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A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid–vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid–vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid–vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity. [ABSTRACT FROM AUTHOR]

Three new Ewald series are derived using a new strategy that does not start with a proposed charge spreading function. Of these, the Ewald series produced using shifted potential interactions for the Ewald real space series converges relatively slowly, while the corresponding expression using a shifted force (SF) interaction does not converge. A comparison is made between several approximations of the Ewald method and the SF route to include Coulomb interactions in molecular dynamics (MD) computer simulations. MD simulations of a model bulk molten salt and water were carried out. The recently derived α′ variant of Ewald, by K. D. Hammonds and D. M. Heyes [J. Chem. Phys. 157, 074108 (2022)], has been developed analytically and found to be more accurate and computationally efficient than SF in part due to the smaller real space truncation distance that can be used. In addition, with α′, the number of reciprocal lattice vectors required is reduced considerably compared with the standard Ewald implementations to give the same accuracy. The invention of the α′ method shifts the computational balance back toward using an Ewald construction. The SF method shows greater errors in the Coulomb pressure and time dependent fluctuation properties compared to α′. It does not conserve the shadow Hamiltonian in a microcanonical MD simulation, whereas the α′ method does, which facilitates long time stability and insignificant drift of properties over time. The speed of the Ewald computer code is improved by using a new lookup table method. [ABSTRACT FROM AUTHOR]

Henchman's approximate harmonic model of liquids is extended to predict the thermodynamic behavior along lines of constant excess entropy ("isomorphs") in the liquid and supercritical fluid regimes of the Lennard-Jones (LJ) potential phase diagram. Simple analytic expressions based on harmonic cell models of fluids are derived for the isomorph lines, one accurate version of which only requires as input parameters the average repulsive and attractive parts of the potential energy per particle at a single reference state point on the isomorph. The new harmonic cell routes for generating the isomorph lines are compared with those predicted by the literature molecular dynamics (MD) methods, the small step MD method giving typically the best agreement over a wide density and temperature range. Four routes to calculate the excess entropy in the MD simulations are compared, which includes employing Henchman's formulation, Widom's particle insertion method, thermodynamic integration, and parameterized LJ equations of state. The thermodynamic integration method proves to be the most computationally efficient. The excess entropy is resolved into contributions from the repulsive and attractive parts of the potential. The repulsive and attractive components of the potential energy, excess Helmholtz free energy, and excess entropy along a fluid isomorph are predicted to vary as ∼T−1/2 in the high temperature limit by an extension of classical inverse power potential perturbation theory statistical mechanics, trends that are confirmed by the MD simulations. [ABSTRACT FROM AUTHOR]

The retraction of thin films, as described by the Taylor–Culick (TC) theory, is subject to widespread debate, particularly for films at the nanoscale. We use non-equilibrium molecular dynamics simulations to explore the validity of the assumptions used in continuum models by tracking the evolution of holes in a film. By deriving a new mathematical form for the surface shape and considering a locally varying surface tension at the front of the retracting film, we reconcile the original theory with our simulation to recover a corrected TC speed valid at the nanoscale. [ABSTRACT FROM AUTHOR]

Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant. [ABSTRACT FROM AUTHOR]

The bulk viscosity, ηb, of the hard sphere (HS) fluid is computed by equilibrium and nonequilibrium molecular dynamics (NEMD) simulations, the latter using an adaptation of the time-stepping method for continuous potential systems invented by Hoover et al. [Phys. Rev. A 21, 1756 (1980)], which employs an imposed cyclic density variation on the system by affine scaling of the particle coordinates. The time-stepping method employed for HS is validated against exact event-driven hard sphere methodology for a series of equilibrium quantities over a wide density range, including the pressure, singular parts of the hard sphere viscosities, and the nonsingular parts of the shear viscosity time correlation functions. The time steps used are typically only a little smaller than those employed in continuous potential simulations. Exact pressure tensor fluctuation expressions are derived for the singular (or infinite limiting frequency) equilibrium parts of the viscosities, which were employed in the simulations. The values obtained agree well with the predictions of the Enskog theory for all densities considered. The bulk viscosity obtained by NEMD is shown to be noticeably frequency dependent for densities in excess of ∼0.8, decaying approximately exponentially to the Enskog and equilibrium simulation values at all densities considered for frequencies in excess of ∼5 in hard sphere units. Temperature profiles during the cycle and the effects of strain amplitude on the computed frequency dependent bulk viscosity are presented. The bulk viscosity increases with the maximum density amplitude. [ABSTRACT FROM AUTHOR]

