Ab Initio Molecular Dynamics Simulations on the Hydrated Structures

Apr 25, 2017 - Ab Initio Molecular Dynamics Simulations on the Hydrated Structures of Na+−Nafion Models. Adelia J. A. Aquino*,†,‡,§ and Daniel ...
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Ab Initio Molecular Dynamics Simulations on the Hydrated Structures of Na+−Nafion Models Adelia J. A. Aquino*,†,‡,§ and Daniel Tunega*,‡ †

Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria § School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, People’s Republic of China ‡

S Supporting Information *

ABSTRACT: Ab initio molecular dynamics (AIMD) calculations were performed to investigate the structural and dynamical properties of different domains (hydrophobic, hydrophilic, and interfacial) occurring in the hydrated Na+−Nafion model systems. Pair distribution functions (PDF) were calculated between different atom pairs to analyze the structural features of the hydration structure of the different Na+−Nafion complexes. The analysis of the H···O PDF curves clearly distinguishes water molecules at the ionomer SO3− interface from the rest of the water molecules. It was found that hydrogen bonding of water molecules to the sulfonate group is weaker than hydrogen bonding among water molecules themselves. The vibrational densities of states (VDOSs) were calculated from the autocorrelation function of velocities. Overall, the calculated VDOSs have a good correspondence with experimental IR spectra. The analysis of the VDOS curves shows that the high frequency shift of the OH stretching modes of water molecules comes from the interface region in comparison to the rest of the water molecules. The interfacial water molecules are the main contributors to the high frequency side peak of the OH stretching modes, in good agreement with the observed FTIR spectra of the hydrated Nafion systems. Analysis of the partial vibrational density of states provided the unambiguous assignment of the stretching modes of the structural units that form the Nafion structure (C−O−C, C−C, C−S, SO3, and CFx). AIMD simulations were also performed for Na+−Nafion models hydrated with HDO and D2O molecules, respectively. The calculated PDF curves for Na+···O and H···O distances showed the same features as PDFs for models with H2O molecules. On the other hand, the O−H and O−D stretching modes in the VDOS spectra of the models with HDO are well separated with a large red shift of about 1000 cm−1 of the O−D frequencies. A similar shift was also observed for the models with pure D2O having nearly identical VDOS band structures of the stretching modes. Additionally, water bending modes are redshifted from ∼1630 cm−1 (H2O) to ∼1440 cm−1 (HDO) and ∼1190 cm−1 (D2O), respectively.

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INTRODUCTION Fuel cells are energy exchange devices that transform chemical energy to electrical energy by means of a direct electrochemical reaction.1 They have received extensive recognition as another energy generation technology possibility being highly efficient and operating in a renewable fuel economy. Nevertheless, fuel cell systems have a high cost which limits their application. Additionally, growing worldwide energy demand imposes severe challenges to ecological security, for the sustainability of natural resources, and consequently for human health. The combustion of fossil fuels over recent decades contributes to the production of greenhouse gases such as CO2, NOx and SOx, which have a harmful influence on the environment. Therefore, there is an urgent necessity for clean and more efficient energy alternative devices. Wide-ranging investigations have been carried out on perfluorinated ionomers as their importance has risen drastically in their use in applications for fuel devices.2−4 Nafion is a polymer electrolyte membrane (PEM) which is extensively used in proton exchange fuel cell (PEFC) © 2017 American Chemical Society

membranes. Even though a large number of different ionomers is available, Nafion has been used as a standard material in fuel cells as a result of its excellent ionic conductivity and resistance under extended operation as it is thermally stable up to 190 °C. It has a large range of application in fuel cells, chloralkali industry, water electrolysis, batteries, sensors, and surface treatment among others. Nafion contains a hydrophobic poly(tetrafluoroethylene) (PTFE) backbone terminated by trifluoromethanesulfonic acid groups (-CF 2SO3 H). The sulfonic acid terminated pendant side chains of the membrane encapsulate its ionic domains. They can be regarded as the activity core inside the Nafion membrane. For example, the interaction of Nafion in an aqueous environment is ruled by these domains.2 Nafion is a very strong acid (pKa ∼ −6)5 which in its protonic form is selectively and greatly absorptive to water. The geometric structure and the properties of both the Received: November 28, 2016 Revised: April 12, 2017 Published: April 25, 2017 11215

