Theoretical Description of the Structural Characteristics of the

Article pubs.acs.org/JPCC

Theoretical Description of the Structural Characteristics of the Quaternized SEBS Anion-Exchange Membrane Using DFT Sergio Castañeda and Rafael Ribadeneira* Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia, Carrera 80 #65-223, Medellín, Colombia ABSTRACT: For four conforming structures of the quaternized polystyreneblock-poly(ethylene-ran-butylene)-block-polystyrene membrane (QSEBS), (a) tetramethylammonium hydroxide (TMA+OH−), (b) benzyltrimetylammonium hydroxide, and (c and d) QSEBS segments with 1 and 2 side chains (DBQSEBS), spatial distribution, bond distances, and charge-density profiles were obtained with density functional theory (DFT) and compared with structural simulations of DBQSEBS for two different hydration levels. Results for the TMA+OH− showed that its constituent ions stay metastable in the vicinity of each other and are joined by donor−acceptor interactions. Also, simulations of the other conforming structures show that, in the absence of water, spatial distribution as well as charge-density profiles of trimethylammonium hydroxide do not change with respect to isolated TMA+OH−, demonstrating that the QSEBS chain is a thermodynamically stable backbone to support the functional group, which is in agreement with the literature. When hydrated, simulations of DBQSEBS for water uptake of 4 show that there is a partial dissociation of hydroxide ions due to donor−acceptor interactions acting competitively on them. For water uptake of 6, this dissociation is completed, and hydroxide ions conform to hypercoordinated structures similar to the square-planar arrangement described for pure water medium, but with some structural differences associated with location, type, and interactions among the molecules involved. ionic conductivity (9.37 mS/cm at 80 °C), thermal stability (up to 190 °C), and chemical stability (weight loss >10% due to oxidation in 3% H2O2/4 ppm Fe2+ solution at 80 °C after 120 h) with respect to other anion-exchange membranes.1,19 Four structures related with the dry QSEBS membrane are described: (a) tetramethylammonium hydroxide (TMA+OH−), (b) benzyltrimetylammonium hydroxide (BZTMA+OH−), (c) a QSEBS segment with a single side chain, and (d) a QSEBS segment with 2 side chains (DBQSEBS). Then, hydrated structures for DBQSEBS segment are generated and analyzed for water uptakes (λ) of 4 and 6. All the descriptions are achieved using DFT due to its high degree of accuracy to describe the structures in the atomistic and molecular scale,17,18,20,21 and also with the consideration that to date there are almost no theoretical studies about structural characteristics of AEM used in simulations of AEMFC.14,16

1. INTRODUCTION Anion-exchange membrane fuel cells (AEMFCs) have great potential for commercialization at low cost with respect to technologies similar to those of the proton-exchange membrane fuel cells (PEMFCs) due to (a) better kinetic characteristics for both the anode and cathode avoiding the high use of platinum,1−8 (b) lower fuel crossover, especially if alcohols are used,2,8−10 and (c) reduced degree of corrosion.8,9,11,12 Despite this, the anion-exchange membranes (AEM) of these devices show low ionic conductivity and chemical stability, which restrict, respectively, the efficiency and durability of this kind of fuel cells. 1−3,9,13,14 The improvement of the aforementioned characteristics could be achieved by understanding the related physicochemical phenomena at the nanoscale with high accuracy,1,13,15,16 which is theoretically possible using techniques based on quantum mechanics as density functional theory (DFT) and related with time as ab initio molecular dynamics (AIMD).16−18 However, to achieve this improvement, it is primordial to have information about the structural characteristics of AEMs used in these fuel cells and how they change in the presence of water. With consideration of the above, the aim of this research is to describe comparatively the structure of a segment of the quaternized polystyrene-block-poly(ethylene-ran-butylene)block-polystyrene membrane (QSEBS) in the absence of water and with two different levels of hydration. This polymer was studied experimentally in ref 19 and was selected as a representative AEM used in fuel cells due to its relatively high © 2015 American Chemical Society

2. THEORETICAL METHODS The QSEBS membrane is synthesized from the block polymer SEBS (acronym of styrene-ethylene-butylene-styrene), which is a segregated phase material that can be functionalized with TMA+OH− to give it anion-exchange capacity.1,19 After the Received: July 23, 2015 Revised: November 17, 2015 Published: November 19, 2015 28235

DOI: 10.1021/acs.jpcc.5b07166 J. Phys. Chem. C 2015, 119, 28235−28246

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The Journal of Physical Chemistry C synthesis, the material takes the configuration shown in Figure 1.

