Effective collision diameter

The secondary electroviscous effect is often interpreted in terms of an increase in the effective collision diameter of the particles due to electrostatic repulsive forces (i.e., the particles begin to feel the presence of other particles even at larger interparticle separations because of electrical double layer). A consequence of this is that the excluded volume is greater than that for uncharged particles, and the electrostatic particle-particle interactions in a flowing dispersion give an additional source of energy dissipation. 

Following Holland [1, 2], a localised atom is assigned to one of the localised quantum states, with energy less than E, associated with an adsorption site (see Fig. 1). Quantum states, whose energies are in excess of, embrace the whole surface and are approximated to be the states of a particle in a two-dimensional box of uniform potential. An adatom in one of these quantum states is able to move about the surface and encounter other adatoms, both localised and mobile, the effective collision diameter always being o,. 

If we introduce the depth of the hole zQ and the distance d at which the energy is just zero (the intersection of the curve for the potential energy with the line V — o, (see Fig. 2) d is the effective collision diameter of the molecule. 

Although the Enskog theory is formally valid for rigid spheres only, fairly accurate results have been obtained for real gases as well provided that the effective collision diameter is appropriately adjusted. 

A at 600°K and compare it with the experimental result. Assume that the effective collision diameter is 5 x 10" cm. 

Our theory is done, then, except for some details concerning p and cr. In general these quantities can be only estimated, so that often an effective collision diameter, f7g, is used. This is defined by... 

Using the appropriate collision-theory rate constant, determine the effective collision diameter for this reaction based on the data above. Is this quantity a function of temperature ... 

Considering the collisions between the part ides AB in configuration space, we must replace the actual collision diameter d by an effective collision diameter d = 2d, where d is the radius of a particle AB corresponding to the collision complex in the physical space. Each particle AB with an effective mass... 

Assuming the activation energy and the value of the rate constant at 373 K from Example 12.6, find the effective collision diameter of a hydrogen molecule and an iodine molecule. Solution... 

This volume fraction represents an increase in the effective particle size to give a collision diameter Reff... 

The separation of the caged radical-ion pair can also be rationalized using the model of Konig and Braun, Rajbenbach, and Eirich.103 The probability %(t) that the radical and the ion are at a distance x at a time t (Equation 6.136) depends on the collision diameter a and the effective diffusion coefficient D of the pair, and A is a normalization constant. 

Neutral molecules, dissolved, dispersed or suspended in a liquid medium, are in continuous random motion (Brownian motion) with a mean free path (x) and collision diameter (xe), depending on c and vex effects. At a far separation distance, is negative, increasing to 0 at xe, where repulsion counterbalances attraction and the amphiphiles are at dynamic equilibrium in a primary minimum energy state. At x High concentrations shorten x and make the collision rate nonlinear with c, (Hammett, 1952). A separation distance of x < xe is sterically forbidden without fusion. 

Fig. 2, Effect of (c) collision diameter and (fa) particle radios upon the total interaction energy profile. Other properties have the same value as in Figure 1, except I — y.s2 = 28 mV in (b).

Because of its small size (collision diameter 0.20 nm), helium would appear to be a useful probe molecule for the study of uitramicroporous carbons. The experimental difficulty of working at liquid helium temperature (4.2 K) is the main reason why helium has not been widely used for the characterization of porous adsorbents. In addition, since helium has some unusual physical properties, it is to be expected that its adsorptive behaviour will be abnormal and dependent on quantum effects. 

Here /is the ionization potential of the quenching molecule and = [c/(Q) + (/(I )] /2 is the distance of closest approach of the collision pair, where the d values are taken as Lennard-Jones collision diameters deduced from viscosity measurements. Thus a plot of In (cr ) versus In aQfj j HI ) would be predicted to be linear. This model also predicts some variability for different v vibrational levels due to Franck-Condon effects, but this can be ignored in the present experiment where mainly the v = 32 level is excited by the 532-nm source. 

Although the model is idealized, the principles of momentum conservation which were used to calculate the transfer properties apply equally well to more realistic models including quantum-mechanical treatments and the results are the same, the chief differences being in the effective molecular diameters and the possibility of inelastic collisions. 

Repulsive The repulsive effect begins when the distance between nuclear centers is less than the sum of the centers van der Waal radii (known as the collision diameter). Collisions are extremely unfavorable energetically and grow rapidly as the distance between nuclear centers diminishes (l/r11). 

The collision cross-section a is related to effective molecular diameters by a = nd2 so d =, a(ji)112... 

Fig. 12.2. Potential of mean force fV for two different solute-solvent diameters. Rough estimates of the effective elastic collision diameters of iodine in inert solvents can be obtained from the known Lennard-Jones o parameters. The mean force potential is also compared with the Morse potential, K...

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