Solute hindrance coefficient

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

It should be pointed out that the characteristics of polymer structure (e.g., porosity, tortuosity, steric hindrance, mesh size, etc.) should be determined in order to calculate the diffusion coefficient of a specific molecule in a particular polymer. For cross-linked polymers, additional polymer properties should be characterized. Even though there are methods to determine these properties, a simple mathematical relationship between the diffusion coefficient of a solute and its molecular weight has been used due to the complexity of the experiment ... 

Based upon Eq. 4 a systematic study was performed with four polar permeants (urea, mannitol, sucrose, and raffinose) in an effort to characterize further the porous permeation pathway through HEM (Peck et al., 1994). Dual-labeled liquid scintillation counting and an experimental protocol that incorporated successive permeability experiments, as outlined in the previous sections, allowed the permeability coefficients for each permeant to be determined for each HEM sample studied. Again, Eq. 4 predicts that, for a porous membrane, the permeability coefficient ratio should be equal to the ratio of the diffusion coefficients for the solutes in the membrane. As a first approximation, if the relative radii of the solutes and the membrane pore radii Rp are such that hindrance considerations are negligible (Deen, 1987), then the ratio PJPy should approach the ratio of the free diffusion coefficients D of the solutes in bulk solution. 

The basis for comparing the ratios of the free diffusion coefficients and permeability coefficients was the assumption that hindrance considerations could be ignored. In the instance that this assumption is valid (i.e., the case of large pore dimensions relative to solute radii), the free diffusion coefficients are a reasonable approximation to the diffusion coefficients of the solutes in the membrane. In the instance that hindrance considerations are not negligible, due to pore dimensions that lead to diffusion-restricting hydrodynamic interactions between the solute and the membrane, the diffusion coefficient of the solute in the membrane is a function of both the solute parameters and the properties of the membrane. In this case, the effective diffusion coefficient can be approximated by the product of the free diffusion coefficient and a diffusional hindrance factor, HQC) (Deen, 1987) ... 

The proton-dissociation reaction of alkylated ANIs in the excited 5) state tends to decrease significantly in A-monoalkylanilines but to increase in the A-dialkylated derivatives, with much larger activation energies111. The differences in the observed kiiss rate coefficient between protonated aniline and protonated alkylated derivatives has been explained on the basis of the charge density on the N-atom in the excited S state, the water structure in the vicinity of the amino group which acts as a proton acceptor and steric hindrance of the alkyl groups. As a consequence, the acidity (pKa values) and fluorescence lifetime of protonated anilines in aqueous solution are remarkably dependent on the substituent position in the ring. 

For a polydisperse polymer solute, both W2 and R2 are functions of the solute molecular weight, M2. If f(M2) is the solute differential weight distributions and W(M2) th corresponding hindrance, the average rejection coefficient, R2 is defined through ... 

There is no equation comparable to the Knudsen equation for diffusion of liquids in small pores, but the pore walls do limit the movement of molecules and cause a decrease in the diffusivity. Diffusion coefficients can be predicted from the bulk diffusivity and a hindrance factor that depends on the pore size and the solute size. For moderate-molecular-weight solutes, the empirical Wilke-Chang equation is used for the bulk diffusivity [13] ... 

Electrolytes are electric conductors, but, in contrast to ordinary conductors, they are decomposed by electric current. The charge transport in electrolytes is carried by ions which start to move if an electric field acts on the electrolyte. Many samples to be studied by sensors are electrolyte solutions, hi such solutions, the ionic concentration may be high enough to cause mutual hindrance by ionic interaction. Such an interaction explains why the activity coefficient assumes values so different from 1. 

When the solute dimension is no longer orders of magnitude smaller than the pore dimensions, the solute molecules experience an additional transport resistance due to the proximity of the pore wall. The effective diffusion coefficient is reduced further by a hindrance factor/ drag factor Gm i i,rp). If the solute molecules are assumed spherical of radius r, and diffusing through the centerline of the pore of radius, tp, Faxen s expression may be used to estimate Gor for (r,rp) < 0.5 (Lane, 1950 Renkin, 1954) ... 

Here, is the concentration of solute i averaged over a pore cross section, G is a convective hindrance factor, accounting for the ratio between the velocity of solute molecules and the averaged pore velocity of the solvent Vz (usually less than 1), and Dip is the diffusion coefficient of solute molecules of species i in the pore (Anderson and Quinn, 1974). We have seen earlier from (3.1.113) that... 

Here, Dm is the diffusion coefficient of solute i in the organic solvent. If there is no hindrance to solute diffusion in the pore due to r Tp (at letist by two orders of tnagnimde). 

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