Spherical tensor theory of long-range intermolecular forces

General expressions are given for the electrostatic, induction and dispersion energies of a pair of interacting, molecules in terms of spherical tensor components of the molecular multipole moments and polarizabilities. The orientation dependence is given in terms of the scalar expansion functions S_l1l2l^k1k2.     

Higher-order contributions to the intermolecular energy in the perturbation treatment of long-range forces in the light of spherical tensor theory

A preliminary account of the full spherical tensor theory of long-range interactions between two molecules based on a Rayleigh-Schrödinger perturbation treatment is given. The isotropic third-order interaction energy expression is then derived. Finally, the interaction between two tetrahedral molecules in the third-order of perturbation is studied as an example. It is shown that, in some cases, higher-order contributions should be taken into account.     

Size of elementary clusters and process period in silver nanoparticle formation

The time dependence of small-angle X-ray scattering (SAXS) curves for silver nanoparticle formation was followed in situ at a time resolution of 0.18 ms, which is 3 orders of magnitude higher than that used in previous reports (ca. 100 ms). The starting materials were silver nitrate solutions that were reacted with reducing solutions containing trisodium citrate. The SAXS analyses showed that silver nanoparticles were formed in three distinct periods from a peak diameter of ca. 0.7 nm (corresponding to the size of a Ag(13) cluster) during the nucleation and the early growth period. The Ag(13) clusters are most likely elementary clusters that agglomerate to form silver nanoparticles.     

High order correlation effects in intermolecular forces

A new approach to the calculation of intermolecular forces is presented. The total hamiltonian is used and no arbitrary separation into “orders” is made. The approach allows the interaction to be calculated, including intraatomic electron correction, to various degrees of approximation, the ultimate being full configuration interaction. The approximations are guided by the choice of wave function and the partitioning of the variational form. In this paper the method is applied to the long range interactions of helium, and in more approximate forms to HHe and LiHe. For He₂, studies are made of two- and three-electron excitations. Three-electron excitations contribute almost 9% to the value of the C₆ coefficient. Our final C₆ coefficient is 1.457 (in atomic units) versus the best semi-empirical value of 1.4618 ≠ 0.0004. The results are compared with other calculations in a formal way so as to demonstrate the value of our alternative expressions.     

Thermal fluctuations of clusters with the long-range interaction

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.     

Role of electrostatic forces in cluster formation in a dry ionomer

This simulation study investigates the dependence of the structure of dry Nafion-like ionomers on the electrostatic interactions between the components of the molecules. In order to speed equilibration, a procedure was adopted which involved detaching the side chains from the backbone and cutting the backbone into segments, and then reassembling the macromolecule by means of a strong imposed attractive force between the cut ends of the backbone, and between the nonionic ends of the side chains and the midpoints of the backbone segments. Parameters varied in this study include the dielectric constant, the free volume, side chain length, and strength of head group interactions. A series of coarse-grained mesoscale simulations shows the morphology to depend sensitively on the ratio of the strength of the dipole-dipole interactions between the side-chain acidic end groups to the strength of the other electrostatic components of the Hamiltonian. Examples of the two differing morphologies proposed by Gierke and co-workers [J. Polym. Sci., Polym. Phys. Ed. 19, 1687 (1981); Macromolecules 15, 101 (1982); J. Membr. Sci. 13, 307 (1982)] and by Gebel [Fuel Cells 5, 261 (2005); Macromolecules 37, 7772 (2004)] emerge from our simulations.     

On the theory for closed shell intermolecular forces

The electron gas model of Gordon and Kim is applied to the interaction of inert gases with a hydrogen molecule. Comparison of the isotropic potential wells with available experimental data shows clearly that modification of the exchange potential along the lines suggested by Rae produces greatly improved agreement when simple power series representations of the dispersion energy are included.     

Hardness of intermolecular forces and thermal diffusion

An approximate momentum transfer theorem leads to a direct relation between the thermal diffusion ratio and the logarithmic derivative of the potential. The correlation with exact results is excellent.     

Modern state of the investigation of long-range surface forces

Development of the concept of surface long-range forces and, in particular, the equilibrium disjoining pressure of liquid and gaseous interlayers has been set forth. Considered are the molecular, adsorption, electrical, structural, and electronic components of disjoining pressure. The contribution of the disjoining pressure to the hydrodynamics of thin layers is considered. The first theory of the frost heaving of soils has been formulated. Stated are the investigations of surface forces, in particular, in the processes of the formation of new interfaces and arising phenomena of the emission of electrons, ions, photons, and neutrons.     