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structures are highly controlled by its water content.28−30 Several experimental works connected to theoretical calculations have been performed to explain the nature of the O−H stretching in an ionomer confined in water. Force field molecular dynamics as well as AIMD calculations have been used for this purpose.21,31 The complete assignment of bands in Nafion ionomers, specifically in a spectroscopic range below ∼1500 cm−1, already generated some controversies. For example, IR spectroscopic study of Nafion (125 and 152) membranes, was performed by Heitner-Wirguin32 in order to explain the vibrational motion of heavy atoms in the Nafion structure. Several specific bands were assigned and compared the spectra with those of sulfonated polyethylene (Redcat) membranes. The observed band split at 960 and 980 cm−1 was assigned to a stretching C− O mode of the C−O−C unit. This assignment was made considering that the replacement of the hydrogen by fluorine atom in the CH2- group lowers the C−O stretching vibrations as the corresponding value in poly(oxymethylene) is found at 1090 cm−1. In an opposite way the absorption band at 980 cm−1 was attributed by Ostrowska and Narebska33 to a C−F stretching in the side chain. This example documents that the assignment of the vibrational modes in the spectral region below 1500 cm−1 is complicated and ambiguous because of strong overlapping of the peaks (often broad and of low intensity) corresponding to frequencies of the stretching and bending modes of the -C−O−C-, -CF2/-CF3, -C−C-, -SO3, and -C−S- structural units. In a recent study substrate overlayer attenuated total reflection (SO-ATR) spectroscopy was used on ordered thin films of Nafion on silicon native oxide and gold substrates. The authors were able to characterize symmetric and asymmetric modes of SO3 and CF2/CF3 groups in the Nafion structure.17 Grosmaire et al.20 used in situ ATR-FTIR (attenuated total reflectance FTIR) spectroscopy in the study of the effect of the hydration degree of the ionomeric membrane (Nafion 112 in that case) on the dissociation state of exchange sites inside the polymer material in protonated and sodium forms. The IR spectra showed changes in vibrational states of the sulfonate group with respect to the degree of hydration. High quality FTIR spectra of Nafion structures with different associated cations (H+, D+, and Na+) and including several levels of hydration (from wet to fully hydrated) were reported by Di Noto and co-workers.34−36 The authors provided a detailed assignment of vibrational modes including the reinterpretation of some older assignments10 (e.g., stretching modes associated with the C−O−C unit). It was shown that the associated cation and the degree of hydration have a significant effect on the vibrational modes of the ionomer perfluoroether side chains.36 Furthermore, the authors also indicated two different helical conformations of the perfluorinated backbone (helixes 103 and 157). Additionally, in a recent publication, experimental (ATR-FTIR) and theoretical studies (DFT calculations on molecular models) have been performed in order to explain changes in the IR spectra upon the level of hydration.37 The aim of this work is to perform a theoretical simulation of the structure and the vibrational dynamics with focus on the detailed characterization of the O−H stretching and bending modes of water in the hydrophobic and ionic regions of the water−Na+−Nafion system by means of high level ab initio molecular dynamics calculations. Further, the work also explains the differences in the C−F, C−O, C−C, C−S, and

backbone and the side chains of the perfluorosulfonic acids play an important role in establishing the hydrated morphology and transportation features mainly in the presence of water.2 The PTFE type ionomers have been extensively investigated both theoretically and experimentally.6−23 Mainly infrared (IR) absorption and Raman scattering measurements have been used to obtain a detailed understanding of the role of the hydration shells surrounding and penetrating such ionomers. Hydration is an important factor determining the ionic conductivity in ionomers which has been studied by means of experiments dedicated to water uptake and dehydration of ionomer membranes. Earlier, Falk18 studied the IR spectra of H2O, D2O, and HDO in hydrated Nafion membranes in the presence of sodium as a counterion. The study was focused on the analysis of hydrogen bonding interactions in different regions of the ionomer. It was found that the hydrogen bonding of water in fully hydrated Nafion is significantly weaker if compared with the hydrogen bonding in liquid water at a similar temperature. In a subsequent work, the tendencies that occur in the IR spectrum of water at low water concentrations in 20 different cationic forms of Nafion were investigated.6 The finding was that if there is a good match between the strengths of the ion pairs, they are reasonably stable and water molecules are inclined to attach on the outside of the ion pair. In the opposite situation, if the ion pair strengths are unbalanced, as is the case for example for small cations of high charge or for large cations of low charge, water molecules tend to be placed between the ion pairs even at the lowest water contents.6 IR and Raman techniques were used to study the conformational properties of Nafion membranes considering the effect of hydration on the PTFE backbones.24 It was observed that the spectral features in the 1500−4000 cm−1 region are strongly influenced by the hydration level of the membrane. Bands at around 3450 and 1650 cm−1 prevail in the completely hydrated membranes belonging to H2O stretching and bending modes, respectively. Fourier transform infrared (FTIR) work indicated microstructural differences between surface and bulk of the Nafion membrane. The micelle structure dominates at the membrane surface and the -SO3H group is free from interactions with the key chain.25 Distinct features of headgroup acidity and different hydration populations have been reported by Smedley et al.16 The authors described hydrogen bonding distribution of water adsorbed in proton exchange membranes and described three different water microenvironments with respect to the sulfonate headgroup. Raman scattering investigation of the state of water in the acid form of Nafion-117 in H2O- and D2O-wet conditions revealed that, in Nafion-117, differently from Nafion with higher molecular weights, basically all water molecules participate in the hydrogen bonding rather than connecting to the fluorocarbon network. It was observed also from the shifts of O−D and O−H bands that the water in Nafion-117 is more bulk-like if compared to membranes of higher molecular weight.26 Modeling based on different theoretical methods has also provided important contributions to the understanding of the structure and role of water in the ionomers. For example, ab initio molecular dynamics (AIMD) simulations indicated that increasing levels of hydration weaken the interactions among the sulfonic acid groups, water, and the hydronium ions in the Nafion ionomer. It is based on the observation of the increase in the number of hydrogen bonds occurring in the different systems.27 The proton conductivity and dynamics in the Nafion 11216

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group in an approximate Na+···O distance of 2.2 Å (model_1 in Figure 1), (ii) water separated Na+ hydrated close to the SO3−

S−O stretching modes by calculating partial vibrational density of states of the structural units of the Nafion structure (CF2/ CF3 and SO3 groups, and C−O−C and C−C units in the backbone). The basic Nafion model used in this work is similar to that used in previous work12,13 and is shown in Scheme 1. Scheme 1. Structural Formula of Nafion Model Used in MD Simulations

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Figure 1. Three different models (a, b, c) of the Nafion ionomer used in the calculations including the initial position of Na+ cations. The remaining water molecules are omitted for clarity.

