Pair Interaction Potential Research Articles

Comparison of integral equationtheories of the liquid state.

The Ornstein-Zernike equationis a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce, e.g., the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equationsfor a given closure and pair interaction potential.

Conserving Approximations to Dilute Equilibrium Systems. Pair Interaction Potential

Conserving Approximations to Dilute Equilibrium Systems. Pair Interaction Potential

Two-dimensional pair-interacting hole gas thermodynamics: Exactly solvable Moshinsky model for lens-shaped quantum dots

The thermodynamic characteristics of a pair-interacting hole gas localized in a Ge/Si lens-shaped quantum dot are studied. The pair-interaction potential is modeled by the oscillator function, which depends on the distance between the particles. The analytical form of the spectra makes it possible to calculate the partition function in Boltzmann approximation. Based on the partition function mean and free energies, heat capacity and entropy of the interacting gas are calculated. Interaction between particles substantially changes the behavior of the thermodynamic properties in comparison with the non-interacting gas case. In particular, the gas undergoes a first-order phase transition driven by the height of the upper (or lower) section of QD, resulting in a changing symmetry of the lens-shaped QD.

From many-body quantum dynamics to the Hartree–Fock and Vlasov equations with singular potentials

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form \pm |x-y|^{-a} , which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree–Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N , and the Planck constant, h . For cases where a\in(0,1/2) , we obtain local-in-time results when N^{-1/2}\ll h \leq N^{-1/3} . Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a\in[1/2,1] , our results hold only within a small time scale or require an N -dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree–Fock equation uniformly in the Planck constant, which holds for a\in(0,1] .

Tracking colloidal silica particles to evaluate their dispersion and interactions in concentrated suspensions under shear force applications.

This study aimed to characterize interactions within colloidal silica particles in their concentrated suspensions, using rheo-confocal measurements and imaging, followed by image analysis. We studied the effect of shear rate (0-500s-1) and solution pH (6, 10) on the dispersion degree of colloidal silica particles via the determination and comparison of interparticle distances and their modeling. Images corresponding to different shear rates were analyzed to identify the coordinates of the particles. These coordinates were further analyzed to calculate the distance among the particles and then their surface-to-surface distance normalized by the particle diameter (H/D). It was found that the population of the particles per unit area of the image and H/D varied with increasing shear rate. The comparison between experimentally measured and theoretically calculated H/D identified that for some particles, the former was shorter than the latter, indicating the unexpected attractions among them against the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Then, the modification of previously reported equations for H/D was suggested and confirmed its validity. Assuming pair potential interaction and hydrodynamic interaction were the main non-DLVO interactions, their magnitudes were calculated and confirmed the significance of pH and shear application strength on particle dispersion/coagulation.

Engineering Ultrasoft Interactions in Stiff All-DNA Dendrimers by Site-Specific Control of Scaffold Flexibility.

A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all-DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small-angle X-ray scattering experiments in concentrated aqueous saline solutions of stiff all-DNA G2 dendritic constructs reveal a novel anomalous liquid-like phase behavior which is reflected in the calculated structure factors as a two-step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site-selective incorporation of single-stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self-organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse-graining, and two theoretical approaches based on effective, pair-potential interactions, remarkably confirmed the origin of this unusual liquid-like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self-assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interactingsystems.

Study on Thermodynamic Properties and Elastic Deformation of Full-Heusler Alloys Co2TaGa and Co2VGa by Statistical Moment Method

Heusler alloy is a ferromagnetic alloy based on the Heusler phase. It is an intermetallic alloy between metallic and non-metallic elements that can be non-ferromagnetic and has a BCC crystal structure. This paper presents the theory of thermodynamics and elastic deformation of full-Heusler A2BC alloy with BCC structure built on the basis of statistical moment method (SMM). The paper presents numerical results for the temperature and pressure dependence of the mean nearest neighbor distance between two atoms, the density, the volume, the thermal expansion coefficient, the isotherm and adiabatic compressibilities, the isothermal elastic modulus, the heat capacities at constant volume and pressure, Young’s modulus, the bulk modulus, longitudinal and transverse wave velocities of alloys Co2TaGa and Co2VGa when using the coordination sphere method and the Mie–Lennard-Jones pair interaction potential. Some SMM calculation results agree well with available ab initio calculation results.

