Diffusion coefficients, solute-water

Figure 2.19 Value of the coefficient n in the Stokes-Einstein equation [Equation (2.87)] required to achieve agreement between calculation and experimental solute diffusion coefficients in water. [26]. Reprinted with permission from the Journal of Chemical Education 47, No. 4, 1970, pp. 261-270, Figure 12, copyright 1970, Division of Chemical Education, Inc.

Fig. 2.11. Self-diffusion coefficients of water ( ), sodium ions ( ), dodecyisul-fate ion ( ) and micelles ( ) in SDS solutions. Data from Refs.37-110- 2>...

For B = A, the tracer diffusion coefficient equals the self-diffusion coefficient, D lba= Dla- 1° Table 6-6 the self-diffusion coefficient of water and some diffusion coefficients of organic solutes in water at infinite dilution calculated with Eq. (6-31) are compared with experimental values (Reid et al., 1987). The experimental value for sucrose is from Cussler (1997). 

Based on the study of Sugano et al. (2000) and our predictive VolSurf model for this series, it can be concluded that factors like size and shape previously reported to affect paracellular permeability are indeed important to explain the local structure-permeability relationship of this chemotype. Usually, permeability via paracellular aqueous pore diffusion depends on the size of the solute and its diffusion coefficient in water. Another important factor is lipophilicity. Between intestinal absorption and both volume and lipophilicity, a negative correlation was reported for this series of thrombin inhibitors. In addition, hydrogen bonding properties and dipolarity are factors that determine... 

The kinematic viscosity of dilute aqueous solutions is ca. 0.01 cm s. So Nernst diffusion layers 5/v between 200 and 30 pm result at flow velocities between 5 and 100 cm s. For small molecules like benzene, tetrachloroethene, etc. the diffusion coefficients in water and in the PDMS membrane are of the same order. Then the time constant is approximately ... 

SOLUTION The amount of water that evaporates from a Stefan tube at a specified temperature and pressure over a specilied time period is measured. The diffusion coefficient of water vapor in air is to be determined. 

Interactions between oppositely charged micelles in aqueous solutions spontaneously form vesicles. The self-diffusion coefficient of water and 2H relaxation of 2H-labeled dodecyl trimethyl ammonium chloride of the dodecyl trimethyl ammonium chloride-sodium dodecyl benzenesulfonate systems show that in these mixtures there is limited growth of the micelles with changes in composition. The vesicles abruptly begin to form at a characteristic mixing ratio of the two surfactants. The transition is continuous.205 Transformation from micelle to vesicle in dodecyl trimethyl ammonium chloride-sodium perfluoro-nonanoate aqueous solution has been studied by self-diffusion coefficient measurements, and it was found that at a concentration of 35 wt% with a molar ratio of 1 1, the self-diffusion coefficient of the mixed micelles is far smaller than that of the two individual micelles.206 The characteristics of mixed surfactant... 

Molecular diffusion coefficients in water are usually determined in the laboratory by using a tracer in agar or gel to insure that the solution is totally free of turbulent motion. Values for gases and ions in pure water are presented in units of cm s in Table 9.1. The molecular diffusion coefficients and their temperature dependence for gases were calculated from the Eyring equation. 

At high solute concentration and low temperature, the viscosity of the system may be greatly enhanced, whereby the diffusion coefficient of water is reduced. Diffusion limitation may now occur. 

Protein crystals commonly contain 40-50 per cent water by weight, sometimes more, and there is much evidence to indicate that the conformation of the protein in the crystal is in general extremely close to that in solution. Hence the crystal studies provide relevant evidence regarding water-protein interactions in dilute solutions. The diffraction patterns obtained require exposures of many hours hence the structures calculated from them represent averaged positions for the atoms and molecules in the structure. Water molecules, in bulk water, at room temperature, have rotational relaxation times of the order of 10" s (lOps). The linear diffusion coefficient of water is near 2 x 10"° cm2 C", so the root mean square linear displacement of a water molecule in lOps would be of the order of 4-5 8. 