COMPUTATIONAL DETAILS Ab initio molecular dynamics calculations within the frame of Kohn−Sham electron density functional theory were performed using the Vienna ab initio simulation package (VASP).38,39 The exchange-correlation energy was expressed in the frame of the generalized gradient approximation (GGA) using the functional proposed by Perdew, Burke, and Ernzerhof (PBE).40 The electron−ion interactions were described using the projector-augmented-wave (PAW) method41,42 in a planewave basis set with an energy cutoff of 400 eV and with the required convergence in total energy of 10−4 eV. Brillouin-zone sampling was restricted to the Γ-point only because of the large computational cells. The Verlet velocity algorithm43 with a time step of 1 fs was chosen for a numerical solution of equations of motion. In the initial thermal equilibration phase of the dynamics, the finite temperature calculations were performed on a canonical ensemble applying the Nosé−Hoover thermostat44 at 300 K with a simulation time of at least 20 ps. The equilibration was controlled through the temporal evolution of parameters such as temperature and potential energy of the system. After equilibration, the system was changed to the microcanonical (NVE) ensemble to obtain power spectra (PS). For the NVE ensemble, the total length of the MD run was 20 ps. Based on these dynamics runs, PS were computed by a Fourier transformation of the velocity autocorrelation functions. Additionally, pair distribution functions (PDFs) were calculated for selected atomic types. The analysis of the MD data was performed using the nMoldyn program.45 The basic Nafion model structure (Scheme 1) was constructed in the following way based on the experience gained with previous DFT/B3-LYP calculations.12 First, a [-CF2-]8 backbone representing a periodic repetition unit was constructed and placed in a periodic box with a perpendicular orientation to the bc plane. Second, one of the F atoms of the CF2 backbone chain was replaced by a side branch -O−CF2− CFCF3−O−CF2−CF2−SO3H (Scheme 1). The b and c vectors were set up to 20 Å and kept constant during the optimization. The third unit cell vector, a, was optimized together with all atomic positions in the structure to get an optimized geometry. A final length of the a unit cell parameter of 10.542 Å was obtained. In all further calculations on the hydrated models, the unit cell parameters were kept constant. The optimized bare model of the Nafion chain was hydrated by insertion of a specific number of water molecules using the program Packmol.46 Then, H+ from the -SO3H headgroup was replaced by sodium cation Na+. Following Falk’s hydration model18 (see also ref 12), three types of hydrated structures with Na+ placed in different initial positions were prepared. These structures were defined as follows: (i) Na+ placed close to the sulfonate

group with Na+···O distance of ∼4.5 Å (model_2 in Figure 1), and (iii) Na+ hydrated close to the hydrophobic region of CF chain and distant from the charged SO3− group (model_3 in Figure 1). The total number of water molecules was ∼90 allowing flexible placement of the Na+ cation in the different domains. After having performed MD simulations on the waterhydrated Nafion cases, we used the last configurations from the MD to continue with calculations on the isotopic effects. In each of the three models, HDO and D2O replaced H2O molecules and MD simulations in the NVE ensemble were performed with a duration of 20 ps. The same analysis of the MD results was carried out as for the simulations with H2O.

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RESULTS AND DISCUSSION Figure 2 displays a snapshot from the MD simulation of the model_2, in which the atoms of interest are presented in a ball

Figure 2. Snapshot (two views) from AIMD of the Na+···Nafion system (model_2).

and stick mode and water molecules in stick mode only. In the following, analysis of the structural features in different domains is performed by calculating and interpreting pair distribution functions (g(r) or PDFs). Further, the vibrational dynamics is described by interpreting calculated PS or equivalently the vibrational density of states VDOS. 1. Structural Analysis. Na+···O PDF Curves. The results for all three models with H2O investigated in this work are shown in Figure 3. Owing to high similarity, PDFs for the models with HDO and D2O were placed into the Supporting 11217

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Figure 3. Pair distribution functions between Na+ cation and all oxygen atoms and oxygen atoms from the SO3− group for all three Na+−Nafion models in water.

