Letter pubs.acs.org/JPCL
Concentration-Dependent Proton Transfer Mechanisms in Aqueous NaOH Solutions: From Acceptor-Driven to Donor-Driven and Back Matti Hellström and Jörg Behler* Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany S Supporting Information *
ABSTRACT: Proton transfer processes play an important role in many fields of chemistry. In dilute basic aqueous solutions, proton transfer from water molecules to hydroxide ions is aided by “presolvation”, i.e., thermal fluctuations that modify the hydrogen-bonding environment around the proton-receiving OH− ion to become more similar to that of a neutral H2O molecule. In particular at high concentrations, however, the underlying mechanisms and especially the role of the counterions are little understood. As a prototypical case, we investigate aqueous NaOH solutions using molecular dynamics simulations employing a reactive high-dimensional neural-network potential constructed from density functional theory reference data. We find that with increasing concentration the predominant proton transfer mechanism changes from being “acceptor-driven”, i.e., governed by the presolvation of OH−, to “donor-driven”, i.e., governed by the presolvation of H2O, and back to acceptor-driven near the room-temperature solubility limit of 19 mol/L, which corresponds to an extremely solvent-deficient system containing only about one H2O molecule per ion. Specifically, we identify concentration ranges where the proton transfer rate is mostly affected by OH− losing an accepted hydrogen bond, OH− forming a donated hydrogen bond, H2O forming an accepted hydrogen bond, or H2O losing a coordinated Na+. Presolvation also manifests itself in the shortening of the Na+−OH2 distances, in that the Na+ “pushes” one of the H2O protons away.
P
solution. For the bulk case, previous work has focused on the presolvation of OH− at low concentrations, but the relative importances of breaking an accepted HB or forming the donated HB have not been quantified. At higher concentrations, where a significant fraction of H2O and OH− are coordinated by counterions, and where the number of available HB donor and acceptor sites is different from the dilute case, even less is known about the influence of presolvation. With the present work we intend to fill several gaps in the understanding of PT in basic aqueous solutions: (i) we identify qualitative changes in the presolvation mechanisms as the hydroxide concentration is increased in bulk solutions, (ii) we extend the presolvation concept to the proton-donating H2O molecules and explicitly consider the role of the counterions (Na+ in this case), and (iii) we unravel to what extent different presolvation mechanisms occur and quantify their relative importances. Experimentally, it is very difficult to obtain reliable information about the OH− diffusion mechanism, especially regarding the effect of the instantaneous local environment on the proton transfer rate. Instead, molecular dynamics (MD) simulations constitute a powerful approach to address this question, provided that the underlying potential is “reactive” and thus can describe proton transfer events. Densityfunctional-theory-based ab initio MD would in principle enable
roton transfer (PT) events are of central importance in many chemical processes, e.g., in enzymatic catalysis, in organic synthetic chemistry, in electrocatalysis, and in protonexchange membrane fuel cells. Consequently, unravelling the mechanisms by which they occur is crucial for understanding several interesting phenomena as well as for commercially relevant applications. Basic aqueous solutions constitute a fundamental PT system, where hydroxide ions (OH−) can diffuse anomalously fast via a “Grotthuss”-like mechanism, in which a proton is transferred from a neighboring H2O, converting this molecule to become the new OH− ion.1,2 Several mechanistic studies of the diffusion of OH− in aqueous solutions have been conducted, that support the notion that PT is aided by presolvation.1,3−7 In dilute hydroxide solutions, H2O molecules usually both accept and donate two hydrogen bonds (HBs), while OH− ions mostly accept four HBs and donate none.8−11 Still, due to their dynamical nature, HBs are continuously broken and formed, and if an OH− ion loses one of its accepted HBs, and donates a HB through its H atom, it has become “presolvated” for proton transfer. If the OH− ion then picked up a proton from one of the HB-donating H2O molecules, the resulting H2O molecule would immediately possess the typical H2O HB pattern, effectively lowering the PT barrier. Similarly, fluctuations in the local hydrogen-bonding environment around the hydrated hydroxyl radical (HO•) have been shown to influence the H-transfer rate.12 Because PT involving OH− is sensitive to the nearby environment, different PT rates and mechanisms are obtained for OH− that is, for example, microsolvated,13 or that is part of one-dimensional water wires,14 as compared to OH− in bulk © XXXX American Chemical Society
