Intrinsic diffusion coefficient components

Various diffusion coefficients have appeared in the polymer literature. The diffusion coefficient D that appears in Eq. (3) is termed the mutual diffusion coefficient in the mixture. By its very nature, it is a measure of the ability of the system to dissipate a concentration gradient rather than a measure of the intrinsic mobility of the diffusing molecules. In fact, it has been demonstrated that there is a bulk flow of the more slowly diffusing component during the diffusion process [4], The mutual diffusion coefficient thus includes the effect of this bulk flow. An intrinsic diffusion coefficient, Df, also has been defined in terms of the rate of transport across a section where no bulk flow occurs. It can be shown that these quantities are related to the mutual diffusion coefficient by... 

The intrinsic diffusion coefficients, Dk and DB, of a binary alloy A-B express the diffusion of the components A and B relative to the lattice planes [7], Therefore, during interdiffusion, a net flux of atoms across any lattice plane is present, where, normally, the diffusion rates of the diffusing particles A and B are different. Subsequently, this interdiffusion process provokes the shift of lattice planes with respect to a fixed axis of the sample, result which is named the Kirkendall effect [9],... 

In the two-component system gas + zeolite, in parallel with a general two-component system, one may consider 5 diffusion coefficients Dab (interdiffusion coefficient of sorbate and zeolite) Da, Db (intrinsic diffusion coefficients, respectively, of sorbate and zeolite) and Da, Db (tracer diffusion coefficients, respectively, of sorbate and zeolite). However, because Db and Db are effectively zero, as for a nonswelling crystal. 

Once an appropriate frame of reference is chosen, a two components (A, B) system may be described in terms of the mutual diffusion coefficient (diffusivity of A in B and vice versa). Unfortunately, however, unless A and B molecules are identical in mass and size, mobility of A molecules is different with respect to that of B molecules. Accordingly, the hydrostatic pressure generated by this fact will be compensated by a bulk flow (convective contribution to species transport) of A and B together, i.e., of the whole solution. Consequently, the mutual diffusion coefficient is the combined result of the bulk flow and the molecules random motion. For this reason, an intrinsic diffusion coefficient (Da and Db), accounting only for molecules random motion has been defined. Finally, by using radioactively labeled molecules it is possible to observe the rate of diffusion of one component (let s say A) in a two component system, of uniform chemical composition, comprised of labeled and not labeled A molecules. In this manner, the self-diffusion coefficient (Da) can be defined [54]. Interestingly, it can be demonstrated that both Da and Da are concentration dependent. Indeed, the force/acting on A molecule at point X is [1]... 

For example, if ethanol evaporates faster than water, a gradient of alcohol will develop and ethanol will diffuse from the interior of the sample at the same time, water will diffuse into the interior. The interdiffusion will affect shrinkage only if the intrinsic diffusion coefficients of the components are different and the permeability of the network is low. (See Fig. 9.) If the diffusion coefficients are equal, the fluxes of the components will be equal and opposite, so no net volume change will occur in the saturated pores. If the diffusion coefficients are different, flow will tend to compensate for the volume change (say, by the rapid diffusion of alcohol to the drying surface and counterflow of the pore liquid into the interior). If the permeability is low, that flow will be inhibited, and the diffusion of the volatile component from the interior will cause the tension to rise in the liquid within the gel. This will compensate for the rising tension in the liquid at the exterior, reducing the differential strain and stress. 

The additional advantage of CARS-CS over DLS and FCS is the spectral selectivity for individual chemical components in their native state, where fluorescent labeling is not desired. This may not only allow mapping of 3D diffusion coefficients, for example inside life cells, but also offer a method to monitor the specific interaction of individual components within complex systems, e.g., aggregation processes of different chemical species. Another prospect is the implementation of CARS cross-correlation spectroscopy that may allow the investigation of correlated fluctuations between two different species. These could be two distinct Raman spectral features of one and the same compound, or a specific intrinsic Raman band and an emission of a more sensitive fluorescence label [160]. 