Practical implementations of the Ewald method used to compute Coulomb interactions in molecular dynamics simulations are hampered by the requirement to truncate its reciprocal space series. It is shown that this can be mitigated by representing the contributions from the neglected reciprocal lattice vector terms as a simple modification of the real space expression in which the real and reciprocal space series have slightly different charge spreading parameters. This procedure, called the α′ method, enables significantly fewer reciprocal lattice vectors to be taken than is currently typical for Ewald, with negligible additional computational cost, which is validated on model systems representing different classes of charged system, a CsI crystal and melt, water, and a room temperature ionic liquid. A procedure for computing accurate energies and forces based on a periodic sampling of an additional number of reciprocal lattice vectors is also proposed and validated by the simulations. The convergence characteristics of expressions for the pressure based on the forces and the potential energy are compared, which is a useful assessment of the accuracy of the simulations in reproducing the Coulomb interaction. The techniques developed in this work can reduce significantly the total computer simulation times for medium sized charged systems, by factors of up to ∼5 for those in the classes studied here. [ABSTRACT FROM AUTHOR]

A reformulation of the Green–Kubo expressions for the transport coefficients of liquids in terms of a probability distribution function (PDF) of short trajectory contributions, which were named "viscuits," has been explored in a number of recent publications. The viscuit PDF, P, is asymmetric on the two sides of the distribution. It is shown here using equilibrium 3D and 2D molecular dynamics simulations that the viscuit PDF of a range of simple molecular single component and mixture liquid and solid systems can be expressed in terms of the same intrinsic PDF (P0), which is derived from P with the viscuit normalized by the standard deviation separately on each side of the distribution. P0 is symmetric between the two sides and can be represented for not very small viscuit values by the same gamma distribution formulated in terms of a single disposable parameter. P0 tends to an exponential in the large viscuit wings. Scattergrams of the viscuits and their associated single trajectory correlation functions are shown to distinguish effectively between liquids, solids, and glassy systems. The so-called viscuit square root method for obtaining the transport coefficients is shown to be a useful probe of small and statistically zero self-diffusion coefficients of molecules in the liquid and solid states, respectively. The results of this work suggest that the transport coefficients have a common underlying physical origin, reflecting at a coarse-grained level the traversal statistics of the system through its high-dimensioned potential energy landscape. [ABSTRACT FROM AUTHOR]

Microcanonical ensemble (NVE) Molecular Dynamics (MD) computer simulations are performed with negligible energy drift for systems incorporating Coulomb interactions and complex constraint schemes. In principle, such systems can now be simulated in the NVE ensemble for millisecond time scales, with no requirement for system thermostatting. Numerical tools for assessing drift in MD simulations are outlined, and drift rates of 10−6 K/μs are demonstrated for molten salts, polar liquids, and room temperature ionic liquids. Such drift rates are six orders of magnitude smaller than those typically quoted in the literature. To achieve this, the standard Ewald method is slightly modified so the first four derivatives of the real space terms go smoothly to zero at the truncation distance, rc. New methods for determining standard Ewald errors and the new perturbation errors introduced by the smoothing procedure are developed and applied, these taking charge correlation effects explicitly into account. The shadow Hamiltonian, Es, is shown to be the strictly conserved quantity in these systems, and standard errors in the mean of one part in 1010 are routinely calculated. Expressions for the shadow Hamiltonian are improved over previous work by accounting for O(h4) terms, where h is the MD time step. These improvements are demonstrated by means of extreme out-of-equilibrium simulations. Using the new methodology, the very low diffusion coefficients of room temperature 1-hexyl-3-methyl-imidazolium chloride are determined from long NVE trajectories in which the equations of motion are known to be integrated correctly, with negligible drift. [ABSTRACT FROM AUTHOR]

