Mobility, average

Key words Transparent thin-film transistor, device physics, effective mobility, field-effect mobility, saturation mobility, average mobihty, incremental mobihty, output conductance... 

For a cylindrical particle oriented at an arbitrary angle between its axis and the applied electric field, its electrophoretic mobility averaged over a random distribution of orientation is given by pav = /i///3 + 2fjLj3 [9]. The above expressions for the electrophoretic mobility are correct to the first order of ( so that these equations are applicable only when C is low. The readers should be referred to Ref. [4-8, 10-13, 22, 27, 29] for the case of particles with arbitrary zeta potential, in which case the relaxation effects (i.e., the effects of the deformation of the electrical double layer around particles) become appreciable. 

If the traps can move, their mobility averages the influence of spatial heterogeneity and in this case [136] Eq. (88) ... 

It is necessary to mark, that the singular dependence on time in the equation (2) appears simultaneously with large-scale fluctuations (inhomogeneity) of traps density. If the traps ean move, their mobility averages the influence of spatial heterogeneity, so the assumptions resulting to (1) will be carried out better. It was shown, that in this case the concentration of the particles drops imder the combined law [4] ... 

The interpretation of termination behavior in the TD region is far more complicated, as monomer conversion is no sufficient measure for characterizing radical mobility. Average polymer size or, even better, size distribution and the extent of branching should additionally be known. The situation may be referred to as history-dependent kinetics, which basically says that kt depends on the characteristics of the polymerizing system, in particular on the properties of the polymer. These properties are determined by the specific mode of polymerization by which a particular conversion has been reached. The pathway thus affects kt under TD conditions via the polymeric structure given by the preceding polymerization. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

The application of a small external electric field A to a semiconductor results in a net average velocity component of the carriers (electrons or holes) called the drift velocity, v. The coefficient of proportionality between E and is known as the carrier mobility p. At higher fields, where the drift velocity becomes comparable to the thennal... 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

The average linear velocity u of the mobile phase in terms of the column length L and the average linear velocity of eluent (which is measured by the transit time of a nonretained solute) is... 

A solute s capacity factor can be determined from a chromatogram by measuring the column s void time, f, and the solute s retention time, (see Figure 12.7). The mobile phase s average linear velocity, m, is equal to the length of the column, L, divided by the time required to elute a nonretained solute. 

The solute can only move through the column when it is in the mobile phase. Its average linear velocity, therefore, is simply the product of the mobile phase s average linear velocity and the fraction of solute present in the mobile phase. 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

Thus when an electric field is appHed to a soHd material the mobile charge carriers are accelerated to an average drift velocity v, which, under steady-state conditions, is proportional to the field strength. The proportionality factor is defined as the mobility, = v/E. An absolute mobility defined as the velocity pet unit driving force acting on the particle, is given as ... 

The ionic mobility is the average velocity imparted to the species under the action of a unit force (per mole), i is the stream velocity, cm/s. In the present case, the electrical force is given by the product of the electric field V in V/cm and the charge per mole, where S" is the Faraday constant in C/g equivalent and Z is the valence of the ith species. Multiplication of this force by the mobihty and the concentration C [(g mol)/cm ] yields the contribution of migration to the flux of the ith species. 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

On average, a molecule will remain in the mobile phase a time (ta) before it is adsorbed. During this time, it will be moving at the mean velocity of the mobile phase (u) and will, thus, move a distance (uta). Thus, in moving a distance (l), the total... 

Figure 4. HETP Curves for the Same Column and Solute Using the Average Mobile Phase Velocity and the Exit Velocity...

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