Self-diffusion of Water Molecules

The rate of exchange of water molecules between the hydration shells of ions and bulk water was considered by Samoilov (1957) to indicate the strength of the hydration and indirectly the effects of the ions on the water structure. The ratio of the average residence time of a water molecule near another one in the hydration shell of the ion, Ti, to that in the bulk (tw = 17 ps) was obtained from the activation Gibbs energy of the exchange, This, in turn, was obtained from the temperature 

The ratio tj/tw of the average residence times is then given by  

Some ions, such as Li+, Na+, Mg , and Ca +, have AGf, 0 and tj tw and were called positively hydrated . For some other ions K+, Cs+, Cr, Br , and I , ACLh 0 and Ti Tw and they were designated as negatively hydrated . These terms are not in general use now, however, but the relation of the residence times to the dynamic extent of hydrogen bonding in the solution is apparent. It should be noted that the residence time of a water molecule in the vicinity of another one, tw = 17 ps is considerably longer than the rotational reorientation of a water molecule, around 2-3 ps, or the mean lifetime of a hydrogen bond, 0.2-0.4 ps, see Sect. 1.1.4. 

In the case of cations, the values of ti deduced from Eq. (3.5) are expected to correspond with the unimolecular rate constants, kj, for water release from their hydration shells, obtained from ultrasound absorption (Marcus 1985). These constants depend on the competition between water molecules and anions for sites in the coordination shell and need to be independent of the anion in order to be valid characteristics of the cation hydration. So far this has not been demonstrated. 

Nowikow et al. (1999) measured the self diffusion of water in 0.94 m BU4NCI at room temperature using quasi-elastic neutron scattering. The residence times of water molecules in the hydration shell of the cation were twice longer than in bulk water. Still, (1 - Z w(E)/-Dw) 0 and the salt is a net structure maker. Sacco et al. (1994) measured the self diffusion coefficient of the water in aqueous CsCl in D2O 

1 Self-diffusion of Water Molecules The rate of exchange of water mole- 

Ions in Solution and Their Solvation, First Edition. Yidiak Marcus. 

The self diffusion coefficients of water molecules in aqueous alkali halide solutions, were obtained at 23°C by McCall and Douglass [4] and at 0°C by Endon et al. [5] from NMR measurements. More recent data, for 25°C, at moderate concentrations and including some divalent metal chlorides, are also available in the report by Muller and Hertz [6], When both cation and anion are structure-breakers, that is, negatively hydrated according to 0 as is the case for KX, RbX, and CsX, where X=Cl, Br, and I, then (1 is negative. When at least one of the ions 

Data on aqueous NaClO, LiClO, and MgCClO ) at 25°C by Heil et al. [7] indicate that the structure-making properties of the cations predominate over those of the structure-breaking perchlorate anion so that (1- ) 0. The self diffusion of 

The D/H isotope effect for the self diffusion coefficient of the water in solutions of CsCl in D O and H O was according to Sacco et al. [16] in agreement with the structure-breaking properties of both ions of this salt and with the more extensive ( stronger ) hydrogen bonded network of the D O relative to H O, see Table 3.8. 

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The properties of liquid water between electrodes are obviously of considerable importance. MD simulations of the system have been reported, with and without an applied electric field [47]. It is concluded that the presence of the walls is structurebreaking for the H-bond networic and that this has significant consequences for the self-diffusion of water molecules near the walls. 

My views (as experimentalist) are rather qualitative mostly based simply in many experimental results and in evaluations of the orders of magnitude of several physical properties. In the paper of 1985 (Teixeira, Bellissent-Funel, Chen, Dianoux) we deduced from the analysis of the quasi-elastic neutron scattering by pure water, that self diffusion of water molecules is mainly due to rotations of the molecule. In my view, at least at low temperatures, when, instantaneously, most of the pairs of molecules are bonded, the molecule can rotate around one bond if the other possible bonds are broken simultaneously. 

Based on the experimental observation that self-diffusion of water molecules in ice has an activation energy similar to that of the dielectric and mechanical relaxations ( — 13.5 kcal./mole), some investigators (I2J) see a connection between the formation and migration of valence defects... 

The self-diffusion of water molecules in LiCl solution changes dramatically in magnitnde as the solution becomes denser. The self-diffusion coefficient of extended simple point charge (SPC/E) water at 25°C is 2.5 x 10 m s and decreases by 42% as the concentration of the LiCl solution increases from 0.22 M to 3.97 M (see Table 4.4). Over the same concentration range, the diffusion coefficient of water in RbCl and Csl shows a slight increase (more apparent in Csl solutions) and finally an overall drop with factors of 21% and 6%, respectively, at 3.97 M from their... 

According to [59], at 25 °C the diffusion coefficient of protons in water is Dh+ = 9.28 10 cm /s, while the self-diffusion of water molecules is three times lower, = 2.8 10" cm /s. The hydrogen-bonded network, that restrains the self-diffusion of water molecules, paves the way for the rather fast proton transfer along the hydrogen bonds. Curiously, ordering water molecules within the network in itself does not accelerate proton transfer. Actually, according to recent data [60], the rate of proton diffusion in the... 

Brown, W Stilbs, P Lindstrom, T, Self-Diffusion of Small Molecules in Cellulose Gels using FT-Pulsed Field Gradient NMR, Journal of Applied Polymer Science 29, 823,1984. Brownstein, KR Tarr, CE, Importance of Classical Diffusion in NMR Studies of Water in Biological Cells, Physical Review A 19, 2446, 1979. 

