Temperature-Dependent Structure and Dynamics of Water

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Temperature-Dependent Structure and Dynamics of Water Intercalated in Layered Double Hydroxides with Different Hydration States Meng Chen, Runliang Zhu, Jianxi Zhu, and Hongping He J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08133 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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The Journal of Physical Chemistry

Temperature-Dependent

Structure

and

Dynamics

of

Water

Intercalated in Layered Double Hydroxides with Different Hydration States

Meng Chen,*, 1 Runliang Zhu,1 Jianxi Zhu,1 and Hongping He1, 2 1. CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences (CAS), Guangzhou 510640, China 2. University of Chinese Academy of Sciences, 19 Yuquan Road, Beijing 100049, China *

Correspondence regarding this manuscript should be sent to [email protected]

ABSTRACT: Properties of water confined in layered double hydroxides (LDH) are relevant with hydration, dehydration and protonic conduction in interlayer galleries. Evolutions of structure and dynamics of water in LDHs (Mg2Al(OH)6Cl•mH2O) with temperature are disclosed through molecular dynamics simulations performed in the range of 300 to 430 K. LDHs with m = 0.78 and 1.44 which characterize two different hydration states are investigated. Water in the lower hydration state is characterized with higher ordered structure. Irrespective of water content, water becomes less hydrogen bonded and more disordered as temperature increases. This leads to a large decrement in dehydration enthalpy, which facilitates dehydration energetically. Irrespective of temperature or water content, water exhibits the preference for being fixed in hydroxyl sites and it diffuses through jumping between neighbor sites. Jump diffusion approximately exhibits an Arrhenius dependence on temperature. A jump is a collective process consisting of water translation and hydroxyl group reorientation, which is reflected in the high activation energy and low attempt frequency. Hydronium ions may be transported through jumping between neighbor sites, making a contribution to proton transfer in interlayer galleries.

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1. INTRODUCTION Water confined in nanometer- or subnanometre-scale space exhibits structure and dynamics distinctly different from bulk water.1-4 The chemistry of the confining interfaces, size and topology of the confining space largely influence properties of confined water. Water confined inside single-walled carbon nanotubes adopts a stacked-ring structure, forming intra- and inter-ring hydrogen bonds.5 Water confined between mica surfaces transits into bilayer ice exhibiting a specific hydrogen-bonding network as the distance between surfaces drops to 0.61 nm.6 These findings evidence that the hydrogen bond (HB) structure of confined water is dependent on surface chemistry and confining geometry. As compared to bulk water, confined water generally exhibits slower dynamics due to van der Waals and electrostatic interactions and hydrogen bonds between water and interfaces.7-8 Structure and dynamics of water confined in nanometer- and subnanometre-scale space are of fundamental importance in science and technology. For example, the adsorption of water into nanopores of zeolite can be applied in solar thermal energy storage.9-10 Layered double hydroxides (LDH) are a family of layered materials with water and anions intercalated in nano- or subnano-scale interlayers. The general formula of LDHs is [M2+(1-x)Me3+x(OH)2]x+(An-)x/n·mH2O, where M2+ can be Zn2+, Mg2+, Co2+, Ni2+, Ca2+ or Cu2+, Me3+ can be Cr3+, Ga3+, Fe3+ or Al3+, and An- are Cl-, SO42-, CO32-, NO3- and so on.11 LDHs are widely used as adsorbing agents, electrode modifiers, catalyst, and so on.12-15 The applications of LDHs are relevant with anion exchanges,16-18 hydration,19 dehydration20-22 and protonic conduction23 in interlayer


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galleries. Hence, revealing how confined water and anions interplay with brucite-like layers is important. Molecular dynamics (MD) simulations of LDHs with the formula Mg3Al(OH)8Cl•3H2O showed on average an intercalated water molecule forms 3.8 HBs, higher than that in bulk liquid water (3.2) but close to that in ice Ih (4).24 A water molecule generally accepts two HBs from two hydroxyl (OH) groups, one from the upper layer, and the other from the lower layer (Figure 1a). And it probably donates two HBs to adjacent water molecules or anions. Thus, it exhibits a tetrahedral structure similar to that in ice Ih.25 The stretching vibration of OH bonds of intercalated water is also close to that of ice Ih.26-27 Thermodynamic studies showed intercalated water gains entropy with respect to ice but loses entropy with respect to liquid water.28 In other words, water confined in LDHs is intermediate between solid ice and liquid water. These studies were at ambient temperature. Since applications of LDHs are often at elevated temperature,22, 29-30 investigating how interlayer structure evolve with temperature is necessary. Thermal decomposition studies of LDHs show dehydration and dehydroxylation occur sequentially upon heating. Generally, complete dehydration of intercalated water appears at 150-200 °C (423-473 K), but the brucite-like layered structure is still maintained.20-21, 31-35

During the dehydration

process as temperature increases, the intensity of the signal manifold in

27

Al magic

angle spinning nuclear magnetic resonance (MAS NMR) spectra increases, which was ascribed to the increased mobility of water in interlayer galleries.22, 36 It probably implies water is less bound by layers at elevated temperature. However, how ice-like structure of confined water at ambient temperature vary as temperature increases, is



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still not clear according to our knowledge.

Figure 1. (a) Schematic structure of a water molecule intercalated in LDHs. It locates in an OH site accepting HBs from two opposite OH groups. (b) Schematic jumping trajectory of an intercalated water molecule. (c) The reaction of a water molecule jumping from one OH site to another.

