Density-dependent Pair Potentials Research Articles

Coarse-graining polymer solutions: A critical appraisal of single- and multi-site models

We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluid-fluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they present a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.

Local density approach for modeling fluids with density-dependent interactions.

In a recent paper [Phys. Rev. Lett. 86, 2038 (2001)] a simple fluid with a particular density-dependent pair potential was shown to exhibit, together with the vapor-liquid transition, a liquid-liquid phase separation and it was evidenced that, in order to adequately define the correct boundaries of stability, a simulation procedure based on the use of local densities had to be devised. It was found that for certain thermodynamic states the potential drives the system toward a phase separation that is otherwise frustrated by the change in the interactions induced by density fluctuations. Therefore, when integral equations or global density simulations are used, the critical points estimated from the thermodynamics are not associated with divergent correlations and vice versa. Here, we will explore in depth this fluid and introduce a detailed account of the proposed local density simulation technique. The results presented bear general significance for density-dependent potentials, like those of liquid metals or charge-stabilized colloids.

The compressibility equation for soft-matter liquids

Effective interactions in soft-matter physics result from a formal contraction of aninitial multicomponent system, composed of mesoscopic and small particles, intoan effective one-component description. By tracing out in the partition functionthe degrees of freedom of the small particles, a one-component system ofmesoscopic particles interacting with a state-dependent Hamiltonian is found.Although the effective Hamiltonian is not in general pairwise additive, it is usuallyapproximated by a volume term and a pair-potential contribution. In this paperthe relation between the structure, for which the volume term plays no role, andthe thermodynamics of a fluid of particles interacting with a density-dependentpair potential is analysed. It is shown that the compressibility equationdiffers from that of atomic fluids. An important consequence is that theinfinite-compressibility line derived from the thermodynamics does notcoincide with the spinodal line stemming from the divergence of correlations.

Evidence of double criticality in a fluid model with density-dependent interactions.

Evidence of a liquid-liquid equilibrium in simple fluids has recently been exposed for a density-dependent pair potential in the framework of a van der Waals theory. Here this double criticality is investigated by means of computer simulation, a perturbation theory, and integral equation theory. It is found that the critical point estimated from the integral equation thermodynamics is not associated with divergent correlations. To cope with these features, a special simulation procedure, based on the definition of local densities, is devised. Monte Carlo calculations confirm the existence of two critical points, in agreement with the predictions of perturbation theory.

Local coordination in relation to electronic structure of condensed conducting phases

Density functional theory (DFT) can be employed to calculate an effective, density-dependent pair potential, mediated by the conduction electrons, in sp liquid metals. The total electronic charge around the metallic ion, say Na+, in an electron gas must perfectly screen the ion, as long-range electric fields cannot exist in a conducting medium. The pair potential thus obtained for liquid Na near freezing, which is consistent with high coordination number, is compared with that obtained by inversion of the liquid structure factor as measured in diffraction experiments. Results of such experiments on the heavy highly expanded liquid alkali Cs, which reveal low coordination numbers, have motivated recent DFT calculations on ordered chains of K atoms, both linear and zig-zag. The ground-state electronic properties are compared and contrasted with those of structures with higher coordination numbers such as diamond and body-centred cubic. Chains of C atoms in C2BN are then briefly referred to, and differences ...

Local coordination in relation to electronic structure of condensed conducting phases

Density functional theory (DFT) can be employed to calculate an effective, density-dependent pair potential, mediated by the conduction electrons, in sp liquid metals. The total electronic charge around the metallic ion, say Na+, in an electron gas must perfectly screen the ion, as long-range electric fields cannot exist in a conducting medium. The pair potential thus obtained for liquid Na near freezing, which is consistent with high coordination number, is compared with that obtained by inversion of the liquid structure factor as measured in diffraction experiments. Results of such experiments on the heavy highly expanded liquid alkali Cs, which reveal low coordination numbers, have motivated recent DFT calculations on ordered chains of K atoms, both linear and zig-zag. The ground-state electronic properties are compared and contrasted with those of structures with higher coordination numbers such as diamond and body-centred cubic. Chains of C atoms in C2BN are then briefly referred to, and differences in conduction properties from recent DFT calculations on a hexagonal layer of CBN are stressed. Finally, some attention is given to the coexistence of metallic and molecular phases, with particular reference to the insulator-metal transition in crystalline I2 under pressure and to very recent studies of fluid molecular H under extreme conditions of pressure and temperature.

Free-energy model for fluid atomic helium at high density.