Figure 1. Structure of the QSEBS membrane.19

In order to obtain the most accurate representation for the QSEBS segments under consideration, six simulations of structural optimizations were made: (a) TMA+OH−, (b) BZTMA+OH−, (c) the QSEBS with a single side chain segment assuming for simplicity values of 1 for the parameters x and y in Figure 1, (d) the DBQSEBS segment assuming also values of 1 for x and y, and (e and f) the DBQSEBS segment obtained in step (d) with water uptakes of 4 and 6 (hydrated DBQSEBS). This procedure is schematically depicted in Figure 2. The structural optimizations were carried out with the Quantum Espresso Package.22 The generalized gradient approximation (GGA) with the exchange-correlation functional Becke−Lee−Yang−Parr (BLYP) was used for the calculations of total energy. The ionic cores were described by ultrasoft pseudopotentials, and the Kohn−Sham one-electron valence states were calculated with plane waves. For all the simulations, a kinetic energy cutoff of 822 eV and three automatic k-points in each direction according to Monkhorst−Pack scheme were fixed, on the basis of convergence and consistency of the final energy and the bond distances between atoms. The cutoff radius for total energy and forces were established as 10−6 Ry and 10−4 Ry/a.u., respectively. The dimensions of the simulation boxes and the number of atoms considered for each simulation are shown in Table 1.

3. RESULTS AND DISCUSSION 3.1. TMA+OH−. Simulations for different initial positions of the hydroxide ion with respect to the tetramethylammonium cation (TMA) were carried out in order to obtain the equilibrium configurations for each case and identify the most consistent configurations. Given the tetrahedral topology of the TMA in which its four methyl molecules are separated by 109° angles, there are only three different positions that could be considered for the hydroxide ion: in front of the nitrogen atom associated with the cation (Figure 3a), in front of a carbon atom belonging to a methyl group and equidistant from its three hydrogen atoms (Figure 3b), and between 2 hydrogen atoms of a methyl group (Figure 3c). The final configurations for the simulations in which initially the hydroxide ion was placed as shown in Figure 3a,c are schematized in Figure 4. In both cases, the oxygen atom of the hydroxide ion is located approximately equidistant from the three closest hydrogen atoms of the TMA (1.92, 1.91, and 1.89 Å for the atoms indicated in Figure 4 as 1, 2, and 3, respectively) and at 3.019 Å from the nitrogen atom. For the situation in which the oxygen atom was initially placed as shown in Figure 3b, the simulation suggests (Figure 5) that the closest methyl group dissociates from the TMA and bonds with the hydroxide ion to form methanol. This

Figure 2. Simulation strategy implemented to represent the dry and hydrated segments of the QSEBS membrane.

Table 1. Number of Atoms and Dimensions of the Simulation Boxes for the Simulations Carried Out molecule

no. of atoms

TMA+OH− BZTMA+OH− QSEBS DBQSEBS hydrated DBQSEBS (λ = 4) hydrated DBQSEBS (λ = 6)

19 29 53 104 128 140

simulation box 10 10 15 20 20 20

× × × × × ×

10 10 10 10 12 12

× × × × × ×

10 12 15 15 18 18

Å Å Å Å Å Å

configuration is in agreement with the final products of the degradation mechanism by hydroxide attack for TMA.23−25 As a key reference, Figure 6 shows the energy paths and structures for the degradation mechanisms of TMA by 28236


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(circled structures), and they correspond to energy minima of the system, and therefore to equilibrium configurations. Since the energy values in Figure 6 were validated with experimental data guaranteeing the accuracy of the involved molecules, and the structures obtained in this research are consistent with them, consequently the aforementioned molecules can be used in other structural simulations involving complete AEM segments like the QSEBS chains studied in this work. Also, the structure shown in Figure 4 represents the cationic group associated with a functionalized anion-exchange membrane, so it will be the configuration to represent the other constituent structures of the QSEBS in this research. Additionally, in Table 2 are shown the distances between the oxygen atom of the hydroxide ion and the hydrogen atoms

Figure 3. Initial configurations considered for the structural simulations of TMA+OH−. Here, oxygen is in red, carbon is in yellow, nitrogen is in gray, and hydrogen is in blue.

