Water bulk-like

On one hand, there are the dielectric properties, which are especially important for polai solvents like water. Bulk properties can, on the other hand, only be modeled by using a supermolecule approach with explicitly defined solvent molecules. 

Simulations of water in synthetic and biological membranes are often performed by modeling the pore as an approximately cylindrical tube of infinite length (thus employing periodic boundary conditions in one direction only). Such a system contains one (curved) interface between the aqueous phase and the pore surface. If the entrance region of the channel is important, or if the pore is to be simulated in equilibrium with a bulk-like phase, a scheme like the one in Fig. 2 can be used. In such a system there are two planar interfaces (with a hole representing the channel entrance) in addition to the curved interface of interest. Periodic boundary conditions can be applied again in all three directions of space. 

The excellent prospects of PEFCs as well as the undesirable dependence of current PEMs on bulk-like water for proton conduction motivate the vast research in materials synthesis and experimental characterization of novel PEMs. A major incentive in this realm is the development of membranes that are suitable for operation at intermediate temperatures (120-200°C). Inevitably, aqueous-based PEMs for operation at higher temperatures (T > 90°C) and low relative humidity have to attain high rates of proton transport with a minimal amount of water that is tightly bound to a stable host polymer.33 37,40,42,43 yj-jg development of new PEMs thus warrants efforts in understanding of proton and water transport phenomena under such conditions. We will address this in Section 6.7.3. 

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 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. ... 

In general, pores swell nonuniformly. As a simplification, fhe random network was assumed to consist of fwo types of pores. In fhis fwo-stafe model, nonswollen or "dry" pores (referred to later as "red" pores) permit only a small residual conductance due to tightly bound surface water, which solvates the charged surface groups. Swollen or "wet" pores (referred to later as "blue" pores) contain extra water in the bulk, allowing them to promote the high bulk-like conductance. Water uptake by the membrane corresponds to the swelling of wef pores and to the increase of their relative fraction. 

In this model, proton transport in the membrane is mapped on a percolation problem, wherein randomly distributed sites represent pores of variable sizes and fhus variable conductance. The distinction of pores of differenf color (red or blue) corresponds to interfacial or by bulk-like proton transport. Water uptake by wet pores controls the transition between these mechanisms. The chemical structure of the membrane is factored in at the subordinate structural levels, as discussed in the previous subsections. 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

The response range of the local environment to the excited Trp-probe is mainly within 10 A because the dipole-dipole interaction at 10 A to that at —3.5 A of the first solvent shell drops to 4.3%. This interaction distance is also confirmed by recent calculations [151]. Thus, the hydration dynamics we obtained from each Trp-probe reflects water motion in the approximately three neighboring solvent shells. About seven layers of water molecules exist in the 50-A channel, and we observed three discrete dynamic structures. We estimated about four layers of bulk-like free water near the channel center, about two layers of quasi-bound water networks in the middle, and one layer of well-ordered rigid water at the lipid interface. Because of lipid fluctuation, water can penetrate into the lipid headgroups, and one more trapped water layer is probably buried in the headgroups. As a result, about two bound-water layers exist around the lipid interface. The obtained distribution of distinct water structures is also consistent with —15 A of hydration layers observed by X-ray diffraction studies from White and colleagues [152, 153], These discrete water stmctures in the nanochannel are schematically shown in Figure 21, and these water molecules are all in dynamical equilibrium. 

The structural diffusion of proton in a PFSA membrane can be described by three reactions depending upon the reactants and the surrounding environment. If the channels that compose the aqueous domain are sufficiently large, there may be a bulk-like region near the center of the channel, where the water stracture is similar to bulk water and where, therefore, we can expect the reaction to take place as in Eq. (2),... 

The relative importance of each of these three reactions is likely a strong function of water content. In order for the bulk-like reaction (Eq. 16a) to take place, one must be at high degrees of hydration, where there is bulk-like water within the membrane. From electronic stracture calculation we are aware that a minimum of three water molecules is required for the dissociation of protons from the sulfonic acid end group, it is likely that the reaction in Eq. (16c) is important only at very low water contents. The reaction in which oxygen atoms of the sulfonate groups act as part of the solvation shell, (Eq. 16b) is likely relevant across a range of intermediate hydration levels. 

The correlation between wrapping and dehydration propensity (Fig. 5.5a) has the following characteristics (a) dehydrons (p < 19) generate T-values in the range 2 < T < 3.6 (b) the upper wrapping bound, p = 28, corresponds to bulk-like water (r = 4) in the desolvation domain and (c) all solvating water is excluded from the desolvation domain for p > 28. 

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