shown, too. Comparing the plots for model_1 and model_2, strong similarities are immediately observed. They indicate that both cases are structurally comparable and that they evolve during the 20 ps NVT equilibration phase to similar configurations albeit having started from a different localization of the Na+ cations (in a direct contact to SO3− group (model_1) and water separated hydrated Na+ (model_2)). Both Na+···O(SO3−) PDF curves show a well distinguished peak at ∼2.2−2.3 Å which is a typical Na+···O distance of the first coordination shell of the sodium cation. The second, less intensive and broad peak, corresponds to the Na+···O(SO3−) distances between 4.0 and 5.0 Å for the two other oxygen atoms of the SO3− group. This means that the Na+ cation is not fully water separated from the SO3− group but is in a direct contact with one of the three O(SO3−) atoms. The width and the intensity of the first Na+···O(SO3−) PDF peak indicates that the Na+···O(SO3−) coordination is relatively stable. This observation is in contrast with predictions from earlier experimental work,55 which report that Na+ exists as a mostly water separated complex from the SO3- group. The plot of the Na+···O(SO3−) PDF curve of the model_3 (Figure 3) demonstrates that the Na+ cation is distant from the SO3− group with a broad peak starting to increase at the distance of 7 Å. The similarities between models 1 and 2 were also confirmed by comparison of the temporal evolution of potential energies of all three models for the NVE ensemble. The energies of the models 1 and 2 showed very similar trends with almost identical average values. Model_3 had a potential energy evolution about 25 kcal/mol higher than model_1 and model_2 documenting its lower stability. Therefore, the results for model_3 will not be discussed further. The higher stability of models 1 and 2 can be assigned to the formation of the electrostatically bound Na+···SO3− pair complex through the direct coordination of the Na+ cation by one oxygen atom of the SO3− group. H···O/F PDF Curves. Aimed at understanding the hydrogen bonding structure in different domains of the hydrated Na+− Nafion models, the PDF curves for the distances from the H atoms of the water molecules to selected atom types were calculated, particularly to all oxygen atoms (Oall), to oxygen atoms of the SO3− group, and to all F atoms of the Nafion backbone and side chains. The PDF plots for all three models with water are displayed in Figure 4. Owing to high similarity,

Information (SI, Figures S1 and S2) and will not be discussed in detail in the following text. Each of the three plots in Figure 3 shows two curves of the Na+···O distances, particularly (a) for all O atoms in the system and (b) for O atoms belonging to the SO3− group (note that these curves are y-scaled by a factor of 5 for a better resolution). The total PDFs show two well resolved peaks for all three models. The first intensive sharp peak located at r ≈ 2.2 Å represents the first hydration shell of the Na+ cations and corresponds very well with the first solvation shell for aqueous solution of Na+ obtained either by experiment or from MD simulations.47−49 The experimental coordination numbers of sodium in solution are found to be between 4 and 8;50,51 the values obtained from theoretical calculations (molecular dynamics or Monte Carlo) are similar in a range of 4− 7.48,52,53 From our calculations, the coordination number of Na+ is about 5 giving good agreement with coordination numbers of Na+ in solution. The first peak of the Na+···O distance is relatively narrow and sharp, documenting the stability of the first hydration shell. The second, less intensive but broad peak starts at ∼3.3 Å and extends up to ∼5.5 Å. This peak corresponds to the second hydration shell of the Na+ cation. AIMD simulation of Na+ and Cl− ions in water by Khalack and Lyubartsev49 showed a distance of ∼3.4 Å for the second hydration shell of Na+. Earlier Clementi and Barsotti54 studied a cluster of 200 water molecules containing a single ion (Li+, Na+, K+, F−, or Cl−) by means of a Monte Carlo approach. They found the second hydration shell of Na+ in a range of 4.5−5.6 Å giving good agreement with our calculations. In contrast to the first Na+···O peak, the second peak is much broader and structurally more complex and it can be attributed to the reduced stability of the second hydration shell and higher fluctuation of the H2O molecules. Moreover, a broad peak starting at the distance of 6 Å is also observed (well distinguished in model_3 in Figure 3), which can be assigned to the higher order hydration shells of the Na+ cation of water molecules confined in ionomer pores. The total Na+···O PDFs contain also small contributions from the Na+···O distances to two O atoms from the Nafion side chain and three atoms from the SO3− group, respectively. Therefore, in order to emphasize the role of the sulfonate oxygens in the coordination of Na in Figure 3 PDF curves containing the Na+···O(SO3−) distances only (black lines) are 11218

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Figure 4. Pair distribution functions between hydrogen and oxygen atoms, and hydrogen and fluorine atoms for all three Na+−Nafion models in water.

etheric unit C−O−C); the dominant component is represented by water molecules. To characterize the ionomer−water interface, H···O PDFs were obtained separately for the three oxygen atoms of the SO3− group (black line in the plots of Figure 4). Whereas the values for the maxima for H···O distances between water molecules are ∼1.77 Å, the value for the H···O(SO3−) distances is constantly shifted to higher values of 1.83−1.85 Å evidencing that hydrogen bonding of the sulfonate group is weaker than hydrogen bonding among water molecules. The well separated and relatively narrow peak demonstrates also a stability of the first coordination shell of water molecules forming hydrogen bonds with the sulfonate group. We did not observe any H··· O(SO3−) peak at distances below 1.5 Å that could indicate extra strong H-bonds or eventually proton transfer to the SO3− group. The observed weaker hydrogen bonding of the SO3− group comparing to H-bonds of water molecules is in accord with the experimental observations from IR measurements explaining the blue shift of the OH stretching frequencies to weaker hydrogen bonding interactions of water with the SO3− interface.12,56−58 This observation was also confirmed later by the analysis of a partial vibrational density of states for water molecules in a vicinity of the SO3− head that are discussed in details further in this work.

the plots of the PDF curves for HDO and D2O were placed into the Supporting Information (Figures S3 and S4). The match between model_1 and model_2 observed from the analysis of the Na+···O PDFs is also evident from the H···O PDF curves. The trends of the PDF curves of model_3 are also very similar as the SO3− group also forms H-bonds with water molecules. Moreover, the SO3− group is not blocked by the Na+ cation so the number of H-bonds to SO3− is larger than in models 1 and 2, respectively. The intensive sharp peak at the distance of ∼1.0 Å of the H··· Oall curve (gray line) corresponds to the O−H bonds in the water molecules. The most interesting H···O PDF peaks are at distances close to 2.0 Å, and their maxima are collected in Table 1 for all three models. These peaks represent hydrogen bonding Table 1. Maxima of H···O PDF Peaks (Å) model

