Hydrated Arrays of Acidic Surface Groups as Model Systems for

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Hydrated Arrays of Acidic Surface Groups as Model Systems for Interfacial Structure and Mechanisms in PEMs A. Roudgar,† S. P. Narasimachary,† and M. Eikerling*,†,‡ Department of Chemistry, Simon Fraser UniVersity, 8888 UniVersity DriVe, Burnaby, BC, V5A 1S6, Canada, and Institute for Fuel Cell InnoVation, National Research Council Canada, 4250 Wesbrook Mall, VancouVer, BC, V6T 1W5, Canada ReceiVed: May 24, 2006; In Final Form: July 18, 2006

We utilize ab initio quantum mechanical calculations in order to explore structural conformations and cooperative mechanisms at a minimally hydrated 2D array of flexible acidic surface groups. This system serves as a model for rationalizing interactions and correlations of protons and water with ionized side chains that are affixed to hydrophobic polymer aggregates in polymer electrolyte membranes (PEMs). The model exhibits two basic minimum energy configurations upon varying the separation of surface groups from 5 to 12 Å. In the “upright” structure at small separation, surface groups are fully dissociated and oriented perpendicular to the basal plane. Together with hydronium ions (H3O+) they form a highly ordered network with long-range correlations. At larger separations we found the transition to a “tilted” structure with clusterlike conformation of surface groups. This structure retains only short-range correlations. Moreover, we investigated the strength of water binding to the minimally hydrated structures. At small separations between surface groups, an additional water molecule interacts only weakly with the minimally hydrated array (binding energy < 0.1 eV) while the energy needed to remove one water molecule exceeds 1 eV. This shows that the minimally hydrated systems are very stable. Ideally, these studies would expedite the design of cheap, highly performing PEMs for fuel cells, with a major focus on membranes that could operate stably at minimal hydration and elevated temperatures (>120°C).

Introduction Ionomer membranes are of great practical importance for a wide range of applications, e.g., in coatings, water electrolysis, catalysis, and chlor-alkali cells.1 Furthermore, their intricate selforganized morphologies and unique transport properties inspire enormous efforts in fundamental research.2-12 In recent years, the use in polymer electrolyte fuel cells (PEFC) has emerged as the primary application of protonconducting ionomer membranes.13,14 Indeed, to a large extent the polymer electrolyte membrane (PEM) determines architecture, feasible operating conditions, and performance measures such as voltage efficiency and power density of the fuel cell system. In addition to high proton conductivity (0.1 S cm-1), PEMs should be impermeable to gases, possess chemical and mechanical robustness, and facilitate water management in the fuel cell. In fuel cell powered vehicles, PEMs should easily adapt to widely varying operation conditions, e.g., start-up at -40 °C.15-18 Presently, the most widely used and tested polymer electrolyte membranes are perfluorinated sulfonated polymers such as Nafion (DuPont), Dow (Dow Chemicals), Flemion (Asahi Glass), and Aciplex. They vary in chemical structure, ion exchange capacity, and thickness. The membrane morphology and the basic mechanisms of proton transport are, however, similar. The base polymer, depicted schematically in Figure 1, * Corresponding author: Department of Chemistry, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada. Tel.: 001 604 291 4463. Fax: 001 604 291 3765. E-mail: [email protected]. † Simon Fraser University. ‡ National Research Council Canada.

Figure 1. Different steps in the evolution of the self-organized structure of polymer electrolyte membranes, as inferred from scattering and diffraction studies.1-4,10 The primary chemical structure on the left with hydrophobic backbones, side chains, and acid headgroups evolves into polymeric aggregates with complex interfacial structure (middle). Randomly interconnected phases of these aggregates and water-filled voids between them form the heterogeneous membrane morphology at the macroscopic scale (right).

consists of Teflon-like backbones with randomly attached pendant side chains, terminated by charged hydrophilic segments or end groups (usually sulfonic acid groups, -SO3H).19,20 The excellent perspectives of PEFCs as autonomic, highly efficient, and environmentally benign energy conversion devices trigger enormous efforts in synthesis and experimental characterization of novel PEMs.8,21-26 A major incentive in this realm is the development of membranes that are suitable for operation at intermediate temperatures (120-200 °C). In state-of-the-art PEMs, the evaporation of weakly bound water at temperatures exceeding 90 °C extinguishes the most favorable mechanism of proton transport through bulk water. Inevitably, aqueousbased PEMs for operation at T > 90 °C have to attain high rates of proton transport with a minimal amount of water that is tightly bound to a stable host polymer.22,25,27 The development