Received: June 30, 2016 Accepted: August 9, 2016
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after the PT, which can take several picoseconds in the cases of A(H 2 O) and A*(OH − ). Thus, none of the possible presolvation steps is strictly necessary for PT, but merely support the PT. At higher concentrations, many of the H2O and OH− are coordinated by Na+. Figure 1b shows the presolvation (and postsolvation) at xNaOH = 0.31 for the shortest Na+−O distance for H2O and OH− that coordinate one or two Na+ before PT: dmin(Na+−OH−) increases to make room for the incoming proton, and dmin(Na+−OH2) increases slightly before it sharply decreases. The shortening of the Na+−OH2 distance before PT can be interpreted as the Na+ “pushing” the proton from the H2O to the OH−. We have calculated the PT rate for all of the occurring values of A*(OH−), A(H2O), D(OH−), D*(H2O), X(OH−), X(H2O), as well as the equilibrium distributions of these quantities, over the entire room-temperature solubility range of NaOH(aq). If the maximum PT rate is obtained for a value that is not the most frequently occurring value, then the PT is clearly aided by presolvation. For example, we have found that, at the low concentration of xNaOH = 0.008, the most common number of HBs for a OH− ion to accept is four (A*(OH−) = 3), and that such OH− ions appear 3 times as often in the simulation as those with A*(OH−) = 2. Nevertheless, the maximum PT rate is obtained when A*(OH − ) = 2. The relative rate
such studies, but this method is computationally very demanding, which prohibits a thorough sampling of phase space. Reactive force-fields constitute an alternative approach, and have recently been used, for example, to model OH− diffusion in anion exchange membranes.15,16 Here, we develop an interatomic potential based on highdimensional neural networks17−19 (NNs) to describe liquid NaOH(aq) solutions. NNs can represent first-principles potential energy surfaces very accurately, and have recently been applied to, for example, neutral and protonated water clusters,20,21 and to explain the density anomality of liquid water.22 Using our newly developed NN, we run equilibrium MD simulations (at 300 K and at a density equilibrated at 1 bar) of NaOH solutions up to the solubility limit of 19 mol L−1, corresponding to a mole fraction xNaOH ≤ 0.33, where xNaOH = n(NaOH)/[n(NaOH) + n(H2O)]. The technical details of the NN potential and of the simulations are given in the Supporting Information (SI). The SI also contains some calculated radial distribution functions, that are compared to those from previous experimental and theoretical works.9−11 Proton transfer occurs within a hydrogen-bonded pair of H2O (donor) and OH− (acceptor), HOH···OH −. We characterize the environment around such a pair by means of six environmental parameters (EPs): the number of accepted HBs, A(H2O) and A*(OH−), the number of donated HBs, D*(H2O) and D(OH−), and the number of counterions Na+ that are within 3 Å of the respective O atom, X(H2O) and X(OH−). For A*(OH−) and D*(H2O), we exclude the HB along the PT coordinate (indicated by the asterisks), i.e., A*(OH−) = A(OH−) − 1 and D*(H2O) = D(H2O) − 1. We employ a common HB definition that requires an OdH···Oa pair with dOO ≤ 3.5 Å and ∠ OaOdH ≤ 30°.23 Figure 1a illustrates how presolvation precedes a PT event at a low concentration of xNaOH = 0.016, where t = 0 indicates the
r(A*(OH−) = 2) r(A*(OH−) = 3)
= 2.1, meaning that 2.1 times as many PT events
happen for OH− ions with A*(OH−) = 2 as for those with A*(OH−) = 3. Similarly, Figure 1a reveals that presolvation also occurs by, for example, an increase of D(OH−). The most common value for D(OH−) at low concentration is 0, but the maximum rate is obtained for D(OH−) = 1. In this case, the relative rate
r(D(OH−) = 1) r(D(OH−) = 0)
= 1.7, which is smaller than the value