Table 2. Distances between the Oxygen of the Hydroxide Ion and the Hydrogen Atoms Indicated as 1, 2, and 3 in Figure 4 for TMA+OH− Obtained in This Work and in Reference 26 Figure 4. Structure for TMA+OH− obtained from the simulations in which the hydroxyl ion was initially placed in front of the nitrogen atom of the cation (left) and between 2 hydrogen bonds associated with a methyl group (right). The color code for the atoms is the same as that for Figure 3.

research

mean distance (Å)

% relative error

this work Davies et al.26

1.918 1.886

1.7%

indicated with numbers in Figure 4, which were obtained in the simulations of this work and the values which are experimentally validated in the simulations of the theoretical research of ref 26. It can be seen that there is high correspondence, in the values of the aforementioned distances, as indicated by the very low error value shown in Table 2, which confirms again the consistency and accuracy of the functional group obtained in this work. It is interesting to note that, in the obtained TMA+OH− structure, the distances between the oxygen atom of the hydroxide ion and the atom of the TMA cation are higher than the normal bond distances between the oxygen and the nitrogen (1.36 Å27) and between the oxygen and the hydrogen (1.1 Å27), which shows that ions of the system are not covalently bonded. However, they stay chemically metastable in the vicinity of each other. If this were not the case, the TMA cation would have dissociated in trimethylammonium and methanol, as was shown in Figure 5.

Figure 5. Structural configuration obtained from TMA + OH − simulations in which the hydroxyl ion was initially placed as shown in Figure 3b. The color code for the atoms is the same as that for Figure 3.

hydroxide attack SN2 and ylide pathways, obtained with DFT in the theoretical study of ref 23. It can be seen that the structures shown in Figures 4 and 5 of this work are in agreement with the structural configuration of structures D and H in Figure 6

Figure 6. Energy paths and structures involved in the TMA degradation mechanisms SN2 and ylide according to ref 23. Here, oxygen is in red, carbon is in cerulean, nitrogen is in dark blue, and hydrogen is in white. The structures of energy minima are circled in yellow. Adapted with permission from ref 23. Copyright 2010 American Chemical Society. 28237


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Figure 7. Electronic charge-density profiles obtained for the TMA+OH− structure with respect to the plane shown in the inset. The color code for the atoms is the same as that for Figure 3.

established between the molecules, there is an interaction associated with electronic charge that keeps them close. This fact can be better appreciated in Figure 8, which shows an

For some insights about the type of interactions established between the TMA cation and the oxygen of the hydroxide ion, Figure 7 shows the electronic charge-density profiles with respect to a two-dimensional plane that passes through the centers of the oxygen of the hydroxide ion and the nitrogen atom of TMA. Five charge concentration peaks on Figure 7 are identified for the chemical elements of TMA+OH−: (a) the oxygen of the hydroxide ion peak, which has the highest electronic charge concentration, (b) the nitrogen atom of the TMA cation, in which the top part of this peak is flatter than the peak of the oxygen, which is representative of the tetrahedral configuration of the cationic group, (c) the methyl group located behind the nitrogen atom of the TMA, aligned with the peaks of the oxygen and the nitrogen, and (d and e) the 2 peaks at the sides of the nitrogen atom of the TMA, which have the lowest charge density, corresponding to hydrogen atoms of side methyl groups of the cationic group. As mentioned above, the distances between the oxygen atom of the hydroxyl anion and the nitrogen and hydrogen of the TMA cation are higher than the normal values, suggesting that they are not formally bonded. However, in the side view of the electronic charge density (Figure 7), a saddle point can be seen between the peaks of the oxygen and nitrogen for a value of electronic charge density of approximately 0.033 e−/bohr3. This demonstrates that although there is not a covalent bond

Figure 8. Electronic charge-density isosurface of 0.033 e−/bohr3 depicted for the TMA+OH− structure. The color code for the atoms is the same as that for Figure 3.

electronic charge-density isosurface of 0.033 e−/bohr3, where this slight bonding interaction between the aforementioned atoms is observed. This interaction can also be appreciated in Figure 9, where the electron localization function (ELF) is depicted, taken from the top view of the electronic chargedensity profile (Figure 7), in which a region of uniform charge density different from zero can be identified in the space between the hydroxide ion and the TMA cationic group. 28238


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Figure 11. Structural configuration obtained from the simulations of the QSEBS segment with a single side chain. The color code for the atoms is the same as that for Figure 3.

