Proton mobility, theory

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. 

J. T. Fermann and S. Auerbach, Modeling proton mobility in acidic zeolite clusters II. Room temperature tunneling effects from semiclassical theory, J. Chem. Phys. 112 (2000), 6787. 

Is Eyring s theory on proton mobility in water successful in predicting the experimental values of mobility The unfortunate answer is that this classical calculation is not acceptable at aU, partly because it gives mobilities that are much smaller than those observed and it does not fit the demanding criterion of h+ d+ = 1 -41. It is necessary to turn to another view. 

One More Step in Understanding Proton Mobility The Conway, Bockris, and Linton (CBL) Theory... 

Can the CBL theory predict experimental values The answa- is a resounding yes, and the results justify printing the lengthy story of an advance made in 1956. The rate of this field-induced water reorientation was faster than the rate of the spontaneous thermal rotation, but turned out to be much slower than the proton tunneling rate. Thus, it is thQ field-induced rotation of water that determines the ovo all rate of proton transfer and the rate of proton migration through aqueous solutions. According to the theory, the estimated value of the proton mobility is 28 x 10 and that observed experimentally is 36 x 10 cm s" V ... 

This notion is supported by a large number of independent experimental data, related to structure and mobility in these membranes. It implies furthermore a distinction of proton mobility in various water environments, strongly bound surface water and liquidlike bulk water, and the existence of water-filled pores as network forming elements. Appropriate theoretical treatment of such systems involves random network models of proton conductivity and concepts from percolation theory, and includes hydraulic permeation as a prevailing mechanism of water transport under operation conditions. On the basis of these concepts a consistent approach to membrane performance can be presented. 

At the same time it is interesting to understand why the intracellular 756 cm 1 mode influences the proton conductivity. As we mentioned above, the polarized optical 99-cm 1 mode activates the proton mobility in the range Tc < T < To, where Tc= 120K and 7o = 213 K. However, the intracellular 756-cm 1 mode is not polarized nevertheless, it is responsible for the proton mobility for T > To. With T > Tc = 120 K, these two modes demonstrate an anomalous temperature behavior and the intracellular mode begins to intensify [47], It is the intensification of the cellular mode with T, which leads to its strong coupling with charge carriers in the crystal studied. A detailed theory of the mixture of the two modes is posed in Appendix D. 

Assuming that the size and shapes of water-filled domains are known, as well as the structure of polymer/water interfaces, proton distributions at the microscopic scale can be studied with molecular dynamics simulations (Feng and Voth, 2011 Kreuer et al., 2004 Petersen et al., 2005 Seeliger et al., 2005 Spohr, 2004 Spohr et al., 2002) or using the classical electrostatic theory of ions in electrolyte-filled pores with charged walls (Commer et al., 2002 Eikerling and Komyshev, 2001). An advanced understanding of spatial variations of proton mobility in pores warrants quantum mechanical simulations. 

See also acid-base theories, -> Eigen complex, - pH, Zundel complex, prototropic charge transport, proton transfer, proton mobility. 

The first attempt to apply microscopic electrolyte theory to study the mobility of protons in PEMs is due to Paddison and co-workers.Because the... 

In our opinion, this book demonstrates clearly that the formalism of many-point particle densities based on the Kirkwood superposition approximation for decoupling the three-particle correlation functions is able to treat adequately all possible cases and reaction regimes studied in the book (including immobile/mobile reactants, correlated/random initial particle distributions, concentration decay/accumulation under permanent source, etc.). Results of most of analytical theories are checked by extensive computer simulations. (It should be reminded that many-particle effects under study were observed for the first time namely in computer simulations [22, 23].) Only few experimental evidences exist now for many-particle effects in bimolecular reactions, the two reliable examples are accumulation kinetics of immobile radiation defects at low temperatures in ionic solids (see [24] for experiments and [25] for their theoretical interpretation) and pseudo-first order reversible diffusion-controlled recombination of protons with excited dye molecules [26]. This is one of main reasons why we did not consider in detail some of very refined theories for the kinetics asymptotics as well as peculiarities of reactions on fractal structures ([27-29] and references therein). 

One of the most successful models for gel electrophoresis is the reptation theory of Lumpkin and Zimm for the migration of double-stranded DNA (Lumpkin, 1982). An in-depth discussion can be found in Zimm and Levene (1992) for a synopsis see Bloomfield et al. (2000). The velocity v of a charged particle in a solution with an electric field E depends on the electrical force Fei = ZqE, in which Z is the number of charges and q is the charge of a proton, and the frictional force l fr = —fv, in which/is the frictional coefficient. At steady state, these forces balance and the velocity is v = ZqE/f. The electrophoretic mobility fi is the velocity relative to the field strength, fi = vE = Zq/f. 

Emi and Bockris suggested a model for this phenomenon that bears some resemblance to the Conway-Bockris-Linton (CBL) theory of the mobility of protons in solution. Here (Section 4.11.6), protons tunnel from their positions attached to a given water to another water when—under the influence of the proton s field—this latter has rotated sufficiently to offer an orbital in which to receive ajumping proton. 

Numerical calculations were carried out for several proteins. They yielded dipole moments of about the same magnitude as actually measured. The Afi apparently becomes fi ly large when the pH is close to the pA" range of the frequently occurring carboxy and amino-groups, respectively. Therefore, sharp maximum values of the dipole must be expected at about pH 4 and 10. Experimental tests of this diaracteristic feature have failed, however. The discrqrancy between the theory and these measurements are so obvious that one must conclude that protons are not sufficiently mobile to contribute significantly to the dielectric polarization of protein solutions. 

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