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.     

Certain results obtained in research on long-range surface forces

Conclusions Research over the last 45 years has revealed the existence of long-range surface forces of three types: molecular, ionic-electrostatic, and structural. These forces lie at the foundation of the theory of stability of disperse systems and colloids, and are the basis of many processes: swelling, frost-heaving of soils, wetting phenomena, and thermoosmotic phenomena. The structural features of boundary layers of polar liquids and water lead to their anisotropy and to changes in their heat capacity and density.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1721–1725, August, 1982.     

Direct measurements of long-range surface forces in gas and liquid media

A modified set-up was applied to carry out direct measurements of the forces of molecular attraction of gold spheres and crossed quartz filaments in air within the region of distances from 10 to 100 nm. Some quantitative deviations from Lifshitz's theory for gold may be attributed to an insufficient reliability of the spectral data used in the calculations. The DLVO theory adequately describes the interaction of glass threads in KCl (10^?3 ÷ 10^?5 N) solutions within the region of 5 to 100 nm. At a distance smaller than 5 nm, the deviations from DLVO theory are attributable to the influence of structural forces.When the contact between crossed hydrophobized quartz threads in water is broken, the attraction forces (which exceed the molecular forces by several orders of magnitude) at a distance of up to 300 nm are detected.     

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.     

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.     

The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

Direct evaluation of DLVO theory for predicting long-range forces between a yeast cell and a surface

Using a combined gradient optical trap and evanescent wave light-scattering force-measurement technique, long-range colloidal forces were measured between a single Candida albicans yeast cell and a flat, bare glass surface in electrolyte concentrations ranging from 0.1 to 100 mM NaCl. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory was compared to experimentally measured equilibrium force curves and found to provide a close approximation to the decay length of the measured forces for electrolyte concentrations up to about 0.23 mM NaCl. At higher electrolyte concentrations (>/=0.5 mM NaCl), decay lengths of force curves in experimental measurements were consistently longer than Debye lengths calculated from the electrolyte concentrations. In electrolyte concentrations of 10 and 100 mM NaCl, most cells attached rapidly, which prevented measurements of long-range forces. The small fraction of cells remaining unattached in these higher electrolyte concentrations displayed purely repulsive forces. These results show that the DLVO theory accurately describes cell-surface interactions when the Debye length is in the range of 20-30 nm but underpredicts the decay length of the interactions at higher electrolyte concentrations.     

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.     

Role of long-range intermolecular forces in the formation of inorganic nanoparticle clusters

An understanding of the role played by intermolecular forces in terms of the electron density distribution is fundamental to the understanding of the self-assembly of molecules in the formation of a molecular crystal. Using ab initio methods capable of describing both short-range intramolecular interactions and long-range London dispersion interactions arising from electron correlation, analyses of inorganic dimers of As(4)S(4) and As(4)O(6) molecules cut from the structures of realgar and arsenolite, respectively, reveal that the molecules adopt a configuration that closely matches that observed for the crystal. Decomposition of the interaction energies using symmetry-adapted perturbation theory reveals that both model dimers feature significant stabilization from electrostatic forces as anticipated by a Lewis acid/Lewis base picture of the interaction. London dispersion forces also contribute significantly to the interaction, although they play a greater role in the realgar structure near equilibrium than in arsenolite.     

New spherical-cutoff methods for long-range forces in macromolecular simulation

New atom- and group-based spherical-cutoff methods have been developed for the treatment of nonbonded interactions in molecular dynamics (MD) simulation. A new atom-based method, force switching, leaves short-range forces unaltered by adding a constant to the potential energy, switching forces smoothly to zero over a specified range. A simple improvement to group-based cutoffs is presented: Switched group-shifting shifts the group–group potential energy by a constant before being switched smoothly to zero. Also introduced are generalizations of atom-based force shifting, which adds a constant to the Coulomb force between two charges. These new approaches are compared to existing methods by evaluating the energy of a model hydrogen-bonding system consisting of two N-methyl acetamide molecules and by full MD simulation. Thirty-five 150 ps simulations of carboxymyoglobin (MbCO) hydrated by 350 water molecules indicate that the new methods and atom-based shifting are each able to approximate no-cutoff results when a cutoff at or beyond 12 Å is used. However, atom-based potential-energy switching and truncation unacceptably contaminate group–group electrostatic interactions. Group-based potential truncation should not be used in the presence of explicit water or other mobile electrostatic dipoles because energy is not a state function with this method, resulting in severe heating (about 4 K/ps in the simulations of hydrated MbCO). The distance-dependent dielectric (? ∝? r) is found to alter the temperature dependence of protein dynamics, suppressing anharmonic motion at high temperatures. Force switching and force shifting are the best atom-based spherical cutoffs, whereas switched group-shifting is the preferred group-based method. To achieve realistic simulations, increasing the cutoff distance from 7.5 to 12 Å or beyond is much more important than the differences among the three best cutoff methods. © 1994 by John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Effect of long-range interactions on the surface tension