Figure 9. Electron localization function (ELF) depicted for the TMA+OH− structure.

From analysis and detailed summary of the previous graphics, the following key information is derived: (a) There is a minimum (critical point) in the electronic charge-density surface between the peaks of the hydroxide ion and the TMA cation. (b) The value of the electronic charge-density in that minimum is higher than 0.01 e−/bohr3 and smaller than 0.1 e−/ bohr3. (c) The Laplacian in that point is positive. (d) The charge density in the region between the ions is uniform; i.e., there are no other maxima or minima of electronic charge density. These aspects allow us to conclude that the most probable interaction between ions, according to the classification of Macchi et al.28,29 and the information in ref 30, is of the donor−acceptor type, and therefore, ions in the system are bound by a coordination bond. This interaction is of the weak closed-shell type and is consistent with the fact that the TMA hydroxide molecule is unstable and tends to dissociate easily, which allows us to demonstrate and to understand the reactive behavior of this molecule. 3.2. BZTMA+OH− and QSEBS Segments. The final structures obtained for BZTMA+OH−, the QSEBS segment with a single side chain, and the DBQSEBS segment are, respectively, shown in Figures 10, 11, and 12.

Figure 12. Structural configuration obtained from the simulations of the DBQSEBS segment. The color code for the atoms is the same as that for Figure 3.

Two characteristics were taken into account to analyze the consistency of the obtained structures: first, the bond distances between the covalently bonded atoms in the molecules were compared with the theoretical values of ref 27 shown in Table 3. It was found in all cases that the relative errors between the values were no higher than 2% showing that the obtained configurations are in thermodynamic equilibrium for all atoms, Table 3. Bond Distances of Covalently Bonded Species Involved in the Obtained BZTMA+OH− and QSEBS Segments with Respect to the Experimental Values of Reference 27

Figure 10. Structural configuration obtained from the simulations of the BZTMA+OH−. The color code for the atoms is the same as that for Figure 3. 28239

bond

obtained distance (Å)

experimental distance (Å)

relative error

OH CH (CH) CH (CH2) CH (CH3) CC (C6H6) CN CH2CH2 CH2CH3 CHCH3 CHCH2 CHC (CC) CH2C (CC)

0.977 1.102 1.096 1.091 1.398 1.508 1.545 1.541 1.544 1.556 1.527 1.514

0.967 1.099 1.095 1.09 1.377 1.485 1.524 1.513 1.524 1.531 1.51 1.502

1.0% 0.3% 0.1% 0.1% 1.5% 1.5% 1.4% 1.9% 1.3% 1.6% 1.1% 0.8%


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lammonium ions would dissociate. This is in agreement with the chemical and thermal stability found experimentally for the QSEBS’s functional groups in ref 19. For the above reasons, it can be concluded that the obtained structure for the QSEBS segments as well as the chemical description obtained from the simulations developed are accurate and consistent with what physically is expected and is reported in experimental research. 3.3. Hydrated DBQSEBS. λ = 4. The configuration obtained for the DBQSEBS segment with a water uptake of 4 is shown in Figure 14. Additionally, in Figures 15 and 16,

which is achieved ensuring the conditions of convergence, stability, and consistency in the DFT simulations. Second, the spatial distribution of the composing atoms of the backbone chain of the QSEBS segments (corresponding to the styrene, ethylene, and butylene groups) shows that the aforementioned chain is in its antibonding gauche configuration, which is the most stable configuration for this kind of polymeric chains that can present conformational isomerism as Nafion 115.31 For these reasons, it is demonstrated that the obtained structures are in its configuration of minimum energy, obtaining low relative error with respect to the experimental values and describing the actual structure of the QSEBS segments. To analyze the structural configuration of the trimethylammonium hydroxide functional group in the BZTMA+OH− and the QSEBS structures, the distances between the oxygen atom of the hydroxide ion and the closest hydrogen atoms (the same depicted in Figure 3) and the nitrogen atom of the trimethylammonium cationic group are shown in Table 4. Table 4. Distances between the Oxygen Atom of the Hydroxide Ion and the Closest Hydrogen Atoms and the Nitrogen of the TMA Cationic Group of TMA+OH−, BZTMA+OH−, and the QSEBS Segment with a Single Side Chain and Two Side Chains param

