Stokes’ ionic radius

That is, nonionic surfactants caused an increase in the Stokes radius (R) of the particles due to penetration of the phospholipid surface layer and unfolding of apoprotein B molecules leading to particle assymetry at molar ratios of surfactant LDL2 of ca. 1000/1. At higher molar ratios, corresponding to 1-2 moles surfactant per mole of phospholipid, ionic surfactants and nonionics with HLB values < 14.6 caused rapid decreases in the Stokes radius due to breakdown of LDL2 into the lipid surfactant and protein surfactant micelles. 

For instance, molar conductivities cannot conceivably be negative. Given this, one may try to look for an ion with very small conductivity, or one may apply Stokes law for motion in a viscous fluid and assume a proportionality between reciprocal ionic radii and the ionic conductivity. It turns out that the Stokes radius of Na+... 

Table 1. Partial Molar Volume (Vj°°). Effective Ionic Radius (rjf), Stokes Radius (rs), and Temperature CoefScient of Walden Product (dln( A °°Tj ldT) at 25 ...

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... 

The use of the macro-d5uiamical method previously in connection with the osmotic theory of force [the diffusion of electrolytes and ionic mobilities by Nemst diffusion and the hydrodynamic (Stokes ) radius of molecules according to W. Sutherland and Einstein] is weU known. An alternative, simple formulation of two-component diffusion, Eq. (10), is possible if another form of the thermod5mamic factor, based upon osmotic pressme is applied ... 

A test of Stokes equation is easily arranged. Table 5.12.1 lists sets of ionic radii, and Table 5.12.2 the so-called Walden products A° 7 for several cations and anions using data drawn from Appendices 5.12.1 to 5.12.12. The first point to notice is that the Walden product for a given ion varies from solvent to solvent and attains approximate constancy only when the ion is very large. In most cases, therefore, the Stokes radius is a function of the solvent as well as of the ion. For ranges... 

Concerning the origin of the peculiar behavior, two models have been proposed and coexisted for long time, which attribute quite different physics to solvent response to a solute displacement. The first model, often referred to as the solventberg model, maintains the classical view of Stokes law but with an effective ionic radius, or the Stokes radius, which takes into account the effect of solvation solvent molecules are regarded firmly bound to the ion, and the radius of the solvated ion plays a role of the Stokes radius. The Stokes radius in this model decreases with increasing ionic radius since the ion-solvent interaction is weakened due to the increased ion-solvent distance. The solventberg model has... 

A Stokes radius may be assigned to an ion, "ist = F I )%Njf) Zi lri. Ionic Stokes radii are commensurate with ri but not directly related to them for some ions even rist < i, although they ought to be larger, pertaining to the hydrated ions. The Walden products are approximately... 

The different hydration numbers can have important effects on the solution behaviour of ions. For example, the sodium ion in ionic crystals has a mean radius of 0 095 nm, whereas the potassium ion has a mean radius of 0133 nm. In aqueous solution, these relative sizes are reversed, since the three water molecules clustered around the Na ion give it a radius of 0-24 nm, while the two water molecules around give it a radius of only 017 nm (Moore, 1972). The presence of ions dissolved in water alters the translational freedom of certain molecules and has the effect of considerably modifying both the properties and structure of water in these solutions (Robinson Stokes, 1955). 

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

AA-gpjj. Conditionally, the ionic atmosphere is regarded as a sphere with radius r. The valnes of approach the size of colloidal particles, for which Stokes s law applies (i.e., the drag coefficient 9 = where r is the liquid s viscosity) when they... 

For very dilute solutions, the motion of the ionic atmosphere in the direction of the coordinates can be represented by the movement of a sphere with a radius equal to the Debye length Lu = k 1 (see Eq. 1.3.15) through a medium of viscosity t] under the influence of an electric force ZieExy where Ex is the electric field strength and zf is the charge of the ion that the ionic atmosphere surrounds. Under these conditions, the velocity of the ionic atmosphere can be expressed in terms of the Stokes law (2.6.2) by the equation... 

Molar ionic conductivity — This quantity, first introduced by -> Kohlrausch, is defined by A = Zi Fui (SI unit Sm2 mol-1), where Zj and 14 are the charge number and -> ionic mobility of an ion, respectively. The molar -> conductivity of an electrolyte M +X (denoted by A) is given by A = u+X+ + i/ A, where A+ and A are the molar ionic conductivities of the cation and anion. The A value of an ion at infinite dilution (denoted by A°°) is specific to the ion. For alkali metal ions and halide ions, their A values in water decrease in the orders K+ > Na+ > Li+ and Br- > Cl- > F-. These orders are in conflict with those expected from the crystal ionic radii, because the smaller ions are more highly hydrated, so that the -> hydrated ions become larger and thus less mobile. Based on Stokes law, the radius of a hydrated ion... 

The Stokes-Einstein equation connecting diffiisivity D, of ionic species i of charge z, and radius r with the viscosity q of the medium in which the diffusion is occurring. 

What is the total charge on an ionic atmosphere around an anion of valence z From the data in the text, examine logy vs. Vm, where tn is the molality of the solution, from 0 to 1 mol dm". The plots always pass through a minimum. Use the fully extended Debye-Hlickel theory, including the Bjerrum-Stokes and Robinson terms, to find the significance of the minimum at which the electrolyte concentration increases with the increase of the cation radius. 

Table IV shows the Stokes shift of the Ce emission in several surroundings. In the 2.2.1 cryptand the Ce Stokes shift is smaller than in some commercial Ce " -activated phosphors (Y2Si05-Ce, Ca2AlSiOv-Ce). It becomes very small in ScBOa (see above) and in CaF2 and CaS04, where it carries an effectively positive charge that will make the Ca site smaller than it is on basis of the Ca " ionic radius.

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