H···Oall

H···O(SO3−)

1 2 3

1.77 1.76 1.77

1.83 1.83 1.85

among water molecules and the SO3− group with water molecules. The curve H···Oall covers all oxygen atoms (including the three from the SO3− group and two from the

Figure 5. Total VDOS of all three Na+−Nafion models in water. 11219

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The Journal of Physical Chemistry C The third curve (dark gray) in the plots of Figure 4 refers to the H···F distances. These curves are practically identical for all three models having no sub-band structure. They start to continuously increase at a distance > 2.0 Å up to 10.0 Å. This type of curve is a clear evidence of the hydrophobicity of the carbon−fluorine (CF) units of the Nafion chains with no participation of the F atoms in the H2O reorientation near the -CF2−CF2- chain. 2. Vibrational Dynamics Analysis. The total PS or VDOS for all three models, calculated from the autocorrelation function of velocities, are displayed in Figure 5. The VDOS spectra are quite similar and can be separated into three spectral domains: (i) low frequency region below 1400 cm−1, (ii) medium frequency region in the interval 1400− 2500 cm−1, and (iii) high frequency region extending from 2500 to 4000 cm−1, respectively. The low frequency region encompasses vibrational modes of the hydrated ionomer and includes a mix of bending, wagging, torsional, skeletal, and librational motions of the system. A detailed analysis of the whole region is beyond the scope of this work, and only modes appearing above ∼700 cm−1 will be discussed here in detail. These modes are attributed dominantly to the stretching vibrations of the heavy atoms in the Nafion skeleton (C, F, O, and S). The typical experimental spectra of Nafion structures have several distinguished peaks in the region 700−1400 cm−1 apart from one broad complex peak in the calculated VDOS spectra shown in Figure 5. Because of the complexity of the vibrational spectra, the assignment of the C− O/C−C/C−F/C−S/S−O stretching modes is difficult and no definitive complete analysis has been given in the literature so far. In the total calculated VDOS the bands of heavy atoms are not directly resolvable because they are strongly overlapping and hidden in the intensive and broad peak, which has the main contribution from the hydrogen atoms dynamics from water molecules (Figure 5). However, from the calculated MD data it is possible to separate partial vibrational density of states (PVDOS) for specific groups of atoms which allows an interpretation of the total VDOS and analysis of the vibrations of individual structural units in the hydrated Na+−Nafion models. Figure 6 shows the PVDOS that are assigned to the stretching modes of the C−O, C−F, C−C, C−S, and S−O bonds, respectively. The assignment of the C−O/C−F/S−O stretching modes in the experimental spectra is difficult, and there is no definitive analysis available in the literature.59−62 The corresponding maxima of the dominant PVDOS peaks (>700 cm−1) displayed in Figure 6 are collected in Table 2. This table also contains a selection of experimental data for the hydrated Nafion ionomers and results from other calculations for Nafion models interacting with water molecules or Na+ cation.17,24,31,37,59,63 It has to be noted, however, that in the previous calculations13,31,37,59 static geometry optimizations were performed on cluster models of the Nafion chains and the vibrational modes were computed in the harmonic approximation. In the opposite, our calculated PVDOS curves automatically include anharmonic effects and obtained peaks represent average vibrational densities of states for specific groups of atoms. Generally, good correspondence is observed between our calculated stretching modes and those from other calculations or experiments for all types of the stretching modes of heavy atoms of the Nafion skeleton. Decomposition of the PVDOS of C−F vibrations resulted in two main peaks assigned to CF2

Figure 6. Partial VDOS of selected structural units of the Na+−Nafion model_2 in water: (a) C−F vibrations, (b) atoms in the Nafion chain, and (c) SO2 and CS vibrations.

(1108 cm−1) and CF3 (1147 cm−1) groups (Figure 6a, Table 2). Both peaks have evident shoulders at the high frequency edge (∼1260 cm−1 for CF2 and ∼1230 cm−1 for CF3). Although our model with the linear perfluorinated backbone does not reflect the supposed helical conformational structures36 (which, consequently, produce more complicated vibrational modes of CFx units in the experimental spectra), the calculated PVDOS peaks of CF2/CF3 groups fit very well with the experimental assignments, which are in the range 1100− 1260 cm−1 (see Table 2 and corresponding references). Figure 6b shows PVDOS of the atoms in the Nafion chain, particularly -C−C- and -C−O−C- units. The vibrational motions of the C−C and C−O−C are mechanically strongly coupled oscillators, which are reflected in broad and relatively complex peaks of two C−O−C units. The maximum is observed at 1068 cm−1, and two shoulders are estimated at 920 and 1195 cm−1, respectively. The first, low frequency shoulder can be assigned to the symmetric vibration of the C−O−C unit corresponding to the experimental assignment (see ref 24; Table 2). Both higher frequencies could be attributed to the asymmetric types of the vibrational motions, and the experimental assignment provided a similar number of 1142 cm−1 (see ref 59; Table 2). The values calculated on the cluster 11220