Effect of substrate roughness on dynamics of wetting and decay of an ultrathin liquid film

In this study, we analyze the dynamics of wetting and decay of an ultrathin liquid film on a rough substrate. The dependence of disjoining pressure on liquid film thickness is derived by the direct numerical calculation for the Lennard-Jones pair interaction potential and 3D rough substrate with a random relief. It is shown that disjoining pressure for a rough substrate can be approximated by a similar function for a smooth one with highly fluctuating parameters over the substrate surface. The equation describing wetting and decay of 3D liquid film is modified, accounting for the calculated coordinate dependence of disjoining pressure the general form of capillary pressure depending on substrate relief. The approach is used for the simulation of drop formation from a nanosized liquid film for substrates with various roughness parameters. It is demonstrated that substrate roughness is responsible for accelerated film rupture and formation of “detectable” drops, increase in their number density, and decrease in average size. At the later stage, liquid film transformation is described by the power-law dependences of number density, average height and size with the exponents depending on substrate roughness. The blocking point of the size distribution function shifts to a larger value for a substrate with a more fine-grained structure. These changes in the growth rate and size distribution function of drops are associated with the change in conditions of liquid flow, which becomes inhomogeneous due to substrate roughness.

Effective Interactions between Double-Stranded DNA Molecules in Aqueous Electrolyte Solutions: Effects of Molecular Architecture and Counterion Valency.

A computational investigation of the effects of molecular topology, namely, linear and circular, as well as counterion valency, on the ensuing pairwise effective interactions between DNA molecules in an unlinked state is presented. Umbrella sampling simulations have been performed through the introduction of bias potential along a reaction coordinate defined as the distance between the centers-of-mass of pairs of DNA molecules, and effective pair interaction potentials have been computed by employing the weighted histogram analysis method. An interesting comparison can be drawn between the different DNA topologies studied here, especially with regard to the contrasting effects of divalent counterions on the effective pair potentials: while DNA-DNA repulsion in short center-of-mass distances decreases significantly in the presence of divalent counterion-ions (as compared to monovalent ions) for linear DNA, the opposite effect occurs for the DNA minicircles. This can be attributed to the fact that linear DNA fragments can easily adopt relative orientations that minimize electrostatic and steric repulsions by rotating relative to one another and by exhibiting more pronounced bending due to the presence of free ends.

Determination of pairwise interactions via the radial distribution function in equilibrium systems interacting with the Mie potential

Particle interactions play a fundamental role in condensed matter physics because they determine both the dynamical behavior and the equilibrium physical properties of a given system at temperature T and density ρ. However, these interactions are not always precisely known in experiments, or in simulations of coarse-grained systems. A direct determination of the pair interaction potential in a given system could help understand observed behaviors and make further predictions. Given a number of equilibrium configurations of a system, it would be desirable to find a method to directly determine the pair potential by only using these snapshots. We propose two simple methods towards this goal for the specific case of the systems in 3 dimensional space with the Mie potential, which includes two exponents as m and s. Well-equilibrated system configurations are produced by molecular dynamical simulations using the Mie potential with different exponent combinations (m,s). In the first method, we construct a correspondence between the value and location of the first peak of the radial distribution function and the couple (m,s), which allows us to determine the potential with an accuracy of 100% when given a set of equilibrium configurations for an unknown potential. In the second method, we train an artificial neural network to learn this correspondence. We find that all (m,s) combinations are correctly predicted. Both methods support the idea that the pairwise interaction can often easily be inferred by using equilibrium snapshots.

Polyelectrolyte Complexes from Oppositely Charged Filamentous Viruses

Here, we present an explorative study on a new type of polyelectrolyte complex made from chemically modified filamentous fd viruses. The fd virus is a semiflexible rod-shaped bacteriophage with a length of 880 nm and a diameter of 6.6 nm, which has been widely used as a well-defined model system of colloidal rods to investigate phase, flow, and other behavior. Here, chemically modified viruses have been prepared to obtain two types with opposite electrical charges in addition to a steric stabilization layer by poly(ethylene glycol) (PEG) grafting. The complex formation of stoichiometric mixtures of these oppositely charged viruses is studied as a function of virus and salt concentration. Furthermore, static light scattering measurements show a varying, strong increase in scattering intensity in some samples without visual macroscopic complex formation. Finally, the results of the complex formation are rationalized by comparing to model calculations on the pair interaction potential between oppositely charged viruses.