10.1021/jp063189v CCC: $33.50 © 2006 American Chemical Society Published on Web 09/19/2006

20470 J. Phys. Chem. B, Vol. 110, No. 41, 2006 of new PEMs, thus, demands efforts in understanding of proton transport mechanisms under such conditions. The random phase-segregated morphology of PEMs has been widely explored in experiment. Recent reviews can be found in refs 8 and 10. Two prevalent structural motifs have emerged. The cluster network model, suggested by A. Eisenberg28 and later on refined by T. D. Gierke and colleagues,29,30 describes the PEM as a network of aqueous pathways (consisting of inverted spherical micelles and aqueous necks) that is embedded in an inert and structureless polymer host. This oversimplified perspective proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells.6,7 It helped to rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks.29,31 In contrast, G. Gebel and colleagues at the CEA in Grenoble developed a more genuine structural picture on the basis of small angle scattering data (SANS, SAXS, and USAXS), in which polymer aggregates were identified as the membrane-forming elements.2-4,32-35 This view opens intriguing perspectives for predictive theories of structure formation in PEMs based on a consistent treatment of interactions between polymer, protons, and water. Three major levels in the structural evolution from primary chemical architecture to polymer aggregates at the nanoscale to random heterogeneous morphology at the macroscale are depicted in Figure 1. Upon hydration, self-organization of polymer backbones leads to the formation of a hydrophobic skeleton that consists of interconnected elongated fibrillar aggregates.2-4 The -SO3H head groups dissociate and release protons as charge carriers into the aqueous subphase that fills the void spaces between aggregates. Polymer side chains remain fixed at the surfaces of those aggregates where they form a charged, flexible interfacial layer. The structure of this interface determines the stability of PEMs, the state of water, the strength of interactions in the polymer/water/ion system, vibration modes of side chains, and mobilities of water molecules and protons. The charged polymer side chains contribute elastic (“entropic”) and electrostatic terms to the free energy. This complicated interfacial region thereby largely contributes to differences in performance of membranes with different chemical architectures. Indeed, the picture of a “polyelectrolyte brush” could be more insightful than the picture of a well-separated hydrophobic/-philic domain structure in order to rationalize such differences.36 Proton conductivities of ∼0.1 S cm-1 at high excess water contents in current PEMs are due to the concerted effect of a high concentration of free protons, liquid-water-like proton mobility, and a well-connected cluster network of hydrated pathways.37-42 The effects of membrane dehydration are multifold. It triggers morphological transitions that have been studied recently in experiment2-4 and theory.9,31,40,43 At water contents below the percolation threshold, the well-hydrated pathways cease to span the complete sample and narrow, poorly hydrated necks control the overall transport.9,43 Moreover, the structure of water and the molecular mechanisms of proton transport change at low water contents. In well-humidified PEMs the activation energy of proton transport is ∼0.12 eV.38,39 This suggests that the well-known relay-type mechanism of prototropic mobility in aqueous media prevails, which is also often referred to as structural diffusion or Grotthuss mechanism.9,31,44-48