Marcelin et al. had suggested water in the two-dimensional interlayers of LDHs diffuses in a jumping way,37 which was later supported by quasi-elastic neutron scattering measurements.38 Our previous study with MD simulations has clearly shown the jump diffusion of confined water with a diffusion coefficient D close to that of ice Ih.39 A water molecule locating in an OH site jumps to a nearest neighbor site occasionally (Figure 1b). In this process it loses HBs from the original OH site and accepts HBs from the nearest neighbor site successively (Figure 1c). The Arrhenius equation is generally used to describe the dependence of D on temperature T:


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= exp −

(1)

where E is the activation energy, D0 the pre-exponential coefficient and k the Boltzmann constant.40 Confined water do not necessarily exhibits an Arrhenius behavior, which depends on how water structure evolve with temperature.41-43 The kinetics of dehydration upon heating is controlled by water diffusion in interlayer galleries. The Arrhenius equation was often used to describe the dependence of dehydration on temperature.21, 44 On the other hand, protonic conduction in LDHs which obeys the Arrhenius law,23 may be related to water diffusion.45 It is interesting to show if diffusion exhibits an Arrhenius behavior. The relationship between water structure and diffusion in interlayer galleries needs to be disclosed. MD simulations have been widely used to disclose hydration properties of LDHs and consistent results with experiments have been presented.24-25, 46-48 In this study, with MD simulations, temperature-dependent structure and dynamics of water intercalated in LDHs (Mg2Al(OH)6Cl•mH2O) are investigated. Thermal evolution of water structure is revealed. We disclose the jump model more or less explains water diffusion at elevated temperature which approximately corresponds to an Arrhenius behavior. A jump of a water molecule is shown to be a collective process and described with the transition state theory. Details can be seen in results of this article. 2. SIMULATION DETAILS AND THEORETICAL BACKGROUNDS 2.1. Simulation Details. X-ray diffraction studies showed the basal (c-axis) spacing of LDHs intercalated with Cl- ions is less than 8 Å under all humidity conditions and is almost non-expandable.19,

49

This basal spacing corresponds to



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LDHs (Mg2Al(OH)6Cl•mH2O) with m < 1.67, in which water appears as monolayers.39 LDHs with m = 0.78 and 1.44 (Mg2Al(OH)6Cl•0.78H2O and Mg2Al(OH)6Cl•1.44H2O) are simulated in this study, so as to show the influence of m on water structure and dynamics. A previous MD simulation study showed, for m ≤ 1.0, the basal spacing is almost constant with m; while for m > 1.0, it is slightly expandable as m increases. For m ≤ 1.0, the hydration energy is quite negative and almost constant, but it increases rapidly as m exceeds 1.0.48 These phenomena imply water in LDHs with m ≤ 1.0 and m > 1.0 belongs to different states. So, investigating LDHs with m = 0.78 and 1.44 in this study is meaningful in revealing properties of intercalated water belonging to different states. According to a previous study, the dehydration of Mg/Al-Cl LDHs is completed below 430 K.22 Thus, the simulated temperature range in this study is set to 300-430 K, corresponding to the stage with water intercalated. For a water content, 27 systems are simulated at T = 300, 305…, 425, and 430 K, respectively. On the other hand, 27 systems without water are also simulated in the same temperature range so as to calculate the dehydration energy. The initial model is built based on the experimentally determined crystal structure, which exhibits rhombohedral (3) symmetry.50 For convenience, hexagonal instead of rhombohedral unit cells are built. A simulated system consists of 9 × 9 × 1 unit cells in the a, b, and c directions, respectively. The layers have a complete Mg/Al ordered arrangement.51 Periodic boundary conditions are applied in all directions. The ClayFF force field52 with SPC water model53 incorporated is used to describe atomic


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interactions. According to Wang et al., the partial charges of O atoms in the layers are modified to make the model electrostatically neutral ( -0.9742 |e| vs -0.9500 |e| in the original force field).54 The SPC model has well reproduced thermodynamic properties of water, e.g., temperature-dependent heat of vaporization,55 and produced diffusion coefficient of the same order as the experimental value.56 The ClayFF force field and SPC model have been widely used in simulations, which describe hydration properties of layered materials well.57 Long-range electrostatic interactions are described by the particle-particle particle-mesh (PPPM) method.58 Short-range Lennard-Jones interactions

are cut off at 10.0 Å. Simulations are performed with LAMMPS.59 The time step is 0.5 fs. The systems are equilibrated in isothermal-isobaric ensemble for 20 ns. The Nosé-Hoover thermostat60-61 and Parrinello-Rahman barostat62-63 are used to achieve target temperature and pressure (1 atm), respectively. Each dimension of the supercell is scaled independently. After equilibration, production runs are performed for another 20 ns in canonical ensemble without pressure coupling. Data are saved every 0.1 ps. 2.2. Theoretical Backgrounds. Diffusion of water in interlayer galleries is studied by calculating the mean-square displacement in the xy-plane (MSDxy(t)), which is described by the Einstein relation:

〈(

#

+ ) − ( )" + $(

#

+ ) − $( )" 〉 = 4

(2)

where t is the time interval, t0 the time origin and D the diffusion coefficient. The average is taken over t0. Thus, D is derived by linearly fitting MSDxy(t). On the other hand, as water diffusion is assumed to be jumping between adjacent OH sites, D is



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related to the total jump rate ()*) through the equation:40

=

1 ( +# 4 )*)

(3)

where + is the jump distance. ()*) is referred to the total rate for a water molecule to jump to an arbitrary nearest neighbor site. It is related to ( , the rate for the molecule to jump to a specific nearest neighbor site, via the equation:

()*) = ,(

(4)

where , is the number of nearest neighbor sites around an OH site. Apparently,

, = 6, as shown in Figure 1b. ( can be described by an Arrhenius equation:64 ( = ./0 123/56

