Diffusing water protons

Diffusive water protons should also be taken into account for considering all contributions to the observed rates (see Section II.A.7). 

Water proton self-diffusion exhibits a break point and begins to increase at a = 0.85. In the case of AOT self-diffusion, a breakpoint also occurs, but AOT self-diffusion continues to slow as a decreases further. These breakpoints in both water and AOT selfdiffusion behavior at a = 0.85 coincide with the breakpoint in electrical conductivity illustrated in Fig. 1, where the onset of electrical conductivity percolation occurs. At a = 0.7 two more breakpoints in the water proton and AOT self-diffusion are seen. Water proton self-diffusion increases more markedly and AOT self-diffusion beings to increase markedly. 

A simple two-state model for the observed water proton self-diffusion may be put forward in the form... 

The order parameter values calculated from the data of Fig. 4 are illustrated in Fig. 5. The data there suggest the existence of two continuous transitions, one at a = 0.85 and another at a = 0.7. The first transition at a = 0.85, denoted by the arrow labeled a in Fig. 5, is assigned to the formation of percolating clusters and aggregates of reverse micelles. The onset of electrical percolation and the onset of water proton self-diffusion increase at this same value of a (0.85) as illustrated in Figs. 2 and 3, respectively, are qualitative markers for this transition. This order parameter allows one to quantify how much water is in these percolating clusters. As a decreases from 0.85 to 0.7, this quantity increases to about 2-3% of the water. 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

In many products, the spin-relaxation properties of the components can be different due to molecular sizes, local viscosity and interaction with other molecules. Macromolecules often exhibit rapid FID decay and short T2 relaxation time due to its large molecular weight and reduced rotational dynamics [18]. Mobile water protons, on the other hand, are often found to have long relaxation times due to their small molecular weight and rapid diffusion. As a result, relaxation properties, such as T2, have been used extensively to quantify water/moisture content, fat contents, etc. [20]. For example, oil content in seeds is determined via the spin-echo technique as described according to international standards [64]. 

Outer sphere relaxation arises from the dipolar intermolecular interaction between the water proton nuclear spins and the gadolinium electron spin whose fluctuations are governed by random translational motion of the molecules (106). The outer sphere relaxation rate depends on several parameters, such as the closest approach of the solvent water protons and the Gdm complex, their relative diffusion coefficient, and the electron spin relaxation rate (107-109). Freed and others (110-112) developed an analytical expression for the outer sphere longitudinal relaxation rate, (l/Ti)os, for the simplest case of a force-free model. The force-free model is only a rough approximation for the interaction of outer sphere water molecules with Gdm complexes. 

Variations of R with A suggest a two-step hydration process solvation and formation of disconnected water clusters centered on polar head groups, followed by the formation of a continuous hydrogen-bond network. At low A, Ri depends logarithmically on co, suggesting bidimensional diffusion of protons in the interfacial region between polymer and water. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

X 10 cm /s at room temperature) and that the diffusion of protonated water molecules makes some contribution to the total proton conductivity (vehicle mechanism " ). This is --"22% when assuming that the diffusion coefficients of H2O and H3O+ (or H502 ) are identical. However, as suggested by Agmon, " the diffusion of H3O+ may be retarded, because of the strong hydrogen bonding in the first hydration shell. 

From the formation reaction of protonic defects in oxides (eq 23), it is evident that protonic defects coexist with oxide ion vacancies, where the ratio of their concentrations is dependent on temperature and water partial pressure. The formation of protonic defects actually requires the uptake of water from the environment and the transport of water within the oxide lattice. Of course, water does not diffuse as such, but rather, as a result of the ambipolar diffusion of protonic defects (OH and oxide ion vacancies (V ). Assuming ideal behavior of the involved defects (an activity coefficient of unity) the chemical (Tick s) diffusion coefficient of water is... 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

The relaxation rates calculated from Eq. (15) are smaller than the measured ones at low field, while they are larger at high field. OST is thus obviously unable to match the experimental results. However, water protons actually diffuse around ferrihydrite and akaganeite particles and there is no reason to believe that the contribution to the rate from this diffusion would not be quadratic with the external field. This contribution is not observed, probably because the coefficient of the quadratic dependence with the field is smaller than predicted. This could be explained by an erroneous definition of the correlation length in OST, this length is the particle radius, whilst the right definition should be the mean distance between random defects of the crystal. This correlation time would then be significantly reduced, hence the contribution to the relaxation rate. 

Fig. 8. The water-proton spin-lattice relaxation rates vs. magnetic field strength plotted as the Larmor frequency at 282 K for hexacyanochromate(II) ion ( ), trioxalatochromate(III) ion ( ), and trimalonatochromate(III) ion (A). The lines were computed using translational diffusion models developed by Freed with and without the inclusion of electron spin relaxation effects 54,121).

In a water solution, a proton (hydrogen ion) is hydrated, forming the hydroxonium ion H30. For the sake of simplicity we write H+ instead of H30. For further simplicity, we assume that the diffusion of protons from the bulk of the solution to the electrode [outer Helmholtz plane (OHP)],... 

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