of 2.1 obtained for A*(OH−). Thus, in this case, the number of HBs that OH− accepts is “more important” than the number of HBs it donates. We can thus define the “most important presolvation step” for each xNaOH as the kind of change in one of the six EPs A*(OH−), A(H2O), D(OH−), D*(H2O), X(OH−) and X(H2O) yielding the highest PT rate relative to that obtained for the most frequently occurring value of the same quantity. In many cases, the highest PT rate is obtained for the most frequently occurring value, in which case no “presolvation” is deemed to occur. For example, at the low concentration of xNaOH = 0.008, most OH− ions have X(OH−) = 0, and most PT events also occur for X(OH−) = 0, so in that case, there is no predominant “presolvation” mechanism of OH− ions with respect to their coordination to Na+, although we will later show that the PT barrier ΔF‡ decreases significantly for OH− bound to Na+. Figure 2 summarizes the most frequently occurring values of the EPs, their values associated with the maximum rate of PT, the relative rates between these, and the most important presolvation steps for each xNaOH, which at low concentrations (xNaOH < 0.11) are acceptor-driven, i.e., governed by changes in A*(OH−) or D(OH−), but at higher concentrations (0.11 < xNaOH < 0.29) become donor-driven, i.e., governed by changes in X(H2O) or A(H2O), and near the solubility limit (xNaOH > 0.29) become acceptor-driven again. In order to explain the variations in the most important presolvation step, Figure 3 shows the average equilibrium values of the EPs (the full distributions are given in the SI).
Figure 1. Time evolution of the average environment before and after a PT event happening at t = 0. (a) Average number of accepted and donated hydrogen bonds for H2O (red and pink) and OH− (blue and purple) at xNaOH = 0.016. Reactions have been considered only if reactants have been in the reactant state for at least 0.75 ps of the 1 ps preceding the PT event. At t > 0, data is included only if the molecule remains in the product state. (b) Average shortest Na+−O distance at xNaOH = 0.31, for H2O (brown) and OH− (green) reactants with counterion number X = 1 (top two lines) or X = 2 (bottom two lines) at t < 0.
time at which the transferred proton is getting closer to the accepting OH− than to the original H2O. Approximately 0.5 ps before the PT, A(H2O) begins to increase and A*(OH−) begins to decrease. At about 0.1 ps before the PT, D*(H2O) decreases and D(OH−) increases. However, such presolvation is not necessarily “complete” before the PT, and all four variables continue to relax toward their new equilibrium values 3303
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The most important presolvation step changes from decreasing A*(OH−) to increasing D(OH−) at around xNaOH = 0.03 (Figure 2b). This is because as the concentration increases, OH− accepts more HBs (Figure 3a), which makes the formation of A*(OH−) = 2 less favorable, and a smaller fraction of PT events occur via that mechanism. Instead, at xNaOH > 0.03, a greater relative rate is obtained by increasing D(OH−) from 0 to 1 as compared to decreasing A*(OH−) from 3 to 2. As the concentration increases further, more and more H2O molecules become coordinated by Na+ (Figure 3c), and consequently H2O accepts fewer hydrogen bonds. Such H2O molecules are less active for PT. At mole fractions xNaOH > 0.1, the majority of H2O are coordinated by at least one Na+, and the most important presolvation step at such concentrations is therefore not acceptor-driven via the loss or addition of HBs by OH−, but rather donor-driven via a decrease in X(H2O) or an increase in A(H2O). At highest concentrations, xNaOH > 0.3, a large enough fraction of H2O has X(H2O) = 2, so that the PT rate is also the highest for this X(H2O). Instead, the most important presolvation step again becomes to decrease A*(OH−), as the maximum rate is obtained at A*(OH−) = 1, while the most frequent value is A*(OH−) = 2. Going beyond the relative PT rates for different environments, we now turn to the investigation of the free energy barriers ΔF‡ that must be overcome during the PT reactions. As in previous works,3,7 we define a PT coordinate δmin for each OH− that accepts at least one HB, as illustrated in Figure 4. When δmin = 0 Å, the proton lies exactly halfway between two O atoms.
Figure 2. (a) The most frequently occurring values for A*(OH−), A(H2O), D(OH−), D*(H2O), X(OH−), X(H2O), and the values yielding the maximum rate of proton transfer, as a function of the mole fraction xNaOH. (b) Some selected relative rates as a function of xNaOH. Thick symbols/lines are drawn for relative rates between values of the environmental parameter with the highest rate and with the greatest occurrence. The background color indicates the most important presolvation step in each xNaOH range.
