Isotropic Pair Potentials Research Articles

Thermodynamic properties of two-dimensional nonideal structures with isotropic pair potential

An approximation is proposed for energy density in two-dimensional nonideal systems for a wide class of isotropic repulsive pair interparticle potentials. The approximation allows one to determine the main thermodynamic functions and characteristics of the system by using well-known thermodynamic formulas. The results obtained with the help of this approximation are compared with the data of numerical simulations of thermodynamic properties of the structures under study. The simulations were performed in a wide range of parameters typical of laboratory dusty plasmas. Main attention was paid to the screened Coulomb potential.

Fast off-lattice Monte Carlo simulations with “soft” repulsive potentials

The basic idea of fast off-lattice Monte Carlo (FOMC) simulations is to use "soft" repulsive potentials that allow particle overlapping in continuum Monte Carlo (MC) simulations. For multichain systems, this gives much faster chain relaxation and better sampling of the configurational space than conventional molecular simulations using "hard" excluded-volume interactions that prevent particle overlapping. Such coarse-grained models are particularly suitable for the study of equilibrium properties of soft materials. Since soft potentials are commonly used in polymer field theories, it is another advantage of FOMC simulations that using the same Hamiltonian in both FOMC simulations and the theories enables quantitative comparisons between them without any parameter fitting to unambiguously reveal the consequences of approximations in the theories. Moreover, FOMC simulations can be performed with various chain models and in any statistical ensemble, and all the advanced off-lattice MC techniques proposed to date can be implemented to further improve the sampling efficiency. We have performed canonical-ensemble FOMC simulations with an isotropic soft pair potential for three systems: we first used (small-molecule) soft spheres to demonstrate the improved sampling of FOMC simulations over conventional molecular simulations; we then used single-chain simulations to show that the effects of excluded-volume interactions can be well captured by the soft repulsive potential; finally, for compressible homopolymer melts, we compared FOMC results with those under the random-phase approximation to demonstrate that FOMC simulations can be used to unambiguously and quantitatively reveal the fluctuation/correlation effects in the system. In addition, we examined in detail in our single-chain simulations the spatial discretization scheme used in all previous FOMC simulations.

The dynamics of formation of monolayer dust structures in a confining electric field

The conditions for formation of monolayer dust structures are investigated for dust grains (interacting via isotropic pair potentials) placed in a confining electric field varying linearly with position. The relationships between the grain interaction potential, the number of grains and the gradient of the confining field of the electric trap are established. A criterion for instability of a monolayer dust structure is proposed.

Two-dimensional fluid with competing interactions exhibiting microphase separation: Theory for bulk and interfacial properties

Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems with isotropic pair potentials between the particles, due to the fact that the pair interaction between the colloids has competing attraction and repulsion over different length scales. Here we present a simple density functional theory for a model of such a two-dimensional fluid. The theory predicts a bulk phase diagram exhibiting cluster, stripe, and bubble modulated phases, in addition to homogeneous fluid phases. Comparing with simulation results for this model from the literature, we find that the theory is qualitatively reliable. The model allows for a detailed investigation of the structure of the fluid and we are able to obtain simple approximate expressions for the static structure factor and for the length scale characterizing the modulations in the microphase separated phases. We also investigate the behavior of the system under confinement between two parallel hard walls. We find that the confined fluid phase behavior can be rather complex.

Simulation of mass transport in systems with repulsive isotropic pair potential

The results of the numerical investigation of mass-transfer processes of extensive quasi-two-dimensional and three-dimensional nonideal dissipative systems are presented. Simulations were performed for different types of model pair potentials for inter-grain interaction that had various combinations of power-law and exponential functions. The parameters of calculations corresponded to the conditions of laboratory dusty plasma experiments. It was shown that the dynamics of grains in nonideal liquid-like systems on short observation times is close to the evolution of thermal oscillations in the crystal lattice.