Wang, JH, Theory of the Self-Diffusion of Water in Protein Solutions. A New Method for Studying the Hydration and Shape of Protein Molecules, Journal of the American Chemical Society 76, 4755, 1954. 

Pulsed field gradient (PFG)-NMR experiments have been employed in the groups of Zawodzinski and Kreuer to measure the self-diffusivity of water in the membrane as a function of the water content. From QENS, the typical time and length scales of the molecular motions can be evaluated. It was observed that water mobility increases with water content up to almost bulk-like values above T 10, where the water content A = nn o/ nsojH is defined as the ratio of the number of moles of water molecules per moles of acid head groups (-SO3H). In Perrin et al., QENS data for hydrated Nation were analyzed with a Gaussian model for localized translational diffusion. Typical sizes of confining domains and diffusion coefficients, as well as characteristic times for the elementary jump processes, were obtained as functions of A the results were discussed with respect to membrane structure and sorption characteristics. ... 

The relaxation of hydrogen nuclei in a fluid confined in pores is determined by the self-diffusion of the molecules within the pores, the bulk relaxation of the liquid, and the surface relaxation at the pore walls (Valckenborg et al. 2000, 2001). For NMR spin-echo times of a few ms, the diffusion length of the water molecules in broad pores is about 1 J.m, and hence the surface relaxation is the dominating process at pore sizes below 0.1 pm (fast diffusion limit Brownstein and Tarr 1979). In this case, a one to one correspondence exists between the observed distribution of relaxation times and the PSD (Halperin et al. 1989, Valckenborg et al. 2000). Since the transverse relaxation time of... 

In Chapter 1, Murgia, Palazzo, and coworkers investigated the physicochemical behaviors of a binary IL bmimBF and water, and the ternary NaAOT, water and bmimBF mixtures essentially through the evaluation of the self-diffusion coefficients of the various chemical species in solution by PGSTE-NMR experiments. The diffusion of water molecules and bmimBF ions were found to be within different domains, which suggested that the systems were nanostructured with formation of micelles having positive curvature and a bicontinuous micellar solution for the former and the later systems, respectively. The remarkable differences between the two systems are attributed to the specific counterion effect between the aforementioned ILs and the anionic surfactant. In Chapter 2, Bermudez and coworkers focused on the characterization of small (conventional surfactants) and polymeric amphiphiles (block copolymers) in different types of ILs (imidazolium, ammonium. 

Lateral density fluctuations are mostly confined to the adsorbed water layer. The lateral density distributions are conveniently characterized by scatter plots of oxygen coordinates in the surface plane. Fig. 6 shows such scatter plots of water molecules in the first (left) and second layer (right) near the Hg(l 11) surface. Here, a dot is plotted at the oxygen atom position at intervals of 0.1 ps. In the first layer, the oxygen distribution clearly shows the structure of the substrate lattice. In the second layer, the distribution is almost isotropic. In the first layer, the oxygen motion is predominantly oscillatory rather than diffusive. The self-diffusion coefficient in the adsorbate layer is strongly reduced compared to the second or third layer [127]. The data in Fig. 6 are qualitatively similar to those obtained in the group of Berkowitz and coworkers [62,128-130]. These authors compared the structure near Pt(lOO) and Pt(lll) in detail and also noted that the motion of water in the first layer is oscillatory about equilibrium positions and thus characteristic of a solid phase, while the motion in the second layer has more... 

Translational motion is the change in location of the entire molecule in three-dimensional space. Figure 11 illustrates the translational motion of a few water molecules. Translational motion is also referred to as self-diffusion or Brownian motion. Translational diffusion of a molecule can be described by a random walk, in which x is the net distance traveled by the molecule in time At (Figure 12). The mean-square displacement (x2) covered by a molecule in a given direction follows the Einstein-derived relationship (Eisenberg and Crothers, 1979) ... 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

Table 2.3 gives the self-diffusion coefficients of some important ions in submerged soils and Figure 2.2 shows the values for the elemental ions plotted against ionic potential ( z /r where z is the absolute ionic charge and r the crystal ionic radius). As the ionic potential increases the hydration layer of water molecules around the ion increases, and therefore the mobility tends to decrease. Also, at the same ionic potential, cations diffuse faster than anions. The mobilities... 

The impedance factor is strictly empirical, accounting primarily for the geometry of the soil pore network bnt also for ion exclusion by negative adsorption from narrow pores, and for the increased viscosity of water near charged surfaces. It is similar for all simple ions and molecules. It can be measured by following the self diffusion of a nonadsorbed ion, such as Cl , for which C = 0lCl and hence D =... 

Mechanisms of Solvent (Water, Methanol) Transport. The following types of transport are considered in this section (i) self-diffusion or tracer diffusion of solvent molecules, which is the unidirec-... 

The opposite signs for the neutron scattering power of hydrogen and deuterium (—0.38 and +0.65) offers the possibility for investigating (slow) self-diffusion between different water sites and/or localization of water molecules with different mobility if diffraction experiments are carried out for a sample where D20 is exchanged in steps vs. H20. 

Figure 5. Experimental self-diffusion coefficient of water molecules in NaX as a function of reciprocal temperature, (a) Mean diameter of the zeolite crystals 3 pm ...

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