Bulk collisions

The simplest and most straightforward idea for producing collisionally polarized molecules in a thermal cell consists of using collisions with the participation of particles which are polarized in the laboratory frame. It seems that the earliest one was the method based on collisions of atoms which have been optically pumped (optically oriented in their ground state) by the Kastler method see Section 1.1, Fig. 1.1. If the gas constitutes a mixture of a molecular and an atomic component, the conditions being specially created in such a way as to produce such optical orientation of the atoms, we must expect, from considerations of spin conservation in molecular reactions, that polarization of the molecular component must also emerge. 

Let us first discuss a system which is traditional for optical pumping in the Kastler sense [106, 224, 226], namely an optically oriented alkali atom A (see Fig. 1.1) in a noble gas X buffer surrounding. It is important to take into account the fact that in alkali atoms, owing to hyperfine interaction, nuclear spins are also oriented. However, in a mixture of alkali vapor with a noble gas alkali dimers A2 which are in the 1SJ electronic ground state are always present. There exist two basic collisional mechanisms which lead to orientation transfer from the optically oriented (spin-polarized) atom A to the dimer A2 (a) creation and destruction of molecules in triple collisions A + A + X — A2 + X (6) exchange atom-dimer reaction 

The dependence of the dissociation constant kj) and the recombination constants kjt in the reaction (a) on the optical polarization of the atoms A was predicted by Bernheim [65] and Kastler [225] and later demonstrated experimentally [7, 363]. The dependence can be understood from the obvious fact that only hydrogen-like atoms with opposite electronic spins may recombine and form a molecule A2(X1E+). Hence we have kR = kft(l — S2), where S is the degree of electron spin polarization of the atoms. A convenient indicator of dimer formation is provided by the kinetics of the laser-induced molecular fluorescence after switching on magnetic resonance which destroys the polarization of the atoms, as performed by Huber and Weber [201] for a Na — Na2 mixture. The se- 

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This may be compared with the usual bulk collision rate (Moelwyn-Hughes, 17) of... 

F is the bulk collision constant, A is a positive dimensionless factor, Vf is the Fermi velocity and R the particle radius. From a classical point of view, this modification is supported by the fact that, when the radius is smaller than the bulk mean free path of the electrons, there is an additional scattering factor at the particle surface. This phenomenon, known as the mean free path effect, is abundantly discussed in [19]. In a quantum approach, the boundary conditions imposed to the electron wave functions lead to the appearance of individual electron-hole excitations (Fandau damping) [21] resulting in the broadening of the SPR band proportional to the inverse of the particle radius as in Eq. (8) [22]. A chemical interface damping mechanism has also been considered, leading to the l/R dependence of F [23]. 

As an example, we look at tire etching of silicon in a CF plasma in more detail. Flat Si wafers are typically etched using quasi-one-dimensional homogeneous capacitively or inductively coupled RF-plasmas. The important process in tire bulk plasma is tire fonnation of fluorine atoms in collisions of CF molecules witli tire plasma electrons... 

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

As a result, collisions with the wall occur more frequently than with other molecules. This is referred to as the Knudsen mode of diffusion and is contrasted with ordinary or bulk diffusion, which occurs by intermolecular collisions. At intermediate pressures, both ordinaiy diffusion and Knudsen diffusion may be important [see Eqs. (5-239) and (5-240)]. 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

After adsorption, species may diffuse on the surface or, eventually, become absorbed in the bulk. Due to collisions between adsorbed species of different kinds the actual reaction step can occur. Of course, this step requires that some energetic and spatial constraints have to be fulfilled. The result of the reaction step is the formation of a product molecule. This product can be either an intermediate of the reaction or its final output. 

Despite the fact that relaxation of rotational energy in nitrogen has already been experimentally studied for nearly 30 years, a reliable value of the cross-section is still not well established. Experiments on absorption of ultrasonic sound give different values in the interval 7.7-12.2 A2 [242], As we have seen already, data obtained in supersonic jets are smaller by a factor two but should be rather carefully compared with bulk data as the velocity distribution in a jet differs from the Maxwellian one. In the contrast, the NMR estimation of a3 = 30 A2 in [81] brought the authors to the conclusion that o E = 40 A in the frame of classical /-diffusion. As the latter is purely nonadiabatic it is natural that the authors of [237] obtained a somewhat lower value by taking into account adiabaticity of collisions by non-zero parameter b in the fitting law. 

The simplest state of matter is a gas. We can understand many of the bulk properties of a gas—its pressure, for instance—in terms of the kinetic model introduced in Chapter 4, in which the molecules do not interact with one another except during collisions. We have also seen that this model can be improved and used to explain the properties of real gases, by taking into account the fact that molecules do in fact attract and repel one another. But what is the origin of these attractive and... 

A collision with a Mars-sized object may have resulted in the formation of the Earth s moon. Our moon is by no means the largest satellite in the solar system, but it is unusual in that it and the moon of Pluto are the largest moons relative the mass of the planets they orbit. Geochemical studies of returned lunar samples have shown that close similarities exist between the bulk composition of the moon and the Earth s mantle. In particular, the abimdances of sidero-... 

Cherry and Papoutsakis [33] refer to the exposure to the collision between microcarriers and influence of turbulent eddies. Three different flow regions were defined bulk turbulent flow, bulk laminar flow and boundary-layer flow. They postulate the primary mechanism coming from direct interactions between microcarriers and turbulent eddies. Microcarriers are small beads of several hundred micrometers diameter. Eddies of the size of the microcarrier or smaller may cause high shear stresses on the cells. The size of the smallest eddies can be estimated by the Kolmogorov length scale L, as given by... 

In addition to bulk liquid turbulence effects, suspended particles maybe involved in collisions with one another or with solid surfaces within the vessel. This phenomenon has been extensively studied in micro-carrier cultures [60] and appears to be significant at high concentrations [61]. Rosenberg [69] and Meijer [72] applied the approach of Cherry and Papoutsakis [60] to the study of collision phenomena involving spherical plant cell aggregates of 190 and 100 pm, respectively. In both cases it was concluded that for typical biomass concentrations, particle-particle interactions were of less significance than particle-impeller collisions. 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

Figure 3.5.2 shows the results obtained using M-5 and TS-500 samples with S/V values of 3.03 x 107 and 3.28 x 107 m 1, respectively, and porosities of 0.936 and 0.938, respectively. Note the significant deviation of the relaxation behavior from that ofbulk CF4 gas (dotted lines in Figure 3.5.2). The experimental data were first fitted to the model described above, assuming an increase in collision frequency due purely to the inclusion of gas-wall collisions, assuming normal bulk gas density. However, this model merely shifts the T) versus pressure curve to the left, whereas the data also have a steeper slope than bulk gas data. This pressure dependence can be empirically accounted for in the model via the inclusion of an additional fit parameter. Two possible physical mechanisms can explain the necessity of this parameter.

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

As shown in Figure 3.5.3, the relaxation time versus pressure curves are dramatically different from those obtained using CF4 at a temperature well above its critical point. Indeed, while the overall form of the Tx curves for CF4 in fumed silica was similar to that of the bulk gas, the shape of the Ti plots for c-C4F8 in Vycor more closely resembles that of an adsorption isotherm (Ta of CF4 in Vycor is largely invariant with pressure, as gas-wall collisions in this material are more frequent than gas-gas collisions). This is not surprising given that we expect the behavior of this gas at 291 K to be shifted towards the adsorbed phase. The highest pressure... 

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