Solute radius

Rikvold and Stell [319,320,365] have developed an expression for the partition coefficient in a random two-phase medium made up of spherical particles. They found the partition coefficient to be essentially an exponential function of the solute radius, which is in qualitative agreement with the Ogston theory. 

This convolution equation takes into account the fact that Kqpc, the distribution coefficient, is a function of both the effective solute radius (f) and the pore radius (r). Even if all the pores of a gel have the same diameter, solutes of... 

The case of transport through microporous membranes is different from that of macroporous membranes in that the pore size approaches the size of the diffusing solute. Various theories have been proposed to account for this effect. As reviewed by Peppas and Meadows [141], the earliest treatment of transport in microporous membranes was given by Faxen in 1923. In this analysis, Faxen related a normalized diffusion coefficient to a parameter, X, which was the ratio of the solute radius to the pore radius... 

Application of the Stokes-Einstein equation requires a value for the solute radius. A simple approach is to assume the molecule to be spherical and to calculate the solute radius from the molar volume of the chemical groups making up the molecule. Using values for the solute radius calculated this way along with measured and known diffusion coefficients of solutes in water, Edward [26]... 

Fig. 14.4. Theoretical critical velocity as a function of separation distance for different values of solute radius/pore radius ratio (A). Solute radius (a) = 5 nm ko= 1.0 (k is the Debye parameter) membrane and solute surface potential = 50 mV. Values of A (a) 0.8 ...

Optical excitations quite often generate considerable changes in fixed partial charges, usually described in terms of the difference solute dipole Amo ( 0 refers here to the solute). Chromophores with high magnitudes of the ratio Amo/Rl, where Rq is the effective solute radius, are often used as optical probes of the local solvent structure and solvation power. High polarizability changes are also quite common for optical chromophores, as is illustrated in Table 2. Naturally, the theory of ET reactions and optical transitions needs extension for the case when the dipole moment and polarizability both vary with electronic transition ... 

Southall NT, Dill KA. The mechanism of hydrophobic solvation depends on solute radius. J. Phys. Chem. B 2000 104 1326-1331. Lee CY, McCammon JA, Rossky PJ. The structure of fiq-uid water at an extended hydrophobic surface. J. Chem. Phys. 1984 80 4448-4455. 

Me is the number-average molecular weight between polymer cross-links M is the number-average molecular weight of the uncross-Unked polymer M is a critical molecular weight between cross-links (p is polymer volume fraction n is solute radius... 

Equation 16.15 shows that, as expected, the gel phase diffusivity approaches zero as the solute radius approaches the mesh size. In a responsive gel, as sweUing increases in response to environmental changes gel phase diffusivity increases with increasing mesh size. Figure 16.16 shows the effect of competitor concentration on predicted gel phase diffusivity assuming a solute radius of 1.5 nm. Using this example and a dextran polymer gel, it is not possible to achieve a cross-link density sufficient to give a predicted mesh size sufficiently small to prevent gel phase diffusivity. However, as Equation 16.12 does not consider the steric effects of the immobilized receptor experimentally determined gel phase diffiisivities are likely to be lower. 

The SEC partition coefficient [6] (.K sec) was measured on a Superose 6 column for three sets of well-characterized symmetrical solutes the compact, densely branched nonionic polysaccharide, Ficoll the flexible chain nonionic polysaccharide, pullulan and compact, anionic synthetic polymers, carboxylated starburst dendrimers. All three solutes display a congruent dependence of K ec on solute radius, R. In accord with a simple geometric model for SEC, all of these data conform to the same linear plot of i sEc versus R. This plot reveals the behavior of noninteracting spheres on this column. The mobile phase for the first two solutes was 0.2M NaH2P04-Na2HP04, pH 7.0. In order to ensure the suppression of electrostatic repulsive interactions between the dendrimer and the packing, the ionic strength was increased to 0.30M for that solute. 

For each filter-solute combination, X was calculated as a ratio of the solute radius to the "rated" pore radius. The predicted value of the rejection coefficient was then calculated from Equation (4). The comparison between the predicted values and those actually measured with Carbowaxes 4000 and 600 is shown in Figure 10a and b, respectively. The measurements were carried out at several values of AP in order to assess the Importance of contribution from concentration polarization. 

Figure 11. Measured apparent rejection of polyethylene oxide (Carbowax) at aP -= 50 psi (a) GPC trace of a blend solution containing 0.02% of each Carbowax 1000,1400,1540, 4000, and 6000 (b) GPC trace of a permeate obtained by UF at AP = 50 psi through Nuclepore 150 A membrane (c) apparent rejection calculated from GPC traces shown in a and b, (Q), as a function of solute radius of gyration. The solid line shows theoretical prediction according to Equation 4.

Tumor Normal tissue Solute radius (nm) Tumor normal permeability Ref. 

The key parameters used in describing hindered transport through cylindrical pores are illustrated in Figure 5.8. A critical parameter is the ratio of the solute radius to the pore radius, X = a/fp. As X approaches 1, the pore walls become an increasingly important obstacle for particle transport. In the limit as X approaches zero, the fluid within the pore can be considered unbounded. 

SouthaU, N.T., Dill, K.A. The mechanism of hydrophobic solvation depends on solute radius. 

The configuration shown in Fig. 8.35 was used by the present author to determine the stress intensity factor for an annular crack located at the equator of a spherical void (Green, 1980). This geometry was meant to simulate the presence of pores in a linear elastic continuum. The solution is shown schematically in Fig. 8.37. As expected, the solution is similar to the edge crack solution for short cracks (a/R<0.1) and the internal circular crack solution (radius (R+a)) for long cracks (a/R>0.5). 

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