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The Journal of Physical Chemistry C Table 2. Selected Stretching Vibrations of Heavy Atoms (cm−1) in Nafion mode

this work model_2

other calc

CF2

1108

1133a νs(CF2) 1145/1156a νas(CF2+CF3)

CF3

1147

1247/1253/1271/1284b νas(CF2+CF3) 1317/1328b νas(CF3)

SO3 sym

984

929/1000a ν(C−S) + νs(SO3) 965−980c νs(SO3) 1004/1047b νs(SO3) + ν(C−S)

SO3 asym

1180

1107/1284a νas(SO3) 1210/1211/1234b νas(SO3) + νas(CF2 + CF3)

C−O−C

920, 1068, 1195

C−C

1117

816a νs(COC) 1054/1084a νas(COC) + νas(CF3) 1265/1269b νas(COC) 1296/1372a ν(C−C) 1194b ν(C−C)

C−S

897, 1066, 1190

929/1000a ν(C−S) + νs(SO3) 1004/1047b νs(SO3) + ν(C−S)

exp 1101/1200a ν(CF2) 1133d,e νas(CF2), 103 1151d,e νs(CF2), 157 1213d,e νas(CF2), 157 1228d,e νas(CF2), 157 1256d,e νas(CF2), 103 1153f νs(CF) 1150g νs(CF2) 1211f νas(CF) 1220g νas(CF2) + νas(SO3) 1148/1216h νas(CF2) 1204h νas(CF2) + νas(SO3) 1060a νs(SO3) 1058i νs(SO3) 1057f νs(SO3) 1058h νs(SO3) 1155/1237a νas(SO3) 1220g νas(CF2) + νas(SO3) 1135h νas(SO3) 970/983h νs(COC) 972/983/992e,j ν(COC) 1142a νas(COC) 1301/1318d,e ν(C−C), 103 1351d,e ν(C−C), 157 1300/1377h ν(C−C) 803d,e ν(C−S) 804a ν(C−S) 805h ν(C−S)

a

Reference 59. (IR: experiment, perfluoro(2-ethoxyethane) sulfonic acid (PES, represents Nafion side chain) in aqueous solution; calculations, B3LYP/6-311G+(d,p) method and PES···Na+ model.) bReference 37. (ATR-FTIR experiment; calculations, LC-BLYP/cc-pVDZ method and cluster model of Nafion structure solvated by 10 H2O molecules + polarizable continuum (CPMC).) cReference 31 (XB3LYP/63111**++, cluster model of side Nafion chain hydrated explicitly by several water molecules.) dReference 34. (ATR-FTIR, 103 and 157 means two different helices of CF backbone of hydrated Nafion−Na+.) eReference 36. (ATR-FTIR, hydrated Nafion−Na+). fReference 63. (ATR-FTIR, hydrated Nafion.) g Reference 17. (SO-ATR-FTIR, Nafion at SiO2/Au surfaces.) hReference 24. (Raman and ATR-FTIR, hydrated Nafion.) iReference 35. (ATRFTIR, hydrated Nafion.) jReference 10. (FTIR, hydrated Nafion.)

Figure 7. VDOS spectra of water molecules from different regions in Na+−Nafion model_2.

at 984 and 1180 cm−1, respectively. In the vibrations of the C− O−C and C−S units, vibrational density of linked C atoms contributes significantly as it is evidenced by the stretching vibrations of the C−C bonds with the maximum localized at ∼1120 cm−1 (Figure 6b). This value is lower than the experimental assignment for the hydrated Nafion ionomer (1300/1377 cm−1; see ref 24; Table 2). However, a value of

models (see refs 37 and 59; Table 2) show a similar trend in the stretching modes of the C−O−C unit. The vibrational motion of the C−S bond is also strongly coupled with the vibrations of the neighboring C−O−C unit and oxygen atoms of the SO3− group. Thus, the whole peak of the stretching C−S mode in the range 800−1300 cm−1 (Figure 6c) has a complex character with the main peak at 1066 cm−1 and two side peaks 11221

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Table 3. Vibrational Frequencies (cm−1) for H2O, HDO, and D2O Computed from ab Initio Molecular Dynamics Compared with Experimental Data of Fully Hydrated Nafion Samples stretching modes this work ref 18 ref 36

