Diffusive processes

The rates of ion exchange are generally determined by diffusion processes the ratedetermining step may either be that of diffusion across a boundary film of solution or... 

Adam G and Delbrtick M 1968 Reduction of dimensionality in biological diffusion processes Structural Chemistry and Molecular Biology ed A Rich and N Davidson (San Francisco Freeman)... 

More exotic diffusion processes have been identified, although they may not be fully understood. One example is the substantial enliancement [25] of the diffusivity of interstitial O by H, resulting in the increased fonnation rate of... 

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

In HMC the momenta are constantly being refreshed with the consequence that the accompanying dynamics will generate a spatial diffusion process superposed on the ini rtial dynamics, as in BGK or Smoluchowski dynamics. It is well known from the theory of barrier crossing that this added spatial... 

The above estimates of pressure variations suggest that their magni-tude as a percentage of the absolute pressure may not be very large except near the limit of Knudsen diffusion. But in porous catalysts, as we have seen, the diffusion processes to be modeled often lie in the Intermediate range between Knudsen streaming and bulk diffusion control. It is therefore tempting to try to simplify the flux equations in such a way as to... 

These effects of differential vapor pressures on isotope ratios are important for gases and liquids at near-ambient temperatures. As temperature rises, the differences for volatile materials become less and less. However, diffusion processes are also important, and these increase in importance as temperature rises, particularly in rocks and similar natural materials. Minerals can exchange oxygen with the atmosphere, or rocks can affect each other by diffusion of ions from one type into another and vice versa. Such changes can be used to interpret the temperatures to which rocks have been subjected during or after their formation. 

Before pursuing the diffusion process any further, let us examine the diffusion coefficient itself in greater detail. Specifically, we seek a relationship between D and the friction factor of the solute. In general, an increment of energy is associated with a force and an increment of distance. In the present context the driving force behind diffusion (subscript diff) is associated with an increment in the chemical potential of the solute and an increment in distance dx ... 

For adsorption from the vapor phase, Kmay be very large (sometimes as high as 10 ) and then clearly the effective diffusivity is very much smaller than the pore diffusivity. Furthermore, the temperature dependence of K follows equation 2, giving the appearance of an activated diffusion process with... 

Uranium hexafluoride is used in the gaseous diffusion process for the separation and enrichment of uranium-235, which exists in low concentration in natural uranium. The enriched UF is converted back into an oxide and used as fuel for the nuclear power industry. 

Many challenging industrial and military applications utilize polychlorotriduoroethylene [9002-83-9] (PCTFE) where, ia addition to thermal and chemical resistance, other unique properties are requited ia a thermoplastic polymer. Such has been the destiny of the polymer siace PCTFE was initially synthesized and disclosed ia 1937 (1). The synthesis and characterization of this high molecular weight thermoplastic were researched and utilized duting the Manhattan Project (2). The unique comhination of chemical iaertness, radiation resistance, low vapor permeabiUty, electrical iasulation properties, and thermal stabiUty of this polymer filled an urgent need for a thermoplastic material for use ia the gaseous UF diffusion process for the separation of uranium isotopes (see Diffusion separation methods). 

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

A. Rott and E. Weyde, Photographic Silver Halide Diffusion Process, Eocal Press, Inc., New York, 1972. 

The diffusion process has not been designed to ensure sterility, although temperatures above 65°C significantly retard microbial activity. Sulfur dioxide, thiocarbamates, glutaraldehyde, sodium bisulfite, and chlorine dioxide are all used, occasionally disregarding their redox incompatibilities, to knock down or control infections. The most common addition point is to the water from the pulp presses as it is returned to the diffuser. Surfactants ate almost... 

Dj IE, ratio of a crack is held constant but the dimensions approach molecular dimensions, the crack becomes more retentive. At room temperature, gaseous molecules can enter such a crack direcdy and by two-dimensional diffusion processes. The amount of work necessary to remove completely the water from the pores of an artificial 2eohte can be as high as 400 kj/mol (95.6 kcal/mol). The reason is that the water molecule can make up to six H-bond attachments to the walls of a pore when the pore size is only slightly larger. In comparison, the heat of vaporization of bulk water is 42 kJ /mol (10 kcal/mol), and the heat of desorption of submonolayer water molecules on a plane, soHd substrate is up to 59 kJ/mol (14.1 kcal/mol). The heat of desorption appears as a exponential in the equation correlating desorption rate and temperature (see Molecularsieves). 

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

Carburization by Thermal Diffusion. Carburization of chemically processed metal or metal-compound powders is carried out through sohd-state, thermal diffusion processes, either in protective gas or vacuum. Carbide soHd solutions are prepared by the same methods. Most carbides are made by these processes, using loose or compacted mixtures of carbon and metal or metal-oxide powders. HaUdes of Group 5 (VB) metals recovered from ores by chlorination are similarly carburized. 

A number of special processes have been developed for difficult separations, such as the separation of the stable isotopes of uranium and those of other elements (see Nuclear reactors Uraniumand uranium compounds). Two of these processes, gaseous diffusion and gas centrifugation, are used by several nations on a multibillion doUar scale to separate partially the uranium isotopes and to produce a much more valuable fuel for nuclear power reactors. Because separation in these special processes depends upon the different rates of diffusion of the components, the processes are often referred to collectively as diffusion separation methods. There is also a thermal diffusion process used on a modest scale for the separation of heflum-group gases (qv) and on a laboratory scale for the separation of various other materials. Thermal diffusion is not discussed herein. 

Natural uranium consists mostly of and 0.711 wt % plus an inconsequential amount of The United States was the first country to employ the gaseous diffusion process for the enrichment of the fissionable natural uranium isotope. During the 1940s and 1950s, this enrichment appHcation led to the investment of several bUHon dollars in process faciHties. The original plants were built in 1943—1945 in Oak Ridge, Teimessee, as part of the Manhattan Project of World War II. 

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