Dispersion constant

A value of 0.693 was calculated for the dispersion constant a by using eq A7 and supplier s fLRn data. 

In the case of the pore filled with adsorbate molecules one must account for adsorbate-adsorbent, and adsorbate-adsorbate-adsorbent interactions. Walker57 expressed the potential energy minimum, e, corresponding to these two respective interactions in terms of two dispersion constants, Ae.a, and Aa.a, as well as the number density of adsorbate and adsorbent atoms per unit area. This potential minimum takes the form ... 

The potential energy minimum, e, can be expressed in term of equation 13, using the dispersion constants from equations 14 and 15. 

The dispersion and repulsion interactions form the Lennard-Jones (Barrer, 1978 Masel, 1996 Razmus and Hall, 1991 Gregg and Sing, 1982 Steele, 1974 Adamson, 1976 Rigby et al., 1986) potential, with an equilibrium distance (r0) where 4 d + 4 r = 0. This distance is taken as the mean of the van der Waals radii of the interacting pair. Once the attractive, dispersion constant, A, is known, B is readily obtained by setting at chp/dr = 0 at r0. Hence, B = Ar /2. The most commonly used expression for calculating A is the Kirkwood-Muller formula ... 

In addition, z is the internuclear distance between the adsorbate and adsorbent molecules, (L - ds) is the effective pore width, and Aas is the dispersion constant, which takes into account the adsorbate-adsorbent interaction. The term Aas is calculated with the help of the Kirkwood-Muller formula [8,13,17-19]... 

Although the above calculation is somewhat oversimplified because the effects of the compressibility of the gas have been neglected, it serves to illustrate that a reduction of the column diameter cannot be fully compensated by an increase in the column length to keep the column dispersion constant. Therefore, when narrow-bore capillary columns are to be used in GC, the extra-column contribution to band broadening will need to be reduced. 

P. L. Edwards, Ultrasonic Signal Distortion and its Effects on Velocity Measurements in Dispersive Constant-Group-Velocity Media , J. Acoust. Soc. Am. 1983, 73, 1608. 

In equation (4), A is the number density of atoms per unit surface area A is the dispersion constant the subscripts 5 and / refer to the adsorbent and adsorbate, respectively and do = 0.S5 asf is the z-coordinate at which the 10-4 potential for a single planar surface passes through its zero-point value. The 10-4 potential is obtained by integration of the Lennard-Jones 12-6 potential over an infinite planar surface. The dispersion constants A and Aff represent the adsorbate-adsorbent and adsorbate-adsorbate interactions, respectively these coefficients are calculated from the Kirkwood-Muller equations in the original HK paper [6], Combining equations (2-4) yields an equation that relates filling pressure to pore width ... 

This form will give complex dispersion, but since the same dispersion constant, X., occurs in both terms, it is the unusual wavelength dependence... 

The origin of nonzero bo values in these cases is not entirely clear, but it can be formally traced to the difference between Xo and values for the simple dispersion of random coils and hence to a failure of the assumption that Xo equals Xo. If K equals Xo, then the first term of the Moffitt equation will of course be the same as the simple Drude expression known to describe the data and, there being no necessity for a second term, bo will vanish. However, if Xo differs from Xo, the Moffitt plot may still be linear but with a nonvanishing slope. Thus dispersion data that are simple when referred to one dispersion constant may appear complex when plotted against another by a form that sees matters as complex, thereby generating what may be properly suspected as pseudocomplexity. The Moffitt equation was initially intended to describe the complex dispersion of polypeptides for which the simple Drude equation is inadequate, but, as will be seen, its form is also applied to protein dispersions which can be expressed equally well by either formula. It is therefore important to examine more fully the relation of the two equations for cases in which both fit the data. 

In this equation, represents the effective lateral diffusion/dispersion constant for laminar flow a value on the order of is suitable, and for turbulent flow the molecular diffusion coefficient in this expression should be replaced by the turbulent diffusion coefficient. Based on these simple relations it can be calculated that under typical conditions, lateral reactant transport takes place only over distances of a few subchannels. In other words, if the gas velocity through the wall channels differs much from the velocity through the central subchannels, the nonuniform flow profile can have a significant effect on the overall reactant conversion. In these situations the CBS model can be expected to give a better estimate of the reactor performance than the CB model. 

The value of, the Hamaker (dispersion) constant is initially guessed for a given contact angle. This initial guess can be obtained from Molecular Dynamics simulation results (if available). 

Figure 3 Variation of the dispersion constant (Ac) with contact angle (Fluids water and PF5060,...

Negligible axial dispersion, constant radial dispersion coefficient Constant axial and radial dispersion coefficients... 

An alternative, yet equivalent, expression for the dipole dispersion constant is the Casimir-Polder formula (Casimir and Polder, 1948) ... 

The composite system of two different linear molecules has hence four independent elementary dipole dispersion constants, which in London form can be written as ... 

For two identical linear molecules, there are three independent dispersion constants since C = B. 

The different components of the C6 dispersion coefficients in the LaTbM scheme for (i) two different linear molecules, and (ii) an atom and a linear molecule, are given in Table 11.2 of Magnasco and Ottonelli (1999) in terms of the symmetry-adapted combinations of the elementary dispersion constants (Equations (4.27). For identical molecules, C = B in (4.27), and the (020) and (200) coefficients are equal. 

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