Structural features of bicomponent dust Coulomb balls formed by the superposition of fields of different origin in plasma

A binary mixture of dust particles in plasma which are in an external electrostatic harmonic confining field as well as in the field consisting of gravitational, thermophoretic, and electrostatic force is simulated. The interparticle interaction is described by the Yukawa isotropic pair potential. The structural properties of the binary mixture of particles depending on composition are investigated. The segregation features of a system of particles of two species under the conditions of recent experiments on Coulomb ball formation are studied. It is shown that particles form a shell structure in which every shell contains only its own species of particles; in so doing, smaller-sized particles make up outer shells with respect to larger-sized particles. When the size difference between the particles becomes more and more pronounced, they are spatially separated up to the formation of two independent Coulomb balls.

Representability problems for coarse-grained water potentials

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.

Global phase diagram for the honeycomb potential

We calculate the global phase diagram using classical statistical mechanics for an isotropic pair potential that has been previously [Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005)] shown to produce the low-coordinated two-dimensional honeycomb crystal as the ground-state structure. Low-coordinated crystals are of practical interest because they have desirable photonic band-gap properties. The phase diagram is obtained from Helmholtz free energies calculated using thermodynamic integration and Monte Carlo simulations. Our results show that the honeycomb crystal remains stable in the global phase diagram even after temperature effects are taken fully into account. Other stable phases in the phase diagram are high and low density triangular phases and a fluid phase. We find no evidence of gas-liquid or liquid-liquid phase coexistence.

Optimized Interactions for Targeted Self-Assembly: Application to a Honeycomb Lattice

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.

Scattering from Polydisperse Melts

Effective isotropic pair potentials for polymer chains in a melt are derived from a phenomenological, coarse grained model of mixing on small distance scales, and the radial distribution functions of chain centers of mass and the scattering are calculated in the hypernetted chain approximation. The systems chosen for illustrative calculations are quasi-binary melts of deuterated and protonated polyethylene and polystyrene, both of which have been reported to exhibit anomalous composition dependence of neutron scattering. Quite large deviations from the Flory−Huggins picture of random spatial mixing of chains are found and the deviations decrease rather slowly with increasing molecular weights. However, nonrandom mixing gives rise to anomalous scattering of significant magnitude only if the mixture is asymmetric in particular ways. Differences in molecular weight (smaller for the deuterated polymer) and polydispersity (larger for the deuterated polymer) of about 10% are sufficient to exhibit anomalous scattering due to errors in the Flory−Huggins entropy of mixing. Smaller differences in the packing energies of the two different monomers, which are associated in the phenomenological model with composition dependent partial monomer volumes, reveal errors in the usual random phase analysis of scattering. Relative volumes of mixing deuterated and protonated polymer must range up to 1% in order to rationalize experimental anomalous scattering.

Dual Critical Points and Related Phenomena in Simple Fluids from the Perspective of (Approximate) Renormalization Theory

It is known that some single component fluids can have coexisting low-density and high-density liquid phases with two, separate, gas–liquid and liquid–liquid, critical points. Such behavior is found both by experiments and in recent molecular-dynamics simulations performed for certain simple isotropic attractive pair potentials with softened repulsive cores. In the present investigation, a “global” renormalization group theory that was employed previously to make predictions for simple Lennard–Jones and square-well fluids over wide ranges of density and temperature, including the critical point, in reasonably good agreement with molecular dynamics and Monte Carlo simulations, is applied to simple shoulder potentials and to square-well potentials with softened repulsive cores. Results using this renormalization approach are compared with some previously reported results for a shoulder potential and expectations regarding dual critical points for water.

Stripe phases from isotropic repulsive interactions.

One of the most striking signatures of self-organization is spontaneous pattern formation. Among the morphologies observed, stripes are intrinsically fascinating and have potential for technological applications including nanolithography and nanoelectricity. Examples of materials featuring stripe patterns include Langmuir monolayers, magnetic films, lipid monolayers, liquid crystals and polymer films. Stripe formation is generally attributed to the competition between short-range attractive forces and long-range repulsion arising from dipole interactions. Here we show that stripe phases may result from a different mechanism based on a purely repulsive isotropic short-range pair potential with two characteristic length scales. We consider a two-dimensional (2D) assembly of particles consisting of a hard core surrounded by a soft corona and find that at densities where the hard-and-soft core radii compete with each other, decreasing the temperature induces a transition from a disordered state to an orientationally ordered phase characterized by stripe patterns.

