Reginald Paul

The nature of proton transport in fully hydrated Nafion

The diffusion of protons has been studied in fully hydrated Nafion® with a recently constructed non-equilibrium statistical mechanical transport model. Radial cross-sectional profiles of the effective friction and diffusion coefficients were computed in an electrolyte membrane pore with a hydration of 22.5 water molecules per sulfonic acid fixed site. Input parameters were taken from recent SAXS measurements of the hydrated membrane and electronic structure calculations of water clusters with CF3SO3H, the associated acid for the side chain termination. The calculations revealed that the effective friction coefficient increases by more than two orders of magnitude as the proton is brought from the center of the pore to within 4 A of the fixed sites. The model calculated a diffusion coefficient of 1.92 × 10−9 m2 s−1, without ‘fitting’ any parameters, for a proton moving along the pore center, in good agreement with experimental measurements. In addition, the model also identified a predominantly vehicular transport mechanism in regions of the cross section of the pore where the proton is within 12 A of the pore wall. This was distinguished from the central region of the pore (within 4 A of the center axis) where a component of the conduction is via the Grotthuss mechanism. This investigation has demonstrated the applicability of this transport model in the prediction of diffusion coefficients in fully hydrated membranes.

Proton friction and diffusion coefficients in hydrated polymer electrolyte membranes: Computations with a non-equilibrium statistical mechanical model

A recently derived mathematical model to compute the effective friction and diffusion coefficients of hydronium ions in hydrated polymer electrolyte membranes is described and tested for dependence on membrane-specific parameters. Contributions to the friction coefficient due to water–polymer, water–hydronium, and hydronium–polymer interactions are determined through computation of force–force correlation functions. The conventional Stokes law friction coefficient of the hydronium ion in bulk water is then “corrected” with these statistically derived contributions and the corresponding diffusion coefficient calculated. For a Nafion® membrane pore with an hydration level of six water molecules per sulfonic acid functional, the model was used to compute friction coefficients for various distributions of the fixed sites, and for different side chain lengths. The model showed substantial sensitivity to these parameters and predicted that for pores of fixed volume and a constant total number of sulfonate group...

A statistical mechanical model for the calculation of the permittivity of water in hydrated polymer electrolyte membrane pores

An equilibrium statistical mechanical model is derived to compute the spatial variation in the permittivity of water within the hydrated pores of ion-containing polymeric membranes. The fixed anionic groups within the pore are modeled as periodic arrays of point charges. The Helmholtz free energy is calculated from a total Hamiltonian of the pore that includes energy from (1) interactions between the fields generated by the fixed charge groups and the dipoles of the water molecules, (2) “hard core” interactions between the water molecules, and (3) dipole–dipole interactions between the water molecules. The free energy is divided into two parts: (a) a reference free energy associated with five water molecules in a cluster interacting with each other through the hard core potentials and with the fixed charge groups and (b) an excess free energy due to the dipolar interactions between the water molecules in two cluster units. In the present work we calculate the polarization and corresponding permittivity fr...

Effects of dielectric saturation and ionic screening on the proton self-diffusion coefficients in perfluorosulfonic acid membranes.

Proton transport in perfluorosulfonic acid (PFSA) membranes is investigated through a statistical mechanical model that includes the effects of the interaction of the tethered sulfonate groups with both the water and solvated protons. We first derive a potential that describes the electrostatic field due to the dissociated sulfonic acid groups by extending the work of Gronbech-Jensen et al. [ Mol. Phys. 92, 941 (1997)] to a finite array of point charges. A highly convergent series is obtained which includes the effects of screening due to the protons. We then investigate the effects of both dielectric saturation and two distinct formulations of ionic screening on the proton self-diffusion coefficient in Nafion membranes over a range of water contents. Our computations show that the two phenomena (i.e., dielectric saturation and ionic screening) under constant temperature conditions result in canceling affects. Our calculations provide a radial dependence of the proton mobility suggesting that the dominant self-diffusion occurs in the central region of the pores, well separated from the sulfonate groups. Through comparison of our calculated diffusion coefficients with the experimental values we derived a slightly smaller average separation distance of the hydronium ion from the sulfonate ions than suggested by either electronic structure calculations or multistate empirical valence bond molecular-dynamics simulations.