(5)

where ./ is the attempt frequency, Δ9 is the activation Helmoholtz free energy, i.e., the free energy needs to carry a water molecule from an initial equilibrium position to a transition point in configuration space. Δ9 instead of Δ: (activation Gibbs free energy) is used here as analyses are based on production runs performed in canonical ensemble. Obviously, even in isothermal-isobaric ensemble, the difference between

Δ9 and Δ: is negligible as volume variation can almost be neglected in the condensed state. Δ9 can be decomposed into energy and entropy contributions:

Δ9 = Δ; − Δ
/56 4

(7)

@

Comparing eq. (7) with eq. (1) shows = +# ,./0 2=/5 and = Δ;. A

3. RESULTS AND DISCUSSIONS 3.1. Hydrogen Bond Structure. At ambient conditions, we have shown for m less


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than ca. 1.2, mostly a water molecule accepts two HBs, one from the upper OH group, and the other from the lower one (Figure 1a).39 These two opposite OH groups constitute an OH site. Such a water molecule fixed in a site is designated as W2. On the other hand, W1 and W2’ are designated to those accepting just one HB in an OH site and two HBs from two adjacent sites, respectively (Inset in Figure 2a). The HB criterion is as follows: The donor−acceptor distance, the hydrogen−acceptor distance, and the hydrogen−donor−acceptor angle are less than 3.5 Å, 2.45 Å, and 30°, respectively.65-66 This criterion is verified with respect to different temperature conditions (Section S1 in Supporting Information). Generally, the average number of HBs (NHB) accepted by a water molecule from OH groups decreases with increasing temperature (Figure 2a, b). These decrements are due to variations in relative ratios of different types of water molecules (Figure 2c, d). For m = 0.78, over ca. 80% water molecules are fixed in OH sites as W2 at ambient temperature. As temperature increases, the number of W2 decreases while those of W1 and W2’ increase. For m = 1.44, just ca. 50% water molecules are W2 at ambient temperature. Increasing temperature leads to the same trend: W2 decreases, while W1 and W2’ both increase. At temperatures over ca. 360 K, the ratio of W1 exceeds that of W2. Based on the above analysis, as temperature increases, or in the higher hydration state, a water molecule is less bound to an OH site.



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Figure 2. (a) Number of HBs per intercalated water molecule accepts from OH groups as a function of temperature for m = 0.78. (b) The same as (a) except m = 1.44. (c) Probabilities of different types of intercalated water molecules as functions of temperature for m = 0.78. (d) The same as (c) except m = 1.44. The HB structure among water and Cl- ions is also investigated. Water can donate HBs to and accept them from other water molecules, or donate them to Cl- ions. The HB criterion between water molecules is the same as that between water and OH groups, but it is different from that between water and Cl- ions, which is defined as: The

donor−acceptor

distance,

the

hydrogen−acceptor

distance,

and

the

hydrogen−donor−acceptor angle are less than 3.7 Å, 2.75 Å, and 30°, respectively.39 These criterions are also verified with respect to different temperatures (Section S1 in Supporting Information). At all temperatures more HBs are formed among water and Cl- ions for m = 1.44 (Figure 3). It implies in the higher hydration state, water is more connected to each other and Cl- ions, but it is less bound to OH sites as shown above. This phenomenon is consistent to the finding that better developed ring structure through HBs of water and Cl- ions appears in the higher hydration state (Section S2 in Supporting Information). Increasing temperature leads to a general decreasing trend


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of NHB among water and Cl- ions (Figure 3), similar to that of NHB accepted from OH groups (Figure 2a, b). The constraint on water molecules due to HBs donated by layer OH groups and formed between interlayer species becomes weaken as temperature increases.

Figure 3. Number of HBs per intercalated water molecule forms with Cl- ions or other water molecules as a function of temperature. The HB structure of a water molecule at ambient temperature, i.e., accepting two HBs from OH groups and donating two HBs to other species in interlayer galleries, is responsible for its ice-like behavior. The ice-like structure can be quantified by the tetrahedral order parameter Q:67 N

A

3 1# 〈1 C = − E E FcosI5J " + K 〉O 8 3 JL@ 5LJM@

(8)

where ψkj is the angle between the vectors connecting the O atom of the water molecule i and the nearest neighbor atoms j and k which can act as HB donors or acceptors (water O atoms, hydroxyl O atoms, and Cl- ions). A larger Q implies a higher tetrahedral order. Q of hexagonal ice (ice Ih) and liquid water are 1 and 0.597, ACS Paragon Plus Environment


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respectively.68 For m = 0.78, at ambient temperature Q (> 0.65) is higher than that of liquid water (Figure 4). Wang et al. showed the largest average order parameter is 0.65 in nano-pores between brucite (001) surfaces,69 close to Q we find here. This high tetrahedral order is largely contributed by the dominance of W2 water molecules which accept HBs from two OH groups. Generally, ordered water in confinement exhibits well developed ring structure through HB connections.5, 70-71 However, water and anions constituting the most popular ring, the 4-membered ring, just account for less than 3% of all interlayer species (Section S2 in Supporting Information). Thus, the ordered structure of water in interlayer galleries for m = 0.78 can be just attributed to the local tetrahedral order, instead of long-ranged ordered arrangement among water molecules and anions. For m = 1.44 also at ambient temperature, Q is obviously smaller than that of liquid water (Figure 4). In the higher hydration state, water is less bound by OH sites and more connected to interlayer species as shown above. Ring structure is better developed here. However, even the most popular rings, 5-membered rings, only account for less than 9% of all water molecules and anions (Section S2 in Supporting Information). In comparison, 6- and 7-membered rings account for more than 50% of all molecules in pure liquid water.72 Thus, without long-ranged structure and well local coordination, it is in a more disordered state. Irrespective of water content, Q decreases as temperature increases, as water molecules are less bound by HBs.


