CONFORMATIONS OF PERFLUOROETHER SULFONIC ACID SIDE CHAINS FOR THE MODELING OF NAFION®
Stephen J. Paddison1, Lawrence R. Pratt,2 and Thomas A. Zawodzinski Jr.1
Materials Science and Technology Division1 and Theoretical Division2
Los Alamos National Laboratory, Los Alamos New Mexico 87545
LA-UR-98-4628.
ABSTRACT
Optimized geometries for the acid side chain CF3OCF2CF(CF3)O(CF2)2SO3H and the side chain with backbone attachment CF(CF2CF3)2—OCF2CF(CF3)OCF2CF2SO3H were determined with electronic structure techniques exclusive of hydration effects. The minimum energy structures are folded with the two ether oxygens in a gauche conformation. Rotation about the outermost ether group provides natural transition path to the partial unfolding of the side chain. The potential energy surface for this rotation was determined and the results showed that the staggered fluorine conformation of the head group is unchanged with rotation. This rotational produced conformations approximately 40% longer (8.5Å) and about 3.5 kcal/mol higher in energy after surmounting a barrier of about 4.6 kcal/mol. Additional searching for stretched conformations of the side chain led to the discovery of an even longer (9.8Å) minimum energy conformation that was entirely unfolded with the ether oxygens located trans relative to one other. This unfolded conformation is essentially isoenergetic (+0.1 kcal/mol) with the (folded) minimum energy conformation. The existence of a small number of well-defined "short" and "long" side chain conformations, with substantially similar head-group chemistry, suggests the speculative view that hydration-dependent equilibria between these conformations should be a significant feature in physical models of the function of Nafion®. Equilibrium geometries were also obtained for both the folded and the unfolded acid side chains, each with an associated single water molecule.
Widespread electrochemical processes and devices utilize Nafion®, a poly(perfluorosulfonic acid) ion exchange membrane. It exhibits good chemical stability [1], remarkable mechanical strength [2], good thermal stability [3], and high electrical conductivity when sufficiently hydrated [4]. While Nafion® initially found extensive application in chloroalkali cells as a cation-exchange membrane [5], other uses have arisen. A few examples include: organic syntheses [6,7], batteries [8], chemically modified electrodes [9,10], and biosensors [11].
A specific interest in perfluorinated ionomers stems from their use in polymer electrolyte fuel cells (PEFCs) [12-14]. A substantial body of experimental work [15-19] has focused on water and ion transport in the hydrated membrane, issues that are critical in optimizing the performance of PEFCs. Key observations arising from that experimental work are: (a) the water self diffusion coefficient increases with increasing water content in the membrane; (b) the proton conductivity increases with increasing hydration of the membrane; and (c) the electroosmotic drag coefficient, the number of waters transported by coupling to a proton flux, remains a constant value of 1 for membranes equilibrated with water vapor and, at room temperature, jumps to values of between 2 and 3 for membranes immersed in liquid water. At elevated temperature, the electroosmotic drag coefficient increases still further for membranes exposed to liquid water. These trends have been verified for several perfluorosulfonic acid membranes. Similar dependence of the water diffusion coefficient and the conductivity on hydration state have been observed for membranes with sulfonated aromatic side chains. Also, the limited available electroosmotic drag measurements for sulfonated aromatic membranes indicate similar values to those observed for immersed perfluorinated sulfonic acid (PFSA) membranes.
Molecular theoretical studies directed towards understanding these remarkable properties of Nafion® have been limited. However, a number of physical models have been developed to understand the mechanisms of water and ion transport in ionomer membranes. Breslau and Miller [20] used a hydrodynamic approach and were able to predict electroosmotic coefficients within 5% of experimental values except for the case of the proton. [21] constructed solubility and transport models based on phenomenological equations and showed that narrow pores dominate transport in the membrane. Pintauro and coworkers [22,23] derived a partition coefficient model treating effects of hydration, electrostatic interactions, and solvent dipole alignment due to fixed wall charges. [24] developed a random network model of a microporous PEM and demonstrated the importance of both the connectivity of the pores and coordination of water, to the overall conductivity of the PEM. Recently, Din and Michaelides [25] reported results of molecular dynamics simulations of water and protons in micropores with uniform charge density on the walls and concluded that the classic Poisson-Boltzmann theory did not accurately predict the distribution of protons within the pores.