A Glimpse into Quantum Triplet Structures in Supercritical 3He.

A methodological study of triplet structures in quantum matter is presented. The focus is on helium-3 under supercritical conditions (4 < T/K < 9; 0.022 < ρN/Å-3 < 0.028), for which strong quantum diffraction effects dominate the behavior. Computational results for the triplet instantaneous structures are reported. Path integral Monte Carlo (PIMC) and several closures are utilized to obtain structure information in the real and the Fourier spaces. PIMC involves the fourth-order propagator and the SAPT2 pair interaction potential. The main triplet closures are: AV3, built as the average of the Kirkwood superposition and the Jackson-Feenberg convolution, and the Barrat-Hansen-Pastore variational approach. The results illustrate the main characteristics of the procedures employed by concentrating on the salient equilateral and isosceles features of the computed structures. Finally, the valuable interpretive role of closures in the triplet context is highlighted.

Sorption and Gas Transport Characteristics of Polyimides Based on a Mixture of Diethyl Toluene Diamine Isomers

The transport of oxygen, nitrogen, and hydrocarbons C1–C4 in polyimides based on 4,4'-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) and biphenyl-3,3',4,4'-tetracarboxylic acid dianhydride (BPDA) and diethyl toluene diamine (DETDA) has been studied. The dependences of the diffusion coefficient on the diffusant effective diameter and the solubility coefficients on the Lennard–Jones potential of pair interaction have been considered. It is shown that the diffusion coefficients of butane are out of the linear dependence of the logarithm of the diffusion coefficient on the square of the effective diameter of the diffusant, which may indicate the plasticization of polymers with butane at a pressure of 1 atm. The permeability of mixtures of gases O2–N2 (29 : 71 v/v) and CO2–CH4 (62 : 38 v/v) has been studied. There are no significant differences in the gas separation parameters in comparison with the experiment for individual gases; however, for a mixture of CO2–CH4, a slight increase in the separation factor has been found as compared to the ideal selectivity. The data on the measurement of sorption isotherms and solubility coefficients O2, N2, and CH4 are also presented in the article. Gas solubility coefficients have been found to be close to the values obtained indirectly as P/D.

A New Study on the Structure, and Phase Transition Temperature of Bulk Silicate Materials by Simulation Method of Molecular Dynamics

In this paper, the structure and phase transition temperature of bulk silicate materials are studied by the simulation method (SM) of molecular dynamics (MD). In this research, all samples are prepared on the same nanoscale material model with the atomic number of 3000 atoms, for which the SM of MD is performed with Beest-Kramer-van Santen and van Santen pair interaction potentials under cyclic boundary conditions. The obtained results show that both the model size (l) and the total energy of the system (Etot) increase slowly in the low temperature (T) region (negative T values) at pressure (P), P = 0 GPa. However, the increase of l determines the Etot value with very large values in the high T region. It is found that l decreases greatly in the high T region with increasing P, and vice versa. In addition, when P increases, the decrease in the Etot value is small in the low T region, but large in the high T region. As a consequence, a change appears in the lengths of the Si-Si, Si-O, and O-O bonds, which are very large in the high T and high P regions, but insignificant in the low T and low P regions. Furthermore, the structural unit number of SiO7 appears at T &gt; 2974 K in the high P region. The obtained results will serve as the basis for future experimental studies to exploit the stored energy used in semiconductor devices.

Structural phase-field crystal model for Lennard–Jones pair interaction potential

A modification of the structural phase-field crystal model for a Lennard–Jones (LJ) pair interaction potential is presented. Formation of 1D and 2D structures for the LJ-potential was studied numerically. The equilibrium lattice parameters for the obtained structures were found consistent to the correspondent LJ-distance parameters. The lattice parameter of 2D triangle’s structure matches the periodical in 1D, which is consistent to the theory of freezing from the isotropic liquids. Numerically obtained phase diagram of two-dimensional structures qualitatively reproduces classical PFC diagram and coincides with the melting region of high-temperature part of LJ diagram.

