Variable Interaction Range Research Articles

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state (EOS) for square-well chain fluid with variable range (SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids (ILs). A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures. The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation (AAD) of 0.36%. A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring's rate theory of viscosity and the SWCF-VR EOS. The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases. The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT, vapor-liquid equilibrium, caloric properties, surface tension, and viscosity.

Novel ballistic to diffusive crossover in the dynamics of a one-dimensional Ising model with variable range of interaction

The idea that the dynamics of a spin is determined by the size of its neighbouring domains was recently introduced (Biswas and Sen 2009 Phys. Rev. E 80 027101) in a Ising spin model (henceforth, referred to as model I). A parameter p is now defined to modify the dynamics such that a spin can sense domain sizes up to R = pL/2 in a one-dimensional system of size L. For the cutoff factor p → 0, the dynamics is Ising like and the domains grow with time t diffusively as t1/z with z = 2, while for p = 1, the original model I showed ballistic dynamics with z ≃ 1. For intermediate values of p, the domain growth, magnetization and persistence show a model-I-like behaviour up to a macroscopic crossover time t1 ∼ pL/2. Beyond t1, characteristic power-law variations of the dynamic quantities are no longer observed. The total time to reach equilibrium is found to be t = apL + b(1 − p)3L2, from which we conclude that the later time behaviour is diffusive. We also consider the case when a random but quenched value of p is used for each spin for which ballistic behaviour is once again obtained.

Liquid/vapor coexistence and surface tension of the Sutherland fluid with a variable range of interaction: Computer simulation and perturbation theory studies

The liquid-vapor phase diagram and surface tension for the Sutherland fluids with a variable range of interaction have been determined by canonical Monte Carlo simulations and compared with the augmented van der Waals analytic theory. The theory, based on a short-range Yukawa reference, performs well for medium-range models but its accuracy deteriorates with the shortening range due to deteriorating accuracy of the underlined analytic mean spherical approximation solution for the reference Yukawa potential. The simulation results are also analyzed from the point of the extended principle of corresponding states and it is shown that the surface tension and also, to a certain degree of accuracy, the vapor-liquid coexistence curve satisfy the principle.

Mean-field theoretical analysis of the corresponding-states behavior of model fluids with variable interaction range

In a recent communication [Fluid Phase Equilib. 272 (2008) 93–95], Duda and Orea suggested the existence of remarkably simple relationships among the critical parameters of several model fluids with variable interaction range. In addition, they introduced a new way of scaling supercritical pressure–volume–temperature ( PVT) data for a pure substance in a corresponding-states representation. Using different mean-field theories for the square-well fluid and the Yukawa fluid, we investigate whether these approximate equations of state adhere to the new criteria formulated by Duda and Orea. It is found that most theories indeed predict the suggested simple linear relationships between the critical pressure and the critical temperature as well as between the critical density and the reciprocal of the critical temperature for long interaction ranges, but deviations from these simple rules occur for short interaction ranges. Some of the theories, however, indicate that the dependence of the critical density on the interaction range might be more complicated for the square-well fluid. The revised scaling concept of representing the reduced pressure P / P c at a given reduced temperature T / T c as a function of the newly defined reduced density ρ σ / ρ c 2 / 3 , where σ denotes the diameter of a particle, does indeed lead to a better agreement of the data for different interaction ranges than the conventional scaling in terms of ρ / ρ c for both model fluids studied here.

