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.     

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.     

Dynamical phase of driven colloidal systems with short-range attraction and long-range repulsion

We study the nonequilibrium dynamics of colloidal system with short-range depletion attraction and screened electrostatic repulsion on a disordered substrate. We find a growth-melting process of the clusters as the temperature is increased. By strengthening the screened electrostatic repulsion, a depinning transition from moving cluster to plastic flow is observed, which is characterized by a peak in threshold depinning force. The corresponding phase diagram is then mapped out. Due to the influences of disorder from substrate, the clusters are polarized by the strong external force, accompanied by the appearance of interesting orientational order parallel to the force and translational order perpendicular to the force. Under the condition of strong external force, the influences of density of pins and temperature are also studied.     

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.     

Cyclic tetraselenadiynes: rigid cycles with long-range van der Waals forces between chalcogen centers

The synthesis of cyclic tetraselenadiynes could be achieved by a stepwise approach. Key steps were the reaction of the lithium salt of trimethylsilylacetylene (1) with alpha,omega-diselenocyanatoalkanes 2(m) (m = 2-5). By treating the bis-lithium salt of the resulting alpha,omega-diselenaalkadiynes 4(m) (m = 2-5) again with 2(n) (n = 2-5) the cyclic tetraselenadiynes 5(m.n) resulted, with methylene chains of length m and n between the SeC triple bond CSe units. The structures of seven ring systems could be investigated in the solid state. These investigations reveal that the molecular structures are determined by the rigid SeC triple bond CSe units, which try to adopt torsion angles of the CH(2)-Se sigma-bonds between 60 degrees and 90 degrees. In the solid state, the systems 5(3.3) and 5(5.5) show columnar structures that can be traced back to close contacts between Se atoms of neighboring rings.     

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.     

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.     

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.

     

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.     

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.     

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.     

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.     

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.     

Analytical calculation of repulsion forces arising when the non-ionic diffuse adsorption layers are overlapped

Summary Calculation of the molecular (Van der Waals) component of disjoining pressure of an solution interlayer is rendered difficult by the non-uniformity of the concentration of a dissolved component in this interlayer. This interferes with the direct application of Lifshits et al.'s calculation method. It is the use of an analogue of Gibbs-Duhem' equation that leads to an expression for the disjoining pressure of the interlayer: one component of this expression is equal to the disjoining pressure of a pure solvent, while the other takes into account the influence of the dissolved component. This influence is determined by an excess (quasi-adsorption) of the dissolved component in the interlayer. For determining this excess, the effective Van der Waals' potential energy of the dissolved molecules in the interlayer is used.By introducing a certain simplification, it is possible to obtain a simple analytical expression for the resultant disjoining pressure of the solution interlayer. As the interlayer becomes thinner, the expression changes its sign, whether from the negative to the positive or from the positive to the negative one, or it retains the negative sign. Such a result is indicative of the influence of the effects of osmotic nature, which are similar to those acting in ionic solutions.

---

Zusammenfassung Die Berechnung der Molekular-(Van-der-Waals)-Komponente des Spaltdruckes einer Lösung wird durch Ungleichmäßigkeit der Konzentration der aufgelösten Komponente in der Zwischenschicht schwierig gemacht. Dies verhindert die unmittelbare Anwendung der Berechnungsmethode von Lifshits u. a. Infolge der Anwendung eines Analogons der Gibbschen-Duhemschen Gleichung wird ein Ausdruck für den Spaltdruck der Zwischenschicht abgeleitet. Eine Komponente dieser Gleichung ist dem Spaltdruck des reinen Lösungsmittels gleich, während die zweite Komponente den Einfluß des aufgelösten Bestandteils berücksichtigt. Dieser Einfluß wird durch Überschuß (Quasiadsorption) am letzteren in der Zwischenschicht bestimmt. Zur Ermittlung dieses Überschusses benutzt man die Berechnung der effektiven Van-der Waalschen Potentialenergie der aufgelösten Moleküle in der Zwischenschicht.Unter Zuhilfenahme einer Vereinfachung leitet man einen einfachen analytischen Ausdruck für die Resultierende des Spaltdruckes der Lösungszwischenschicht ab.Im Laufe der Verdünnung der Zwischenschicht ändert dieser Ausdruck sein Vorzeichen vom negativen zum positiven oder vom positiven zum negativen ab, oder schließlich behält er das negative Vorzeichen bei.

     

Analytical calculation of repulsion forces arising when the non-ionic diffuse adsorption layers are overlapped

Calculation of the molecular (Van der Waals) component of disjoining pressure of an solution interlayer is rendered difficult by the non-uniformity of the concentration of a dissolved component in this interlayer. This interferes with the direct application of Lifshits et al.'s calculation method. It is the use of an analogue of Gibbs-Duhem' equation that leads to an expression for the disjoining pressure of the interlayer: one component of this expression is equal to the disjoining pressure of a pure solvent, while the other takes into account the influence of the dissolved component. This influence is determined by an excess (quasi-adsorption) of the dissolved component in the interlayer. For determining this excess, the effective Van der Waals' potential energy of the dissolved molecules in the interlayer is used.

By introducing a certain simplification, it is possible to obtain a simple analytical expression for the resultant disjoining pressure of the solution interlayer. As the interlayer becomes thinner, the expression changes its sign, whether from the negative to the positive or from the positive to the negative one, or it retains the negative sign. Such a result is indicative of the influence of the effects of osmotic nature, which are similar to those acting in ionic solutions.