Roudgar et al. In minimally hydrated membranes, which could only retain the strongly bound water molecules near polymeric aggregates, the proton conductivity decreases tremendously. It levels, however, off at a finite residual value. This indicates that samplespanning pathways of proton transport along lowly hydrated acidic side chains persist at small water contents, although the continuously connected network of well-hydrated pores is disrupted. A corresponding increase in activation energy of proton transport to >0.35 eV was observed in refs 38 and 39. The microscopic mechanism of proton transport changes since narrow pores or necks in minimally hydrated PEMs could not perpetuate the high bulk-like proton mobility. In this regime, strong correlations at the polymer/water interface become vital. The compelling, yet unresolved questions are as follows: What are the correlations and mechanisms of proton transport in the interfacial layer? Is high proton mobility possible under conditions of minimal hydration? The complications for the theoretical description of proton transport in the interfacial region are caused by fluctuations of the side chains, their random distributions at polymeric aggregates, and their partial penetration into the bulk of waterfilled pores. The importance of an appropriate flexibility of hydrated side chains has been explored recently in extensive molecular modeling studies.49 Continuum dielectric approaches and molecular dynamics simulations have been utilized to explore the effects of interfacial charge distributions on proton mobility in single-pore environments of PEMs.41,42,50,51 Molecular level simulations were employed in order to study side chain correlations and examine direct proton exchange between water of hydration and surface groups.12,49,52 A trifluoromethane sulfonic acid monohydrate (TAM) solid was explored in ref 52. The regular structure of the crystal53 provides a proper basis for performing controlled ab initio molecular dynamics. Rearrangement of neighboring sulfonate groups led to the formation of an activated state with activation energy ∼0.3 eV. These calculations suggested that an appropriate flexibility of anionic side chains could be vital for high proton mobility in PEMs under conditions of minimal hydration and high anion density. The model system considered in ref 52 is, however, rather stiff, in the sense that chemical composition and water content of the crystal are fixed. Only minimal hydration of the system could be considered. Instead, in the present work, we present molecular-level calculations for a regular hexagonal array of acidic surface groups in 2D. Optimization studies based on DFT calculations reveal a wealth of structural conformations and transitions in such arrays under conditions of minimal hydration. We explore the effects of chemical composition of the surface groups and their density on structure and correlations in this system. Model System and Parameters Figure 2 illustrates the model system considered in this work. It emerges from the self-organized morphology of the membrane at the mesoscopic scale as indicated in the middle panel of Figure 1. The random array of hydrated and ionized side chains is tethered to the surface of aggregated hydrophobic polymer backbones. Relevant structural properties include the shape, thickness, persistence length of aggregates, and the density and effective lengths of side chains on their surface. This system is, however, too complex for our goal of studying the correlated side chain dynamics by full quantum mechanical calculations. A computationally feasible model can be constructed on the basis of the following considerations. We assume that to a first

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Figure 2. In the model, the interfacial structure of hydrated and ionized side chains that are tethered to fibrillar polymeric aggregates is mapped onto a 2D array with fixed end points, as schematically depicted in (a). The simulated system with unit cell (3 × [CF3-SO3-H + H2O]) is shown in (b) in side and top view.

approximation the highly correlated interfacial dynamics of side chains, protons, and water decouples from the dynamics of the polymeric aggregates. We thus imply that these supporting aggregates form a fixed frame of reference for the surface groups. As a further simplification, we remove the supporting substrate altogether, considering it in first approximation as an inert basal plane. (In our calculations, we will ensure that acid head groups and water molecules are located on one side of the basal plane only. This treatment is equivalent to describing the polymer aggregates by excluded volume interactions, as considered in ref 19.) We fix the terminal carbon atoms of the surface groups at the positions of a regular hexagonal grid on this basal plane, while all remaining degrees of freedom are unconstrained. The resulting primitive model consists, thus, of a regular hexagonal array of surface groups with fixed end points, as depicted in Figure 2. As we will see below, despite the highly simplified structure this model retains essential characteristics for studying structural conformations, stability, and the concerted dynamics of polymer side chains, water, and protons at polymeric aggregates in PEMs. Our approach implies that the effect of polymer dynamics on processes inside pores is primarily due to the distribution of side chains, their protrusion lengths into the aqueous domains, their orientation relative to the basal plane, their flexibility, and the corresponding transient charge distributions. In this first publication we present results for the shortest acidic surface groups, viz. CH3SO3H and CF3SO3H. In our standard simulations, the hexagonal unit cell of the 2D hexagonal array contains three surface groups and three water molecules, i.e., overall 36 atoms, as indicated in Figure 2b. In this first publication utilizing this model system, we focus on a minimally hydrated layer (1 water molecule per surface group). The lattice constant a is related to the separation dCC between the end points of the surface groups by dCC ) x2/2a. Side chain separations have been calculated recently in MD-based studies of the membrane morphology. It was found that the average side chain distances are in the range 6.0 Å e dCC e 6.8 Å.54 We consider values in the range 5 Å e dCC e 12 Å, which encompasses the relevant range of variation for prototypical membranes.29,33-35 Upon deswelling of the membrane, side chain separations are likely to decrease.9,29,31 The surface charge