Figure 4. An OH− accepting two hydrogen bonds. Here, the protontransfer coordinate δmin = d4 − d3 (between the OH− and HOβH), because d4 − d3 < d2 − d1.
The relative rates in Figure 2 were determined, as explained in the SI, from the free energy landscape during PT as a function of δmin: ΔF{EP}(δmin) = −kBT ln W{EP}, where W{EP} is the number of times that a HOH···OH− pair with the given δmin-value and with some specific values for the environmental parameters {EP} appear in the simulation trajectory. Such functions are characterized by a minimum ΔFm around δmin = 0.3−0.6 Å, a maximum ΔFM at δmin ≈ 0 Å, and a barrier ΔF‡ = ΔFM − ΔFm. Free energy barriers for PT have previously been shown to be lowered by nuclear quantum effects;3 leaving this aspect for future work, here our main focus is on relative rates and barriers, which we expect to depend much less on such effects due to cancellations of this contribution. Figure 5a shows the free energies involved in PT at xNaOH = 0.016 for different (A*(OH−), A(H2O)) pairs. For example, the (3,2) → (2,3) reaction shows, at negative δmin (left-hand side), the free energy landscape for an HOH···OH− pair with A*(OH−) = 3 and A(H2O) = 2 (these are the most common values at this xNaOH, Figure 2a), that react to form, at positive δmin, an HO−···HOH pair with A*(OH−) = 2 and A(H2O) = 3. The minimum at δmin < 0 is deeper than at δmin > 0, so the reactant state is more stable, as expected from the equilibrium
Figure 3. Average values for the environmental parameters as a function of xNaOH: (a) accepted hydrogen bonds A(H2O) and A*(OH−), (b) donated hydrogen bonds D*(H2O) and D(OH−), (c) coordination by Na+, X(H2O) and X(OH−).
Notably, Na+ preferentially coordinates to H2O. As the concentration increases, H2O becomes a better HB donor, but a worse acceptor because a larger fraction of H2O is bound to Na+, which partially occupies the space that an HB donor would need. D(OH−) increases from about xNaOH = 0.12, and A*(OH−) increases until it reaches a maximum at xNaOH = 0.12, and then decreases again. The maximum for A*(OH−) arises because the presence of Na+ stabilizes OH− ions that accept five HBs, as also reported previously9 (see also SI). At higher concentrations, more OH− directly coordinate to Na+, decreasing the average A*(OH−). 3304
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The PT barriers (and rates) are also influenced by the HB donation numbers [D(OH−), D*(H2O)]. Figure 5b splits the (2,2) → (2,2) reaction from Figure 5a into the four possible combinations of [D(OH−), D*(H2O)]. The nonpresolvated reaction mechanism ((2,2)[0,1] → (2,2)[1,0]; ΔF‡ = +1.5 kBT) has the highest elementary barrier. In this case, presolvating the H2O by the loss of a donated HB ((2,2)[0,0] → (2,2)[0,0]; ΔF‡ = +0.8 kBT) decreases the elementary barrier more than presolvating the OH− by the formation of a donated HB ((2,2)[1,1] → (2,2)[1,1]; ΔF‡ = +0.9 kBT). Nevertheless, the overall rate is highest via the (2,2)[1,1] → (2,2)[1,1] mechanism, indicating that presolvating the OH− donor is more important than presolvating the H2O donor, given that the OH− is already presolvated with respect to A*(OH−). Figure 5a also shows the barriers for different {X(OH−), X(H2O)} pairs at xNaOH = 0.016. Almost all proton transfer events involve species that are not coordinated by Na+. For the {0,0} → {0,0} reaction, the barrier ΔF‡ = +1.6 kBT. It increases considerably if the H2O is coordinated by Na+ ({0,1} → {1,0}; ΔF‡ = +2.7 kBT), and decreases if OH− is coordinated by Na+ ({1,0} → {0,1}; ΔF‡ = +0.7 kBT). This is also in line with the presolvation concept: Because Na+ has a higher affinity for H2O than for OH−, PT barriers are higher for H2O coordinated by Na+ and smaller for OH− coordinated by Na+. The situation is similar at higher concentrations. Figure 5c shows the free energy landscape for PT events for the most predominant combinations of X(OH−) and X(H2O) at xNaOH = 0.31. The most frequently occurring X(OH−) = 0, and the most frequently occurring X(H2O) = 2 (Figure 2a), but ΔF‡ for the {0,2} → {2,0} reaction is very high (+4.5 kBT). The maximum rate is obtained for the {2,2} → {2,2} (presolvated OH−) and {1,1} → {1,1} (presolvated OH− and H2O) mechanisms. Overall, the relative rate r({2, x} → {x , 2}) = 2 indicates that twice r({0, x} → {x , 0})