Morphological features influence transport in these membranes. In addition to transport measurements, Nafion® has been studied by a host of experimental techniques including: small and wide angle x-ray scattering [26,27], dielectric relaxation [28], and a number of microscopic [29-31] and spectroscopic [32-36] studies. The emerging picture of the morphology of hydrated Nafion® is that of a two-phase system made up of a water-containing ion cluster network surrounded by a hydrophobic polytetrafluoroethylene (PTFE) medium. The integrity and structural stability of the membrane is provided by the PTFE backbones and the hydrophilic clusters facilitate the transport of ions and water in the membrane. These clusters or pores have been conceptually described as lined by an interfacial region of hydrated, sulfonate-terminated perfluoroether side chains surrounding a central region of ‘bulk-like’ water. Counterions such as H
Upon uptake of water, the dimensions and shape of the clusters are determined by osmotic equilibrium and the elasticity of the organic matrix [39]. There is, however, no consensus on the structure of the electrolyte-containing clusters. [27,40,41] proposed that the clusters were spherical inverted micelles of 40-50Å diameter, interconnected by channels with characteristic dimensions of 10—20Å. On the basis of their small angle X-ray data they concluded that the pores (hydrated with water vapor) contained approximately 70 side chains and 1000 water molecules. Although the model of [27,40,41] has gained fairly wide acceptance, others have suggested that the spherical shape and uniform spacing of the clusters are oversimplifications. On the basis of an infrared study, Falk [33] concluded that the hydrated clusters are non-spherical with frequent fluorocarbon intrusions. Falk [33] also suggested that a significant fraction of the water interacts with the fluorocarbon material. Additional X-ray diffraction and differential scanning calorimetry measurements by Starkweather [42] led him to propose a lamellar hexagonal structure of the fluorocarbon backbones with the side chains extending perpendicular to the alignment of the PTFE backbones and into the ionic cluster domains. More recently, Litt [43] reexamined the data of [27,40,41] and proposed a lamellar morphology for Nafion® where the side chains are located in planar domains. With hydration of the membrane, the water simply collects in the polar domains pushing the non-polar domains (PTFE backbones) further apart subject to extensions of disordered backbone segments. Similar lamellar micelle structures were observed by [44] for Nafion® solubilized in DMF and by [30] for Nafion® with incorporated silicon oxide.
Despite the wide application of the ionomer, the morphology and transport mechanisms of the membrane are not fully understood on a molecular basis. However, the optimal use of the membrane in any of these applications requires understanding the ion aggregation and hydration, factors that directly affect conductivity and water transport.
A factor limiting a more complete description of the membrane via modeling efforts is the paucity of molecular scale and chemical information of the polymer electrolyte membrane (PEM) upon hydration. The local sulfonic acid/water interactions are undoubtedly important in the transport of water and protons in PFSA membranes. We previously reported electronic structure and dielectric model calculations on components of the side chain of Nafion® with and without a water molecule [45,46]. Here we present structural and energetic results on conformations of a typical complete side chain of Nafion®. Minimum energy structures were determined for conformations of the acid side chains: CF3OCF2CF(CF3)O(CF2)2SO3H and CF(CF2CF3)2—OCF2CF(CF3)OCF2CF2SO3H. In addition, we give structures and energies for binding a probe water molecule to the side chain head group. A principal goal of this work is to provide this necessary information for future modeling of ion and water transport in PEMs based on a detailed understanding of the interfacial region of the water/polymer system.
Standard ab initio molecular orbital calculations were performed using the GAUSSIAN 94 system of programs [47]. Fully optimized geometries were computed using gradient methods [48] for the CF3OCF2CF(CF3)O(CF2)2SO3H and CF(CF2CF3)2—OCF2CF(CF3)OCF2CF2SO3H side chains initially using Hartree-Fock theory and the STO3-G* basis set and then subsequently refined with density functional theory (B3LYP [49]) and the 6-31G** basis set [50].
