Repulsion constant

Strong (repulsive) - constant force or constant distance... 

From this equation, we can see that the total nonideality correction (in braces) contains a negative contribution (first bracketed term) that is indeed proportional to the attractions constant a, while the positive contribution (second bracketed term) is proportional to the finite-volume repulsions constant b, as was supposed in the interpretation of experimental Z behavior in Fig. 2.2. One can also see that the attractions term is linearly proportional to density n/V, whereas the repulsions term is proportional to squared density (,njV)2, so that the former must always prevail at low density (low P) and the latter at high density (high P), as was shown in Fig. 2.2. Furthermore, one can recognize from the 1 /RT prefactor that the entire nonideality correction must diminish with increasing P, as was noted in Fig. 2.3. Thus, regardless of the particular values chosen for a and b, the Van der Waals equation is expected to exhibit both pressure and temperature dependences that are qualitatively consistent with the observed Z(P, T) behavior. 

Guests larger than ethane cannot fit into the small cage of sll and therefore the repulsive constants are zero. Due to the lack of si compositional data, the repulsive constant for only one of the hydrate cages could be regressed. Due to lack of sH compositional data, the volume of sH hydrates was assumed to be independent of composition (Table 5.5). 

Regressed Repulsive Constants and Guest Diameters for Hydrate Volume... 

No theoretical expression for the repulsion constant,, has been developed it can, however, be evaluated in terms of the equilibrium separation, z = ze, where the potential function has its maximum value. At z — ze., dP/dz = 0 hence... 

In this table we have omitted interactions of multipoles higher than the quadrupole. Since very little is known about forces 7-11, they are often neglected. The repulsive energy takes the general form Bjr orB exp(— rjp). Here B is the repulsive constant , p is a constant related to the compressibility and is a constant whose value is usually 9eh.e3o.e3i some... 

The introduction of the expression for the binary interaction potential discussed in Sect. 2.1.11.4 into this equation leads to the formula (92) for the repulsion constant , ii ... 

Fig. 22 Experimental values of the repulsion constant , u, in isotherm (93) for iodide adsorption at Bi-water interface (points are shown with their dispersion) as a function of the eiectrode potentiai in the rational scale, (p = E — Eo=o- The theoretical curve (solid line) was calculated from Eq. (92) for A = 0.71 with the use of experimental data for the compact- and diffuse-layer capacitances of the same interface in a surface-inactive electrolyte solution.

Similar results have been obtained for the other systems listed in the preceding text. In particular, the values of the repulsion constant , v, were found within the limits of 0.6 and 3.5 nm per adsorbed ion. These results represent an additional confirmation of the prediction of strong intensity and long-range of the binary interaction potential discussed in Sect. 2.1.11.4. One should keep in mind that the attempt to interpret the same experimental data with the use of the single-image expression (86) would result in the values of the ion-metal distance, Uj, well beyond the usual length of... 

Strong (repulsive)—constant force or constant height Weak (attractive)—vibrating probe Strong (repulsive)—vibrating probe... 

To estimate the dispersion-repulsion forces for larger molecules for which Lennard-Jones force constants are not available it is customary to retain the general form of Eq. (2.3) but to replace the attractive and repulsive constants (4 o and 4 o ) by the semiempirical constants A and B ... 

The value of the repulsion constant B may therefore be estimated by setting equal to the mean of the van der Waals radii. 

Somewhat closer agreement between theory and experiment for the rare gases in various forms of zeolite X was obtained by Broier et al. who used the Kirkwood-Muller expression, The calculated values are however quite sensitive to the choice of equilibrium radii, which determine the repulsion constants. The choice of radii is not clearly specified by Broier et al. and it seems likely that the values selected may have been adjusted, within physically reasonable limits, to improve the fit. There is also some uncertainty in the choice of physical parameter values for the estimation of the dispersion constants as well as in the charge distribution. 

The constants of a Urey-Bradley force field for NF3 [46, 47] are either physically unreasonable or very badly reproduce observed frequencies if the repulsion constants F and F are subject to the Lennard-Jones condition F = -1/10 F [46]. Better agreement between observed and calculated frequencies is obtained if a nonbonded interaction between the lone pair at nitrogen and the fluorine atoms is taken into account. However, the number of force constants to be determined may then rise to 8, and some of them have to be estimated merely by physical intuition [48, 49]. 

The first derivative of the potential expresses the parameter A as a function of the repulsion constant b, and the set of parameters defined above... 

---