The effect of long-range interactions on the surface tension at a liquid-gas interface was considered. An analytical expression for the correction to the surface tension for the cutoff of the particle interaction potential at the distance r _c was derived based on a step density profile. For the Lennard-Jones fluid, this correction was calculated numerically from the results of computer simulations of the density profiles. It was established that, in the vicinity of the triple point, the correction is as great as ～6% at the potential cutoff radius r _c=6.78 molecular diameters, a quantity insensitive to the form of the density profile in the interfacial layer.     

Effects of long-range electrostatic forces on simulated protein folding kinetics

Molecular dynamics simulations are a useful tool for characterizing protein folding pathways. There are several methods of treating electrostatic forces in these simulations with varying degrees of physical fidelity and computational efficiency. In this article, we compare the reaction field (RF) algorithm, particle-mesh Ewald (PME), and tapered cutoffs with increasing cutoff radii to address the impact of the electrostatics method employed on the folding kinetics. We quantitatively compare different methods by a correlation of quantitative measures of protein folding kinetics. The results of these comparisons show that for protein folding kinetics, the RF algorithm can quantitatively reproduce the kinetics of the more costly PME algorithm. These results not only assist the selection of appropriate algorithms for future simulations, but also give insight on the role that long-range electrostatic forces have in protein folding.     

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures.     

Effect of long-range hydrodynamic and direct intermacromolecular forces on translational diffusion

Within the framework of recently formulated microscopic theories of macromolecular diffusion it is shown that hydrodynamic forces act always to diminish the influence of direct forces, but never to reverse the sign of the correction term due to direct forces alone. Although the correction term D(k) to the intrinsic diffusion coefficient may vary with scattering vector |k|, it is shown that a reversal in sigh of the correction term with increasing |k|, if it occurs, must be associated with an amplitude of less than 10% of the correction term at |k| = 0. At |k| = 0 direct repulsive forces are predicted to always increase the apparent diffusion constant, even after accounting for hydrodynamic interactions. Although experiments on polylysine (1 mg/ml) at salt concentrations above 0.01 M are in qualitative accord with the theory, below 10^?3 M salt the apparent diffusion coefficient is reduced by a factor of about 20, concomitant with a much reduced intensity of scattered light. The strong contradiction of the theory implied by this observation is attributed to a dramatic rise in Stokes friction arising from long-range interionic forces in the low-salt solutions.     

Forces in nematic liquid crystals: from nanoscale interfacial forces to long-range forces in nematic colloids

In this paper we give an overview of experiments that provided an insight into the nature of forces between surfaces and objects in a nematic liquid crystal. These forces, also called ‘structural forces’, are the consequence of the long-range orientational order and orientational elasticity of nematic liquid crystals. Owing to their fundamental as well as technological importance, forces between objects in liquid crystals have been a subject of growing interest during the last decade. Experimental observations and studies of structural forces are described from nanoscale interfacial forces, measured by an atomic force microscope, to the micro-scale forces between colloidal particles in nematics, studied by laser tweezers and optical video microscopy.     

Wetting and surface forces

In this review we discuss the fundamental role of surface forces, with a particular emphasis on the effect of the disjoining pressure, in establishing the wetting regime in the three phase systems with both plane and curved geometry. The special attention is given to the conditions of the formation of wetting/adsorption liquid films on the surface of poorly wetted substrate and the possibility of their thermodynamic equilibrium with bulk liquid. The calculations of contact angles on the basis of the isotherms of disjoining pressure and the difference in wettability of flat and highly curved surfaces are discussed. Mechanisms of wetting hysteresis, related to the action of surface forces, are considered.     

A systematic investigation of the ground state potential energy surface of H3+

Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.