Vehicular diffusion

Figure 26. Vehicular diffusivity of the proton which measures the movement of the centre of mass of the hydronium ion is given as a function of temperature — bold line, non-reactive system triangle, RSI square, RSII dot-dashed line, estimated using Eq. (13).

The vehicular diffusion components from the non-reactive system, RSt and RStt are plotted in Fig. 26. Diffusivities from the classical MD simulation, Dy h can be used as the reference value for comparison. The expected vehicular component, can also be generated based on the experimental total diffusivity and the... 

The simulated and experimental hydronium diffusivities both increase with increasing water contents. The simulated values are lower than the experimental values, presumably, due to the fact that the simulations report only the vehicular contribution to the proton diffusivity, whereas the experiment measures the total proton diffusivity. Experimentally, Nafion has higher proton diffusivity than SSC at low water contents and lower proton diffusivity than SSC at high water contents. The vehicular diffusion coefficients of the hydronium ion measured from simulation are higher for Nafion than in SSC PFSA at all water contents. Clearly a detailed understanding of the total proton diffusivity as a function of polymer architecture requires a model capable of structural diffusion. 

The Li cation self-diffusion coefficient in a binary EOi2/LiTFSI electrolyte was dominated (90%) by Li" vehicular diffusion of the Li" with an EO12 solvent. In EO12TFSI /Li" molten salt electrolyte, half of the Li" motion was attributed to... 

Kreuer etal. [21] provided an in-depth review of the basic mechanisms of transport in proton conductors. Transport of the proton can occur by two mechanisms structural diffusion and vehicular diSusion. Vehicular diffusion is the classical Einstein diffusive motion. The structural diffusion is associated with hopping of the proton along water molecules (the so-called Grotthuss mechanism). In the nanosized confined hydrophihc spaces within the membrane, both mechanisms are operative. What is important here is that the underlying mechanism of transport in PEMs changes as a function the level of hydration. Understanding the nature of these mechanisms and their dependence on the level of hydration and molecular structure is important in the development of advanced PEM materials that are more tolerant of higher temperatures and lower levels of saturation. 

Choi et al. proposed a pore transport model to describe proton diffusion within Nafion." The diffusion coefficients are predicted. The surface diffusion coefficient is 1.01 X10 cm /s at room temperature the vehicular diffusion coefficient is 1.71x10 cm /s and the Grotthuss diffusion coefficient is 7x10 cm /s. The Grotthuss diffusion is the fastest proton transport mechanism within Nafion. The surface diffusion coefficient is much lower than the other two diffusion coefficients. The surface diffusion does not contribute significantly to the overall conductivity of protons except at low water levels. 

Structural diffusion is favored by conditions that enhance the stiffness of the hydrogen-bonded network between water molecules low temperatures and low acid concentration. The decrease in water content leads to an effective increase in the concentration of acid protons, which in turn suppresses the contribution of structural diffusion, as found in aqueous acidic solutions. This agrees with the finding of an enhanced contribution of vehicular transport in PEMs at low hydration. Such an observation is also supported by recent studies of molecular mechanisms of proton transport in PEMs at minimal hydration. ... 

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... 

A word of cantion is in order. A better connectivity in SSC cannot be instantly eqnated to higher condnctivity. In the simulations of Nafion and SSC, the same amount of water is distributed in the same volume. A change in connectivity is almost certainly accompanied by a change in the characteristic dimension and geometry of the cluster channel. In other words, if one stretches out clusters in SSC in order to better connect them, under the constraint that the volume of the aqueous domain is the same as that in Nafion, then one must accept that the dimension of a channel in a clusters in SSC is smaller. (That the characteristic channel width in SSC is smaller than in Nafion has also been observed experimentally at least for the medium and high water contents.) This change in dimension can affect the environment of the water and hydronium ions. If the channel is smaller and more spread out in SSC PFSA membrane than in Nafion, then it has more surface area with the hydrophobic phase per unit volume. This additional interaction with the hydrophobic phase can be characterized as additional confinement. The effects of confinement on both the diffusion of water and the vehicular and structural components of diffusion of the proton are not fully understood. Thus it is important to corroborate the suggestions of this water cluster distribution analysis with other measures of structure and transport. 

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. 

The classical MD simulations performed in task I provide self-diffusion coefficients for water and also for hydronium ions, which is strictly the vehicular component of the proton diffusivity. These diffusion coefficients are calculated from the mean square displacement of H2O and HsO using the Einstein relation. The numerical values for Nation and SSC membranes at the four hydration levels are hsted in Table 5 along with the experimental values. ... 

Going beyond an atomistic description of the aqueous phase and the membrane, Paddison and coworkers [79-88] employed statistical mechanical models, incorporating solvent friction and spatially dependent dielectric properties, to the calculation of the proton diffusion coefficient in Nation and PEEKK membrane pores. They concluded from their studies that, in accordance with NMR based evidence [50], the mechanism of proton transport is more vehicular (classical ion transport) in the vicinity of the pore surface and more Grotthus-like in the center. 

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