density, proton density distribution, and corresponding electrostatic interactions will thus increase and explicit side chainside chain correlations will become more pronounced. On the other hand, experimental data also suggest that mean side chain separations in the dry state should not drop significantly below ∼7 Å since otherwise random ionomers could not form stable aggregates upon hydration. At the lowest separations, direct proton transfer between stiff SO3- groups would still not be possible.40,50 This situation could change, however, when random configurations of side chains, their flexibility, and fine structure and smearing of charges of sulfonate groups are taken into consideration.42 Computational Details We have performed ab initio calculations using the Vienna Ab-initio Simulation Package (VASP) based on density functional theory (DFT).55-58 The exchange correlation effects are incorporated within the generalized gradient approximation (GGA) using the Perdew-Wang (PW-91) functional. The ionic cores are represented by projector-augmented waves (PAW). The Kohn-Sham one-electron valence states are expanded in a basis of plane waves with cutoff energies of Ecut ) 400 eV. A Γ-point sampling of the Brillouin zone is used. We employ a periodic super cell approach; i.e., the unit cell repeats itself along x, y, and z directions. In the z-direction repeating unit cells are separated by a vacuum space of ∼12 Å so that interactions between them could be neglected. We calculated the corrections to the total energy due to factitious dipole-dipole interactions between unit cells in the z-direction. Depending on the separation between surface groups, we found correction energies between 0.003 and 0.030 eV. These values do not affect our results. For optimization studies, a conjugate-gradient algorithm was used to relax ions into their ground state. We started with the smallest separation dCC and increased it stepwise by 0.35 Å between 7 and 12 Å. For points close to the minima of the formation energy we used a step width of 0.2 Å. At each value of dCC we used the optimized geometry at the previous dCC to generate the new initial configuration by scaling up the lattice constant while keeping all intramolecular distances fixed. This

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Roudgar et al.

Figure 3. Formation energy per unit cell, Euc f , of the minimally hydrated interfacial layer of CF3-SO3-H groups as a function of the separation between surface groups, dCC, showing “upright” and “tilted” structures, respectively. The numbered points refer to structural conformations that are discussed in the text.

procedure provided a faster ionic convergence and reduced computation time. At intermediate dCC, we explored the configuration space of the simulated system in more detail by performing a series of ab initio molecular dynamics (AIMD) calculations. AIMD helped to find transitions between different structures, which represent local minima in total energy. We, thereby, found a remarkable conformational multiplicity of the system. The AIMD simulation has been performed with time step t ) 0.2 fs in the NVT ensemble. The temperature was controlled by a Nose-Hoover thermostat59,60 at T ) 300 K. All calculations have been performed on the PEMFC and BUGABOO Linux clusters at Simon Fraser University and on WESTGRID. The net CPU time for the entire calculation amounts to around 60 days using continuously 16 nodes on SGI clusters. Due to a large number of additional calculations, not reported here, waiting times, etc., the actual calculations have consumed much more time. Results and Discussion Formation Energy and Structural Transitions. We considered first the regular array of triflic acid, CF3-SO3-H, as the shortest surface group with hydrophobic tail. For the minimally hydrated array with a unit cell 3 × [CF3-SO3-H + H2O], optimized formation energies per unit cell, denoted as Efuc, are shown as a function of the carbon-carbon separation, dCC, in Figure 3. This formation energy, Euc f , is defined as the difference between the optimized total energy for a given value of dCC, Etotal(dCC), and the total energy of a system of three independent surface groups, each with one water molecule, corresponding to the limit of infinite separation, E∞total, ∞ Euc f ) Etotal(dCC) - Etotal

(1.1)

According to this definition, Euc f incorporates correlation energies between surface groups due to electrostatic interactions and hydrogen bonding in the hydrated interfacial layer. The most stable configuration of this 2D array is found at dCC ) 6.2 Å with Euc f ) -2.78 eV, corresponding to the highest formation energy. As can be seen in Figure 4a, in this conformation, acidic surface groups are fully dissociated. They are oriented upright with an average angle θ ≈ 90° relative to the basal plane. H3O+ ions and SO3- groups form a highly ordered hydrogen-bonded network in 2D. Each of the H3O+ ions has saturated its number of hydrogen bonds with three