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Figure 4. Tetrahedral order parameter Q of water as a function of temperature. Q of liquid water is denoted by a broken line.

Water in LDHs with m ≤ 1.0 and m > 1.0 belongs to two different states, as revealed by different basal spacings and hydration energies previously.48 This study clearly shows the former is more bound by OH sites, less connects to interlayer species, and exhibits local tetrahedral ordered structure. On the other hand, the latter is less bound by OH sites, and exhibits even more disordered structure than liquid water. So, in the latter situation water is in an energetically unfavorable state and it may escape from interlayers. With increasing temperature, water becomes less hydrogen bonded, and more disordered. Even in the lower hydration state, its structure becomes less ordered than liquid water at temperatures higher than 400 K (Figure 4). Thus, water in interlayer galleries becomes energetically less stable, which may lead to dehydration. Further analysis on dehydration enthalpy can be seen in Section 3.3. 3.2. Water Distribution in Interlayer Galleries. After the disclosure of HB structure, now we investigate how water distribution in interlayer galleries vary with



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HB structure. Water maintains monolayer structure throughout the temperature range in this study (Section S3 in Supporting Information). The distribution of water in the monolayer is disclosed by calculating the two-dimensional radial distribution function (RDF) g(r) (Figure 5). r is referred to the projection of the distance between a central Oh atom and a surrounding Ow atom on the x-y plane. An Oh atom is referred to the O atom of OH groups, while an Ow atom is the O atom of water. Irrespective of temperature, the distance between peaks in g(r) is ca. 3.2 Å, corresponding to the distance between OH sites. Water is favored to be fixed in OH sites, consistent to our previous finding based on two-dimensional atomic density distributions.39

Figure 5. Two-dimensional RDF g(r) of water molecules surrounding an OH group on the x-y plane for m = 0.78 (a) and 1.44 (b) at different temperatures. Insets show ∆g (the difference between the maximum and minimum values of g(r)) as functions of temperature.

For m = 0.78 (Figure 5a), the first peak of g(r) locates at ca. 0.5 Å, implying a ACS Paragon Plus Environment

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water molecule tends to deviate a little from the center of an OH site. This deviation should be the result of achieving higher tetrahedral ordered structure. At ambient temperature, in the range of the first peak of g(r) (r < 1.0 Å), NHB accepted from the central OH site is close to 2 and Q is higher than 0.60 (Section S4 in Supporting Information). So, a water molecule belonging to the first peak is mostly a W2 one with high tetrahedral order. Beyond 1.0 Å but within 2.0 Å, i.e., in the region where

g(r) approaches minimum, NHB accepted from central OH groups decreases rapidly (Figure S6 in Supporting Information), implying the increasing ratio of W1 and W2’ water. The minimum of g(r) implies an energy barrier, so that W1 and W2’ water molecules are in unstable states. Also at ambient temperature, for m = 1.44 (Figure 5b), although the peak of g(r) is sharper, in the peak range less HBs (ca. 1.6) are accepted from OH groups and the tetrahedral order (ca. 0.55) is even lower than that of liquid water (Section S4 in Supporting Information). The number of accepted HBs implies, in the peak range, slightly more than half water molecules belong to W2, while the others are probably W1. The appearance of a comparable amount of W1 water is probably due to the higher interlayer spacing (Section S3 in Supporting Information). The peak of g(r) does not deviate from the center of an OH site. In this case, water is more located in OH sites, but less bound by OH groups, exhibiting less ordered structure. W2 and W1 can both be in stable states corresponding to peaks in g(r), in contrast to the situation of the lower hydration state. Irrespective of water content, with increase of temperature, the fluctuation of g(r)



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becomes less pronounced, as shown by the decreasing trend of ∆g (the difference between the maximum and minimum values of g(r)) (Figure 5). It implies more water locating in edges of OH sites. Such molecules in edges are mostly W1 and W2’ (Section S4 in Supporting Information). Thus, the variation of g(r) with temperature corresponds to increases in ratios of W1 and W2’ (Figure 2c,d). Energetically water tends to approach the center of OH sites as to achieve higher ordered structure. However, the entropic effect leads to a disordered distribution, which becomes more important at higher temperatures. As a result, g(r) becomes less pronounced as temperature increases. Low temperature and low water content favor W2 water in centers of OH sites exhibiting well-ordered structure. Increase of temperature or water content leads to part of W2 replaced by W1 and W2’, which exhibit less ordered structure. NMR studies have shown, as temperature increases, the intensity of the signal manifold in 27Al MAS NMR spectra increases, while peaks in 1

H NMR spectra becomes broader and weakened.22, 36 These phenomena are probably

caused by water being less bound by layers and more disordered as temperature increases. 3.3. Dehydration Enthalpy. The dehydration of water from interlayer galleries of LDHs was shown to be an endothermic process.73-74 So, thermodynamically dehydration is entropy-driven. The relative variations in enthalpy and entropy with temperature determine when dehydration is induced. The dehydration enthalpy ∆U is calculated with respect to temperature, according to the equation:

∆U = +

〈;(0)〉 − 〈;(VW )〉 VW


(9)

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where 〈;(VW )〉 is the average potential energy of the system with VW mol water molecules, 〈;(0)〉 the average potential energy of the system without water, the gas constant, and temperature. ∆U can be seen as the molar heat of water dehydrated from interlayers into ideal gas.75 Volume variation is neglected in the equation as simulations are at ambient pressures.47,