Bulk viscosity of gaseous argon from molecular dynamics simulations.

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150-500K and is found to be proportional to density squared in the investigated range of densities 0.001-1 kg m^{-3}. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

Polarons and bipolarons in two-dimensional systems

Polarons and bipolarons in two-dimensional (2 D) crystals with a simple conduction band are considered in the work. A study of the potential of pair interaction for the singlet states of polarons was carried out in the region intermediate coupling. The effective functional of exchange-coupled pair of polarons was obtained by the Buimistrov-Pekar method. Variational calculations of the singlet states energies were carried out taking into account the direct dependence of the wave function of the system on the interelectron distance. The variational functions have been selected in the form of a multiparameter system of Gaussian functions with exponentially correlated multipliers. The region of existence of a two-dimensional bipolaron was determined as a function of the crystal parameters. It has been shown that a single-center configuration (a configuration similar to a two-dimensional helium atom) is stable. The minimum corresponding to the two-center configuration (“polaron molecule”) is secondary extremum that disappears when the electronic correlations associated with the direct dependence of the wave function of the system on the distance between electrons are taken into account. The main energy minimum corresponds to single-center configuration. The study of the fulfillment of the virial theorem for polaron and bipolaron functionals was carried out. The results of variational calculations were compared with the calculations performed by other authors. Two-center configuration of a 2D bipolaron is unstable. The only minimum corresponds to a one-center 2D bipolaron. Exchange energy of two 2D polarons is antiferromagnetic.

Exploring quantum quasicrystal patterns: A variational study

We study the emergence of quasicrystal configurations produced purely by quantum fluctuations in the ground-state phase diagram of interacting bosonic systems. By using a variational mean-field approach, we determine the relevant features of the pair interaction potential that stabilize such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of super-quasicrystals, i.e. supersolid-like quasicrystalline states in which the long-range non-periodic density profile coexist with a non-zero superfluid fraction. Our calculations show that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this work.

Kinetic Equations of Physicochemical Processes with Allowance for Multi-Particle Effects in the Lattice Gas Model

A way of deriving kinetic equations of physicochemical processes in dense phases is developed on the basis of the discrete–continuous description of the spatial distribution of components in the lattice gas model (LGM), with allowance for multi-particle effects. The emergence of multi-particle effects is associated with the simultaneous influence of all neighbors on the rate of the elementary stage with the participation of a given particle. They include multi-particle potentials of interaction, including quantum–chemical energy calculations, the effect the configurations of neighboring molecules have on the internal motion of the central particle, and the effects of the indirect correlation of interacting particles that occurs for any potential of pair interaction, assuming the internal motions of particles do not depend on the local configurations of neighbors. Multi-particle effects take models beyond the quasi-chemical approximation, which reflects direct correlations of interacting particles through pair distribution functions, and require the use of correlation functions for a larger number of particles in describing their kinetics. The rates of elementary one- and two-node stages are calculated within the theory of absolute rates of reactions in non-ideal reaction systems. Ways of calculating approximate rates of the elementary stages of mono- and bimolecular processes are discussed, along with the possibilities of generalizing the derived equations.

To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables

Based on a chain of BBGKI equations with a modified boundary condition that takes into account multiparticle correlations, kinetic equations in the approximate "pairs" collisions and in the polarization approximation, taking into account the interaction through the third particle, obtained. The specifics of the model representation of the pair potential of particle interaction through short-range and long-range parts were taken into account. In the case of the short-range potential in the form of the potential of solid spheres, the contribution of Enskog's revised theory to the complete integration of the collision of the kinetic equation is obtained. The collision integrals include paired quasi-equilibrium distribution functions that depend on the nonequilibrium mean values of the particle number density and the inverse temperature. The method of collective variables Yukhnovskii is applied for the calculation of pair quasi-equilibrium distribution function with an allocation of short-range and long-range parts in the potential of the interaction of particles. In this case, the system with short-range interaction is considered as a frame of reference.