J. Phys. Chem. C 2010, 114, 11965–11976
11965
A Reactive Molecular Dynamics Algorithm for Proton Transport in Aqueous Systems Myvizhi Esai Selvan, David J. Keffer,* Shengting Cui, and Stephen J. Paddison Department of Chemical and Biomolecular Engineering, UniVersity of Tennessee, KnoxVille, Tennessee 37996-2200 ReceiVed: NoVember 5, 2009; ReVised Manuscript ReceiVed: April 27, 2010
We present a model that incorporates the structural diffusion of a proton into a classical molecular dynamics simulation using a reactive molecular dynamics (RMD) algorithm. The transition state for proton transfer obtained from ab initio calculations is mapped onto a set of geometric and energetic triggers to describe the structural diffusion of the proton in the simulation. Numerical values of these triggers are parametrized to satisfy the experimental values of rate constant and activation energy in order to capture the molecular and macroscopic features of structural diffusion. The algorithm partitions the structural diffusion of a proton into three steps: (i) satisfaction of the triggers, (ii) instantaneous reaction, and (iii) local equilibration. The final step ensures that the ending point of the reaction provides the correct structure and heat of reaction. Hence, the reactivity is incorporated by the algorithm rather than through the development of a reactive potential. We have applied this scheme to study proton transport in bulk water and solutions of HCl. Total charge diffusion along with the structural and vehicular decomposition is studied as a function of temperature (280-320 K). The two components are found to be uncorrelated and the structural diffusion contributes 60-70% of the total charge diffusion in bulk water. The method is applied to HCl solutions (0.22-0.83 M) to study the effect of concentration on proton transport. The reduction in the total diffusivity of the charge with an increase in concentration is due to the reduction in structural diffusion. I. Introduction The relationship between the hydrated morphology of proton exchange membranes (PEMs), commonly employed as the electrolyte in fuel cells, and proton conductivity continues to be of great interest.1 A fundamental understanding of this structure-property correlation should enable the effort to develop PEMs with superior performance across a wide range of operating conditions.2,3 The connection between structure and transport, however, remains unclear4 due to the uncertainty in the mechanism of proton transport within the aqueous domains of the hydrated membrane. Proton transport in bulk water occurs through a combination of both vehicular diffusion (movement of the center of mass of hydronium ions) and structural diffusion5,6 (transfer of protons among water molecules). However, it is unclear to what extent these two mechanisms continue to function in a highly acidic and extremely confined aqueous region of a hydrated PEM.7,8 There is evidence from theory and simulation suggesting that both proton transport mechanisms are active in PEMs9-13 with an increase in structural diffusion occurring at high hydration levels.4 Structural diffusion of a proton involves breaking and forming of covalent and hydrogen bonds, and hence a quantum mechanical (QM) description is warranted to accurately describe this process. Zundel and Eigen cations are two of the predominant solvation complexes of the hydrated proton involved in structural diffusion.5,14 The proton transport occurs via structural defects due to continual interconversion between covalent and hydrogen bonds with these as the limiting structures.15 Extensive experimental work has been conducted to study proton transport in water to understand its high mobility. The finding of Eigen16 and Zundel cations17 motivated the study of * To whom correspondence should be addressed. E-mail: dkeffer@ utk.edu.
protonated clusters H+(H2O)n (n ) 4 to 27), using vibrational predissociation spectroscopy.18-21 A detailed structural analysis and thermodynamics of these clusters, including their charge delocalization, were obtained from O-H stretching spectral signatures in the region of 0-4000 cm-1 and through ab initio calculations.22 Insight into the average residence time of a proton on a water molecule was obtained from NMR spectroscopy. These studies23-31 determined the activation energy and rate constants for the proton exchange reaction rates using water enriched with 17 O. They were obtained by measuring the proton spin-lattice relaxation in the rotating frame/low frequency or spin-spin relaxation or 17O line widths as a function of temperature and pH using techniques including field-cycling, pulse, and spin-echo. Both structure and structural fluctuations were investigated in real time using ultrafast vibrational spectroscopy.32 Proton rattling along a hydrogen bond was found to take place at a time scale of