76

Positive ∆U confirms

dehydration is an endothermic process (Figure 6). The range of ∆U here is consistent to the measured ∆U (ca. 55 kJ/mol) through thermal analysis.77 Generally, ∆U we derived is smaller for m > 1, consistent to the previous finding based on MD simulations at ambient temperature.48 The increment in could lead to more than ca. 10 kJ/mol decrement in ∆U in the temperature range studied here. In contrast, through ab initio calculations Costa et al. showed in the temperature range 298-548 K variation in enthalpy is less than 1.5 kJ/mol.78 In the ab initio calculations, vibrational modes of the systems are assumed to be the same throughout the temperature range, and the harmonic approximation is used to derive enthalpy based on the static structure at 0 K. Obviously, these assumptions are at odds with the finding here that the structure of intercalated water varies with temperature. As temperature increases, water becomes more disordered, and energetically less favorable states are appearing, which have been shown in previous sections. This structure variation contributes to increase in energy ;(VW ). As a result, a large decrement of ∆U is observed. Ab initio calculations deduced the dehydration reaction is mainly controlled by the entropy term.78 As shown here, the entropy of hydrated systems should increase with temperature as water is more disordered. Thus, the entropy contribution to



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dehydration is less important than in the ab initio result. Although dehydration is still entropy-driven shown by the positive ∆U , the large decrement in ∆U due to structure variation of water plays an important role.

Figure 6. Dehydration enthalpy as a function of temperature for m = 0.78 and 1.44.

3.4. Diffusion of Water in Interlayer Galleries. According to eq. (2), diffusion coefficient D is derived by fitting MSDxy(t), which becomes linear with t in a long time scale (Figure S11a in the Supporting Information). Approximately, D increases exponentially with decrease of 1/T (Figure 7), corresponding to the Arrhenius behavior. Through fitting data with eq. (1), activation energy E and pre-exponential coefficient D0 are derived (Table 1). Due to the data scattering, we cannot guarantee an Arrhenius behavior without doubt. A non-Arrhenius behavior corresponds to different diffusion mechanisms in different temperature ranges, which generally arise from distinct structure variation.42-43 In the following, we will verify if the diffusion mechanism, i.e., the jump model,39 is the same at different temperatures. We suppose water still diffuse through hopping between OH sites irrespective of temperature, as


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water always exhibits the preference for being fixed in OH sites (Figure 5).

Figure 7. Diffusion coefficients derived by fitting mean square displacements, and calculated with jump models utilizing different definitions of stable states, as functions of temperature. Data are fitted with eq. (1). Table 1. Pre-exponential coefficient D0, activation energy E, activation entropy Δ< and attempt frequency ./ for m = 0.78 and 1.44. m

D0 (cm2/s)

E (kJ/mol)

Δ< (kJ/mol/K)

./ (s-1)

0.78

3.1 [ 101N

32

0.032

4.0 [ 10@

1.44

1.1 [ 101#

36

0.047

2.6 [ 10@

A water molecule stably fixed in an OH site is viewed as in a stable state. A jump is similar to a chemical reaction, during which a water molecule rapidly transits from one stable state into another. Based on the stable state approach,79-80 a jump is described by the cross-correlation function:



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\]^ ( ) = 〈,] ( ),^ (

+ )〉

Page 20 of 50

(10)

where ,] (t0) is 1 if the water molecule is in a stable reactant (R) state at time origin t0, and ,^ (t0+t) is 1 if it is in a stable product (P) state after a time interval ; Otherwise, their values are 0. The average is taken over t0. The adsorbing boundary condition is used in calculating \]^ ( ). The decay time of 1 − \]^ ( ) is jump time

`, i.e., the average time for a jump to happen. As to derive `, stable states, i.e., R and P states, should be well defined. In the previous study, we defined a stable state based on if a water molecule stably accepts two HBs from two OH groups in a site (a stable W2 state).39 The stability is defined by strict HB geometric criterions. In this study, we have shown comparable amounts of water molecules just accept one HB from an OH group (a W1 state) at higher temperatures or in the higher hydration state. The stable state criterion may need to be revised. However, assuming the interconversion between W2 and W1 in an OH site is much more frequent than a jump between adjacent sites, we can still define a stable W2 state as a stable state. This assumption is verified in Section S5 of Supporting Information. Two geometrical criterions are tested in defining a stable W2 state: 1. The donor−acceptor distance, the hydrogen−acceptor distance, and the hydrogen−donor−acceptor angle are less than 2.8 Å, 1.8 Å, and 11°, respectively; 2. Those parameters are less than 3.2 Å, 2.0 Å, and 15°, respectively, which is a looser criterion. Based on these two criterions,

1 − \]^ ( ) are calculated and fitted with exp(− /`) (Figure S13 in Supporting Information). Because ()*) = 1/` , according to eq. (3), ` is related to D via the following equation:40


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+# = 4`

(11)

where the jump distance d is assumed to be the average distance between adjacent OH sites (3.22 Å). This assumption is verified in Section S6 of Supporting Information. D derived with this method is compared to that derived by fitting MSDxy(t) (Figure 7). For m = 0.78, the jump model, irrespective of criterions used for defining stable states, more or less predicts the Arrhenius dependence of diffusion on temperature (Figure 7a). For m = 1.44, using the first criterion, the dependence of D on T deviates significantly from that derived by fitting MSDxy(t) (Figure 7b). The jump model with the first criterion largely underestimates D at high temperatures, although it gives better results while temperature is lower. On the other hand, with the second criterion, the jump model gives a much better prediction throughout the temperature range. The artifacts in stable state definition lead to such deviations. The first criterion is a “too strict” one for m = 1.44 at high temperatures. Hydrogen bonds are statistically elongated at high temperatures (Section S1 in Supporting Information). Thus, under this “too strict” criterion, even though a water molecule jumps to a nearest neighbor site, it may not be regarded as in a stable P state. As a result, the jump time ` is artificially extended, which leads to the underestimate of D. More details about how artifacts are induced due to stable state definitions can be seen in Section S6 of Supporting Information. Nevertheless, the jump model has more or less predicted the Arrhenius dependence of diffusion on temperature, revealing the intrinsic of water diffusion in interlayers is a sequence of jumps between adjacent OH sites. Pisson et al. showed a high diffusion rate of water in interlayer galleries is