We develop a free-energy model aimed at describing the thermodynamics of fluid atomic helium at high density and high temperature. This model represents a step towards a consistent description of the pressure ionization of helium, as encountered in astrophysical situations and high-pressure experiments. In the present paper, a perturbation theory is developed to derive the configuration energy of helium at high density, and the modification of internal states in the partition function due to N-body effects is treated self-consistently within an occupation probability formalism. A scaling relationship between the internal levels and the ground state of helium is presented, which reproduces the experimental energy spectrum of helium within 3%. We also develop a density-dependent pair potential for helium, which reduces to the ab initio Ceperley-Partridge potential [D. M. Ceperley and H. Partridge, J. Chem. Phys. 84, 820 (1986)] at low density and includes implicitly the many-body effects at high density. The theoretical Hugoniot curves and the speed of sound derived from our free-energy model are in excellent agreement with the available experimental data, thereby assessing the validity of the present model at high density. These calculations are the extension of a former model for hydrogen [D. Saumon and G. Chabrier, Phys. Rev. A 44, 5122 (1991)] to nonhydrogenic, two-electron systems. The present free-energy model can be used to derive an accurate equation of state for the outermost layers of Jovian planets, brown dwarfs, and white dwarfs.

Density dependence of excess electronic ground-state energies in simple atomic fluids

The ground-state energies of an excess electron E0 as a function of solvent density are computed using model electron–atom pseudopotentials in fluid helium, argon, and xenon. E0 is a lower bound to the experimentally measurable threshold to photoconductivity, V0. The nonuniqueness of the pseudopotential description of electron–molecule interactions is demonstrated. We find that when many-body polarization effects are included, our calculated E0 results are in close agreement with experimental V0 values indicating that the conduction-band energy lies close to the ground-state energy across a broad range of densities in these polarizable fluids. If the many-body nature of the polarization interaction is ignored the ground-state energies deviate significantly from the V0 results highlighting the importance of accurate treatment of many-body polarization interactions. It is shown that a mean-field theory of polarization gives substantial agreement with full many-body calculations. This allows us to introduce a mean-field, density-dependent pair potential which greatly simplifies such many-body calculations. In the more polarizable systems, it is found that the spatial extent of the ground-state wave function as a function of solvent density is correlated with the density dependence of both V0 and the electron mobility, and it becomes uniformly spread throughout our simulation cell as the electron mobility goes through its maximum value at intermediate solvent densities.

Density-dependent pair potentials and the compressibility problem

The consistent treatment of the static and dynamic properties of metallic systems using interatomic potentials which are based on a one-body potential plus pair interactions containing volume or mean density dependence is examined. The focus is on the discrepancy between the compressibility of metals calculated in two alternative and legitimate ways, i.e. from elastic constants deduced from the long-wavelength limit of phonon spectra and from a homogeneous deformation. A simple, physically motivated resolution of this long-standing 'compressibility problem' is proposed which for simple metals provides an interpretation of earlier treatments involving third- and fourth-order perturbation terms in the total energy. The resolution hinges on taking reasonable account of inhomogeneities in the electron density which modulate the one-body and pair potentials. Subtleties in the interplay between these two terms in the particular case of interatomic potentials based on weak pseudopotential theory are exposed and pitfalls are pointed out in the haphazard application of empirical interatomic potentials. The consequences of the work for the phonon spectra are investigated and a first-principles method for treating this and related situations is outlined.

Departures from Joule's Law in Dense Liquids near Freezing Related to Vacancy Properties in Hot Crystals

Abstract The departures from Joule's Law that the internal energy U is independent of volume V are first expressed in dense liquids in terms of specific heats and the isothermal compressibility. For condensed rare gases, described by density independent pair potentials, (∂U/∂V)T is shown to be closely related to the vacancy formation energy Ev , a correction term dependent on the density dependence of the pair function being displayed explicitly. For metals with density-dependent pair potentials, (∂U/∂V)T is shown to involve the vacancy formation volume.

The energy and elastic constants of simple metals in terms of pairwise interactions

Second order perturbation theory enables the author to write U, the energy of a simple metal, as a large volume dependent part F(V) plus a small term which is the sum over pairs of ions of the central interaction Phi (R; rho ), R being the ion-ion distance. It is noted that Phi is a density dependent pair potential; hence the additional argument. The physics of this representation is discussed. Expressions for the pressure P and bulk modulus B are derived. The author derives formulae and gives numerical results to show a violation of the Cauchy relations and a correction to the conventional lattice dynamical theory of B. Without reference to a particular model an estimate of this correction is obtained.

The compressibilities of simple liquid metals

The application is discussed of the expression for the compressibility, in terms of the long wavelength limit of the structure factor, to a liquid metal. Taking density-dependent pair potentials obtained by perturbation of the electron gas by a model potential, it is shown that in order to obtain agreement with the result obtained by direct differentiation of the pressure with respect to volume when phi q, the Fourier transform of the pair potential, is calculated to second order in the model potential for a general q, the contributions of second order in the model potential must be included in the mean value phi 0. These terms arise as the q to 0 limits of the terms which for a general q are of third and fourth order in the model potential. The author also shows by direct calculation, using the Ashcroft model potential, that the resulting contribution to the compressibilities of the simple liquid metals is considerable.