bending modes

H2O

HDO

D2O

H2O

HDO

D2O

3441/3811 3524/3668/3714 3238/3375/3597

3417/3811 2451/2714 3520/3660 2588/2695

2463/2734 2572/2652/2708 2395/2483/2580/2676

1630 1630 1639

1438

1187

1213 cm−1 for the pure poly(tetrafluoroethylene) polymer was assigned for the C−C stretching mode by Raman spectroscopy,64 which is a value closer to our result indicating that the experimental assignments of the bands > 1300 cm−1 to the C− C modes could be not correct. Two theoretical calculations provided two different results for the C−C stretching modes with a difference of about 100 cm−1.59 For the sulfonate unit, the PVDOS shows two distinguishable peaks at 984 and 1180 cm−1, respectively (Figure 6c and Table 2). The peaks are assigned to the symmetric (lower frequency) and asymmetric (higher frequency) stretching modes of the SO3 group, in accordance with experimental assignments17,24,59,63 and theoretical predictions.31,37,59 Symmetric stretching modes determined experimentally are higher by about 70 cm−1 than our predicted value. However, our results agree well with other theoretical values. The asymmetric stretching mode at 1180 cm−1 shows a good correspondence with both experimental and theoretical results (Table 2). The second, medium frequency range (1400−2500 cm−1) contains one dominant peak at ∼1630 cm−1 (Figure 7). This peak is unambiguously assigned to the bending modes of the water molecules. The value obtained agrees very well with the predicted bending frequencies of water molecules of several cluster Na+−Nafion−H2O models (1590−1640 cm−1) calculated by means the B3LYP/SVP approach. 13 In the experimental IR spectra the peaks of the bending modes have a more complicated structure usually composed of two peaks at ∼1630 and ∼1730 cm−1, respectively.20,63 The band with lower frequency perfectly fits with our predicted number and experimentally was assigned to the bending modes of water molecules. The band with the higher frequency was assigned to the hydronium−water clusters such as Zundel and Eigen cations, of which the intensity decreases progressively with increasing water content in the Nafion matrix.20,63 The high frequency region above 2500 cm−1 has a dominant broad peak spanning over a range of ∼1200 cm−1. This peak consists of a superposition of two OH stretching modes (symmetric and asymmetric, ν1 and ν3) of interacting water molecules confined in a Nafion structure. Apart from bulk water, which has a broad, apparently structureless OH stretching peak, the peaks in Figure 5 show a structural feature (a broad peak with maximum at ∼3400 cm−1 and a side high frequency peak at ∼3800 cm −1 ) that resembles the experimental FTIR spectrum of hydrated Nafion.12 Note, however, that the OH stretching region in the experimental spectra has a more complicated nature. Falk18 observed a shoulder at a low frequency edge (∼3250 cm−1), which was assigned to a Fermi resonance (mixing of 2ν2 overtone with ν1 fundamental OH stretching). This feature is not accessible in the calculated VDOS as they are obtained from Newtonian dynamics. The PS spectra (Figure 5) show a clearly distinguishable subhigh-frequency peak at ∼3810 cm −1 , whereas in the experimental spectrum two closely spaced peaks were

1206

observed,12 which were assigned to the water molecules at the ionomeric−water interface. The observed blue shift was assigned to weaker hydrogen bonding of H2O molecules to the SO3− heads. To confirm that this assignment is correct, the partial VDOSs were calculated for selected sets of water molecules representing different regions of the water envelope. Particularly, the water molecules forming hydrogen bonds with the SO3− group were identifiedthey are those that mainly contribute to the first H···O PDF peak in Figure 4. In addition to this set, two H2O molecules from the second coordination shell of the SO3− group were added to the calculation of the partial VDOS. The second set of water molecules consisted of the water molecules from the first and second coordination shells of Na+ cation. The analysis of the temporal evolution of the H···O(SO3−) hydrogen bonds and Na+···OH2 distances showed that selected water molecules are relatively stable in their positions without significant fluctuation or exchange with water molecules from other regions. The calculated PVDOS of these two sets together with the overall VDOS of all H2O molecules for the high frequency region are displayed in Figure 7. Clearly, the water molecules from the first set (H-bonded to SO3−) show a significant shift of the OH stretching modes to higher frequencies where a double peak in a range 3550−3850 cm−1 is observed. These peaks can be assigned to the OH stretching modes of the OH groups that are involved in the direct hydrogen bonding with the oxygen atoms of the SO3− group, whereas bands at the low frequency side (below 3500 cm−1) can be mainly assigned to OH groups which form Hbonds with neighboring H2O molecules. The partial VDOS of the second set of water molecules shows a certain structure of the vibrational density of states of OH stretches. But, overall, the structure of the broad PVDOS band is a repetition of the main dominant peak of the total VDOS of the H2O molecules. Thus, the water molecules at the ionomer interface that forms weaker hydrogen bonds with the SO3− group are the main source of the high frequency band observed at ∼3810 cm−1, which is in agreement with experimental assignments.12 This supports also the fact of why the third model has the high frequency peak better developed than the models 1 and 2 (Figure 5). This can be explained by the fact that the SO3− group of the model_3 is fully hydrated in contrast to models 1 and 2. In these latter models one O(SO3−) atom is involved in the Na+ coordination and overall the number of the hydrogen bonds to SO3− group is smaller than in the case of model_3. The bending modes of the first set of water molecules are shifted a bit to lower frequency (∼1620 cm−1), whereas the second set of water molecules has the peak shifted to the higher frequency of ∼1650 cm−1 (Figure 7). The superposition of both peaks provides the main peak of the bending modes of all water molecules at 1630 cm−1. 3. Solvation by HDO and D2O. The use of deuterated water (specifically HDO) in the experiment has the advantage of eliminating Fermi resonances because of the wide separation 11222

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(below 1000 cm−1) did not change in comparison to models with H2O.

of the three fundamental bands (ν1, ν2, and ν3), which simplifies the IR spectrum and its interpretation. PDOS calculations were performed for both HDO and fully deuterated water (D2O) for all three models. The calculated PDFs for the same sets of atoms as selected for the H2O models were nearly identical with the PDFs shown in Figures 3 and 4 and are not discussed in this section. No difference was also observed for the H···O D···O hydrogen bond distances. As expected, pronounced changes were observed for the calculated VDOS spectra, specifically in the high frequency region. Figure 8 shows the total VDOS obtained for model_2. The peak