TMA+OH−

BZTMA+OH−

QSEBS

DBQSEBS

O−H1 (Å) O−H2 (Å) O−H3 (Å) O−N (Å)

1.918 1.918 1.924 3.019

1.913 1.888 1.904 3.048

1.889 1.919 1.885 3.036

1.933 1.910 1.927 3.064

It was found from the simulations that the spatial distribution of the trimethylammonium hydroxide is practically the same with respect to TMA+OH−. There were slight differences in some of the distances between the oxygen and its closest hydrogen atoms, but these differences are mostly due to the convergence of the numerical method since they are not significant (lower than 0.05 Å) and do not follow a clear pattern from one structure to another that could suggest changes in the way the ions are interacting. This last aspect can be appreciated in the electronic charge-density isosurface for a value of 0.033 e−/bohr3 shown in Figure 13 for the TMA+OH− and the QSEBS segments, where it can be seen that the electronic charge-density isosurface for the QSEBS segments is almost unaffected with respect to the TMA+OH− and the interaction between the trimethylammonium and the hydroxide ion is still of the donor−acceptor type. In consequence, it can be inferred that the considered SEBS segment is a thermodynamically stable chain to support the trimethylammonium hydroxide functional group, because otherwise hydroxide and trimethy-

Figure 14. Structural configuration obtained from the simulations of the hydrated DBQSEBS segment for λ = 4 (a, front view; b, back view). The color code for the atoms is the same as that for Figure 3.

respectively, the distances are shown between some atoms of water molecules and hydroxide ions and their closest neighbors, and isosurfaces for different electronic charge-density values in the region where water molecules and hydroxide ions are located. According to the obtained structure, hydroxide ions associated with the polymer side chains are surrounded by 3

Figure 13. Electronic charge-density isosurface of 0.033 e−/bohr3 depicted for the TMA+OH− structure and the trimethylammonium hydroxide functional group associated with the obtained QSEBS segments. The color code for the atoms is the same as that for Figure 3. 28240


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established interactions are of the donor−acceptor type, and therefore, hydroxide ions are bonded to water molecules by coordination bonds (see analysis criteria in section 3.1). This is consistent with the fact that anionic species belonging to side chains of anion-exchange membranes are solvated in the presence of water. The electronic charge-density minimum has similar magnitudes for all water molecules interacting with hydroxide ions except for water molecule 8 in Figure 14, which has a value of 0.027 e−/bohr3, since it is located farther from ion β than molecules 6 and 7 in Figure 14. Values of electronic charge-density minima between hydroxide ions and water molecules exceed by more than twice the value of 0.033 e−/bohr3 found for the interaction between hydroxide ions and the trimethylammonium functional groups. This implies that the strength of the coordination bonds between the water molecules and hydroxide ions is higher than the bond between hydroxide ions and polymer side chains. Therefore, and as can be seen in Figure 15, the distances between the hydroxide ions and their respective trimethylammonium groups increase with respect to the structure in absence of water. This suggests that a certain dissociation of ions occurred. However, that dissociation is not complete because although Figure 16a,b indicates that interactions between ions α and β and the polymer side chains are no longer present, Figure 16c,d shows that those interactions just decreased in magnitude, and thus, the trimethylammonium cationic groups continue to be bonded to the ions by coordination bonds of low magnitude. This can be corroborated in the electronic charge-density profiles depicted in Figure 18, where electronic charge-density minima in the region between hydroxide ions α and β and their closest trimethylammonium groups can also be identified (labeled as δ and ε, respectively, in Figure 14). It is important to note that the spatial distribution of the water molecules and hydroxide ions is very similar to the square-planar configuration for hydroxide ions in pure aqueous medium described in detail in refs 32−34. According to them, hydroxide ions establish coordination bonds with 4 water

Figure 15. Distances in Å between atoms of water molecules and hydroxide ions and their closest neighbors for the structure of Figure 14b. The color code for atoms is the same as that for Figure 3.

water molecules which, according to Figure 16a,b, are establishing interactions due to charge densities higher than 0.023 e−/bohr3. These interactions have a notorious effect on the reorientation of the hydroxide ions, which have in this configuration their hydrogen atoms pointing at different directions with respect to the structure in absence of water (Figure 11). Figure 17 depicts the electronic charge density versus distance for a plane which cuts the centers of the oxygen atom of the hydroxide ion α (see nomenclature in Figure 14) and the closest hydrogen of water molecule 4 (Figure 17a), and for a plane which cuts the oxygen atom of the hydroxide ion β and the closest hydrogen of water molecule 7 in Figure 14 (Figure 17b). It can be seen in both cases that there is an electronic charge-density minimum with a magnitude of 0.074 and 0.076 e−/bohr3 respectively. This allows inferring that the