A minimum energy conformation (determined at the HF/STO-3G* level) of the acid side chain of Nafion® is presented in Figure 1; the numbering scheme for the atoms is indicated for reference. Figure 1 indicates that staggered fluorines on adjacent carbons are an important feature of this minimum energy structure. The ether oxygens are also staggered relative to one another. The chain is folded onto the C(1) attachment to the backbone. The intra-atomic distance between C(1) and the acid proton H(26) is taken as a measure of the length of the side chain and in Figure 1 that distance is 7.8Å. This structure is surprising in view of the model of [18,31,32] described earlier. That model suggested that in a cluster with a diameter of 50Å there were up to 70 sulfonate sites and at least 1000 water molecules. Side chains with folded geometry in such a system would seem to be precluded on the basis of packing and space considerations. The lamellar morphology for the hydrated membrane proposed by Litt [34] also points to an elongated geometry in the side chains. In either case, the length of the side chains has a direct bearing on the separation between ionic domains, where the majority of the water resides, and the nonpolar domains.
Calculations were performed at a higher level of theory to test this prediction of folding in the sidechain. Starting from this HF/STO-3G* structure, a similar optimization was performed but using the 6-31G** basis set. This geometry was subsequently refined at the B3LYP/6-31G** level and is displayed in Figure 2. This conformation of the acid side chain is geometrically similar to the HF/STO-3G* but substantially more folded. The O(5)C(6)C(9)—O(15) dihedral angle is again about 60°, but the length of the chain only 6.0Å. This increased folding of the chain is mainly due to rotation about the C(9)—O(15) bond and to a lesser extent the result of rotation about the C(16)—C(19) and C(19)—S(22) bonds.
The structures in Figures 1 and 2 do not contain any substantial portion of the PTFE backbone, a factor that might affect the geometry of the side chain. The minimum energy conformation (B3LYP/6-31G**) of the acid side chain with the addition of two perfluoroethylene units is displayed in Figure 3. Comparison of Figure 2 with Figure 3 indicates that the included portion of the backbone has made no discernible difference in the overall conformation of the side chain. The side chain exhibits similar folding and the length is again approximately 6.0Å.
We emphasize that these results do not account for the effects of hydration. As outlined above, experimental measurements suggest increased separation of the hydrophobic and hydrophilic regions of the membrane with hydration.
These computations also suggest that the natural means for substantial chain extension is rotation about the C(6)C(9)—O(15)C(16) dihedral angle. The conformational potential energy surface for rotation about that C(9)—O(15) bond was determined, initially at the HF/STO-3G* level at 10° intervals, and is displayed in Figure 4. A portion of the Hartree-Fock potential energy surface was refined at the B3LYP/6-31G** level. The revised potential energies are also plotted in Figure 4. These results show a barrier of approximately 4.6 kcal/mol separating the folded conformation from conformations that are partially unfolded. They also indicate that the unfolded conformations are about 3.5 kcal/mol higher in energy. Since the energy changes obtained here are comparable to H-bonding energies, we expect hydration effects to be important; the side chain should sample the extended conformations found in the well between maxima in Figure 4, particularly when hydrated.
The conformations at 0°, 80°, and 120° for rotation about the C(9)—O(15) bond were examined specifically. Comparison of these structures with the minimum energy conformation indicated that the rotation about the C(9)—O(15) bond has not resulted in any substantial changes to the geometry of either the upper portion of the chain (atoms 1 through 14) or the lower portion of the chain (atoms 16 through 26) despite the fact that all the degrees of freedom of these parts of the chain were optimized. The O(5)C(6)C(9)—O(15) dihedral angle varied by only 20° and the oxygens of the C(6)—C(9) bond remained gauche to one another.
In order to locate a complete unfolded conformation, we initiated an optimization from the all trans geometry; the resulting structure is displayed in Figure 5. The length of this unfolded conformation is 9.9Å, considerably longer than the structure in Figure 2 or any of the other local energy minimum structures obtained on the rotational potential energy surface (Figure 4). Here the ether oxygens remained trans. This unfolded conformation is essentially isoenergetic (+0.1 kcal/mol) with the folded conformation (Figure 2). This result is consistent with the arguments of Litt34 and Starkweather33 requiring an elongated side chain geometry.