The shear viscosity, η, of model liquids and solids is investigated within the framework of the viscuit and Fluctuation Theorem (FT) probability distribution function (PDF) theories, following Heyes et al. [J. Chem. Phys. 152, 194504 (2020)] using equilibrium molecular dynamics (MD) simulations on Lennard-Jones and Weeks–Chandler–Andersen model systems. The viscosity can be obtained in equilibrium MD simulation from the first moment of the viscuit PDF, which is shown for finite simulation lengths to give a less noisy plateau region than the Green–Kubo method. Two other formulas for the shear viscosity in terms of the viscuit and PDF analysis are also derived. A separation of the time-dependent average negative and positive viscuits extrapolated from the noise dominated region to zero time provides another route to η. The third method involves the relative number of positive and negative viscuits and their PDF standard deviations on the two sides for an equilibrium system. For the FT and finite shear rates, accurate analytic expressions for the relative number of positive to negative block average shear stresses is derived assuming a shifted Gaussian PDF, which is shown to agree well with non-equilibrium molecular dynamics simulations. A similar treatment of the positive and negative block average contributions to the viscosity is also shown to match the simulation data very well. [ABSTRACT FROM AUTHOR]

The Green–Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states. [ABSTRACT FROM AUTHOR]

The shadow energy, Es, is the conserved quantity in microcanonical ensemble (NVE) molecular dynamics simulations carried out with the position Verlet central-difference algorithm. A new methodology for calculating precise and accurate values of Es is presented. It is shown for the first time that Es rather than E is constant during structural changes occurring within a supercooled liquid. It is also explained how to prepare and conduct microsecond range bulk-phase NVE simulations with essentially zero energy drift without the need for thermostating. The drift is analyzed with block averaging and new drift functions of the shadow energy. With such minimal drift, extremely small and accurate standard errors in the mean for quantities like Es, E, and temperature, T, can be obtained. Values of the standard error for Es of ≈10−10 in molecule-based reduced units can be routinely achieved for simulations of 108 time steps. This corresponds to a simulation temperature drift of ≈10−6 K/μs, six orders of magnitude smaller than generally considered to be acceptable for protein simulations. We also show for the first time how these treatments can be extended with no loss of accuracy to polyatomic systems with both flexible degrees of freedom and arbitrary geometric constraints imposed via the SHAKE algorithm. As a bonus, estimates of simulation-average kinetic and total energies from high order velocity expressions can be obtained to a good approximation from 2nd order velocities and the average mean square force (for polyatomics, this refers to per site, including any constraint forces). [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations have been carried out along four Lennard-Jones (LJ) fluid isomorphs close to the freezing line, covering a temperature, T, in the range of 0.8–350 and a number density, ρ, in the range of 1.1–3.0 in LJ units. Analysis of the transport coefficients is via the Green-Kubo time correlation function method. The radial distribution function, percolation threshold connectivity distance, self-diffusion coefficient, and shear viscosity are shown to be invariant along an isomorph to a very good approximation when scaled with Rosenfeld's macroscopic units, although there are some small departures for T ≃ 1 and lower temperatures. The thermal conductivity is shown for the first time also to be isomorph invariant. In contrast, the Einstein and moment-based frequencies, and especially the bulk viscosity, ηb, show poor isomorphic collapse at low T but not surprisingly tend to an "inverse power" potential limiting value in the high T limit. In the case of the bulk viscosity, the significant departures from invariance arise from oscillations in the pressure autocorrelation function at intermediate times, which scale for inverse power potential systems but not for the LJ case, at least in part, as the pressure and bulk elastic moduli are not isomorph invariant. [ABSTRACT FROM AUTHOR]

The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, Di, and rotational diffusion coefficient, Dr, are reported as a function of m and ρ or volume fraction, ξ. The mDi data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m3Dr against ρ at low densities but as ∼m6Dr at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and Di scale approximately as m and m−1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented. [ABSTRACT FROM AUTHOR]

