Van der Waals forces calculation

FIG. 2 Interaction forces between glass surfaces upon compression in ethanol-cyclohexane mixtures. The dashed and solid lines represent the van der Waals force calculated using the nonretarded Hamarker constants of 3 X 10 1 for glass/cyclohexane/glass and 6 X 10 J for glass/ethanol glass, respectively. 

Table 2. Hamaker constants used for van der Waals force calculation.

As two bubbles approach at any reasonable rate, there must arise a hydrodynamic repulsive force, due to the need to expel water molecules from the film between bubbles. In water, coalescence is observed. Thus, there must exist an attractive force that overcomes the hydrodynamic repulsion. The attractive van der Waals force calculated between two bubbles in water is found to be orders of magnitude smaller than the hydrodynamic repulsion present at reasonable approach rates. As bubbles are highly hydrophobic (/air-water = 72mjm 2) it is reasonable to assume that the "hydrophobic force" is present, and acts to produce coalescence. Available force measurements are found to give an attraction of sufficient magnitude to overcome the hydrodynamic repulsion. This implies that for salts and sugars to reduce bubble coalescence, the attractive hydrophobic force is reduced in their... 

The traditional approach to van der Waals force calculations employing Hamaker theory is illustrated in a series of papers [5.87-91] discussing anisomeric and layered-particle interactions. These papers give numerous explicit results including both indication of the conditions for repulsive interaction and the effects of geometry on the interaction forces. Their formulas are useful for qualitative purposes, but the limitations of the method raise questions both as to their general validity and certainly as to their potential for quantitative predictions. 

Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)...

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

The Debye temperature 9d can be calculated from the slope of the line. The value obtained for Kr is 72 K. This small 9o results from the weak van der Waals forces that hold the Kr atoms together in the solid. 

The van der Waals forces for these substances are due mainly to dispersion forces, which decrease with decrease in atomic number for atoms of similar structure. London s calculations (F. London, Z. Physik 63, 245 (1930) have shown the interaction of permanent dipoles to contribute only a small amount to the van der Waals forces for a substance such as hydrogen chloride. 

Typical forces profdes measmed between glass surfaces in ethanol-cyclohexane mixtures are shown in Fig. 2. Colloidal probe atomic force microscopy has been employed. In pure cyclohexane, the observed force agrees well with the conventional van der Waals attraction calculated with the nometarded Hamaker constant for glass/cyclohexane/glass. 

The interaction of drug molecules with biological membranes is a three-dimensional (3D) recognition that is mediated by surface properties such as shape, Van der Waals forces, electrostatics, hydrogen bonding, and hydrophobicity. Therefore, the GRID force field [5-7], which is able to calculate energetically favorable interaction sites around a molecule, was selected to produce 3D molecular interaction fields. 

Results have shown that the properties of solids can usually be modeled effectively if the interactions are expressed in terms of those between just pairs of atoms. The resulting potential expressions are termed pair potentials. The number and form of the pair potentials varies with the system chosen, and metals require a different set of potentials than semiconductors or molecules bound by van der Waals forces. To illustrate this consider the method employed with nominally ionic compounds, typically used to calculate the properties of perfect crystals and defect formation energies in these materials. 

CNT can markedly reinforce polystyrene rod and epoxy thin film by forming CNT/polystyrene (PS) and CNT/epoxy composites (Wong et al., 2003). Molecular mechanics simulations and elasticity calculations clearly showed that, in the absence of chemical bonding between CNT and the matrix, the non-covalent bond interactions including electrostatic and van der Waals forces result in CNT-polymer interfacial shear stress (at OK) of about 138 and 186MPa, respectively, for CNT/ epoxy and CNT/PS, which are about an order of magnitude higher than microfiber-reinforced composites, the reason should attribute to intimate contact between the two solid phases at the molecular scale. Local non-uniformity of CNTs and mismatch of the coefficients of thermal expansions between CNT and polymer matrix may also promote the stress transfer between CNTs and polymer matrix. 

Scoring systems are set up to quantitatively calculate how well the ligand docks with the active site in terms of alignment, hydrogen bonding, van der Waals forces, and electrostatic and hydrophobic interactions. In addition, flexibilities of both the ligands and protein in the binding process as they accommodate each other have to be considered. 

The van der Waals forces [7,8], which link the particles to the substrates, can easily be calculated in the case of spherical particles ... 

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