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associated with high proton conductivity.45 Surprisingly, the activation energy for protonic conduction they disclosed (40-60 kJ/mol) is close to E for water diffusion derived here (Table 1). Proton transfer in water has long been described with the Grotthuss mechanism, which requires well interconnected HB network.72 However, ring structure characterizing the interconnection between water is not well developed in interlayer galleries (Section S2 of Supporting Information). Ludueña et al. showed, in proton conducting polymers where water is confined in channels, the Grotthuss mechanism must be supported by a short-distance transport of hydronium ions to neighboring acid sites.81 Similarly, the short-distance transport of hydronium ions, characterized by water hopping between neighboring sites disclosed here, could play an important role in proton transfer in LDHs. The finding E for water diffusion is close to that of protonic conduction supports this suggestion. Of course, it needs further investigation, which is currently beyond the scope of this study. 3.5. Water Hopping Explained by the Transition State Theory. A water molecule jumps from one OH site (Site a) into another (Site b), transiting from one stable state being W1 or W2 into another (Figure 8). The average structure variation with time during a jump is disclosed. b is the distance between an Ow atom of water and an Oh atom of Site a, while c is the distance between the Ow atom and f an Oh atom of Site b. Vde is the number of HBs donated by an OH group in Site a, g while Vde is the number of HBs donated by an OH group in Site b. As a jump b c happens, b , c , Vde and Vde all exhibit rapid variations, irrespective of

temperature or water content (Figure 9). Significant increase of b and decrease of


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c are observed at the same time (Figure 9a,b). The coordination of site a decreases while that of site b increases at the same time, as shown by the reverse variations of b c Vde and Vde (Figure 9c,d). It implies a water molecule rapidly leaves site a and

becomes fixed in site b. Thus, a jump is a rapid transition from one stable state to another, similar to the jump reorientation of OH bonds of water.65 This temperature independent phenomenon further verifies the nature of the Arrhenius dynamic is the same jump mechanism. At the moment just before the sudden increase of b and b c decrease of Vde , i.e., at the time just before a jump, Vde decreases sharply (Figure

9c,d). It implies site b is undercoordinated on average before a jump. An unoccupied site is prone to accept a water molecule which hops from a nearest neighbor site.

Figure 8. Schematic view of a water molecule hopping from Site a to Site b.



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f g Figure 9. Variations of b , g , Vde , and Vde , while a water molecule jumps from one OH site to another, for m = 0.78 (a, c) and 1.44 (b, d) at 300 and 400 K.

According to the transition state theory, the activation Helmoholtz free energy ∆h for a jump (eq. (5)) can be calculated with probabilities of transition (i)j ) and stable states (ik)) in configuration space:64

∆h = −(ln i)j − ln ik) )

(12)

In the transition state, a water molecule originally from Site a has moved to the gap, and an OH group from Site b has reoriented to donate a HB to it (Figure 8). Thus, i)j mW d* mW can be decoupled as a product of i)j and i)j . i)j is the probability of a water d* molecule originally from Site a being in the gap between two OH sites, while i)j is

the probability of a Ho atom (hydroxyl H atoms) from Site b being in the gap and mW forming a HB with the water molecule. Similarly, ik) is decoupled into ik) and d* ik) , where the former is the probability of a water molecule being stably fixed in Site


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a, and the latter is the probability of the Ho atom also being in the stable state. Thus, eq. (12) can be rewritten as: mW mW d* d* ∆h = ln ik) − ln i)j " + ln ik) − ln i)j "

(13)

where the first part is designated as ∆h@ , while the second part is ∆h# . ∆h@ accounts for the free energy difference of water, while ∆h# accounts for that of a Ho mW mW d* d* , i)j , ik) , and i)j are derived by the two-dimensional RDF between atom. ik)

different couples of atoms (Figure 10). The first peak in RDF(Oh-Ow) corresponds to a water molecule stably fixed in the central OH site (Site a), which has been shown in mW Section 3.2. Obviously the peak value corresponds to ik) . The second peak in

RDF(Oh-Ho) corresponds to a Ho atom stably locating in the nearest neighbor OH d* site (Site b), whose value is ik) . The first minimum in RDF(Oh-Ow) corresponds to

a water molecule locating in the middle between Site a and Site b. And the first minimum in RDF(Oh-Ho), which is close to 0, more or less corresponds to the position where a Ho atom forms a HB with the water molecule in the gap. These two mW d* minimums correspond to ik) and ik) , respectively. Thus, with eq. (13), ∆h@, ∆h#,

and ∆h are derived. Apparently, ∆h# , the activation energy for the reorientation of an OH group, plays a much more important role (Figure 10). A water molecule fixed by HBs from Site a occasionally moves to the gap between OH sites. However, without the reorientation of an OH group from Site b leading to the formation of a new HB, a jump would not happen. Reorientation of an OH group is rare, which probably happens while Site b is unoccupied by water or anions, as shown by the g small Vde before a jump (Figure 9c,d). The rare reorientation of an OH group partly



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explains the rare jump rate.

Figure 10. Two-dimensional RDF of Ow and Ho atoms around a central Oh atom for m = 0.78 at 400 K. A(n) calculated from the equation 9(n) = − ln i(n) are also shown in the figure.

