bulk values extracted from the in-plane profiles suggest that each interfacial state examined has distinct equilibrium values from each other and significantly deviates from those of the bulk solid and liquid phases, and indicate that the complexion (or phase) diagrams for the Cu(111)/Pb(l) interface bears a resemblance to that of the eutectic binary alloy systems, instead of the monotectic phase diagram for the bulk CuPb alloy. The reported data could support the development of interfacial complexion (or phase) diagrams and interfacial phase rules and provide a new guide for regulating heterogeneous nucleation and wetting processes.

cond-mat.mtrl-sci↗

arXiv2022

Atomistic characterization of the SiO2 high-density liquid/low-density liquid interface

The equilibrium silica liquid-liquid interface between the high-density liquid (HDL) phase and the low-density liquid (LDL) phase is examined using molecular-dynamics simulation. The structure, thermodynamics, and dynamics within the interfacial region are characterized in detail and compared with previous studies on the liquid-liquid phase transition (LLPT) in bulk silica, as well as traditional crystal-melt interfaces. We find that the silica HDL-LDL interface exhibits a spatial fragile-to-strong transition across the interface. Calculations of dynamics properties reveal three types of dynamical heterogeneity hybridizing within the silica HDL-LDL interface. We also observe that as the interface is traversed from HDL to LDL, the Si/O coordination number ratio jumps to an unexpectedly large value, defining a thin region of the interface where HDL and LDL exhibit significant mixing. In addition, the LLPT phase coexistence is interpreted in the framework of the traditional thermodynamics of alloys and phase equilibria.

cond-mat.mtrl-sci↗

arXiv2022

Local collective dynamics at equilibrium BCC crystal-melt interfaces

We present a classical molecular-dynamics study of the collective dynamical properties of the coexisting liquid phase at equilibrium body-centered cubic (BCC) Fe crystal-melt interfaces. For the three interfacial orientations (100), (110), and (111), the collective dynamics are characterized through the calculation of the intermediate scattering functions, dynamical structure factors and density relaxation times in a sequential local region of interest. An anisotropic speed up of the collective dynamics in all three BCC crystal-melt interfacial orientations is observed. This trend differs significantly different from the previously observed slowing down of the local collective dynamics at the liquid-vapor interface [Acta Mater 2020;198:281]. Examining the interfacial density relaxation times, we revisit the validity of the recently developed time-dependent Ginzburg-Landau (TDGL) theory for the solidification crystal-melt interface kinetic coefficients, resulting in excellent agreement with both the magnitude and the kinetic anisotropy of the CMI kinetic coefficients measured from the non-equilibrium MD simulations

cond-mat.mtrl-sci↗

arXiv2020

Kinetics of Crystallization and Orientational Ordering in Dipolar Particle Systems

The kinetic mechanisms underlying bottom-up assembly of colloidal particles have been widely investigated in efforts to control crystallization pathways and to direct growth into targeted superstructures for applications including photonic crystals. Current work builds on recent progress in the development of kinetic theories for crystal growth of body-centered-cubic crystals in systems with short-range inter-particle interactions, accounting for a greater diversity of crystal structures and the role of the longer-ranged interactions and orientational degrees of freedom arising in polar systems. We address the importance of orientational ordering processes in influencing crystal growth in such polar systems, thus advancing the theory beyond the treatment of the translational ordering processes considered in previous investigations. The work employs comprehensive molecular-dynamics simulations that resolve key crystallization processes, and are used in the development of a quantitative theoretical framework based on ideas from time-dependent Ginzburg-Landau theory. The significant impact of orientational ordering on the crystallization kinetics could be potentially leveraged to achieve crystallization kinetics steering through external electric or magnetic fields. Our combined theory/simulation approach provides opportunities for future investigations of more complex crystallization kinetics.

cond-mat.mtrl-sci↗

arXiv2014

Parameterizing the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy $γ$ and the excess adsorption $Γ$ are of central importance. For theoretical studies closed expression of $γ$ and $Γ$ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for $γ$ and $Γ$, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for $γ$ and $Γ$ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterizations show significant deviation at high density. In this work, we propose new parameterizations for $γ$ and $Γ$ that agree with the simulation data within statistical error over the entire fluid density range.

cond-mat.stat-mech↗

arXiv2014

Evaluation of Constant Potential Method in Simulating Electric Double-Layer Capacitors