Theoretically computed proton diffusion coefficients in hydrated PEEKK membranes

A recently derived molecular structure–function model based on non-equilibrium statistical mechanics has been used to compute proton friction and diffusion coefficients in 65% sulfonated PEEKK membranes at various degrees of hydration. Morphological parameters, taken from recent SAXS measurements, including pore radius and average separation distance of the sulfonate fixed sites within the pore, along with results from electronic structure explicit water calculations for para-toluene sulfonic acid, were used as input parameters in the model. For membranes where the hydration levels (λ) were 15, 23, and 30 H2Os/SO3−, the model predicted proton diffusion coefficients of 4.13 × 10−10, 1.23 × 10−9, and 1.54 × 10−9 m2 s−1, respectively. These values were obtained without any attempt at fitting to the results obtained from pulsed-field gradient NMR experiments. These computed diffusion coefficients are all within approximately 15% of the measured values; demonstrating the substantial predictive capability of the model. Furthermore, this investigation has shown that at the lower water content (λ = 15) the transport of the proton may be adequately described as vehicular in nature, while at the two higher water contents (λ = 23, 30) there is a contribution via structural diffusion.

Integrated planar concentric ring dielectrophoretic (DEP) levitator

Abstract In the present paper, the design, fabrication and testing of a microchip based planar concentric ring DEP levitator is presented. The performance of the planar microchip levitator is verified using model plant cells and compares favorably with the conventional 3D cone–plate used in previous work. Broad frequency band DEP levitation measurements on plant protoplasts suggest that the microchip based positive DEP levitation is certainly practical and perhaps a more suitable alternative to the conventional 3D electrode system. Furthermore, integration of on chip cell position sensing and control electronics will provide a microchip based automated noninvasive tools for manipulating and fingerprinting individual living cells.

Applications of the Quantum‐Mechanical Green's Functions to the Study of Chemical Reactions. II

Starting from a field theoretical representation of chemical reactions, the rate equation is developed in terms of the quantum mechanical Greens functions. The equation is valid for non‐Markowian behavior and the approximations that are necessary in order to obtain the conventional (Markowian) rate equation are investigated. The effect of finite collision times is also discussed.

Statistical‐Mechanical Analysis of the Theory of Diffusion‐Controlled Chemical Reactions. III

The theory of diffusion‐controlled chemical reactions, as presented by Waite [T. R. Waite, Phys. Rev. 107, 463 (1957)] using phenomenological arguments, is analyzed from a statistical‐mechanical standpoint, and the approximations needed to arrive at Waites starting equation are examined.

Hysteresis loops in the low frequency region of the Clausius-Mossotti polarization factor: the result of non-linear boundary conditions at the particle interface

Abstract A mathematical model involving a non-linear displacement vector at the interface of a spherical particle with a linear medium, is developed to explain the recent experimental observations of multiple Clausius-Mossotti factors in the low frequency (10 Hz to 1 kHz) domain in the dielectrophoretic spectrum of tobacco protoplasts. The model is the simplest possible extension of the existing spherical model, and is exactly solvable. This model also clearly demonstrates the active role of the electric field in influencing the physical properties of the medium-particle interface. Suitable choice of the second-order parameters in permittivity and conductivity result in good qualitative agreement with the experimentally observed low frequency hysteresis loops (neglecting anomalous dielectrophoresis).

Comparison of the effective dipole method for the computation of the torque with the Maxwell's stress tensor method in non-lossy systems

In all experiments that involve electrorotation the motion of the cells is a direct result of the torque that is exerted upon them by the field. As a consequence of this the theoretical study of the origin of the torque has been of some interest. Two methods of calculating the torque have evolved: (1) an effective dipole moment induced on the cell by the external electromagnetic field is first computed and then the torque exerted on this by the latter is calculated by using standard formulae from classical mechanics; and (2) the force per unit area exerted on the surface of the cell by the electromagnetic field is calculated by using Maxwells stress tensor. and from this the torque is obtained by taking a vector cross product with the radius vector followed by an integration over the entire surface of the cell. In this study. the torque experienced by an ellipsoidal cell in a rotating frequency-independent electrical field is calculated by using the Maxwell stress tensor approach, and the limits under which this result yields the torque, commonly computed from an effective dipole moment method, are examined. The applied electrical field is taken to be independent of the frequency in order to ensure that complications due to energy dissipation are eliminated and a simple comparison of the two methods is made possible.<<ETX>>