The bounded inverse power (BIP) interaction pair potential, ϕ (r) = 1 / ( a q + r q ) n / q , where a and the exponent, n, are constants which control the interaction softness, q is a positive integer, and r is the pair separation, is shown to exhibit isomorphic scaling as does the well-known inverse power potential, i.e., where a = 0. If T is the temperature and ρ is the number density of particles, two state points are isomorphic if a reference state, ρ0, T0, a0 and another state, ρ, T, a are related through the relationships ρ n / 3 / T = ρ 0 n / 3 / T 0 and a = a 0 ρ 0 / ρ 1 / 3 = a 0 T 0 / T 1 / n . The potential form is therefore density dependent along an isomorph. Molecular dynamics simulations and solutions of the Ornstein-Zernike integral equation for q = 2 demonstrate the existence of isosbestic points (IBPs) in the radial distribution function and structure factor for 6 ≤ n ≤ 18 and a wide range of a and ρ values. For the BIP potentials with not too small a values and over a wide density range, the IBP distance is insensitive to the number density and is equal to the distance, rT, defined through ϕ(rT) = T. For exponential potentials of the general form, ϕ(r) = C exp(−rm) with 1 ≤ m ≤ 3, there are also IBPs which are at r values that are typically ∼10–15% larger than predicted by the formula for rT. [ABSTRACT FROM AUTHOR]

The density functional method of Jari'c and Mohanty [Phys. Rev. B 37, 4441 (1988)] for calculating the elastic moduli of crystalline solids is considered here from the perspective of some new findings. The very slow convergence of the reciprocal-lattice vector summations and presence of the three body term in the method's computational scheme identified in [J. Chem. Phys. 118, 6594 (2003)] is confirmed and discussed. The sensitivity of the results to the scheme parameters, such as the width of the Gaussian density profiles and the Percus-Yevick approximation used for the direct correlation function is explored. The calculations are for a hard-sphere crystal but most conclusions can be applicable to model crystalline solids in general. [ABSTRACT FROM AUTHOR]

The transport coefficients of model monatomic fluids are explored within the context of isomorph theory. An extension of our previous study in this field to the thermal conductivity of Lennard-Jones (LJ) fluids is reported here. The relationship to and comparisons with the behavior of the LJ system and those of hard spheres (HS), which form perfect isomorphs at all densities are made. The HS and LJ transport coefficients obtained by MD simulations when scaled by socalled macroscopic ('isomorph') units, and the density is scaled by the freezing density, form curves which are extremely similar, and in near quantitative agreement apart from close to freezing in most cases. It is shown that to a large extent the excellent 'isomorph' scaling of the transport coefficients exhibited by the LJ system, even at low densities, can be traced back to the dominance of the repulsive part of this potential for these dynamical quantities, which can reasonably accurately be accounted for by the scaling behavior of hard spheres. Numerical support for this conclusion using molecular dynamics data for the HS and LJ model fluids is presented. [ABSTRACT FROM AUTHOR]

The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics (NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring’s model (EM) for shear thinning are derived. It is argued that an “incremental viscosity,” ηi, or IV which is the derivative of the steady state stress with respect to the shear rate is a better measure of the physical state of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shear stress divided by the strain rate). The stress relaxation function, Ci(t), associated with ηi is consistent with Boltzmann’s superposition principle and is computed by NEMD and the EM. The IV of the Eyring model is shown to be a special case of the Carreau formula for shear thinning. An analytic solution for the transient time correlation function for the EM is derived. An extension of the EM to allow for significant local shear stress fluctuations on a molecular level, represented by a gaussian distribution, is shown to have the same analytic form as the original EM but with the EM stress replaced by its time and spatial average. Even at high shear rates and on small scales, the probability distribution function is almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formula approximately satisfies the Fluctuation Theorem, which may in part explain its success in representing the shear thinning curves of a wide range of different types of chemical systems. [ABSTRACT FROM AUTHOR]

The second virial coefficient (SVC) of bounded generalizations of the Mie m:n potential φ(r) = λ[1=(aq + rq)m/q - 1=(aq + rq)n=q], where λ, a, q, m, and n are constants (a ≥ 0), is explored. The particle separation distance is r. This potential could be used as an effective interaction between polymeric dispersed colloidal particles of various degrees of interpenetrability. The SVC is negative for all temperatures for a, greater than a critical value, ac, which coincides with the range of a, where the system is thermodynamically unstable. The Boyle temperature and the temperature at which the SVC is a maximum diverge to +∞as a→ac from below. Various series expansion expressions for the SVC are derived following on from those derived for the Mie potential itself (i.e., a = 0) in the study of Heyes et al. [J. Chem. Phys. 145, 084505 (2016)]. Formulas based on an expansion of the exponential in the Mayer function definition of the SVC are formally convergent, but pose numerical problems for the useful range of a < 1. High temperature expansion (HTE) formulas extending those in the previous publication are derived, which in contrast converge rapidly for the full a range. The HTE formulas derived in this work could be useful in guiding the choice of nucleation and growth experimental conditions for dispersed soft polymeric particles. Inter alia, the SVC of the inverse power special case of the Bounded Mie potential, i.e., φ(r) = 1=(aq + rq)m/q, are also derived. [ABSTRACT FROM AUTHOR]

