Structural Diffusion of Protons

To date, our reactive molecular dynamics simulations of proton transport have been limited to bulk water. However, the extension of Ae RMD algorithm to proton transport in PFSA membranes is analogous to what has been done in bulk water and simi- 

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), 

Along the walls of the aqueous domain, where the sulfonate groups are tethered, hydration of the reactants (either the hydro-nium ion or the water molecule) is possible by the oxygen atoms in SOs because hydrated protons form Zundel-ion-like and Eigen-ion-like configurations with the end groups. This reaction can be represented by the following equation 

The third and final reaction is the dissociation of the protons from the sulfonic acid groups and is given by 

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. 

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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. ... 

The structural diffusion of proton can be represented by the following equation ... 

But one has to be careful with generalizations. There is no apparent reason why the structure diffusion of protons should be initiated only by molecular diffusion processes, as is probably the case for aqueous solutions. Why should not local modes, which have a momentum in the direction of a hydrogen bonded chain, be able to trigger reversal of the direction of polarization in the chain The pressure dependence of the proton conductivity of HUAs, for instance, shows a sudden drop of the activation enthalpy and the pre-exponential factor around 2.5 GPa, suggesting an onset of structure conductivity. Whether the process is released by molecular diffusion has not yet been proven. 

The total electro-osmotic coefficient nd = nhydr + nmoi includes terms due to hydrodynamic coupling nhydr, and a molecular coupling nmoi, that is related to the structural diffusion of protonic defects. The relative contributions of nhydr and nmol depend on the mechanism of proton transport in pores. 

Ab initio methods provide elegant solutions to the problem of simulating proton diffusion and conduction with the vehicular and Grotthuss mechanism. Modeling of water and representative Nation clusters has been readily performed. Notable findings include the formation of a defect structure in the ordered liquid water cluster. The activation energy for the defect formation is similar to that for conduction of proton in Nafion membrane. Classical MD methods can only account for physical diffusion of proton but can create very realistic model... 

Figure 3.3.5 (A) Chemical structure of sulfonated perfluorinated polyethylene (Nafion ). (B) Schematic illustration of the microscopic structure of hydrated Nafion membrane perfluorinated polyethylene backbone chains form spherical hydrophobic clusters. Sulfonic end groups interface with water-filled channels and mediate the migration and diffusion of protons. The channels are filled with water and hydronium ions. Figure adapted from [4].

Structural diffusion is provided by various complexes bare hydronium ion, Eigen complexes, and - Zundel complexes. Structural diffusion of bare hydronium ion and Eigen complexes occurs by proton hops between two water molecules. Two or more protons and several water molecules are involved in the structural diffusion of Zundel complexes. The contribution of mechanisms to the overall mobility depends on the temperature. Eigen and Zundel complexes prevail at room temperature, whereas bare hydronium ions dominate at high temperatures. Excess proton mobility of water has Arrhenius-like (-> Arrhenius equation) temperature dependence with the - activation energy about 0.11 eV. 

In this work, we have approaehed the understanding of proton transport with two tasks. In the first task, deseribed above, we have sought to identify the moleeular-level stmeture of PFSA membranes and their relevant interfaees as a funetion of water content and polymer architecture. In the second task, described in this Section, we explain our efforts to model and quantify proton transport in these membranes and interfaces and their dependence on water content and polymer architecture. As in the task I, the tool employed is molecular dynamics (MD) simulation. A non-reactive algorithm is sufficient to generate the morphology of the membrane and its interfaces. It is also capable of providing some information about transport in the system such as diffusivities of water and the vehicular component of the proton diffusivity. Moreover, analysis of the hydration of hydronium ion provides indirect information about the structural component of proton diffusion, but a direct measure of the total proton diffusivity is beyond the capabilities of a non-reactive MD simulation. Therefore, in the task II, we develop and implement a reactive molecular dynamics algorithm that will lead to direct measurement of the total proton diffusivity. As the work is an active field, we report the work to date. 

Figure 25. The estimated (bold line) structural diffusivity of the proton from Eq. (11) as a function of temperature is used as the reference for the structural diffusivi-ties obtained from RSI (triangle) and RSII (square).

We suppose the reason for the highly porous character of the SU8 structures lies in the chemical composition of the resist and the cross-linking reaction based on the diffusion of protons. This UV-induced reaction is strongly heat dependent and results in highly nano-porous sidewalls by choosing very long post-exposure times. Thus, one can achieve very slim and tapered ultra-hydrophobic surfaces, with relatively large and square structures on the UV mask. 

The simplest possible version of the chemiosmotic model visualizes the membrane in a fluid moasaic structure in which the various enzyme complexes are freely diffusable and energetically coupled through the circulation of protons.-No barrier for the diffusion of protons is assumed between the aqueous bulk compartments,facing both sides of the membrane,and the proton releasing or accepting sites of the proton translocating enzymes. 

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

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