neighboring SO3- groups, resulting in nine hydrogen bonds per unit cell. Strong long-range correlations render this structure rather stiff, resembling a 2D monohydrate crystal. The strong directional hydrogen bonds suppress the dynamics of protons and water molecules. Due to the high electronegativity of the hydrophobic residual groups, the oxygen atoms in H3O+ ions are repelled from the interface. The average vertical separation between the H3O+ ions (position of O atom) and the SO3groups (position of S atom) is 1.0 Å. The average hydrogen bond length is dOO ) 2.6 Å. The average OH bond length in H3O+ ions is 1.02 Å, a value that is slightly larger than OH bond lengths in water (dOH ) 0.98 Å). Upon gradually increasing dCC, the fully dissociated “upright” structure becomes less stable. The average hydrogen bond distance increases from dOO ) 2.6 Å (at dCC ) 6.2 Å) to dOO ) 2.7 Å (at dCC ) 7.1 Å), resulting in weaker hydrogen bonds and therefore lower absolute values of the formation energy, e.g., Euc f ) -1.67 eV at dCC ) 7.1 Å. Figure 3 reveals that a transition between fully dissociated and fully nondissociated states of the surface groups would occur in the “upright” conformation at dCC ≈ 7.2 Å (point 1 in Figure 3). Figure 5a shows that the number of hydrogen bonds decreases from 9 to 3 upon this transition. The “upright” conformation becomes, however, unstable at dCC ) 6.5 Å (point 2 in Figure 3). For dCC > 6.5 Å, a transition to a fully dissociated “tilted” structure is energetically more favorable, as is evident from Figure 3. In this structure the three surface groups in each unit cell are inclined toward each other. In comparison to the “upright” structure, the surface groups are rotated around their C-S axis and one H3O+ ion is shifted laterally. Upon increasing dCC, the tilting angle decreases monotonically from θ ) 75° for dCC ) 6.0 Å to θ ≈ 14° for dCC > 10 Å as shown in Figure 5b. At dCC ) 7.4 Å the number of hydrogen bonds per unit cell decreases from 9 to 7, cf. Figure 5a. At this point, the inter-unit-cell hydrogen bonds are broken, leading to the formation of disconnected clusters of three surface groups and three H3O+ ions each. Optimized geometries of the fully dissociated “tilted” structure with nine and seven hydrogen bonds are shown in Figure 4b (at dCC ) 7.1 Å) and Figure 4c (at dCC ) 8.1 Å), respectively. Strong intracluster correlations persist for dCC > 7.4 Å and stabilize the “tilted” structure relative to the “upright” structure. A transition from fully dissociated to partially dissociated “tilted” conformation occurs at dCC ) 8.7 Å with two H2O and one H3O+ remaining per unit cell (point 3 in Figure 3). At dCC ) 9.2 Å another transition from the partially dissociated to a nondissociated configuration occurs (point 4 in Figure 3). The optimized geometry of the nondissociated conformation at dCC ) 10.4 Å is shown in Figure 4d. Upon further increasing dCC, every acid group has only one hydrogen bond with the closest water molecule. The intracluster hydrogen bonds are broken and the formation energy approaches Euc f ) 0. As corroborated in refs 12, 49, 61, and 62, a single water molecule per independent surface group is not sufficient for dissociation. We have performed ab initio molecular dynamics simulations at dCC ) 7.1 Å and T ) 300 K for about 6 ps. While such an MD trajectory is by far too short to observe proton transport, it helped us in finding the transition to a new conformation of the hydrated interfacial layer that is the most stable conformation for 7.1 Å e dCC e 7.4 Å. The formation energy Euc f is higher in absolute value by ∆Euc ) 0.2 eV in comparison to that of f the “tilted” structure. In the corresponding configuration, fully dissociated surface groups are inclined toward the basal plane with tilting angle θ ) 7°. They form a hexagonal ring structure

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Figure 4. Optimized geometries of the CF3-SO3-H system at various surface group separations: (a) fully dissociated “upright” structure at dCC ) 6.7 Å, (b) fully dissociated “tilted” structure at dCC ) 7.1 Å, (c) fully dissociated “tilted” structure at dCC ) 8.1 Å, and (d) nondissociated “tilted” structure at dCC ) 10.6 Å.

Figure 5. (a) Number of hydrogen bonds as a function of dCC for “upright” and “tilted” structures. (b) Average tilting angle as a function of dCC for the “tilted” structure.

in which each of the three H3O+ ions can retain its three hydrogen bonds. Two H3O+ ions per unit cell are located above the basal plane and one H3O+ ion is located below it. This