Molecular theory of three-pulse photon echoes for solutes in non-polar fluids

For a simple molecular solute in a simple non-polar liquid solvent the potential energy can be reasonably modeled by a sum of isotropic pair potentials. In this case various time-correlation functions, including the solute's (transition) frequency–frequency time-correlation function (also called the solvation correlation function), can be calculated semi-analytically without recourse to computer simulation. If the interactions in the system are such that the solute's dynamic transition frequency fluctuations describe a Gaussian process, this then leads to a semi-analytic theory for various spectroscopic observables, including the three-pulse photon echo intensity. In this paper we describe such a theory of the photon echo intensity. For two different model systems our theoretical results compare well with those from molecular dynamics simulation.

Short-Range Structure of Vitreous P<SUB>2</SUB>O<SUB>5</SUB> by MD Simulation

We have performed molecular dynamics (MD) simulations for vitreous P2O5 using isotropic pair potentials composed only of coulombic and repulsive interactions. The P–O pair distribution function obtained had the two distinguishable peaks expected from the results of neutron diffraction experiments, in the nearest-neighbor P–O correlation. The neutron-weighted real-space correlation function was also in semi-quantitative agreement with that obtained from the experimental results. The distribution of the coordination number for O around P and P around O showed that most P atoms form tetrahedral PO4 units in the glass, and that three-fifths of O atoms are bridging oxygen atoms, OB, and the remaining are terminal oxygen atoms, OT. The pair distribution functions for P–OB and P–OT show that the PO4 units have three long P–OB bonds and one short P–OT bond. We have concluded that the short-range structure obtained for vitreous P2O5 agrees well with the picture derived from many experiments. This fact indicates that the short-range structure of vitreous P2O5 can be described mainly by both charge ordering and packing based on the differences in ionic charge and size between cation and anion.

Ground state of a two-dimensional lattice system with a long-range interparticle repulsion: Stripe formation and effective lowering of dimension

It has been shown that particle ordering into stripes and effective lowering of dimension reside universally in the ground state of two-dimensional lattice systems with a long-range interparticle repulsion for any geometry of the host lattice and any physically reasonable isotropic pair potential. Examples are adatom systems and ensembles of self-localized charge carriers in layered or two-dimensional narrow-band conductors. On the basis of this fact a general analytical procedure has been formulated to describe fully the ground-state space structure of the above systems and the zero-temperature dependence of their filling factor on the chemical potential. The results obtained enable us to suggest that charge ordering into stripes revealed in copper-oxide superconductors can be caused solely by a long-range Coulomb hole-hole repulsion.

Nonadditive three-body polarizabilities of molecules interacting at long range: Theory and numerical results for the inert gases, H2, N2, CO2, and CH4

Collision-induced light scattering spectra of the inert gases and hydrogen at high densities provide evidence of nonadditive three-body interaction effects, for which a quantitative theory is needed. In this work, we derive and evaluate the three-body polarizability Δα(3) for interacting molecules with negligible electronic overlap. Our results, based on nonlocal response theory, account for dipole-induced-dipole (DID) interactions, quadrupolar induction, dispersion, and concerted induction-dispersion effects. The contribution of leading order comes from a DID term that scales as α3d−6 in the molecular polarizability α and a representative distance d between the molecules in a cluster. Quadrupolar induction effects are also large, however, ranging from ∼35% to 104% of the leading DID terms for equilateral triangular configurations of the species studied in this work, at separations approximately 1 a.u. beyond the van der Waals minima in the isotropic pair potentials. For the same configurations, the dispersion terms range from 2% to 7% of the total Δᾱ(3). The dispersion and induction-dispersion contributions are derived analytically in terms of integrals over imaginary frequency, with integrands containing the polarizability α(iω) and the γ hyperpolarizability. For H, He, and H2, the integrals have been evaluated accurately by 64-point Gauss–Legendre quadrature; for heavier species, we have developed approximations in terms of static polarizabilities, static hyperpolarizabilities, and van der Waals interaction energy coefficients (C6 and C9). In the isotropic interaction-induced polarizability Δᾱ, the three-body terms are comparable in magnitude to the two-body terms, due to a cancellation of the first-order, two-body DID contributions to Δᾱ. For the heavier species in this work (Ar, Kr, Xe, N2, CH4, and CO2) in the configurations studied, the three-body contributions to Δᾱ range from −7 to −9% of the two-body terms for equilateral triangular arrays and from 35% to 47% of the two-body terms for linear, centrosymmetric systems.