A major challenge in the molecular simulation of electric double layer capacitors (EDLCs) is the choice of an appropriate model for the electrode. Typically, in such simulations the electrode surface is modeled using a uniform fixed charge on each of the electrode atoms, which ignores the electrode response to local charge fluctuations induced by charge fluctuations in the electrolyte. In this work, we evaluate and compare this Fixed Charge Method (FCM) with the more realistic Constant Potential Method (CPM), [Reed, et al., J. Chem. Phys., 126, 084704 (2007)], in which the electrode charges fluctuate in order to maintain constant electric potential in each electrode. For this comparison, we utilize a simplified LiClO$_4$-acetonitrile/graphite EDLC. At low potential difference ($ΔΨ\le 2V$), the two methods yield essentially identical results for ion and solvent density profiles; however, significant differences appear at higher $ΔΨ$. At $ΔΨ\ge 4V$, the CPM ion density profiles show significant enhancement (over FCM) of "partially electrode solvated" Li$^+$ ions very close to the electrode surface. The ability of the CPM electrode to respond to local charge fluctuations in the electrolyte is seen to significantly lower the energy (and barrier) for the approach of Li$^+$ ions to the electrode surface.

physics.comp-ph↗

arXiv2012

Solid-liquid interfacial premelting

We report the observation of a premelting transition at chemically sharp solid-liquid interfaces using molecular-dynamics simulations. The transition is observed in the solid-Al/liquid-Pb system and involves the formation of a liquid interfacial film of Al with a width that grows logarithmically as the bulk melting temperature is approached from below, consistent with current theories of premelting. The premelting behavior leads to a sharp change in the temperature dependence of the diffusion coefficient in the interfacial region, and could have important consequences for phenomena such as particle coalescence and shape equilibration, which are governed by interfacial kinetic processes.

cond-mat.mtrl-sci↗

arXiv2012

Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces

Using molecular-dynamics simulation, we have calculated the interfacial free energy, γ, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η= ρσ^3/6, where ρand σare the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that γfor a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to ηabout 0.42. In addition, earlier results for γfor this system [Bryk, et al., Phys. Rev. E, 68, 031602 (2003)] using a geometrically-based classical Density Functional Theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above ηabout 0.42, γ(R) shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle, to determine $γ$ for any sufficiently smooth surface immersed in a hard-sphere fluid.

cond-mat.stat-mech↗

arXiv2003

Direct calculation of the crystal-melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system

Extending to continuous potentials a cleaving wall molecular-dynamics simulation method recently developed for the hard-sphere system [Phys.Rev.Lett 85, 4751 (2000)], we calculate the crystal-melt interfacial free energies, $γ$, for a Lennard-Jones system as functions of both crystal orientation and temperature. At the triple point, T* = 0.617, the results are consistent with an earlier cleaving potential calculation by Broughton and Gilmer [J. Chem. Phys. {\bf 84}, 5759 (1986)], however, the greater precision of the current calculation allows us to accurately determine the anisotropy of $γ$. From our data we find that, at all temperatures studied, $γ_{111} < γ_{110} < γ_{100}$. Comparison is made to the results from our previous hard-sphere calculation and to recent results for Ni by Asta, Hoyt and Karma [Phys. Rev. B, 66 100101(R) (2002)].

cond-mat.mtrl-sci↗

arXiv2002

Structure and dynamics of the interface between a binary hard-sphere crystal of NaCl type and its coexisting binary fluid

Molecular dynamics simulations are performed to study the [100] and [111] orientations of the crystal-melt interface between an ordered two-component hard sphere with a NaCl structure and its coexisting binary hard-sphere fluid. The diameter ratio of the two types of hard spheres making up the mixture is taken to be 0.414. This work complements our earlier interface simulations [J. Chem. Phys.116, 3410] for the same diameter ratio at lower pressures where the smaller component is immiscible in the solid and the fluid mixture coexists with a pure FCC crystal of large particles. Density profiles and diffusion coefficient profiles are presented for the AB interfacial system. We find that for this system, the transition from crystal-like to fluid-like behavior of both the density and diffusion constant profiles occurs over a narrower region than that seen in our previous studies [J. Chem. Phys. 116, 3410] of the FCC/binary fluid system. But similar to what was found in the FCC/binary fluid interface the transition region for the large particle diffusion constant is shifted about the size of the large particles toward the fluid phase relative to that for the small particles.

physics.chem-ph↗

arXiv2002

Generating Generalized Distributions from Dynamical Simulation

We present a general molecular-dynamics simulation scheme, based on the Nose' thermostat, for sampling according to arbitrary phase space distributions. We formulate numerical methods based on both Nose'-Hoover and Nose'-Poincare' thermostats for two specific classes of distributions; namely, those that are functions of the system Hamiltonian and those for which position and momentum are statistically independent. As an example, we propose a generalized variable temperature distribution that designed to accelerate sampling in molecular systems.

