Van der Waals potentials

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

Tang K T and Toennies J P 1984 An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients J. Chem. Phys. 80 3726... 

Figure Bl.20.2. Attractive van der Waals potential between two curved mica surfaces measured with the SFA. (Reproduced with pemiission from [4], figure 11.6.)...

Fraser G T and Pine A S 1986 Van der Waals potentials from the infrared speotra of rare gas-HF oomplexes J. Chem. Phys. 85 2502-15... 

The potential energy of a molecular system in a force field is the sum of individnal components of the potential, such as bond, angle, and van der Waals potentials (equation H). The energies of the individual bonding components (bonds, angles, and dihedrals) are function s of th e deviation of a molecule from a h ypo-thetical compound that has bonded in teraction s at minimum val-n es. 

L1948. Steric Effects. I. Van der Waals Potential Energy Curves. Journal of Chemical Physics 16 399-04. 

Figure 4-15 A van der Waals Potential Energy Function. The Energy minimum is shallow and the interatomic repulsion energy is steep near the van der Waals radius.

From one force held to the next, the balance of energy terms may be different. For example, one force held might use a strong van der Waals potential and no electrostatic interaction, while another force held uses a weaker van der Waals potential plus a charge term. Even when the same terms are present, different charge-assignment algorithms yield systematic differences in results and the van der Waals term may be different to account for this. 

Fig. 6. Van der Waals potential energy-distance curve showing regions of operation of contact, noncontact, and intermittent contact or tapping-mode afm...

Fig. 7. The van der Waals potential between droplets is increasingly negative with reduced interdroplet distance, whereas the electric double-layer potential...

The relative value of the two potentials reveals the destabdization action of salts added to the emulsion. Addition of an electrolyte to the continuous phase causes a reduction of the electric double-layer repulsion potential, whereas the van der Waals potential remains essentially unchanged. Hence, the reduced electric double-layer potential causes a corresponding reduction of the maximum in the total potential, and at a certain concentration of electrolyte the maximum barrier height is reduced to a level at which the stabdity is lost. 

Liquid crystals stabilize in several ways. The lamellar stmcture leads to a strong reduction of the van der Waals forces during the coalescence step. The mathematical treatment of this problem is fairly complex (28). A diagram of the van der Waals potential (Fig. 15) illustrates the phenomenon (29). Without the Hquid crystalline phase, coalescence takes place over a thin Hquid film in a distance range, where the slope of the van der Waals potential is steep, ie, there is a large van der Waals force. With the Hquid crystal present, coalescence takes place over a thick film and the slope of the van der Waals potential is small. In addition, the Hquid crystal is highly viscous, and two droplets separated by a viscous film of Hquid crystal with only a small compressive force exhibit stabiHty against coalescence. Finally, the network of Hquid crystalline leaflets (30) hinders the free mobiHty of the emulsion droplets. 

Fig. 15. The slope of the van der Waals potential vs interdroplet distance becomes extremely small in the coalescence step between two droplets covered by...

Let us now calculate the three components of the van der Waals attraction by first calculating these interactions between two molecules. Subsequently, the total van der Waals potential between bodies will be determined by assuming that the molecules belong to two different materials and integrating the molecular interactions over the volumes of the materials. 

A more sophistieated model, whieh permits assoeiative adsorption on the erystalline lattiees, has been introdueed in Refs. 82, 83. The model assumes that the atoms forming the erystal lattiee interaet with fluid partieles not only via the van der Waals potential but also via assoeiative forees. The assoeiative adsorption is eharaeterized by a high degree of Realization of the adsorbed partieles as a eonsequenee of a strong bonding between the bulk... 

We should mention here one of the important limitations of the singlet level theory, regardless of the closure applied. This approach may not be used when the interaction potential between a pair of fluid molecules depends on their location with respect to the surface. Several experiments and theoretical studies have pointed out the importance of surface-mediated [1,87] three-body forces between fluid particles for fluid properties at a solid surface. It is known that the depth of the van der Waals potential is significantly lower for a pair of particles located in the first adsorbed layer. In... 

The calculations have been carried out for a one-component, Lennard-Jones associating fluid with one associating site. The nonassociative van der Waals potential is thus given by Eq. (87) with = 2.5a, whereas the associative forces are described by means of Eq. (60), with d = 0.5contact with an attracting wall. The fluid-wall potential is given by the Lennard-Jones (9-3) function... 

Figure 6-12. Model for Ihe Calculation of the van der Waals potential experienced by a single T6 molecule on a Tfi ordered surface. Each molecule is modeled as a chain of 6 polarizable spherical units, and the surface as 8-laycr slab, each layer containing 266 molecules (only pan of the cluster is shown). Tire model is based on X-ray diffraction and dielectric constant experimental data. The two configurations used for evaluating the corrugation of the surface potential are shown. Adapted with permission front Ref. [48].

X 10, and 7.8 X 10 kg/mol-ns respectively. Note that these values are at the level which we identified with the onset of configurational motion inhibition. In glassy polymers, we expect the effective value of 7c to be significantly larger than the roughly 5 x 10 kg/mol-ns calculated above because the actual repulsive part of the van der Waals potential is much steeper than a quadratic fit of Equation 2. Let us emphasize again the approximate... 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

Fig. 1 a Model bead-spring chain interacting through bond potential Dj, bond angle potential Uq, and van der Waals potential C7v(jw> and b the form of the bond angle potential Ug... 

Figure 4.13 shows the free energy profile as a function of the helix-helix distance. Equation (4.47) allows the computation of the contributions to the profile by the different intermolecular potentials. The helix-helix and helix-solvent interactions were considered. The helix-helix van der Waals potential shows a significant minimum... 

T. L. Hill, Steric effects. I. van der Waals potential energy curves, J. Chem. Phys. 

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