The most important limitation of these results for the understanding of hydrated Nafion® is the absence of molecular hydration. Treatment of these effects will require subsequent effort. However, we also determined conformations of the folded and unfolded acid side chain with a probe water molecule. It is clear (Figure 6) that the additional water molecule has only a local effect on the head group, not on the chain conformations. The position of the water molecule in the two acid chains is similar; both exhibit typical hydrogen bonding with a water oxygen—O(25) distance of 2.60Å. The position of the water molecule relative to the sulfonic acid group in these structures is essentially identical to that obtained previously for triflic acid.15
From the total electronic energies of each of the minimum energy structures of the side chains (folded and unfolded) both with and without a water molecule, the binding energy for the interaction of this first water molecule was calculated. At the B3LYP/6-31G**, the water binding energies for the folded conformation was 18.6 kcal/mol and for the unfolded conformation was 17.1 kcal/mol and both of these were substantially higher than those obtained with Hartree-Fock theory.
These calculations show that the side chains can exist in nearly isoenergetic folded and extended conformations with substantial difference in length: the length in the equilibrium structure of the folded side chain was found to be 6.0Å, while that of the entirely unfolded chain was 9.9Å. A natural transition path is rotation involving the outermost ether linkage during which the —(CF2)2SO3H portion of the chain is invariant holding a staggered fluorine conformation. However, consistent with previous work [45], the rotations of the sulfonate group and of the acid OH are quite facile. The estimate here of the energy barrier for that unfolding path is about 4.6 kcal/mol. The position of the first water of hydration has been determined for both the folded and extended side chains. The water adopts a doubly H-bonded configuration with a traditional H-bond in addition to a short H-bond involving the acid proton. This H-bonded configuration is similar to that reported in an investigation with trifluoromethane sulfonic acid, suggesting that the position of additional water molecules may be determined satisfactorily considering only the head group [51]. The existence of a small number of well-defined "short" and "long" side chain conformations, with substantially similar head-group chemistry, suggests that hydration-dependent equilibria between these conformations should be a significant feature in physical models of Nafion® function.
We acknowledge the support of this work by the Los Alamos National Laboratory LDRD program for the funding and the US Department of Energy under contract W-7405-ENG-36. We also thank R. L. Martin for helpful discussions. LA-UR-98-4628.
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FIGURES
Figure 1. HF/STO-3G* optimized acid side chain showing atomic numbering scheme. Significant parameters: C(1)—H(26) = 7.80 Å; O(5)C(6)C(9)—O(15) = -60.5°, C(6)C(9)O(15)—C(16) = 155.9°.
Figure 2. Minimum energy conformation of the acid side chain obtained at the B3LYP/6-31G** level. C(1)—H(26) = 6.01 Å; O(5)C(6)C(9)—O(15) = -60.4°, C(6)C(9)O(15)—C(16) = 120.8°.
Figure 3. Optimized structure (B3LYP/6-31G**) of the acid side chain with inclusion of two perfluorinated ethylene units. C(1)—H(26) = 6.01 Å; O(5)C(6)C(9)—O(15) = -56.2°, C(6)C(9)O(15)—C(16) = 118.8°.
Figure 4. Potential energy surface for rotation about the outermost ether linkage, the C(9)—O(15) bond in the folded side chain. The points indicated by square boxes were obtained at the B3LYP/6-31G** level and the circles at the HF/STO-3G* level.
Figure 5. Optimized (B3LYP/6-31G**) structure for the fully extended acid side chain. C(1)—H(26) = 9.93 Å; O(5)C(6)C(9)—O(15) = -180.0°, C(6)C(9)O(15)—C(16) = 118.7°.
(top)
(bottom)
Figure 6. Minimum energy conformations (B3LYP/6-31G**) for the placement of a single ‘probe’ water molecule relative to the terminal group in the following acid side chains: (top) folded, C(1)—H(26) = 4.9 Å, Water O—O(25) = 2.58 Å; and (bottom) extended, C(1)—H(26) = 10.0 Å, Water O—O(25) = 2.60 Å.