cond-mat.stat-mech↗

arXiv2002

Constant-temperature molecular-dynamics algorithms for mixed hard-core/continuous potentials

We present a set of second-order, time-reversible algorithms for the isothermal (NVT) molecular-dynamics (MD) simulation of systems with mixed hard-core/continuous potentials. The methods are generated by combining real-time Nose' thermostats with our previously developed Collision Verlet algorithm [Mol. Phys. 98, 309 (1999)] for constant energy MD simulation of such systems. In all we present 5 methods, one based on the Nose'-Hoover [Phys. Rev. A 31, 1695 (1985)] equations of motion and four based on the Nose'-Poincare' [J.Comp.Phys., 151 114 (1999)] real-time formulation of Nose' dynamics. The methods are tested using a system of hard spheres with attractive tails and all correctly reproduce a canonical distribution of instantaneous temperature. The Nose'-Hoover based method and two of the Nose'-Poincare' methods are shown to have good energy conservation in long simulations.

physics.chem-ph↗

arXiv2002

Simulations of binary hard-sphere crystal-melt interfaces:Interface between a one- component fcc crystal and a binary fluid mixture

The crystal-melt interfaces of a binary hard-sphere fluid mixture in coexistence with a single-component hard-sphere crystal is investigated using molecular-dynamics simulation. In the system under study, the fluid phase consists of a two-component mixture of hard spheres of differing size, with a size ratio $α=0.414$. At low pressures this fluid coexists with a pure fcc crystal of the larger particles in which the small particles are immiscible. For two interfacial orientations, [100] and [111], the structure and dynamics within the interfacial region is studied and compared with previous simulations on single component hard-sphere interfaces. Among a variety of novel properties, it is observed that as the interface is traversed from fluid to crystal the diffusion constant of the larger particle vanishes before that of the small particle defining a region of the interface where the large particles are frozen in their crystal lattice, but the small particles exhibit significant mobility. This behavior was not seen in previous binary hard-sphere interface simulations with less asymmetric diameters.

physics.chem-ph↗

arXiv2001

The solid-liquid interfacial free energy of close-packed metals: hard spheres and the Turnbull coefficient

Largely due to its role in nucleation and crystal-growth, the free energy of the crystal-melt interfacial free energy is an object of considerable interest across a number of scientific disciplines, especially in the materials-, colloid- and atmospheric sciences. Over fifty years ago, Turnbull observed that the interfacial free energies (scaled by the mean interfacial area per particle) of a variety of metallic elements exhibit a linear correlation with the enthalpy of fusion. This correlation provides an important empirical "rule-of-thumb" for estimating interfacial free energies, but lacks a compelling physical explanation. In this work we show that the interfacial free energies for close-packed metals are linearly correlated with the melting temperature, and are therefore primarily entropic in origin. We also show that the slope of this linear relationship can be determined with quantitative accuracy using a hard-sphere model, and that the correlation with the enthalpy of fusion reported by Turnbull follows as a consequence of the fact that the entropy of fusion for close-packed metals is relatively constant.

cond-mat.mtrl-sci↗

arXiv2000

On the approximation of Feynman-Kac path integrals for quantum statistical mechanics

Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function space, by restricting the integration to a subspace of all admissible paths. Using this process, a wide class of methods can be derived, with each method corresponding to a different choice for the approximating subspace. The traditional ``short-time'' approximation and ``Fourier discretization'' can be recovered from this approach, using linear and spectral basis functions respectively. As an illustration, a novel method is formulated using cubic elements and is shown to have improved convergence properties when applied to a simple model problem.

cond-mat.stat-mech↗

arXiv2000

Direct calculation of the hard-sphere crystal/melt interfacial free energy

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy, $γ$, for a system of hard spheres of diameter $σ$. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with $γ$ = 0.62$\pm 0.01$, 0.64$\pm 0.01$ and 0.58$\pm 0.01 k_BT/σ^2$ for the (100), (110) and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments measuring the crystal nucleation rates from colloidal fluids of polystyrene spheres that have been interpreted [Marr and Gast, Langmuir {\bf 10}, 1348 (1994)] to give an estimate of $γ$ for the hard-sphere system of $0.55 \pm 0.02 k_BT/σ^2$, slightly lower than the directly determined value reported here.

cond-mat.mtrl-sci↗