∆h can be decomposed into contributions of ∆; and ∆< (eq. (6)). ∆; is known, as Δ; = which has been derived by fitting () (Table 1). We now verify if ∆h and ∆; derived with different approaches are consistent. Using values of ∆; as constants, ∆h() is linearly fitted with eq. (6) (Figure 11). Although data scatterings of ∆h are observed, the fitted lines locate in the range of the data. It implies ∆h derived with the transition state approach is probably reasonable. Through the linear fitting, ∆< is derived (Table 1). Positive ∆< implies the transition state is a more disordered state, but the absolute value of ∆< is with doubt @

due to data uncertainty. As = +# ,./0 2=/5 (eq. (7)), with derived by fitting A

() (Table 1), ./ is achieved and also shown in Table 1. ./ is of the order 10@ s-1, obviously smaller than the vibrational frequency ( 10@# s-1) characterizing translational motion of water (Section S7 in Supporting Information). ./ is approximately the vibrational frequency around the equilibrium state but in the


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direction of the reaction path. Generally, ./ is of the order of the Debye frequency of the lattice (10@# to 10@N s-1),40 the same as that of the frequency characterizing water translation in interlayer galleries. For example, the attempt frequency for He diffusion in olivine is of the order 10@# s-1.82 However, unlike atomic diffusion in lattice, a jump of a water molecule is a collective process consisting of translation of a water molecule and reorientation of an OH group, as shown above. Thus, the vibration in the direction of the reaction path should be a collective motion of water and OH groups. This explains the low order of ./ disclosed here.

Figure 11. Activation Helmoholtz free energy ∆h as functions of temperature for m = 0.78 and 1.44. ∆h are fitted with linear functions (solid lines).

4. CONCLUDING REMARKS Molecular dynamics simulations have been performed to study structure and dynamics

dependences

on

temperature

of

water

intercalated

in

LDHs

(Mg2Al(OH)6Cl•mH2O). Two hydration states (m = 0.78 and 1.44) have been investigated. In the lower hydration state, at ambient temperature, a water molecule generally accepts two HBs from two opposite OH groups, exhibiting ice-like ordered



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

structure. In the higher hydration state, it is characterized with a better interconnection between interlayer species, but less HBs accepted from OH groups, and more disordered structure. Irrespective of water content, as temperature increases, water becomes less bound by HBs, more disordered, and more uniformly distributed in interlayer galleries. Water with more disordered structure at higher temperatures or in the higher hydration state is in favor of dehydration energetically. Dehydration enthalpy ∆U is smaller for the system in the higher hydration state. In the temperature range studied here (300 to 430 K), more than 10 kJ/mol decrement in ∆U as temperature increases is observed. This result is at odds with that derived from ab initio calculations (less than 1.5 kJ/mol from 298 to 548 K), which did not take structure variation with temperature into account explicitly.78 This study discloses enthalpy variation should play a more important role in dehydration than previously thought. Although water distribution becomes more uniform with increasing temperature, it still shows the obvious preference for being fixed in OH sites. Water diffuses through jumping between OH sites, irrespective of temperature or water content. A jump is a collective process, consisting of translation of a water molecule from a stable site into a gap, and reorientation of an OH group in a neighbor site to donate a HB to the water molecule. This collective behavior is reflected in the attempt frequency, which is much lower than the frequency characterizing the translational vibrational motion of water. The activation energy consists of contributions of water translation and reorientation of an OH group, in which the latter plays a much more important role.


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The collective behavior explains the rare jump rate of water in interlayer galleries. The hopping diffusion of intercalated water approximately exhibits an Arrhenius dependence on temperature with activation energy close to that for protonic conduction,45 implying possible relationship between diffusion and proton transfer. A water molecule may achieve a proton from an OH site, and transport it through hopping between neighboring sites. It is a similar mechanism as protonic conduction in polymer channels.81 The verification of this suggestion needs further investigations.

ACKNOWLEDGEMENTS This work was financially supported by Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS) (QYZDJ-SSW-DQC023-4), and National Natural Science Foundation of China (41602034). We are grateful to the National Supercomputer Center in Guangzhou for using the high performance computing facility.

ASSOCIATED CONTENT Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org: Analysis on hydrogen bond parameters; more analyses on structure of intercalated water; analysis on transition of water between different hydrogen-bonded states; discussion on artifacts due to stable state definitions; vibrational frequency of intercalated water; time correlation functions for water hopping between sites.



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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; Tel: +86-20-85290252; Fax: +86-20-85290252. Notes The authors declare no competing financial interest.

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51. Sideris, P. J.; Nielsen, U. G.; Gan, Z.; Grey, C. P. Mg/Al Ordering in Layered Double Hydroxides Revealed by Multinuclear NMR Spectroscopy. Science 2008, 321, 113-117. 52. Cygan, R. T.; Liang, J.-J.; Kalinichev, A. G. Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field. J. Phys. Chem. B 2004, 108, 1255-1266. 53. Berendsen, H. J.; Postma, J. P.; van Gunsteren, W. F.; Hermans, J. Interaction Models for Water in Relation to Protein Hydration. In Intermolecular forces, Springer: 1981; pp 331-342. 54. Wang, J.; Kalinichev, A. G.; Kirkpatrick, R. J. Effects of Substrate Structure and Composition on the Structure, Dynamics, and Energetics of Water at Mineral Surfaces: A Molecular Dynamics Modeling Study. Geochim. Cosmochim. Acta 2006, 70, 562-582. 55. Jorgensen, W. L.; Jenson, C. Temperature Dependence of TIP3P, SPC, and TIP4P Water from NPT Monte Carlo Simulations: Seeking Temperatures of Maximum Density. J. Comput. Chem. 1998, 19, 1179-1186. 56. Mizan, T. I.; Savage, P. E.; Ziff, R. M. Molecular Dynamics of Supercritical Water Using a Flexible SPC Model. J. Phys. Chem. 1994, 98, 13067-13076. 57. Kirkpatrick, R. J.; Kalinichev, A. G.; Bowers, G. M.; Yazaydin, A. Ö.; Krishnan, M.; Saharay, M.; Morrow, C. P. NMR and Computational Molecular Modeling Studies of Mineral Surfaces and Interlayer Galleries: A Review. Am. Mineral. 2015, 100, 1341-1354. 58. Hockney, R. W.; Eastwood, J. W. Computer Simulation Using Particles. CRC Press: 1988. 59. Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1-19. 60. Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1695. 61. Nosé, S. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Mol. Phys. 1984, 52, 255-268.