Onsager's theory of the isotropic-nematic phase separation of rod shaped particles is generalized to include particle softness and attractions in the anisotropic interparticle force field. The procedure separates a scaled radial component from the angular integral part, the latter being treated in essentially the sameway as in the original Onsager formulation. Building on previous treatments of more idealised hard-core particle models, this is a step toward representing more realistic rod-like systems and also allowing temperature (and in principle specific chemical factors) to be included at a coarse grained level in the theory. The focus of the study is on the coexisting concentrations and associated coexistence properties. Prolate and oblate ellipsoids are considered in both the small and very large aspect ratio limits. Approximations to the terms in the angular integrals derived assuming the very large (prolate) and very small (oblate) aspect ratios limits are compared with the formally exact treatment. The approximation for the second virial coefficient matches the exact solution for aspect ratios above about 20 for the prolate ellipsoids and less than ca. 0.05 for the oblate ellipsoids from the numerical evaluation of the angular integrals. The temperature dependence of the coexistence density could be used to help determine the interaction potential of two molecules. The method works at temperatures above a certain threshold temperature where the second virial coefficient is positive. [ABSTRACT FROM AUTHOR]

The phase behavior of a confined liquid at high pressure and shear rate, such as is found in elastohydrodynamic lubrication, can influence the traction characteristics in machine operation. Generic aspects of this behavior are investigated here using Non-equilibrium Molecular Dynamics (NEMD) simulations of confined Lennard-Jones (LJ) films under load with a recently proposed wall-driven shearing method without wall atom tethering [C. Gattinoni et al., Phys. Rev. E 90, 043302 (2014)]. The focus is on thick films in which the nonequilibrium phases formed in the confined region impact on the traction properties. The nonequilibrium phase and tribological diagrams are mapped out in detail as a function of load, wall sliding speed, and atomic scale surface roughness, which is shown can have a significant effect. The transition between these phases is typically not sharp as the external conditions are varied. The magnitude of the friction coefficient depends strongly on the nonequilibrium phase adopted by the confined region of molecules, and in general does not follow the classical friction relations between macroscopic bodies, e.g., the frictional force can decrease with increasing load in the Plug-Slip (PS) region of the phase diagram owing to structural changes induced in the confined film. The friction coefficient can be extremely low (~0.01) in the PS region as a result of incommensurate alignment between a (100) face-centered cubic wall plane and reconstructed (111) layers of the confined region near the wall. It is possible to exploit hysteresis to retain low friction PS states well into the central localization high wall speed region of the phase diagram. Stick-slip behavior due to periodic in-plane melting of layers in the confined region and subsequent annealing is observed at low wall speeds and moderate external loads. At intermediate wall speeds and pressure values (at least) the friction coefficient decreases with increasing well depth of the LJ potential between the wall atoms, but increases when the attractive part of the potential between wall atoms and confined molecules is made larger. [ABSTRACT FROM AUTHOR]

System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (~10), with the variances being inversely proportional to the SV volume, O. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes. [ABSTRACT FROM AUTHOR]