The ground state of the “frozen” electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension

In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons’ hopping, resulting in formation of a “frozen” electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a zero-band-width limit the “frozen” electron phase is a classical lattice system with a long-range interparticle repulsion. The ground state of such systems has been considered in the case of two dimensions for an isotropic pair potential of the mutual particle repulsion. It has been shown that particle ordering into stripes and effective lowering of dimension resides universally in the ground state for any physically reasonable pair potential and for any geometry of the conductor lattice. On the basis of this fact a rigorous general procedure for describing the ground state fully has been formulated. Arguments have been adduced that charge ordering into stripes in high-Tc superconductors testifies to the presence of a “frozen” electron phase in these systems.

Molecular theory of electronic spectroscopy in nonpolar fluids: Ultrafast solvation dynamics and absorption and emission line shapes

We present a theory of time- and frequency-domain spectroscopy of a dilute nonpolar solute in a nonpolar liquid or supercritical fluid solvent. The solute and solvent molecules are assumed to interact with isotropic pair potentials. These potentials, together with the solute and solvent masses, are the only input in the theory. We arrive at expressions for the absorption and emission line shapes, which include the possibility of motional narrowing, and for the time-resolved fluorescence and transient hole-burning observables, by assuming that the solute’s fluctuating transition frequency describes a Gaussian process. These expressions depend only on the average and variance of the transition frequency distributions in absorption and emission and on the normalized frequency fluctuation time-correlation functions. Within our formalism the former are obtained from the solute-solvent and solvent-solvent radial distribution functions, which are calculated using integral equations. The time-correlation functions involve the time-dependent solute-solvent Green’s function. Its solution depends upon the solute and solvent diffusion constants, which in turn are determined from the radial distribution functions. The theory compares favorably with computer simulation results of the same model. We then investigate the dependence of the various spectroscopic observables on the solvent density, the temperature, and the difference between the ground- and excited-state solute’s pair interaction with the solvent molecules. For example, since our theory for the time-correlation functions captures both their short- and long-time behavior, we can see how the crossover from inertial to diffusive dynamics depends on these variables. Our results are similar to a variety of experiments on solutes in both nonpolar and polar solvents.

Thermodynamic properties and phase equilibrium of fluid hydrogen from path integral simulations

The thermodynamic properties of normal and para-hydrogen are computed from multiple time-step path integral hybrid Monte Carlo (PIHMC) simulations. Four different isotropic pair potentials are evaluated by comparing simulation results with experimental data. The Silvera–Goldman potential is found to be the most accurate of the potentials tested for computing the density and internal energy of fluid hydrogen. Using the Silvera–Goldman potential, simulation and experimental data are compared on isobars ranging from 0.1 to 100 MPa and for temperatures from 18 to 300 K. The Gibbs free energy is calculated from the PIHMC simulations by an adaptation of Widom's particle insertion technique to a path integral fluid. A new method is developed for computing phase equilibria for quantum fluids directly by combining PIHMC with the Gibbs ensemble technique. This Gibbs–PIHMC method is used to calculate the vapour–liquid phase diagram of hydrogen from simulations. Agreement with experimental data is good.

Pair potential from neutron diffraction on argon at low densities.

We report the results of measurements of the static structure factor S(\ensuremath{\kappa}) for gaseous $^{36}\mathrm{Ar}$ at 140 K and four (subcritical) low densities from which, for the first time, we derive the well of the isotropic pair potential directly by means of a simple Fourier transform inversion.