The "barrier-effect" also reduces the average translational self-diffusion of protons and is most acute in this case with low coverages. The presence of high concentrations of solute, the physical obstruction of the pore surfaces, and the presence of almost impermeable barriers (such as the liquid-air surface) will result in a pure steric effect reducing the self-diffusion coefficient of water molecules. This is termed the barrier effect... 

The diffusion coefficient of oxygen in sucrose solution decreases much more rapidly with increasing sucrose concentrations than does the diffusion coefficient of water (King, 1988). According to King (1988) when diffusional limitations exist, the local oxygen concentrations may be different from those that would be expected if the head space or surrounding air were instantly and continuously maintained in equilibrium. 

DIFFUSION COEFFICIENTS IN WATER AND GASES 1.2.1 Diffusion coefficient of salts (electrolytes) in aqueous solutions... 

Neutron scattering data for Li- and Na-vermiculite, on the other hand, gave no indication of water protons being immobile on the neutron scattering time scale.This result is consistent with the behavior of water molecules in aqueous solution, since the residence time in the primary solvation shell of a monovalent cation is about 10" s, well within the time scale probed by neutrons. However, as shown in Table 2.4, the self-diffusion coefficients of water molecules on Li- and Na-vermiculite were found to be much smaller than the bulk liquid value at 298 K. These data suggest that, even in the two-layer hydrate, the solvating water molecules exhibit only about 5 per cent of the mobility they have in the bulk liquid phase and about 10 per cent of that in the primary solvation shell of a monovalent cation in aqueous solution (Dg 1.3 x 10" m s" ) . This reduction in water molecule mobility is evidently produced by interactions with the charge distribution on the siloxane surface. 

FIGURE 39.4 Thijssen theory of selective diffusion. Diffusion coefficients of water and acetone in coffee extracts and maltodextrin solutions (0.1%w/w acetone, 25°C) acetone volatile molecule). 

As mentioned earlier, the first signature of the influence of the protein surface on the dynamics of water came from the measurements of the rotational and translational diffusion coefficients of water in aqueous protein solutions. Analysis based on hydrodynamic formulas (such as Stokes-Einstein and Debye-Stokes-Einstein (DSE)) showed that an explanation of the observed values required a larger than actual radius of the protein to be used in the Stokes expression of the friction (from hydrodynamics). This indicated the presence of a substantially rigid water layer around the protein surface. However, the story turned out to be more complex. We have already discussed some of these aspects - we now turn to a more detailed discussion of several experimental results. 

The diffusion coefficients of ionic solutes show nonideal behavior with variation of composition of the solvent mixture in water-methanol binary mixtures. The degree of non-ideality of the solute diffusion is found to be similar to the nonideality that is observed for the diffusion of water and methanol molecules in these mixtures and is attributed to the enhanced stability of the HBs and formation of interspecies complexes in the mixtures. The diffusion coefficient of water is found to be minimum at 0-5 and that of methanol shows the minimum at = 0.7. However, the observed deviation from linear behavior with composition is found to be a bit weaker than that found in simulations of water-DMSO mixtures [11,12],... 

Figure 20 Double-water experiment, the aqueous analogy of the double-oil experiment, performed on an AOT microemulsion as a function of temperature. The polar solvent is a 5% A-methyl formamide (NMF) solution in heavy water (D2O). The ratio of the water (here measured as trace impurities of HDO) and NMF diffusion coefficients is monitored as a function of temperature (c). Also shown as (a) the individual self-diffusion coefficients of water (O). NMF ( ), and AOT ( ) and (b) the relative diffusion coefficient of water. Kq = 1.73 is the diffusion coefficient ratio in the pure water-NMF mixture and is indicated as a broken line in (c). The phase boundary at 75"C is indicated as a vertical broken line. The behavior with increasing temperature is completely analogous to that of the nonionic system (Fig. 19) and illustrates a transition from reverse micelles to a bicontinuous structure via growing droplets that become attractive. (Data from Ref 49.)... 

High-intensity electric field pulses accelerated osmotic dehydration of carrot [18], A Fickian diffusion coefficient for water and solute increased exponentially with electric field strength. This effect was attributed to increased cell wall permeability, which was also manifested by the softening of product. 

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