Mobility and diffusivity

Trinh et al. [399] derived a number of similar expressions for mobility and diffusion coefficients in a similar unit cell. The cases considered by Trinh et al. were (1) electrophoretic transport with the same uniform electric field in the large pore and in the constriction, (2) hindered electrophoretic transport in the pore with uniform electric fields, (3) hydrodynamic flow in the pore, where the velocity in the second pore was related to the velocity in the first pore by the overall mass continuity equation, and (4) hindered hydrodynamic flow. All of these four cases were investigated with two different boundary condi-... 

He, Q Johnson, CS, Two-Dimensional Electrophoretic NMR for the Measurement of Mobilities and Diffusion in Mixtures, Journal of Magnetic Resonance 81, 435, 1989. 

Slater, GW Guo, HL, Ogston Gel Electrophoretic Sieving How Is the Fractional Volume Available to a Particle Related to Its Mobility and Diffusion Coefficient(s) , Electrophoresis 16,11, 1995. 

Iodine and bromine adsorb onto Au(l 11) from sodium iodide or sodium bromide solutions under an applied surface potential with the surface structure formed being dependent on the applied potential [166]. The iodine adsorbate can also affect gold step edge mobility and diffusion of the Au surface. Upon deposition of a layer of disordered surface iodine atoms, the movement of gold atoms (assisted by the 2-dimensional iodine gas on the terrace) from step edges out onto terraces occurs. However, this diffusion occurs only at the step edge when an ordered adlayer is formed [167]. 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

Capillary zone electrophoresis, an up-to-date high resolution separation method useful for proteins and peptides, has been shown to be a useful method for determining electrophoretic mobilities and diffusion coefficients of proteins [3], Diffusion coefficients can be measured from peak widths of analyte bands. The validity of the method was demonstrated by measuring the diffusion coefficients for dansylated amino acids and myoglobin. 

Table 1 summarizes several of the experimental methods discussed in this chapter. A need exists for new or revised methods for transport experimentation, particularly for therapeutic proteins or peptides in polymeric systems. An important criterion for the new or revised methods includes in situ sampling using micro techniques which simultaneously sample, separate, and analyze the sample. For example, capillary zone electrophoresis provides a micro technique with high separation resolution and the potential to measure the mobilities and diffusion coefficients of the diffusant in the presence of a polymer. Combining the separation and analytical components adds considerable power and versatility to the method. In addition, up-to-date separation instrumentation is computer-driven, so that methods development is optimized, data are acquired according to a predetermined program, and data analysis is facilitated. 

Y Walbroehl, J Jorgenson. Capillary zone electrophoresis for determination of electrophoretic mobilities and diffusion coefficients. J Microcolumn Separ 1 41, 1989. 

Early CE-NMR experiments were aimed at understanding the effects of eleetro-phoresis on NMR spectral properties and determining physicochemical properties such as electrophoretic mobilities and diffusion coefficients. Since then, CE-NMR has garnered attention as an effective hyphenated technique with a variety of applications... 

It may be noted that data on the diffusion coefficient of the salt and on the limiting transport numbers permit the individual ionic mobilities and diffusion coefficients in the membrane to be evaluated by conventional means. 

Such easy reactivity and selechvity working under rather mild conditions is probably favored by the lack of relevant solvation effects and by a controlled mobility and diffusion corresponding to few collateral reactions and consequently high selechvity. 

Equation (2.158) is the Einstein relation relating the mobility and diffusivity tensors. 

Example 3.7 Use molar ionic conductivity data in Table 3-1 to calculate the mobility and diffusivity of Na+, Cl and NaCl at infinite dilution and 298.15 K. 

The first step always occurs since, attractive forces between the undissociated molecule and the surface usually exist. This step may involve adsorption into a so-called precursor state where the molecule is mobile and diffuses across the... 

There are several different approaches that are commonly used to determine particle size distributions in air. One of them, impaction, has been discussed earlier. Multistage impactors with different cut points are used extensively to obtain both mass and chemical composition data as a function of size for particles with diameters > 0.2 /xm. Others, including methods based on optical properties, electrical or aerodynamic mobility, and diffusion speeds, are described briefly in the following section. The condensation particle counter (CPC) is used as a detector in combination with some of these size-sorting methods. 

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

Consequently, while the effect of an electric field dependence of both drift mobility and diffusion coefficient and also hydrodynamic repulsion decreases, the recombination probability, dielectric saturation and relaxation effects increase the recombination probability. 

Hong and Noolandi [72], Berg [278], and Pedersen and Sibani [359] have also noted the connection between the survival probability and homogeneous density distribution. Finally, the escape probability of an ion pair formed with a separation, r0, with an arbitrary monotonically decreasing potential energy of interaction and with electric field-dependent mobility and diffusion coefficient ions was found by Baird et al. [350] to be (see also Tachiya [357])... 

The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

Another use of relaxation times is to provide insight into mobility and diffusion as shown by Nagata et al. where 35C1 NMR was used to analyse the effect of temperature on sodium chloride mobility in crab meat37... 

Because colloidal particles have finite size, their mobility and diffusion coefficients depend not only upon their size but also upon, the distance from the collector surface. This variation with distance stems from friction between the collector surface and the fluid which increases the force required to push the fluid out of the path of the approaching particle. In the usual transport equation containing only convective and diffusive terms, the size of the molecules is small enough for the thickness in to be small compared to the length du, where fim and Bp are explained in Table 1. Other situations arise In which these conditions are not met, or in which London or gravitational forces are important To identify the limiting cases, it is useful to seek some quantity for each mechanism which allows the ordering of its relative importance. 

Length over which the mobility and diffusion coefficients vary appreciably with radial distance. 

According to the Nernst-Eicstein equation ( > = mkT) the mobility and diffusion coefficients are proportional. Then, using Equation (5), the diffusion coefficient of the particles can be expressed as... 

Mobility and diffusion coefficients were evaluated from Equations (6) and (6), The associated boundary condi-... 

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