structure thus violates the requirement that all H3O+ ions and H2O molecules should be located on one side of the basal plane, owing to the volume exclusion effect of the hydrophobic polymer aggregates. We, therefore, subsequently disregard it. The number of hydrogen bonds per unit cell, cf. Figure 5a, is a measure of correlations in the interfacial layer. It determines the structure at the interface. Strong long-range correlations exist at dCC < 7.4 Å, for which each H3O+ ion could attain its optimum number of hydrogen bonds. Short-range correlations within clusters persist at intermediate separations between surface groups, 7.4 Å e dCC < 10.5 Å. At dCC g 10.5 Å surface groups are more or less independent with the correlation energy approaching zero. We would like to stress that the transition between “upright” and “tilted” structures upon increasing dCC is not a gradual activationless process. It corresponds in fact to a true surface transition via an activated state. During transiting from “upright” to “tilted” structures, an H3O+ ion is shifted laterally and it literally flips over its back after clipping off a hydrogen bond between unit cells. Thereafter, it forms a new intracluster hydrogen bond, while surface groups rotate simultaneously in order to relax into the “tilted” conformation. We are currently calculating the activation energy for this process. Preliminary results suggest a value in the range ∼0.5 eV or smaller. Effect of Different Chemical Compositions of Surface Groups. For a rudimentary study of the effect of the chemical composition of the side chains, we have performed the same sequence of DFT calculations with surface groups CH3-SO3H. The formation energy Euc f (dCC) is shown in Figure 6. The qualitative findings are very similar to those for CF3-SO3-H. The most stable “upright” conformation with formation energy Euc f (dCC) ) -2.25 eV is obtained at dCC ) 6.2 Å. The absolute value of the formation energy, |Euc f (dCC)|, at the position of the minimum is lower by 0.52 eV than that obtained for the CF3-

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Figure 6. Formation energy, Euc f , as a function of dCC for the system with unit cell 3 × [CH3-SO3-H + H2O]).

SO3-H array. This is expected, since CF3-SO3-H is a stronger acid than CH3-SO3-H due to the stronger electron-withdrawing effect of the fluorocarbon residual group. We found that the average vertical separation between the H3O+ ions (position of O atom) and the SO3- groups (position of S atom) is ≈0.1 Å, i.e., ∼0.9 Å smaller than the value found for the CF3-SO3-H system. At the same dCC, H3O+ ions are, thus, more deeply embedded into the interfacial layer for the CH3-SO3-H system, indicating that interactions between H3O+ ions and the hydrophobic parts of the side chain are significantly less repulsive. As illustrated in Figure 6, we observe a similar sequence of transitions involving “upright” and “tilted” conformations as well as varying degrees of dissociation upon variation of dCC. The transition from dissociated “upright” structure to dissociated “tilted” structure occurs at dCC ) 6.2 Å. This value is 0.3 Å smaller than the corresponding value for the CF3-SO3-H system. Strength of Water Binding to the Interfacial Layer. The most severe limitation of sulfonic acid based ionomers is the low proton conductivity at low levels of hydration. At temperatures exceeding T ≈ 90 °C the conductivity steeply decreases even at water partial pressures exceeding ∼1 atm. Under these conditions, weakly bound water molecules that could be needed to bridge the typical separations of 7-10 Å between neighboring sulfonic acid groups evaporate. It has, however, been demonstrated in ref 25 that the proton conductivity in low hydrated ionomers could level off at

Roudgar et al. relatively high residual values of about 4 × 10-2 S cm-1 in the temperature range 130-170 °C if the sulfonic acid groups are spatially less separated and/or possess sufficient conformational flexibility. It can be expected that under such conditions the strength of binding of residual water molecules to the interface and the dynamics of the interfacial layer are crucial for sustaining an effective mechanism of proton transport. As a preliminary step, before one could explore in detail the feasible mechanisms of proton transport in such systems, it is expedient to explore our model of the low hydrated interfacial layer (with CF3-SO3-H surface groups) with respect to the strength of binding of an extra water molecule and study its stability with respect to the removal of a water molecule. We have, thus, calculated the binding energy of one additional water molecule, Eb, as well as the defect energy, Ed, i.e., the change in Euc f (dCC), upon removal of one water molecule from the minimally hydrated layer. To examine the unit cell with respect to the binding energy of the additional water molecule, Eb, we generated a regular 10 × 10 grid of points in the xy-plane, spanning the complete unit cell. The xy coordinates of the oxygen atom in the additional water molecule were fixed successively at all 100 grid points. At each of these positions we performed a geometry optimization including the remaining degrees of freedom (while carbon end points of surface groups remain fixed). We were, thus, able to generate a contour plot of binding energies of the additional water molecule. The contour plot for the upright structure at dCC ) 6.3 Å is depicted in Figure 7a (darker regions correspond to higher binding energies). We have thereafter performed a full geometry optimization with the water molecule placed initially at the positions corresponding to the highest binding energies in the contour plot. Figure 7b shows the corresponding optimized conformation found with one extra water molecule at dCC ) 6.3 Å. In Figure 8a we show Eb as a function of dCC. For the “upright” structure the additional water is weakly attached to two neighboring -SO3- groups, cf. Figure 7b. For 6.7 Å < dCC < 9.9 Å, we found that the additional water molecule and one H3O+ ion form a Zundel ion, H5O2+, in the “tilted” structure. This region is highlighted in Figure 8a and a typical conformation that exhibits the formation of a Zundel ion is shown in Figure 9. The additional water molecule is weakly bound in the strongly correlated regime, for dCC < 7.0 Å. Notably, in this region values of |Eb| could be significantly smaller (|Eb| < 0.1 eV for dCC
7.4 Å, the additional water molecule will be strongly bound with |Eb| > 0.5 eV. A sharp transition from low |Eb| to high |Eb| occurs at dCC ≈ 7 Å. This is expected since at larger dCC the number of hydrogen bonds is reduced to 7, cf. Figure 5a, and long-range correlations disappear. The maximum binding energy |Eb| ) 0.92 eV is obtained at dCC ) 7.4 Å. The results depicted in Figure 8a are of vital significance for our future work on mechanisms of proton transport along the hydrated interfacial layer. For small surface group separations the interface could be equilibrated with the minimum number of one water molecule per surface group, whereas at large separations a larger, yet to be determined, number of water

