Solute Stokes radii

On the basis of either model, ii is clear ihat dialytic transport will dectesse with increasing solute molecular size, not only beeause of the smeller solution diffusivity of a large molecule bur also because of incransmg values of q. This effect is seen in Fig. 21.1-4. where the ratio of diffusivity in the membrane (3Dm) to difliisivity in solution (3D) is plotted as a function of solute Stokes radii for several dialysis membranes. 

FIGURE 2.8 Determination of relative clearance of dextran as a function of solute size. Please note that Stokes radius (left curve) will yield too low a value for the renal clearance barrier. [Reproduced from Hagel et al. (1993), with permission.]... 

A prerequisite condition for the increase in conductivity being caused by added ligands is a high association constant of the salt in the absence of added ligand. If the association constant is low, as it is for AN-based solutions, a decrease of conductivity may occur, because the Stokes radius of the solvated Li+ ion is increased by ligands with molecular diameters larger than that of AN, entailing lower cation mobility [214],... 

If, however, the Stokes radius of the solute bears some simple relationship to its molecular weight, the latter may be determined directly from gel chromatography by means of the Laurent-Killander equation.54 Sims and Folkes59 have pointed out that equation 4 may be more simply expressed in the form... 

Squire63 used a model of the gel phase in which the volume elements available to solvent within the gel were regarded as a combination of cones, cylinders, and crevices, and derived expressions for the volumes available to a solute of Stokes radius a in these three types of pore. Certain arbitrary assumptions regarding the distribution of solute among the different types of pore gave the following equation ... 

Ackers64 has interpreted gel chromatography in terms of steric and frictional resistance to the diffusion of the solute in the gel pores, and, on this basis, he has used an equation originally proposed by Renkin65 for deriving the following relationship between Kd and the Stokes radius, a, of the solute ... 

The theoretical basis of the transport of solute ions during iontophoresis can be compared to electrophoresis through a gel network. When the ionized solute has a mean Stokes radius smaller than the average mesh size (hole in the network), the solute is considered as a rigid sphere undergoing Brownian movement, with a mobility dependent on the frequency of solute interaction with the porous network. The sphere mobility is assumed to be proportional to the fractional volume of the pore that is accessible to the sphere [92]. The electrophoretic mobility, u, of such a solute sphere has been shown to be directly related to the molecular weight of the solute [93] ... 

The electrophoretic mobility of a species in agarose or polyacrylamide gel is determined by the Stokes radius, the effective charge, the nature of the counter-ions, the potential gradient, the concentration of agarose or polyacrylamide and, to a lesser extent, by the number of cross-links. For a solute molecule of appreciable size there will be a gel concentration at which the mobility is so diminished that the molecules do not enter the gel. The mobility in fact is a smooth function of the gel concentration, which must therefore... 

However, surfactants incorporated into the electrolyte solution at concentrations below their critical micelle concentration (CMC) may act as hydrophobic selectors to modulate the electrophoretic selectivity of hydrophobic peptides and proteins. The binding of ionic or zwitterionic surfactant molecules to peptides and proteins alters both the hydrodynamic (Stokes) radius and the effective charges of these analytes. This causes a variation in the electrophoretic mobility, which is directly proportional to the effective charge and inversely proportional to the Stokes radius. Variations of the charge-to-hydrodynamic radius ratios are also induced by the binding of nonionic surfactants to peptide or protein molecules. The binding of the surfactant molecules to peptides and proteins may vary with the surfactant species and its concentration, and it is influenced by the experimental conditions such as pH, ionic strength, and temperature of the electrolyte solution. Surfactants may bind to samples, either to the... 

Stokes radius of a solute (X) rejection coefficient wall surface area of cores (cm /g) thickness of adsorbed layer (X) volume of pore cores (cm /g) volume of cylindrical pores (cm /g)... 

Figure 5.11 Relationship of permeability coefficients of neutral molecules (urea, glucose and saccharose) through the cation exchange membrane NEOSEPTA CM-1 and the same membrane with a polypyrrole layer to the Stokes radius of the solutes. ( ) Cation exchange membrane without the layer (NEOSEPTA CM-1) (O) membrane with a polypyrrole layer facing the dilute side in the measurement (A) membrane with polypyrrole layer facing the concentrated side. One surface of ferric ion form NEOSEPTA CM-1 was in contact with an aqueous pyrrole solution for 10 min to form a polypyrrole layer (polymerization time 10 min.).

While the Stokes-Einstein equation is strictly applicable only in cases where the diffusing particle is large when compared to the surrounding solvent molecules (so that the fluid can be considered a continuum), it has proven to be useful for solute-solvent pairs in which the radius, a, is only two to three times the solvent radius. For a solute with radius comparable to the solvent radius, the 6 in Equations 4-3 and 4-4 should be replaced by a 4, since the assumption of no slip at the solute surface is no longer valid [48]. 

The size of the solute molecules is characterised by their hydrodynamic radius (Stokes radius) in a particular solvent. Using SEC it is... 

---