as many PT events take place for OH− that bridge two Na+ compared to “free” OH−, in spite of there being 68% more “free” OH− than bridging OH−. Overall, the elementary barrier is highest for X(OH−) = 0 and X(H2O) = 2. The previous two examples for xNaOH = 0.016 and xNaOH = 0.31 illustrate the complexity of PT processes in hydroxide solutions: There are many competing mechanisms, that all contribute to various extents. We have seen that the elementary reaction barrier is lower for OH− that accept fewer than four HBs, that donate HBs, and that are coordinated to Na+. In most cases, the opposite is true for H2O: the reaction barrier is lower if the H2O is “hypercoordinated” and accepts three HBs, or if it has lost its second donated HB (the one donated by the H that is not transferred toward OH−), or if the H2O is not coordinated by Na+. In summary, our neural-network-based molecular dynamics simulations have revealed that the most important presolvation step for proton transfer in NaOH(aq) solutions changes from being acceptor-driven, to being donor-driven, and back to acceptor-driven as the concentration increases toward the room-temperature solubility limit. For the lowest concentrations, the most important presolvation step is for the OH− to lose one of its accepted HBs. As the concentration increases, the average number of HBs accepted by OH− increases. As a result, the most important presolvation step becomes for OH− to donate a HB. For even higher concentrations, a majority of H2O molecules become coordinated by Na+, and because the PT barriers for such H2O are high, the most important presolvation step is to decrease the number of Na+ near the
Figure 5. (a) Proton transfer free energy landscapes for different (A*(OH−), A(H2O)) pairs at xNaOH = 0.016, averaged over all combinations of D(OH−), D*(H2O), X(OH−), and X(H2O); and {X(OH−), X(H2O)} pairs averaged over D(OH−), D*(H2O), A*(OH−), and A(H2O). The points represent bins with a width of 0.03 Å. (b) The (2,2) ↔ (2,2) reaction from (a) decomposed into [D(OH−), D*(H2O)] contributions. (c) Proton transfer free energy landscapes for different {X(OH−), X(H2O)} pairs at xNaOH = 0.31.
distributions. The forward barrier is ΔF‡ = +2.5 kBT, which is considerably larger than the average barrier of +1.6 kBT. However, the barrier can be decreased by presolvation, which means either decreasing A*(OH−) (the (2,2) → (2,2) reaction; ΔF‡ = +0.9 kBT), or increasing A(H2O) (the (3,3) → (3,3) reaction; ΔF‡ = +1.5 kBT). Thus, presolvating the OH− lowers the elementary reaction barrier more than presolvating the H2O does. More PT reactions proceed via the presolvated OH− than r without the presolvation: (2,2)→ (2,2) = 2.0. Similarly, the PT rate r(3,2) → (2,3)
through presolvated H2O is also higher than without any r presolvation, but by a smaller amount: (3,3)→ (3,3) = 1.1. r(3,2) → (2,3)
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H2O, or for H2O to accept more hydrogen bonds. Finally, for the highest concentrations, the most important presolvation step is to break one or more of the hydrogen bonds that OH− accepts.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b01448. Supplementary results (radial distribution functions, hydroxide ion lifetimes and PT barriers for all mole fractions, equilibrium and rate distributions for the six EPs, relative rate constants, and tabulated data for Figure 5), detailed description of the methods, and free-energy landscapes at xNaOH = 0.255 calculated with ab initio MD (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge useful discussions with Tobias Morawietz. This work was supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft, and the DFG Heisenberg fellowship Be3264/6-1.
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REFERENCES
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