Diffusion coefficients in pure water

In both equations, Dw is the solute diffusion coefficient in pure water, rs is the molecular radius of the solute, ls is its characteristic size, Vw is the water free volume, Mc is the molecular weight between crosslinks in the amorphous phase, Mn is the number average molecular weight of the polymer before crosslinking, M is the minimum value of Mc below which the solute cannot diffuse, 4>(V) is the free volume function mentioned earlier, and k3 is a constant. 

Figure 1.5 Experimental oxygen diffusion coefficients in pure water. Note that the label of...

Table 1.4. O2 Diffusion Coefficients in Pure Water at Different Temperatures and 1.0 atm O2 Pressure...

The influence of a cut-off relative to the full treatment of electrostatic interactions by Ewald summation on various water parameters has been investigated by Feller et al. [33], These authors performed simulations of pure water and water-DPPC bilayers and also compared the effect of different truncation methods. In the simulations with Ewald summation, the water polarization profiles were in excellent agreement with experimental values from determinations of the hydration force, while they were significantly higher when a cut-off was employed. In addition, the calculated electrostatic potential profile across the bilayer was in much better agreement with experimental values in case of infinite cut-off. However, the values of surface tension and diffusion coefficient of pure water deviated from experiment in the simulations with Ewald summation, pointing out the necessity to reparameterize the water model for use with Ewald summation. 

The diffusion coefficient for water in the cytoplasm of various cells has been determined with a satisfactory precision. It has been found that the movement of water molecules inside living cells is not much different and is reduced by a factor of between 2 and 6, compared with the self-diffusion coefficient for pure water. According to Mild and Lpvtrup (1985), the most likely explanation of the observed values is that part of the cytoplasmic water, the vicinal water close to the various surface structures in the cytoplasm, is structurally changed to the extent that its rate of motion is significantly reduced, compared with the bulk phase. 

Cw = 10" gm cm" the value of D is found to be 10 cm sec which compares favourably with the experimental value of 5 X 10 1 cm sec from measurements on a thin natural rubber sample (vulcanizate A, 0.3 mm thick) immersed in distilled water. The factor of 5 is not regarded as significant in view of the uncertainties in the values of the constants used. It is noteworthy that the apparent diffusion coefficient is four orders of magnitude lower than the estimated true diffusion coefficient in pure rubber. 

The diffusion coefficient in the middle of the water layer (z 33 A) is comparable to that observed in pure water (-0.77 x W cm s at 323 K Note that modified TIP3P water [76] used here overestimates the experimental diffusion coefficient by a factor of 2). If we construct the system with a larger concentration of water, it will be expected that the diffusion coefficient in the water layer completely coincides with that of bulk water. Although a slightly smaller diffusion coefficient observed in the middle of water layer is, in this sense, a finite... 

The ratio of the effective diffusion coefficient in soils or mineral materials to the diffusion coefficient in free water is, however, also influenced by other effects than only the complexity of the diffusion paths in the pore spaces of a soil. For example, the viscosity of water can decrease in narrow pore spaces, with corresponding effects on the diffusion coefficients of the dissolved substances. Apparent tortuosity factors calculated from measured values can therefore be smaller than the value suggested by geometry. It is therefore justifiable to find a conservative estimate of diffusion coefficients for pollutants in soil water, for example when considering mineral landfill liners for which no measured values are available, to use this pure... 

The part played by the so-called obstruction factor should not be ignored in the interpretation of diffusion measurements. Indeed, it has been shown that in micellar systems, using DgO as the solvent, the observed coefficient of heavy water, D bs, is related to the diffusion coefficient of the micelle, to the fraction of bound water and to the diffusion coefficient of pure water, D ... 

The Desmopressin diffusion coefficient in the cubic phase at 40 C (D=0.24 x 10-10 m2s-l) is about a factor 9 smaller than in 2H20-solution at 25 C (D=2.25 x 10-10 m s" ), a difference which is larger than what is expected from pure obstruction effects a reduction factor of three is expected from the inclusion of a solute in the water channels of the cubic phase (13). Thus, the results indicate an interaction between the peptide and the lipid matrix and/or membrane surface, especially since the peptide and lipid diffusion coefficients are very similar in the cubic phase (Table... 

The classical equation for 7 sis provided in Section VII.A of Chapter 2. It depends only on the spin quantum number S, on the molar concentration of paramagnetic metal ions, on the distance d, and on a diffusion coefficient D, which is the sum of the diffusion coefficients of both the solvent molecule (Dj) and the paramagnetic complex (Dm), usually much smaller. The outer-sphere relaxivity calculated with this equation at room temperature and in pure water solution, by assuming d equal to 3 A, is shown in Pig. 25. It appears that the dispersions do not have the usual Lorentzian form. 

