Van der Waal forces constant

Empirical constant used in the calculation of the van der Waals force constant of integration Concentration of salt Electrolyte concentration Correction factor for Reynolds equation accounting for the mobility of the film surfaces Concentration of Na ions near the surface... 

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.)...

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

With the reader bearing in mind this framework, the Lifshitz theory of van der Waals interactions can readily be understood. According to the Lifshitz theory, van der Waals forces arise from the absorption of photons of frequency tu by a material with a complex dielectric constant... 

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. 

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as ... 

Refinements in the theory of interparticle long-range van der Waals forces (the Landau-Lifshitz theory) are within reach. New techniques are now available for measuring the complex dielectric constants of various media required for the implementation of that theory. 

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. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

From the ideal gas equation, it is found that for 1 mole of gas, PV/KT = 1, which is known as the compressibility factor. For most real gases, there is a large deviation from the ideal value, especially at high pressure where the gas molecules are forced closer together. From the discussions in previous sections, it is apparent that the molecules of the gas do not exist independently from each other because of forces of attraction even between nonpolar molecules. Dipole-dipole, dipole-induced dipole, and London forces are sometimes collectively known as van der Waals forces because all of these types of forces result in deviations from ideal gas behavior. Because forces of attraction between molecules reduce the pressure that the gas exerts on the walls of the container, van der Waals included a correction to the pressure to compensate for the "lost" pressure. That term is written as w2a/V2, where n is the number of moles, a is a constant that depends on the nature of the gas, and V is the volume of the container. The resulting equation of state for a real gas, known as van der Waals equation, is written as... 

Van Deemter rate theory analychem A theory that the sample phase in gas chromatography flows continuously, not stepwise. van dam tar rat. the a re ) van der Waals adsorption physchem Adsorption in which the cohesion between gas and solid arises from van der Waals forces. van dar, w6lz ad.sorp shan ) van der Waals attraction See van der Waals force. van dar, w6lz a.trak shan ) van der Waals covolume physchem The constant b in the van der Waals equation, which is approximately four times the volume of an atom of the gas in question multiplied by Avogadro s number. van dar, w6lz ko val yam ) van der Waals equation phys chem An empirical equation of state which takes into account the finite size of the molecules and the attractive forces between them p = RT/(v — b) - (a/v ). where p is the pressure, v is the volume per mole, T is the absolute temperature, R is the gas constant, and a and b are constants. van dar, w6lz i,kwa-zhan ... 

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