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CONCLUSIONS Structural and dynamical properties of several hydrated Na+− Nafion models were obtained from ab initio molecular dynamics to characterize three different domains in the systems (hydrophobic, hydrophilic, and interfacial). Calculated Na+···O PDF curves showed a higher stability of the structure with the SO3− group in direct coordination with the Na+ cation through one sulfonate oxygen atom than the structure with Na+ cation localized nearby hydrophobic C−F domain, far from the SO3− head. The sodium cation first shell coordination is completed by water molecules with an average coordination number ∼ 5. The analysis of the H···O PDF curves clearly distinguished water molecules at the ionomer−SO3− interface from the rest of the water molecules. It was found that hydrogen bonding of water molecules to the sulfonate group is weaker than hydrogen bonding among water molecules themselves. This conclusion was also confirmed by calculating partial vibrational density of states showing a high frequency shift of the OH stretching modes of water molecules at the interface in comparison to the rest of the water molecules. The interfacial water molecules are the main contributors to the high frequency side peak of the OH stretching modes that are also observed in FTIR spectra of the hydrated Nafion systems. Also overall calculated VDOS have a good correspondence with experimental IR spectra. Further, the analysis of the frequency region below 1400 cm−1 by using partial vibrational density of states allowed unambiguous assignment of the stretching models of the -SO3−, -C−O−C-, -C−C-, -C−S-, and -CFx structural units. It was found that the particular bands are in a relatively narrow spectral range, and in the total VDOS they are strongly overlapping and not directly resolvable. This finding also explains the difficulty with a complete assignment of the S−O, C−O, C−C, C−S, and C−F stretching modes in the experimental spectra. The AIMD calculations were also performed for Na+−Nafion models hydrated with HDO and D2O molecules, respectively. The calculated PDF curves for Na+···O and H···O distances showed the same features as PDFs for models with H2O molecules. On the other hand, expected large separation of the O−H and O−D stretching modes was observed in the VDOS with significant shifting of the O−D modes to lower frequencies. The effect of deuterium was also observed on the bending H−O−D and D−O−D modes with the low frequency shift giving very good agreement with experiment. Generally, the AIMD simulations showed that the Na+ cations in the Nafion ionomeric channels are better stabilized near the negatively charged sulfonate heads. It can be concluded that an ionic transport in the hydrated Nafion channels will depend on the density and configuration of the SO3− groups (i.e., some effective distance between the heads) at the interface with water and the level of hydration.

Figure 8. VDOS of the Na+−Nafion (model_2) in HDO (a) and D2O (b).

maxima of the OH/OD stretching and H−O−D/D−O−D bending modes are collected in Table 3 together with frequencies obtained from FTIR measurements on hydrated H2O/HDO/D2O−Nafion samples.18,36 For the HDO solvation a pronounced splitting of the HDO stretching modes (high frequency peaks) is observed with preserving band structure (one dominant peak plus one side peak). The maxima of the main peaks are at 2451 and 3417 cm−1 and the side peaks have maxima at 2714 and 3817 cm−1, respectively (Figure 8a, Table 3). The OH−OD splitting agrees very well with the experimental spectrum (two OH and two OD stretching modes by Falk18 in Table 3). Moreover, the experimental spectrum has a simplified shape (double-band peak due to the elimination of the Fermi resonance) and resembles the calculated VDOS spectrum in Figure 8a. The VDOS spectra of Nafion models with pure D2O have only OD stretching peaks in a range 2000−3000 cm−1 with a shape that is very similar to the H2O−Nafion VDOS spectra (Figure 5). The OD stretching maxima are about 10−20 cm−1 higher than those obtained for the HDO models (Table 3). This blue shift is also observed for the HDO/D2O−Nafion samples (Table 3; refs 18 and36). Again, experimental spectra have a more complicated shape, similar to H2O, due to re-established Fermi resonance. The determined VDOS maxima of the OH/OD stretching modes also correspond to calculated OH/OD stretching frequencies computed at the DFT level for the Nafion cluster models with explicitly added water/HDO/D2O molecules as solvated medium.13 The effect of deuterium is also observed on the bending modes of HDO/D2O molecules. Whereas for H2O the peak of bending frequencies was observed at ∼1630 cm−1 (Figure 7, Table 3), for models with HDO it decreased to ∼1400 cm−1 and with D2O to ∼1200 cm−1, respectively (Figure 8; Table 3). These shifts are in very good agreement with the measured D− O−D bending frequency of 1206 cm−1 obtained by Negro at al.36 The overall shapes of the VDOS spectra of the Nafion models with HDO and D2O in the low frequency region

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11946. Pair distribution functions (PDFs) of the distances of Na+ and all oxygen atoms and for O···H and H···F distances in HDO and D2O (PDF) 11223

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AUTHOR INFORMATION

Corresponding Authors

*(A.J.A.A.) E-mail: [email protected]. * (D.T.) E-mail: [email protected]. ORCID

Adelia J. A. Aquino: 0000-0003-4891-6512 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Profs. Hans Lischka and Carol Korzeniewski for fruitful discussions. We are thankful for computer time at the Vienna Scientific Cluster (VSC), Project No. 70544, at the cluster Robinson in the TTU Department of Chemistry & Biochemistry whose purchase was funded by the National Science Foundation under the CRIFMU Grant CHE-0840493, and at the computer cluster Arran of the School of Pharmaceutical Science and Technology of the Tianjin University.

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