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62. Nosé, S.; Klein, M. Constant Pressure Molecular Dynamics for Molecular Systems. Mol. Phys. 1983, 50, 1055-1076. 63. Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182-7190. 64. Vineyard, G. H. Frequency Factors and Isotope Effects in Solid State Rate Processes. J. Phys. Chem. Solids 1957, 3, 121-127. 65. Laage, D.; Hynes, J. T. A Molecular Jump Mechanism of Water Reorientation. Science 2006, 311, 832-835. 66. Laage, D.; Hynes, J. T. On the Molecular Mechanism of Water Reorientation. J. Phys. Chem. B 2008, 112, 14230-14242. 67. Chau, P.-L.; Hardwick, A. A New Order Parameter for Tetrahedral Configurations. Mol. Phys. 1998, 93, 511-518. 68. Alabarse, F.; Haines, J.; Cambon, O.; Levelut, C.; Bourgogne, D.; Haidoux, A.; Granier, D.; Coasne, B. Freezing of Water Confined at the Nanoscale. Phys. Rev. Lett. 2012, 109, 035701. 69. Wang, J.; Kalinichev, A. G.; Kirkpatrick, R. J. Molecular Modeling of Water Structure in Nano-Pores between Brucite (001) Surfaces. Geochim. Cosmochim. Acta 2004, 68, 3351-3365. 70. Zangi, R. Water Confined to a Slab Geometry: A Review of Recent Computer Simulation Studies. J. Phys.: Condens. Matter 2004, 16, S5371. 71. Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Effect of Pressure on the Phase Behavior and Structure of Water Confined between Nanoscale Hydrophobic and Hydrophilic Plates. Phys. Rev. E 2006, 73, 041604. 72. Hassanali, A.; Giberti, F.; Cuny, J.; Kühne, T. D.; Parrinello, M. Proton Transfer through the Water Gossamer. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 13723-13728. 73. Xu, Z. P.; Zeng, H. C. Decomposition Pathways of Hydrotalcite-like Compounds Mg1-xAlx(OH)2(NO3)x·nH2O as a Continuous Function of Nitrate Anions. Chem. Mater. 2001, 13, 4564-4572. 74. Zhang, J.; Xu, Y. F.; Qian, G.; Xu, Z. P.; Chen, C.; Liu, Q. Reinvestigation of Dehydration and Dehydroxylation of Hydrotalcite-Like Compounds through


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TOC Graphic


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Figure 1. (a) Schematic structure of a water molecule intercalated in LDHs. It locates in an OH site accepting HBs from two opposite OH groups. (b) Schematic jumping trajectory of an intercalated water molecule. (c) The reaction of a water molecule jumping from one OH site to another. 76x102mm (300 x 300 DPI)



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Figure 2. (a) Number of HBs per intercalated water molecule accepts from OH groups as a function of temperature for m = 0.78. (b) The same as (a) except m = 1.44. (c) Probabilities of different types of intercalated water molecules as functions of temperature for m = 0.78. (d) The same as (c) except m = 1.44. 161x137mm (300 x 300 DPI)


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Figure 3. Number of HBs per intercalated water molecule forms with Cl- ions or other water molecules as a function of temperature. 76x63mm (300 x 300 DPI)



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Figure 4. Tetrahedral order parameter Q of water as a function of temperature. Q of liquid water is denoted by a broken line. 226x180mm (300 x 300 DPI)


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Figure 5. Two-dimensional RDF g(r) of water molecules surrounding an OH group on the x-y plane for m = 0.78 (a) and 1.44 (b) at different temperatures. Insets show ∆g (the difference between the maximum and minimum values of g(r)) as functions of temperature. 76x102mm (300 x 300 DPI)



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Figure 6. Dehydration enthalpy as a function of temperature for m = 0.78 and 1.44. 222x181mm (300 x 300 DPI)


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Figure 7. Diffusion coefficients derived by fitting mean square displacements, and calculated with jump models utilizing different definitions of stable states, as functions of temperature. Data are fitted with eq. (1). 76x94mm (300 x 300 DPI)



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Figure 8. Schematic view of a water molecule hopping from Site a to Site b. 82x50mm (300 x 300 DPI)


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Figure 9. Variations of Ra, Rb, NHBa, and NHBb, while a water molecule jumps from one OH site to another, for m = 0.78 (a, c) and 1.44 (b, d) at 300 and 400 K. 104x100mm (300 x 300 DPI)



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Figure 10. Two-dimensional RDF of Ow and Ho atoms around a central Oh atom for m = 0.78 at 400 K. A(r) calculated from the equation A(r) = -kT ln (g(r)) are also shown in the figure. 76x58mm (300 x 300 DPI)


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Figure 11. Activation Helmoholtz free energy ∆A as functions of temperature for m = 0.78 and 1.44. ∆A are fitted with linear functions (solid lines). 76x64mm (300 x 300 DPI)



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TOC Graphic 75x36mm (300 x 300 DPI)


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Temperature-Dependent Structure and Dynamics of Water

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