The high sensitivity of radiotracer techniques makes these very attractive for determination of diffusion coefficients. Self-diffusion (i.e. diffusion of the intrinsic components of the substance) is of special interest and can only be measured by indicator methods. 

Here the subscript i refers to the solvent, whereas the superscript (A or B) refers to the component homopolymer. For example, ai is the thermal diffusion coefficient of a homopolymer consisting of component B in solvent 1. Parameters [rj]i and Xi are the intrinsic viscosity and retention parameter measured on the copolymer in solvent i T g in equation 9c is the temperature at the center of gravity of the retained polymer zone in solvent i, while rjo is the viscosity of solvent i at Teg- Equations 7 through 9 are applicable to copolymers with only two components similar equations could be derived for n-component copolymers, in which case My and Xa are determined from retention and viscosity data in n separate solvents. 

Separation from mixtures is achieved because the membrane transports one component more readily than the others, even if the driving forces are equal. The effectiveness of pervaporation is measured by two parameters, namely flux, which determines the rate of permeation and selectivity, which measures the separation efficiency of the membrane (controlled by the intrinsic properties of the polymer used to construct it). The coupling of fluxes affecting the permeability of a mixture component can be divided into two parts, namely a thermodynamic part expressed as solubility, and a kinetic part expressed as diffusivity. In the thermodynamic part, the concentration change of one component in the membrane due to the presence of another is caused by mutual interactions between the permeates in the membrane in addition to interactions between the individual components and the membrane material. On the other hand, kinetic coupling arises from the dependence of the concentration on the diffusion coefficients of the permeates in the polymers [155]. 

Finally, a phenomenon called concentration quenching or static quenching can lead to upward curvature of Stern Volmer plots even at moderate quencher concentrations (c q > 0.01 M). Molecules that are located next to a quencher at the time of excitation will be quenched immediately. Therefore, the fluorescence decay curve will be nonexponential initially, exhibiting a very fast initial component. Moreover, the initial depletion of these molecules will result in an inhomogeneous distribution of the remaining excited molecules around the quenchers. As a result, the diffusion coefficient kA is no longer a constant, but becomes a function of time, kd(t), until the statistical distribution of excited molecules is re-established. The impact of these effects has been analysed in detail.231 Intrinsic rates of electron transfer in donor acceptor contact pairs can be extracted from the resulting curvature in Stern Volmer plots.232... 

The intrinsic simplicity of the single-component system renders it ideal for measurements of basic reaction in chemistry like the kinetics of recombination in Coulomb cage (Forster and Volkers, 1975), the diffusion coefficient of a proton in water (Gutman et al., 1981) or solids like ice or urea (Pines, 1981). Due to the indirect applicability of these subjects to biochemistry, these subjects will not be further discussed. 

In (5.51), r stands for the intrinsic reaction rate at liquid bulk conditions. For worst-case-estimations, one should use a highest rate value possible in the considered RD column. In this respect it should be kept in mind that the reaction rates under RD conditions strongly depends on the operating pressure that influences the boiling temperatures, that is the reaction temperature. D g/ represents the effective diffusion coefficient of a selected reaction component inside the catalyst particles. One should use the component with the lowest mole fraction Xj in the liquid bulk mixture as key component [35]. Its effective diffusion coefficient can be estimated from the diffusion coefficient at infinite dilution Dg((/ = (sfr)D with the total porosity e and the tortuosity r of the applied catalyst. Based on (5.51) one can say that intraparticle diffusion resistances will be negligible, if 1. 

At the other end of the spectrum, however, in transdermal systemic delivery, the molecular attributes required are rather different. In this case, compounds are required to partition into the relatively lipophilic stratum corneum, diffuse rapidly across the stratum corneum and partition easily into the more hydrophilic viable epidermis and dermis prior to vascular removal. The intrinsic requirements of compounds for transdermal delivery are, therefore, a medium polarity (a log octanol-water partition coefficient of 1-3), a low molecular volume and a lack of potential to bind to skin components (e.g., via hydrogen bonding). 

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