A note on the theory of interatomic long-range forces

A comment is made on the multipolar expansion formula of the long-range force between hydrogen atoms previously obtained. The second-order perturbation energy neglecting exchange in the framework of the Unsöld approximation is evaluated exactly. An extension is made to helium atoms, and to other s-electron interactions. An approximate method is suggested to estimate the interatomic force between two atoms in general.     

Role of adsorption in formation of inorganic nanoparticles: Kinetic model

A simple kinetic model is proposed for the formation of inorganic nanoparticles in the presence of additives of readily adsorbing organic compounds. Additives and monomers may occupy the same sites on the surface of a growing particle. The maximum sizes and size distribution of formed particles are estimated under the assumption that the surface curvature of a growing particle has equivalent effects on the rate constants of the growth and adsorption. Equations are derived that relate the polydispersity indices for particle mass and radius distributions to the variances of particle radius distribution. The conditions are determined for the formation of virtually monodisperse nanoparticles.     

Gaussian representations of charge overlap effects in intermolecular forces

The ground state H? H⁺ and H? H interactions are used as model interactions for investigating the feasibility of using Gaussian basis sets for representing charge overlap effects in intermolecular forces. The non-expanded charge-induced dipole energy and the non-expanded dipole-dipole dispersion energy, respectively, for these interactions are calculated using two types of Gaussian basis functions to represent the first order wave function, Ψ⁽¹⁾. Very good results for these interaction energies, which include charge overlap effects, are obtained for all interatomic separations by using small Gaussian basis sets to represent the interaction, that is Ψ⁽¹⁾, and/or the isolated atoms (the zeroth order wave function).     

Super-molecule calculations of intermolecular forces between long-chain molecules

Intermolecular interactions between paraffin chains (C₃C₉) in four different mutual orientations have been studied by PCILO and INDO methods. The PCILO method is found to be superior. It is observed that polarity optimization is not required for these interaction studies although it most certainly would be for molecules with more polar bonds. The calculated interaction energies per carbon atom extrapolated to long-chain length are (0.09–0.22) kcal mol^?1 depending upon the orientation and geometry. The effect of a polar head group on the intermolecular interactions of long-chain molecules is also studied using the propionic acid dimer as model. Lone-pair interactions cause one of the dimer orientations to be totally repulsive.     

The current state of the theory of long-range surface forces

Interactions between surfaces and particles are considered on the basis of isotherms of disjoining pressure ∏(h), which include molecular, electrostatical, structural and steric forces. A review of the present day theory of long-range surface forces is given with special attention to the structural forces of hydrophilic repulsion and hydrophobic attraction. Effects of electrolyte concentration, degree of hydrophilization and temperature on the structural forces are discussed.     

On long-range forces of repulsion between biological cells

We have established experimentally that when biological cells, for example, blood, are suspended in concentrated solutions of inorganic electrolytes (for instance, in a 15% solution of sodium chloride) then around some cells (leucocytes, especially tumour cells) there form haloes, i.e., circular spaces free from background cells (erythrocytes, yeast cells, colloidal particles of Indian ink). In the medium made up of erythrocytes the haloes form during 5–10 min as a result of the background cells drawing apart from the central halo-forming cell (HFC) at a distance of 10–100 μm and more.

In the medium made of the Indian ink particles, the haloes form during 2–4 s and attain a thickness of about 10–20 μm. The erythrocytes and the haloes forming in their medium can be preserved for about three to five days at room temperature.

It has been established that, when tumour HFCs are present at sufficient concentrations, they form hexagonal periodic structures having a mean spacing between cells of up to 60 μm.

The authors put forward as one probable suggestion that the formation of haloes is largely determined by long-range repulsive forces arising from the phenomenon of diffusiophoresis generated by the diffusion currents that emerge from the surface of halo-forming cells.     

Application of Ewald summations to long-range dispersion forces

Results illustrating the effects of using explicit summation terms for the r(-6) dispersion term on the interfacial properties of a Lennard-Jones fluid and SPC/E water are presented. For the Lennard-Jones fluid, we find that the use of long-range summations, even with a short "crossover radius," yields results that are consistent with simulations using large cutoff radii. Simulations of SPC/E water demonstrate that the long-range dispersion forces are of secondary importance to the Coulombic forces. In both cases, we find that the ratio of the box size L( parallel) to the crossover radius r(c) (k) plays an important role in determining the magnitude of the long-range dispersion correction, although its effect is secondary when Coulombic interactions are also present.     

On the theory of intermolecular forces between inert gas atoms

The method described by Gordon and Kim and modified by Rae has been further modified to restrict the self-exchange correction to an electron gas composed of the outer shell electrons. Revised results are presented for the interaction potentials between various pairs of inert gas atoms.