Figure 16. Isosurfaces for different electronic charge-density values depicted for the region where the water molecules and hydroxide ions are located in the structure of Figure 14b. The color code for the atoms is the same as that for Figure 3. 28241


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Figure 17. Electronic charge-density profiles for planes which cut, respectively, the centers of oxygen atoms of the hydroxide ions α (a) and β (b) and the closest hydrogen atoms of water molecules 4 and 7 in Figure 14.

molecules which each donate a hydrogen bond. Now, with the charge-density analysis taken into account, it can be determined that, in the hydrated DBQSEBS system, hydroxide ions also receive four hydrogen bonds: three from surrounding water molecules and a fourth bond from one of the methyl groups associated with their respective cationic functional group. However, there are some differences with respect to the hypercoordinated structure in an aqueous medium. Radial distribution functions for the square-planar structure of hydroxide in water are shown in refs 34 and 35 where the length of the coordination bonds between the oxygen atom of the hydroxide ion and water molecules solvating it can be determined, which is approximately 1.61 Å. In this study, such a value is only comparable with the length of the coordination bond between hydroxide ion α and water molecule 4 (Figure 15), whereas the other bonds have lengths ranging between 1.4 and 2.4 Å. These variations are principally due to the fact that the system under consideration is chemically more complex than the aqueous medium without the polymer, and there are a lot of donor−acceptor interactions involved that are competing among them: On one hand, water molecules seek to establish coordination bonds with the hydroxide ions promoting their

dissociation from the trimethylammonium cationic groups. However, at the same time, cationic groups seek to keep their interaction with the anions preventing their distancing. This is consistent with the bond distance analysis: hydroxide ions moved away from the polymer side chains (0.506 and 0.265 Å for the hydroxide ions α and β, respectively, in Figure 14), but not enough to eliminate completely the interaction with them. With this in consideration, the resultant hypercoordinated structures are formed with the water molecules arranging with respect to the position of the hydrogen bond donated by the trimethylammonium cationic groups. On the other hand, almost all the water molecules are interacting not only with the hydroxide ions but also with other water molecules and the methyl groups of the polymer side chains (see Figure 16b−d). Thus, it is consistent that the bond lengths between water molecules and hydroxide ions change with respect to their position and type of molecules in their surroundings. This is for example the case for water molecule 8 in Figure 14, which is interacting with the hydroxide ion β and water molecule 4 at the same time; however, with consideration of the higher magnitude of the interaction with the latter, which seeks to attract it as much as possible (at least to approximately 1.77 Å, 28242


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Figure 18. Electronic charge-density profiles for planes which cut, respectively, the centers of oxygen atoms of the hydroxide ions α (a) and β (b) and the hydrogen atoms of their closest trimethylammonium groups (labeled as δ and ε in Figure 14).

the average length of the coordination bond between water molecules36), the length of the coordination bond between the hydroxide ion β and water molecules 8 in Figure 14 is higher than the others. The mentioned effect of the location of molecules is also reflected in the differences with respect to the spatial distribution of the conforming species of the hypercoordinated structures of the ions. In Figure 19 are displayed the angles

between the coordination bonds involved in the hypercoordinated structures of ions α and β. It can be seen that the structure of hydroxide ion β, which is surrounded by 2 benzyltrimetylammonium chains and 4 water molecules, is close in distribution and angles between bonds to the squareplanar arrangement (angles close to 90°) for hydroxide ions in pure water. However, the hypercoordinated structure of hydroxide ion α, which is surrounded by just one benzyltrimetylammonium chain and 4 water molecules, shows a square topology but is more pyramidal than planar (which is reflected in the fact that half the angles between coordination bond are significantly lower than 90°). Those particular characteristics are explained taking into account that the confinement of hydroxide ion β between 2 polymer side chains makes its solvation and dissociation harder than if they were not present. For that reason, on this ion the interaction of the cationic functional group is stronger (see Figure 16c,d and 18), and as a result, the hypercoordinated structure around hydroxide ion β is more stable and welldefined. By the other side, the hydroxide ion α is not as restricted as ion β so the water molecules have more influence on it. This allows them to move a little down the ion in order to increase the force exerted on it seeking the dissociation. However, although they diminish in higher grade the

