Protonic percolation

Fig. 15. Critical exponent for protonic percolation on purple membrane. Hydration dependence of the conductivity for HjO (O) and ( ) hydration of lyophilized...

Protonic percolation may be the event that imposes a lower limit on the hydration level for onset of enzyme activity, for those enzymes dependent on general catalysis. The hydration level at which chymotrypsin first displays activity, 0.12 h, is in agreement with this suggestion. The chymotrypsin mechanism includes general catalysis, but not significant substrate rearrangement in the rate-determining step. As noted, other enzymes show a critical hydration level between 0.1 and 0.2 h. 

Careri G, Giansanti A, Rupley lA. Proton percolation on hydrated lysozyme powders. Proc. Nat. Acad. Sci. U.S.A. 1986 83 6810-6814. 

Careri, G., Giansanti, A., and Rupley, J.A. Critical exponents of protonic percolation in hydrated lysozyme powders, Phys. Rev. A, 37, 2703, 1988. 

An increased electrolyte concentration within the membrane may enhance accessibility and improve rates of proton sorption and permeation though the membrane. Maintenance of constant electrolyte concentration may be desirable for obtaining stable proton conductivity, and replenishment of vaporized or leached electrolyte may be continuously performed during operation. On a morphological level, dynamic fluctuations between electrolyte domains may provide conductive pathways through the polymeric continuous phase. Thus, the ability of the polymeric phase to mechanically comply with the anodic proton flux may enable proton percolation though the membrane and enhance conductivity. 

P. Pissis, A. Anagnostopoulou-Konsta, Protonic percolation on hydrated lysozyme powders studied by the method of thermally stimulated depolarization currents, J. Phys. D Appl. Phys. 23... 

J. A. Rupley, L. Siemankowski, G. Careri, F. Bruni, Two-dimensional protonic percolation on lightly hydrated purple membrane, Proc. Natl. Acad. Sci. U.S.A. 85 (1988) 9022-9025. 

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. 

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. 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

Fig. 2.9.3 Proton spin density diffusometry in a two-dimensional percolation model object [31]. The object was initially filled with heavy water and then brought into contact with an H2O gel reservoir, (a) Schematic drawing ofthe experimental set-up. The pore space is represented in white, (b) Maps ofthe proton spin density that were recorded after diffusion times t varying from 1.5 to 116 h. Projections of the...

Fig. 2.9.13 Qu asi two-dimensional random ofthe percolation model object, (bl) Simulated site percolation cluster with a nominal porosity map of the current density magnitude relative p = 0.65. The left-hand column refers to simu- to the maximum value, j/jmaK. (b2) Expedited data and the right-hand column shows mental current density map. (cl) Simulated NMR experiments in this sample-spanning map of the velocity magnitude relative to the cluster (6x6 cm2), (al) Computer model maximum value, v/vmax. (c2) Experimental (template) for the fabrication ofthe percolation velocity map. The potential and pressure object. (a2) Proton spin density map of an gradients are aligned along the y axis, electrolyte (water + salt) filling the pore space...

In H-NMR spectra, the acrylates showed a characteristic ABX pattern in the region of 8 6.8-6.0 with a pair of doublet couplings for each vinyl proton, while the methacrylates showed a characteristic AB pattern in the region of 8 6.5—5.8 with an equivalent singlet peak for each vinyl proton. The monomers purified by percolation over alumina contained no detectable hydrate water or polymerized impurities. 

Based on GebeTs calculations for Nafion (where lEC = 0.91 meq/g),i isolated spheres of ionic clusters in the dry state have diameters of 15 A and an intercluster spacing of 27 A. Because the spheres are isolated, proton transport through the membrane is severely impeded and thus low levels of conductivity are observed for a dry membrane. As water content increases, the isolated ionic clusters begin to swell until, at X, > 0.2, the percolation threshold is reached. This significant point represents the point at which connections or channels are now formed between the previously isolated ionic clusters and leads to a concomitant sharp increase in the observed level of proton conductivity. 

This oversimplified random network model proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells. - - - It helped rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks linking them. ... 

In this section, we describe the role of fhe specific membrane environment on proton transport. As we have already seen in previous sections, it is insufficient to consider the membrane as an inert container for water pathways. The membrane conductivity depends on the distribution of water and the coupled dynamics of wafer molecules and protons af multiple scales. In order to rationalize structural effects on proton conductivity, one needs to take into account explicit polymer-water interactions at molecular scale and phenomena at polymer-water interfaces and in wafer-filled pores at mesoscopic scale, as well as the statistical geometry and percolation effects of the phase-segregated random domains of polymer and wafer at the macroscopic scale. 

Proton conductivities of 0.1 S cm at high excess water contents in current PEMs stem from the concerted effect of a high concentration of free protons, high liquid-like proton mobility, and a well-connected cluster network of hydrated pathways. i i i i Correspondingly, the detrimental effects of membrane dehydration are multifold. It triggers morphological transitions that have been studied recently in experiment and theory.2 .i29.i ,i62 water contents below the percolation threshold, the well-hydrated pathways cease to span the complete sample, and poorly hydrated channels control the overall transports ll Moreover, the structure of water and the molecular mechanisms of proton transport change at low water contents. 

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. 

The physical mechanism of membrane water balance and the formal structure of modeling approaches are straightforward. Under stationary operation, the inevitable electro-osmotic flux has to be compensated by a back flux of water from cathode to anode, driven by gradients in concentration, activity, or liquid pressure of water. The water distribution in PEMs that is generated in response to these driving forces decreases from cathode to anode. With increasing/o, the water distribution becomes more nonuniform. the water content near the anode falls below the percolation threshold of proton conduction, X < X. This leaves only a small conductivity due to surface transport of water. As a consequence, increases dramatically this can lead to failure of the complete cell. 

The highest level, at structural scales >10 nm, is that over which long-range transport takes place and diffusion depends on the degree of connectivity of the water pockets, which involves the concept of percolation. The observed decrease in water permeation with decreasing water volume fraction is more pronounced in sulfonated poly(ether ketone) than in Nafion, owing to differences in the state of percolation. Proton conductivity decreases in the same order, as well. 

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