Aspects of the second virial coefficient, b2, of the Mie m : n potential are investigated. The Boyle temperature, T0, is shown to decay monotonically with increasing m and n, while the maximum temperature, Tmax, exhibits a minimum at a value of m which increases as n increases. For the 2n : n special case T0 tends to zero and Tmax approaches the value of 7.81 in the n → ∞ limit which is in quantitative agreement with the expressions derived in Rickayzen and Heyes [J. Chem. Phys. 126, 114504 (2007)] in which it was shown that the 2n : n potential in the n → ∞limit approaches Baxter's sticky-sphere model. The same approach is used to estimate the n-dependent critical temperature of the 2n : n potential in the large n limit. The ratio of T0 to the critical temperature tends to unity in the infinite n limit for the 2n : n potential. The rate of convergence of expansions of b2 about the high temperature limit is investigated, and they are shown to converge rapidly even at quite low temperatures (e.g., 0.05). In contrast, a low temperature expansion of the Lennard-Jones 12 : 6 potential is shown to be an asymptotic series. Two formulas that resolve b2 into its repulsive and attractive terms are derived. The convergence at high temperature of the Lennard-Jones b2 to the m = 12 inverse power value is slow (e.g., requiring T ≃ 104 just to attain two significant figure accuracy). The behavior of b2 of the ∞ : n and the Sutherland potential special case, n = 6, is explored. By fitting to the exact b2 values, a semiempirical formula is derived for the temperature dependence of b2 of the Lennard-Jones potential which has the correct high and low temperature limits. Published by AIP Publishing. [ABSTRACT FROM AUTHOR]

The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML. [ABSTRACT FROM AUTHOR]

An investigation is carried out of the association and clustering of mixtures of Gaussian charge distributions (CDs) of the form ~Q exp(-r²/2α²), where Q is the total charge, r is the separation between the centers of charge and a governs the extent of charge spreading (α → 0 is the point charge limit). The general case where a and Q are different for the positive and negatives charges is considered. The Ewald method is extended to treat these systems and it is used in Molecular Dynamics (MD) simulations of electrically neutral C D mixtures in the number ratios of 1:1 and 1:4 (or charge ratio 4:1). The M D simulations reveal increased clustering with decreasing temperature, which goes through a state in which each large C D is overlapped by four of the oppositely signed CD in the 1:4 case. At very low reduced temperatures, these mini-clusters progressively coalesce into much larger tightly bound clusters. This is different from the 1:1 mixture case, where the low temperature limit is a random distribution of neutral dimers. At higher temperatures, the M D radial distribution functions g(r) agree well with those from the hypernetted chain solution of the Ornstein-Zernike integral equation, and (at not too high densities) a previously introduced mean field approximation extended to these charge distribution systems. [ABSTRACT FROM AUTHOR]

The article presents an overview of localized momentum constraint for non-equilibrium molecular dynamics simulations, which is used to control momentum evolution in sub-regions in molecular dynamics simulations, is derived from Gauss’s principle of least constraint and is based on the physics equations of Irving and Kirkwood. A discussion of the practical uses of the constraint, which can can prescribe arbitrary flow fields in non-equilibrium molecular dynamics simulations and can form a mathematical framework for introducing coupling constraints at the boundary between continuum and discrete systems in the field of physics, is presented.

The article presents research on formulas to compute planes pressure or stress tensor for a spherical subvolume of radius (R). Topics include the Method of Planes (MoP) spherical geometry formula by Todd et al. in a 1995 issue of "Physics Review;" the proposed Control Volume formulation by E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki in a 2012 issue of "Physics Review;" the radial-dependence of the pressure tensor calculated y the Molecular Dynamics simulation; and the Radial Irving-Kirkwood formula.

The electrostatic interaction between finite charge distributions, ρ(r), in a neutralizing background is considered as an extension of the one component plasma (OCP) model of point charges. A general form for the interaction potential is obtained which can be applied to molecular theories of many simple charged fluids and mixtures and to the molecular dynamics (MD) simulation of such systems. The formalism is applied to the study of a fluid of Gaussian charges in a neutralizing background by MD simulation and using hypernetted-chain integral equation theory. The treatment of these interactions is extended to a periodic system using a Fourier Transform formulation and, for a rapidly decaying charge distribution, an application of the Ewald method. The contributions of the self-energy and neutralizing background to the system's energy are explicitly included in the formulation. Calculations reveal differences in behavior from the OCP model when the Wigner-Seitz radius is of order and less than the Gaussian charge density decay length. For certain parameter values these systems can exhibit a multiple occupancy crystalline phase at high density which undergoes re-entrant melting at higher density. An exploration of the effects of the various length scales of the system on the equation of state and radial distribution function is made. [ABSTRACT FROM AUTHOR]

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF2), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory. [ABSTRACT FROM AUTHOR]