Vapor-liquid critical and interfacial properties of square-well fluids in slit pores

Vapor-liquid phase equilibria of square-well (SW) fluids of variable interaction range: lambdasigma=1.25, 1.75, 2.0, and 3.0 in hard slit pores are studied by means of grand-canonical transition-matrix Monte Carlo (GC-TMMC) simulation. Critical density under confinement shows an oscillatory behavior as slit width, H, reduced from 12sigma to 1sigma. Two linear regimes are found for the shift in the critical temperature with the inverse in the slit width. The first regime is seen for H>2.0sigma with linear increase in the slope of shift in the critical temperature against inverse slit width with increasing interaction range. Subsequent decrease in H has little consequence on the critical temperature and it remains almost constant. Vapor-liquid surface tensions of SW fluids of variable well extent in a planar slit pore of variable slit width are also reported. GC-TMMC results are compared with that from slab based canonical Monte Carlo and molecular dynamics techniques and found to be in good agreement. Although, vapor-liquid surface tension under confinement is found to be lower than the bulk surface tension, the behavior of surface tension as a function of temperature is invariant with the variable pore size. Interfacial width, xi, calculated using a hyperbolic function increases with decreasing slit width at a given temperature, which is contrary to what is being observed recently for cylindrical pores. Inverse scaled interfacial width (xi/H), however, linearly increases with increase in the scaled temperature (T(c,bulk)-T)/T(c,bulk).

Nonextensive thermodynamics and glassy behaviour

An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium dynamics which can be considered paradigmatic for nonextensive systems. In this short paper we illustrate the interesting anomalous pre-equilibrium dynamics, focusing on the novel connections to the generalized nonextensive thermostatistics and the recent links to glassy systems.

Fracture model with variable range of interaction.

We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function that can interpolate between the two limiting cases of load redistribution, i.e., the global and the local load sharing schemes. By varying the range of interaction, several features of the model are numerically studied and a crossover from mean-field to short-range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.

Crossover scaling in two dimensions

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the reduced temperature as well as in the finite-size crossover variable, it has up to now largely evaded a satisfactory numerical determination. Using a new Monte Carlo method, we could obtain accurate results for sufficiently large interactions ranges. Our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal. Also the so-called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region.

Monte Carlo study of percolation of random discs in two dimensions: Variable range interaction

Monte Carlo study of percolation of random discs in two dimensions with variable range of interaction is carried out. The critical exponents β and γ are found to be the same when analysed as a function of range of interaction or critical area fraction, for all levels of dilution.

Percolation and cluster distribution. II. layers, variable-range interactions, and exciton cluster model

Monte Carlo simulations for the site percolation problem are presented for lattices up to 64 x 106 sites. We investigate for the square lattice the variable-range percolation problem, where distinct trends with bond-length are found for the critical concentrations and for the critical exponentsβ andγ. We also investigate the layer problem for stacks of square lattices added to approach a simple cubic lattice, yielding critical concentrations as a functional of layer number as well as the correlation length exponentν. We also show that the exciton migration probability for a common type of ternary lattice system can be described by a cluster model and actually provides a cluster generating function.

Percolation and cluster distribution II: Layers, variable range interactions and other site problems : By J. Hoshen, R. Kopelman and E. M. Monberg; Department of Chemistry, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Percolation and cluster distribution II: Layers, variable range interactions and other site problems : By J. Hoshen, R. Kopelman and E. M. Monberg; Department of Chemistry, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Phase transitions in a simple model ferroelectric. II. Comments on the self-consistent phonon approximation

The self-consistent phonon approximation is appled to the treatment of a simple model of a ferroelectric crystal. The range of applicability of this approximation scheme for the prediction of phase transitions in such a system is examined. In particular, an intercell coupling with a variable range of interaction is employed to determine what dependence the order of the transition has on the character of this coupling. It is also shown that the so-called mean-field approximation is a special case of the self-consistent phonon approximation in the limit where the intercell coupling is infinitely long range in character.

Self-consistent approximation schemes for the treatment of a prototype ferroelectric

Abstract As a simple prototype of a ferroelectric crystal we treat a system of coupled anharmonic oscillators in order to determine the range of applicability of different self-consistent approximation schemes. In particular, we examine the self-consistent phonon approximation with an intercell coupling which possesses a variable range of interaction. In the limit where the interaction is of sufficiently long range, the density matrix of the system is obtained numerically exactly.