Interaction-radii

This involves the diffusion coefficients DA and DB for the two colliding partners and the encounter radii RAB = aA + Cb sum of the interaction radii (Figure 6.1), p is a probability factor per encounter. The diffusion coefficients are given by the Stokes-Einstein equation... 

Interaction radii, Re (A), distances, R0, and sums of the gas-kinetic radii of the reagents, 1 M + for the reactions of the alkaline metal atoms with iodine Na is the excited Na atom. 

For harpoon reactions of alkaline metal atoms with iodine molecule I2, the interaction radii, Re, calculated using the formula Re = (ajji) 12 from the experimentally measured cross-sections a, are compared in Table 3 with the distances, Ru, calculated with the help of eqn. (40) and the sums of the gas-kinetic radii i M + i l2 of the reagents. In these calculations, effective radii of alkaline metal atoms have been used as RM, while the radii of the molecule I2, calculated from the data on the viscosity of I2 vapour at T > co and at T = 273 K, have been used as i l2 (the values of RM + i ,2 given in brackets correspond to the latter) [71], It is seen that the values of Re exceed Rm + Rh, i.e. electron transfer occurs at large impact parameters. 

The interaction radii beyond which the various intercell quantities appearing in equations (5) and (6) can be cut off are very different 12-15>18... 

Cylinder-cylinder (crossed at 90°) interactions (radii Rf, R2, respectively)... 

Application of Eqs. (21)-(27) to the calculations of the nucleation rates J for various alloy models revealed a number of interesting results, in particular, sharp dependence of J and embryo characteristics on the supersaturation, temperature, interaction radius, etc. These results will be described elsewhere. 

Increasing the cation-solvent interaction radius from 8 to 10 A while the solvent-solvent interactions remain at 8 A results in only a small change (< 0.1 kcal/mol) in the free energy. However, if the solvent-solvent interaction radius is also increased to 10 A the change in the free energy becomes +0.4 kcal/mol which is much larger than would be expected from the water-image effect. It appears that for this mutation the choice of cutoff radius for the solvent-solvent interactions is more important than the radius for the cation-... 

On further assumption that the interaction radius and the kinetic radius are equal, i.e. a = r, and the probability factor p = 1, we have the final form of the equation for efficient reaction,... 

The role of the non-equilibrium charge screening is emphasized by calculations neglecting such screening, i.e., when equations (5.1.54) are omitted and Uv r) — L/r is postulated. In this case mutual repulsion of similar particles accompanied by the attraction between dissimilar particles are characterized by the infinite interaction radius between particles which leads immediately to the Coulomb catastrophe - an infinite increase in K(t) in time shown in Fig. 6.47. This effect is independent of the choice of the initial defect distributions for both similar and dissimilar particles. On the other hand, incorporation of the Coulomb screening makes equations (6.4.1), (6.4.2) asymptotically valid for any initial distribution of particles. 

The lattice-gas model allows to use it for studying the effect of the lateral interactions between the adspecies on the surface process rate or, in other words, to consider the non-ideality of the reaction system in the surface process kinetics. In the lattice-gas model the interaction of adspecies / and j in sites / and g at the distance r is set by the energy parameter sjg(r). In the homogeneous lattice systems such distances can be conveniently determined with the use of the numbers of the (c.s.) where site g is located relative to site /. In this case in the parameter y(r) the index r runs a discrete series of values from 1 to R, where R is the interaction radius 1 1) = 0, one deals with the nearest-neighbors... 

In the general case, the structure of Eq. (B.l) also makes it possible to substantially lower the dimension of the system of equations to (s — 1 )Rt, where R is the interaction radius and t is the number of site types. This is achieved by converting the system of equations for the two-body functions into the identities 1=1 with the aid of the substitution... 

Particles can be regarded as point masses which exert no force on each other beyond a separation distance r > R (R is known as the interactive radius). At r < R there is an infinite repulsive force between the particles involved. They therefore behave like perfectly elastic spheres of radius R/2. 

In the case of nonpolar solute molecules, the third and fourth as well as the fifth term in Eq. (6-2) is zero, thus the solvent dependence will be determined by dispersion interactions and only the second term is essential. The solvent shift, compared to the vapour state, will be approximately 70 to 3000 cm to lower wavenumbers (general red shift) depending only on the function f (cf Eq. (6 )). If, on excitation, there is a sufficiently large change in dipole moment, the third and fourth terms have to be taken into account. In the case of an increase in the dipole moment, these terms cause a batho-chromic shift, and in the case of a decrease, a hypsochromic shift of the absorption band. It has been calculated that for a molecule with an interaction radius aw = 6 10 cm, a dipole moment = 10 Cm (6 D), and a dipole change (// — =... 

Veg and Veg are the wavenumbers of the electronic transitions for absorption and fluorescence in the gas phase, respectively the other terms are as in Eq. (6-2). Eq. (6-5a) has been widely used for the determination of dipole moment changes from the solvent dependence of spectra. The main source of error is the Hmited accuracy of the estimated value for the interaction radius uw of the solute molecule since Av is a cubic function of Uw. 

Hansen Parameters and Interaction Radius of some Polymers and... 

If two colliding particles can be considered hard elastic spheres of radii r and r2, their collisional cross section is equal to 7r(ri +r2). Obviously, interaction radius and cross section can exceed corresponding geometric sizes because of the long-distance nature of forces acting between electric charges and dipoles. On the other hand, if only a few out... 

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