J. Phys. Chem. B, Vol. 110, No. 41, 2006 20475 molecules will be needed for equilibrating the interface in MD calculations. Correspondingly, different PT mechanisms will be operative in these regimes. At intermediate separations, dCC ≈ 7 Å, the strength of water binding is highly sensitive to dCC. In this intermediate regime, the strong coupling between local fluctuations in arrangements of surface groups and fluctuations in the strength of binding of extra water molecules could trigger sequences of trapping and releasing of water molecules from the interface. In Figure 8b we show the energy Ed needed for removing one water molecule from a unit cell and transferring it to infinite separation as a function of dCC. In this calculation, we removed the water molecule with the lowest binding energy. Values of Ed > 1 eV for dCC < 10 Å affirm the extraordinary stability of the minimally hydrated array layer. The maximum value Ed ≈ 1.6 eV is found at dCC ≈ 7.1 Å. For dCC > 11.0 Å, Ed approaches a value that corresponds to the latent heat of vaporization of water molecules from a free liquid water surface (∼0.5 eV). Overall, these results suggest that the minimally hydrated layer is very stable in the strongly correlated regime at dCC < 7.0 Å. While it is energetically highly unfavorable to remove one water molecule from the interfacial layer (Ed > 1 eV), additional water molecules are only weakly attached to it (|Eb| < 0.1 eV) and thus easily evaporate at elevated temperatures. The sharp increase in |Eb| at dCC ≈ 7 Å by ∆Eb ≈ 1 eV coincides with the transition from a highly ordered surface conformation with long-range correlations to a less correlated structure with pronounced tendency of cluster formation at dcc > 7.4 Å. In further systematic molecular dynamics calculations, we expect to find strong fluctuations in the transition region at dCC ∼ 7 Å, which distinguish it as the primary region for exploring the dynamics in the interfacial layer. As a support in favor of this conclusion, we observed the formation of a Zundel ion for 6.7 Å < dCC < 9.9 Å upon addition of the extra water molecule, which is regarded as a vital relay group in pertinent proton transport mechanisms in aqueous systems. In summary, our study demonstrates that the simple model of the minimally hydrated interface in PEMs exhibits a number of distinct structural conformations and transitions. The minimally hydrated interfacial conformation is very stable over the whole range of considered surface group separations. It could persist even at elevated temperatures. Presumably, with adjustment of the surface group separation a regime could be found at intermediate surface group separations, in which the strength of long-range correlations and the flexibility of surface groups are attuned in such a way as to enable high rates of proton transport along the interfacial layer. At small separations between surface groups, the stiffness of the interfacial configuration due to strong hydrogen bonding will suppress the mobility of protons and water molecules. At large separations, on the other hand, surface groups and their associated water molecules will be uncorrelated and, thus, highly flexible; longrange proton transport would only be possible upon the addition of a sufficient number of water molecules that could bridge the separation between surface groups. A viable mechanism of proton transport under conditions of minimal hydration warrants an optimized tradeoff between correlations in the interfacial layer and conformational flexibility of the surface groups. As our results suggest, this could be realized at intermediate separations of dCC ≈ 7 Å. Further exploration of this model could thus be highly insightful for lowly hydrated PEMs at elevated temperatures, as considered recently in experiment.25 Moreover, the molecular level understanding of mechanisms of lateral proton transport