Figure 19. Angles between coordination bonds involved in the hypercoordinated structures of ions α (left) and β (right) in Figure 14. The views were obtained for a plane perpendicular to the hydrogen bond of each hydroxide. The color code for the atoms is the same as that for Figure 3. 28243


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The Journal of Physical Chemistry C interaction with the cationic group than in the case of ion β, is not enough to achieve a complete dissociation, and consequently the resultant hypercoordinated structure shows an irregular arrangement. λ = 6. The final configuration obtained for the DBQSEBS system with a water uptake of 6 is shown in Figure 20. As in the

Figure 22. Electronic charge-density isosurface of 0.033 e−/bohr3 depicted for the region where the water molecules and hydroxide ions are located in the structure shown in Figure 20. The color code for the atoms is the same as that for Figure 3.

and the hydroxide ions that were identified in the previous structures (neither a charge-density connection nor chargedensity minima were found). This aspect, and the factor discussed in part a, allows us to conclude that for this degree of hydration the hydroxide ions are totally dissociated from their cationic functional groups, which is coherent with what experimentally is well-known about the behavior of anionexchange membranes in the presence of a large enough amount of water. It is important to note that hydroxide ion β has undergone stronger changes in the distance to its related cationic functional group than hydroxide ion α. This is explained taking into account that, in the previous structure, the interaction between cationic group ε and hydroxide ion β was determined and was found to be stronger than the interaction of cationic group δ and hydroxide ion α. Therefore, dissociation for the first case requires that water molecules pull ion β stronger from its cationic group to break off the interaction between them, while hydroxide ion α just required a change of ≈0.08 Å to achieve its dissociation. (c) Since the interaction between hydroxide ions and their cationic functional groups is not present, a fourth water molecule, as can be seen in Figure 20, is now involved in the hypercoordinated structure of each hydroxide ion by donating the hydrogen bond supplied initially by the methyl group of the polymer side chains. (d) Now the hypercoordinated complexes that conformed around ions α and β are more similar to the structures described in the literature for the pure aqueous medium but with some slight differences. Angles between coordination bonds of the structure of hydroxide ion α (shown schematically in Figure 23) are all close to 90° and have similar values between them, which resembles very well the square-planar arrangement reported in refs 32−34. However, the structure of hydroxide ion β shows a higher change in its angles which gives a reason for the

Figure 20. Structural configuration obtained from the simulations of the hydrated DBQSEBS segment for λ = 6. The color code for the atoms is the same as that for Figure 3.

Figure 21. Distances in Å between atoms of water molecules and hydroxide ions and their closest neighbors for the structure of Figure 20. For convenience of visualization, the displayed structure is slightly rotated with respect to Figure 20. The color code of for the atoms is the same as that for Figure 3.

previous case, Figures 21 and 22 show, respectively, the distances among some atoms of water molecules and hydroxide ions and their closest neighbors, and an electronic chargedensity isosurface of 0.033 e−/bohr3 for the region where water molecules and hydroxide ions are located. With an increase in its degree of hydration from 4 to 6, the DBQSEBS system undergoes some important changes in its structural configuration: (a) Distances between the hydroxide ions α and β and their respective cationic functional groups increase further with respect to the previous hydrated structure. Now hydroxide ions α and β are, respectively, separated 2.503 and 3.065 Å from trimethylammonium groups δ and ε in Figure 20. (b) Figure 22 and analysis of electronic chargedensity profiles revealed the total absence of the donor− acceptor interactions between the cationic functional groups

Figure 23. Angles between coordination bonds involved in the hypercoordinated structures of ions α (left) and β (right). The views are obtained from Figure 21. The color code for the atoms is the same as that for Figure 3. 28244


