Diffusion coefficient solvent viscosity effect

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent environment and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diffusion coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [69]... 

Dioxane is a cyclic diether forming a six-membered ring [20]. Thus it is a nearly nonpolar symmetric molecule. 1,4-Dioxane is an extraordinary solvent, capable of solubilizing most organic compounds, and water in all proportions, and many inorganic compounds. The self-diffusion coefficient of dioxane is 1.1 x 10 cm /s, about half that of a water molecule. The effective diameter of dioxane is 5.5 A - about twice that of a water molecule. One should not forget that a water-dioxane mixture narrowly avoids a lower critical consolute point. However, the effects of criticality are reflected in the values of ffie mutual diffusion coefficient and viscosity. Note that binary mixtures are often chosen so that they are mixable (do not phase separate). Thus, the two components interact attractively and strongly. 

Equation (10.4 ) relates a diffusion coefficient to the effective radius of a diffusing particle of substance 2 and the viscosity of the solvent ... 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

The Hl value is reduced by an increase in the viscosity of the solvent or by a decrease in the temperature. Longitudinal diffusion can thus be reduced by decreasing the diffusion coefficient and increasing the flow rate however, these two actions are counter-effective in liquid chromatography because of the mass transport term. 

Much of the recent impetus for temperature control has focused on exploiting the effects of elevated temperature on viscosity and diffusion coefficients [2], These lead to faster separations and also allow smaller particle diameters to be employed with conventional HPLC hardware. As the viscosity of solvents decreases, the column pressure drops. This can be exploited by using faster flow rates and smaller particle diameters. All of this leads to faster separations. In one experiment in this laboratory, a separation which required 8 min at room temperature was reduced to 2 min at 50°C without changing the column. Speed enhancements of as much as 50-I00-fold have been reported [13] as shown in Figure 9.1. 

In the concentration range regarding the ED processes, the effective diffusion coefficient (Z>B) can be predicted via the Gordon relationship (Reid et al, 1987), which accounts for the partial derivative of the natural logarithm of the mean molal activity coefficient (y+) with respect to molality (m) and solvent relative viscosity (rjr) ... 

The proper choice of a solvent for a particular application depends on several factors, among which its physical properties are of prime importance. The solvent should first of all be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapour pressure, and their temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity also need to be considered. Electrical, optical and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant too. Furthermore, molecular characteristics, such as the size, surface area and volume, as well as orientational relaxation times have appreciable bearing on the applicability of a solvent or on the interpretation of solvent effects. These properties are discussed and presented in this Chapter. 

In addition to elucidation of molecular structures, NMR can also extract valuable information about physicochemical parameters. Because of the omnipresence of protonated solvents in CE/CEC, mobile-phase events can be monitored with NMR. Early studies using E-NMR involved the calculation of diffusion coefficients, electrophoretic mobilities, and viscosity [27]. Stagnant mobile-phase mass transfer kinetics and diffusion effects [60] and fluid mass transfer resistance in porous media-related chromatographic stationary phases [61] have been studied with NMR spectroscopy. NMR imaging of the chromatographic process [62] and NMR microscopy of chromatographic columns [63] have also been reported. Several applications of NMR to on-line studies of CE/ and CEC/ NMR are highlighted. 

These thermodynamic approaches to hydrophobic effects are complemented by spectroscopic studies. Tanabe (1993) has studied the Raman spectra manifested during the rotational diffusion of cyclohexane in water. The values of the diffusion coefficients are approximately half those expected from data for other solvents of the same viscosity, and the interpretations made are in terms of hindered rotation arising from the icebergs presumably formed (c/. Frank and Evans) around the cyclohexane. 

It has also been shovm that the diffusion coefficients in a solvent are inversely proportional to its viscosity. The viscosity changes with temperature, composition, and the concentration of the feed. When the column is operated at a constant reduced velocity, v = udp)/Dj, the efficiency constant. The effect of a change of viscosity due to an adjustment in any of the parameters just Hsted will have Ht-tle effect on the pressure required to keep the reduced velocity constant (since the product of the viscosity and the diffusion coefficient remains constant) but it will markedly affect the retention times (which will increase with increasing viscosity) and, in preparative applications, the production rate. Thus, conditions under which the viscosity is low should be preferred. 

This relationship is known as the Stokes-Einstein equation. Strictly speaking it should only be applied at infinite dilution to monoatomic ions. However, in practice it is applied to more complex ions and at finite ionic strengths. If the diffusion coefficient for the ion is measured experimentally, an effective radius for the ion can be estimated using the viscosity of the pure solvent. 

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