20476 J. Phys. Chem. B, Vol. 110, No. 41, 2006 along biological membranes and lipid monolayer films is a longstanding issue.63-69 Interestingly, the authors of ref 64 identified a surface group separation of ∼7 Å as a critical value for the occurrence of long-range proton conduction. This value is in agreement with the critical separation that we have found in our calculations. Likewise for PEMs as well as in the context of bioenergetics it is thus of great current interest to understand how structuring and interactions at the hydrated interface vary with the density of charged surface groups and how these variations affect the mechanisms of proton transport. Conclusions The present work explores interfacial conformations and cooperative mechanisms at surfaces of hydrated polymeric aggregates in PEMs. The primary objective is to rationalize interactions and correlations of proton complexes and water with ionized side chains that are affixed to the hydrophobic skeleton of the membrane. This insight helps to understand better the relations between the chemical architecture of PEMs and their proton-conductive abilities. Our model system consists of a 2D hexagonal array of acidic surface groups with end points fixed at a basal plane. Due to its simple regular structure, this model provides a viable basis for ab initio quantum mechanical calculations. It allows for the systematic variation of the density of surface groups, their chemical structure, and the degree of hydration. Here, we present results for arrays of the simplest surface groups, CF3-SO3-H and CH3-SO3-H, under conditions of minimal hydration, i.e., with one water molecule added per group. We considered the density of surface groups as the major parameter and investigated its effect on correlations and stability of the hydrated interfacial layer. We explored surface group separations from 5 to 12 Å, spanning the values encountered in prototypical membranes. At the lowest surface group separations, ionized surface groups and hydronium ions form a highly ordered, stiff network. Due to the strong correlations, the dynamics of the interfacial layer will be suppressed and it is unlikely to find long-range proton transfer under such conditions. In the opposite limit, at the largest separations, surface groups are found to be only weakly correlated and they are nondissociated. Hence, additional weakly bound water molecules would be needed in order to facilitate proton mobility. The twist is that in order to promote long-range proton transport along minimally hydrated arrays, the surface groups should be sufficiently correlated but at the same time they should remain flexible enough. Variation of the surface group separation in the intermediate range could be the proper way to optimize the tradeoff between correlations and flexibility. A transition from an “upright” conformation of surface groups with long-range order to a “tilted” conformation with cluster formation occurs at a separation of ∼7.0 Å. Furthermore, we found that correlations between surface groups determine the strength of water binding to the interfacial layer. In the strongly correlated regime for 7.0 Å. The binding energy of the extra water varies by ∼0.9 eV in this relatively narrow region. In our future work, we will explore whether the strong fluctuations between weak and strong binding of the extra water molecule as well as the observed formation of a Zundel ion at such separations are sufficient for generating high rates of proton transfer at lowly hydrated interfaces. The energy needed to remove one water molecule was found to be >1 eV for surface group separations 100 °C. In terms of the approved stability of minimally hydrated structures and the suggested viability of effective mechanisms of proton transport under conditions of elevated temperature and minimal hydration, our results could be compared with experimental data in ref 25. Those measurements demonstrate that PEMs could sustain high proton conductivities at temperatures exceeding 140 °C, if the chemical structure of the side chains and their density are properly adjusted. Overall, our results suggest that the 2D regular array of surface groups could be a viable model system for exploring interfacial mechanisms of proton transport in PEMs that involve strong correlations among protons, water, and charged polymer groups. Starting from molecular level calculations, we plan to systematically increase the complexity of the system, by considering longer, more complex surface groups that more closely resemble the side chains in PEMs and explore proton transfer events in such polymer brushes of acidic surface groups with varying degrees of hydration. In part, the present work is inspired by the feasibility of fabricating brushes of acid functionalized surface groups. While the structural conformations of such brushes are widely investigated in experiment and theory,63 their lateral transport properties are still an emerging field of research. Systematic studies on such well-defined model systems could tremendously facilitate the understanding of the role of side chain arrangement and flexibility on interfacial mechanisms of proton transport in PEMs. In studies on real PEMs such an understanding is obstructed by randomness at multiple scales. Acknowledgment. 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