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support the trimethylammonium hydroxide group, which is in agreement with the chemical and thermal stability found experimentally for the QSEBS’s functional groups in ref 19. This allowed us to conclude that it accurately represented the real structure and behavior of the QSEBS segment. For a water uptake of 4, hydroxide ions of the DBQSEBS system receive 3 hydrogen bonds from surrounding water molecules and one from the methyl groups associated with their respective cationic functional group, which shows an incomplete dissociation of hydroxide ions due to several donor−acceptor interactions acting competitively on them. The resulting hypercoordinated structures are similar to the squareplanar arrangement described in the literature for hydroxide ions in pure water but with some differences in their configurations given by the location, type, and magnitude of interactions among the molecules involved. By increasing the water uptake up to 6, complete dissociation of hydroxide ions is achieved and the trimethylammonium cationic groups are replaced in the hypercoordinated complexes by a water molecule. These hypercoordinated structures are more similar to the square-planar arrangements in pure water than in the previous case. However, they have differences in their distances and angles between coordination bonds associated with the same factors of location and type of atoms as for λ = 4. This allows us to conclude that polymer side chains, although not directly interacting with the hydroxide ions, still have a considerable effect on the structural configurations of hydrated structures and the behavior of mobile species in the system. It can be concluded that all the simulated structures related with the DQSEBS segment, in absence of water and hydrated, are consistent with what physically is expected and reported in the literature. Therefore, it is considered that the obtained structures in this work are accurate and can be used in future studies using AIMD simulations to describe transport properties for hydrated AEMs used in AEMFCs in order to improve their operation.

conformation of a square-planar structure but a bit distorted. Like in the previous case, these key differences between structures can be explained taking into account the position and the surroundings of each ion. Water molecules surrounding hydroxide ion β (5 to 8 in Figure 20) are close to the polymer side chains (which are hydrophilic and would try to establish coordination bonds with them) and to water molecules 11 and 12 in Figure 20 (which also seek to establish coordination bonds). The interactions established among them diminishes the degrees of freedom of water molecules, which inhibits the arrangement in the same way that they would have in a pure aqueous medium. At the same time, water molecules surrounding hydroxide ion α do not have that restriction and have more independence to adopt a preferential configuration as similar as possible to pure aqueous medium. In fact water molecules 9 and 10 in Figure 20 are arranged in a similar way to those of a second hydration shell, with is also a key characteristic of the square-planar hypercoordinated complex in aqueous medium.32−34 It is important to remark that the obtained hydrated structures for λ = 4 and λ = 6 have a fundamental role in chemical reactions involving transfer of charge defects as seen in other works with similar systems, for instance those describing the photoreduction of 4,4-bipyridine in aqueous medium.37 Considering this and all the analysis carried out, it is considered that the obtained configurations and tendencies analyzed are accurate and represent appropriately the DBQSEBS system in absence of water and for the two levels of hydration studied. Additionally, the information obtained from the simulated structures is a contribution to the understanding of how the ionic species of this AEM behave in the presence of water. This is a fundamental aspect required to study further processes like degradation and transport which are fundamental to carry out the task of improvement of conductive polymers for AEMFCs and therefore the performance of these promissory devices. Also, the methodology presented can be extended to other types of membranes and processes of anion-exchange in general.

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4. CONCLUSIONS Different simulations were carried out with DFT to describe the structure of a hydrated segment of the AEM QSEBS with two side chains in absence of water and with two different levels of hydration. They include structural optimizations of the constitutive molecules TMA+OH−, BZTMA+OH−, a QSEBS segment with one and two side chains (DBQSEBS), and the hydrated structure for water uptakes of 4 and 6. These simulations contribute to the understanding of the structure of these molecules and their behavior in the presence of water, taking into account that there is almost no theoretical and experimental information about them. It was found from the simulations of TMA that the oxygen atom of the hydroxyl ion is located approximately equidistant from the 3 closest hydrogen atoms of the TMA. Also, it was found from electronic charge-density and ELF profiles that the ions in the system keep them close through closed-shell interactions of the donor−acceptor type according to the classification of Macchi et al.28,29 and the information in ref 30; since it is a weak interaction, it allows us to have insights about the reactivity of the TMA group and why it is susceptible to dissociate. It was inferred from this work that the simulated QSEBS segment is a thermodynamically stable backbone polymer to

AUTHOR INFORMATION

Corresponding Author

*Phone: (+57) 4 4255380. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Special acknowledgment to Universidad Nacional de Colombia, ́ Departamento de Procesos y Energia,́ especially Sede Medellin, to the Kimera research group for their support. Thanks also to the “Excellent graduate students’ scholarship” and the Advanced Numerical Calculation UnitUNICA, for making the resources and computational tools to carry out this research available.

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Theoretical Description of the Structural Characteristics of the

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