Stephen J. Paddison

Molecular modeling of the pendant chain in Nafion

Ion transport through perfluorosulfonic acid ionomers such as Nafion{reg_sign} is controlled by both the microstructure of the polymer and the charge and water distribution in the hydrated polymer. The authors present here the results of theoretical calculations on the side chain of Nafion{reg_sign}, establishing microscopic information for the modeling of water modeling of water modeling of water and proton transport in the membrane. Optimized geometries for the trifluoromethane sulfonic acid fragment (CF{sub 3}SO{sub 3}H), the di-trifluoromethane ether fragment (CF{sub 3}OCF{sub 3}), and the side chain (CF{sub 3}{single_bond}OCF{sub 2}CF(CF{sub 3})OCF{sub 2}CF{sub 2}SO{sub 3}H) were determined by means of both ab initio Hartree Fock theory with second order Moeller-Plesset electron correlation corrections, and density functional theory with Becke`s three parameter hybrid method. Several rotational potential energy surfaces were calculated to assess chain flexibility and proton accessibility. A probe water molecule was added to each of the fragments to characterize hydrophilic sites. These calculations confirmed that the sulfonic acid group is hydrophilic and the ethers are hydrophobic. Molecular dynamics simulations were then performed on the side chain to check the conditions required to stretch the pendant chain. Thermal averages of several structural parameters assessing the flexibility and stretch of the chain were computed from selected conformations produced in the simulation and these results indicate that although the sulfonate group is free to rotate, the chain stretches little. The construction of a potential energy surface for rotation about the second ether group suggests that the side chain exists in a folded or curled up conformation. A physical continuum dielectric solvent model was used to obtain free energies of electrostatic interaction of the fragments and the full chain with the solvent.

High frequency dielectric studies of hydrated Nafion

Abstract This study reports high frequency dielectric measurements (0.045–30 GHz) on Nafion® 117 at various states of hydration. A novel technique to measure the broad band frequency dependent real and imaginary parts of the relative permittivity is described. The basic experimental configuration and numerical data analysis are reported along with a discussion of several difficulties encountered and experimental validation of the method. The preliminary results show a strong dependence of the dielectric constant of the Nafion® 117 membrane with water content. The dielectric constant for all hydrated membrane samples was observed to be constant over the initial part of the frequency span, ranging from a maximum of 20 in the samples with 13 waters per sulfonate to a minimum of four in very dry samples. The results reflect the decreasing polar environment of the water at low water contents as well as the increasing extent of binding of the water at the fixed ionic site at low water content. A ‘roll off’ in the dielectric constant, the extent of which was dependent on water content, was observed also in the frequency spectrum. Several possible origins for this ‘roll-off’, including real effects of dipolar relaxations occurring in the hydrated polymers and experimental effects due to the similarity of the wavelength of radiation to the sample dimensions are discussed. Finally, the conductivity of the membranes at various water contents and at frequencies below 5 GHz was extracted from the loss factor spectra. These values agreed well with previous conductivity measurements (obtained at lower frequencies) suggesting that no relaxations are observed in the intervening frequency range (roughly 5–50 MHz).

Molecular modeling of trifluoromethanesulfonic acid for solvation theory

Abstract Reported here are theoretical calculations on the trifluoromethanesulfonic (triflic) acid with and without an additional water molecule, establishing molecular scale information necessary to molecular modeling of the structure, thermodynamics, and ionic transport of Nafion® membranes. The optimized geometry determined for the isolated triflic acid molecule, obtained from ab initio molecular orbital calculations, agrees with previous studies. In order to characterize side chain flexibility and accessibility of the acid proton, potential energy and free energy surfaces for rotation about both carbon–sulfur and sulfur–oxygen(hydroxyl) bonds are presented. A continuum dielectric solvation model is used to obtain free energies of electrostatic interaction with the solvent. Electrostatic solvation is predicted to reduce the free energy barrier to rotation about the F3C–SO3 bond from 3.5 kcal/mol to about 2.7 kcal/mol. This electrostatic effect is associated with slight additional polarization of the CF bond in the eclipsed conformation. The energetic barrier to rotation of the acid hydroxyl group away from the sulfonic acid oxygen plane, out into the solvent is substantially flattened by electrostatic solvation effects. The maximum free energy for those solvent accessible proton conformations is about 1.0 kcal/mol. We carried out additional ab initio electronic structure calculations with a probe water molecule interacting with the triflic acid. The minimum energy structures found here for the triflic acid molecule with the probe water revise results reported previously. To investigate the reaction path for abstraction of a proton from triflic acid, we found minimum energy structures and energies for isolated molecular fragments, and solvation free energies for: (a) a docked configuration of triflate anion and hydronium cation and (b) a transition state for proton interchange between triflic acid and a water molecule. Those configurations are structurally similar but energetically substantially different. The activation free energy for that proton interchange is predicted to be 4.7 kcal/mol above the reaction end-points.