The first theory of transport through nonporous gels was presented by Yasuda et al. [150] and was proposed as a result of previous experimental results [151, 152]. This theory relates the ratio of diffusion coefficient in the polymer membrane and diffusion coefficient in the pure solvent to the volume fraction of solvent in the gel membrane or in Yasuda s terminology, the degree of hydration of the membrane, H (g water/g swollen polymer). Yasuda et al. use the... 

We also examined the swelling and shrinking kinetics of the gels in the slurries in comparison to kinetics in pure water. The rates were reduced in slurry somewhat - swelling and shrinking diffusion coefficients dropped by 60-70%. But the rates were fairly independent of slurry concentration over the range of 20 to 70 wt % solids. 

Diffusion is a physical process that involves the random motion of molecules as they collide with other molecules (Brownian motion) and, on a macroscopic scale, move from one part of a system to another. The average distance that molecules move per unit time is described by a physical constant called the diffusion coefficient, D (in units of mm2/s). In pure water, molecules diffuse at a rate of approximately 3xl0"3 mm2 s 1 at 37°C. The factors influencing diffusion in a solution (or self-diffusion in a pure liquid) are molecular weight, intermolecular... 

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. 

Table 9.1. Molecular diffusion coefficients, D, for gases and ions in pure water Diffusion coefficients, D, have units of 10 cm s and were multiplied by 10 before tabulating. For example, Dh+ (25°c) = 93.1 X KT cm s- ... 

Figures 2-4 show the thermal and ionic conductivity, and water self-diffusion coefficient measured in these same systems. Also shown are the transport properties of PEO solutions of molecular weights ranging from 200 to 14,000 (12). The predictions of the Hanai and Maxwell relations are indicated, which were calculated on the assumption that the ionic conductivity or self-diffusion coefficient of the water or suspending electrolyte is equal to that of the pure liquid and that of the oil and emulsifier combined is zero. Also shown are similar results from the PEO solutions of various molecular weights. The thermal conductivity of the microemulsions and PEO solutions are shown in separate figures because the limiting thermal conductivity at zero water content is slightly different (0.27 times that of water for the microemulsion, vs. 0.31 for the PEO).

Trypsin in aqueous solution has been studied by a simulation with the conventional periodic boundary molecular dynamics method and an NVT ensemble.312 340 A total of 4785 water molecules were included to obtain a solvation shell four to five water molecules thick in the periodic box the analysis period was 20 ps after an equilibration period of 20 ps at 285 K. The diffusion coefficient for the water, averaged over all molecules, was 3.8 X 10-5 cm2/s. This value is essentially the same as that for pure water simulated with the same SPC model,341 3.6 X 10-5 cm2/s at 300 K. However, the solvent mobility was found to be strongly dependent on the distance from the protein. This is illustrated in Fig. 47, where the mean diffusion coefficient is plotted versus the distance of water molecules from the closest protein atom in the starting configuration the diffusion coefficient at the protein surface is less than half that of the bulk result. The earlier simulations of BPTI in a van der Waals solvent showed similar, though less dramatic behavior 193 i.e., the solvent molecules in the first and second solvation layers had diffusion coefficients equal to 74% and 90% of the bulk value. A corresponding reduction in solvent mobility is observed for water surrounding small biopolymers.163 Thus it... 

The diffusion coefficient (App) of the redox substrate in these films or solids coated on an electrode has usually been very small. An entirely solid-state voltammogram using a conventional three-electrode system has not been reported yet (see Experiment 14-4, Section 14.5). Electrochemical reactions have been successfully achieved in a tight solid made of polysaccharide and water [107]. In this solid, conventional electrochemical reactions and measurements could be performed using a normal three-electrode system as in pure water without any outer water phase and vessel, and the electrochemical reactivity was almost the same as in pure water. 

Anderson and Wennerstrom [33] calculated the geometrical obstruction factors of the self-diffusion of surfactant and solvent molecules in ordered bicontinuous microstructures, which serve as good approximations also for the disordered bicontinuous microemulsions and L3 (sponge) phases. The geometrical obstruction factor is defined as the relative diffusion coefficient DIDq, where D is the diffusion coefficient in the structured surfactant system and Z)q is the diffusion coefficient in the pure solvent. In a bicontinuous microemulsion the geometrical obstruction factor depends on the water/oil ratio. An expansion around the balanced (equal volumes of water and oil) state gives, to leading order. 

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