Interlaminar Anionic Transport in Layered Double Hydroxides

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Interlaminar Anionic Transport in Layered Double Hydroxides: Estimation of Diffusion Coefficients Guillermo Nieto-Malagón, Cristina Cuautli, and Joel Ireta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10384 • Publication Date (Web): 13 Dec 2017 Downloaded from http://pubs.acs.org on December 25, 2017

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The Journal of Physical Chemistry

Interlaminar Anionic Transport in Layered Double Hydroxides: Estimation of Diffusion Coefficients Guillermo Nieto-Malagón,† Cristina Cuautli,†,‡ and Joel Ireta∗,† †Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, Ciudad de México 09340, México. ‡Current address: Centro de Investigaciones Químicas, Universidad Autónoma del Estado de Morelos, México. E-mail: [email protected]

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Abstract Layered double hydroxides (LDHs) are materials with capacity of conducting anions. To get insight into the mechanisms controlling LDH intrinsic anionic transport properties, it is investigated the effect of composition on the anion diffusion coefficients in LDHs containing Mg or Zn as divalent cation, Al or Ga as trivalent cation and OH− or Cl− as interlaminar anion. Diffusion coefficients are estimated simulating diffusion with a kinetic monte carlo algorithm on a potential energy surface (PES) associated to the dry interlayer anion. The PES is calculated using density functional theory. We find that at room temperature, diffusion coefficients increase as the difference in electronegativity between metal atoms composing the layers grows. However, at higher temperatures, systems with narrower PES basins become the ones with larger diffusion coefficients, owing to shorter residence times prior hopping to a neighbor basin. We also find that Cl− has smaller diffusion coefficient than OH− owing to the less capacity of the former to form hydrogen bonds than the latter. These results illustrate the connection between the LDH atomic composition and its properties, knowledge that is desirable for rationally design LDHs with improved properties.

Introduction Two-dimensional materials like the layered double hydroxides (LDHs) have attracted increasing interest in fields like catalysis, semiconductors and energy storage, owing to the facile tunability of their composition, structure and morphology. 1 Several composite materials based on LDHs have already been rationally designed and employed in supercapacitors, batteries and electrocatalysis for enhancing performance. 1 LDH compounds are formed by stacked two-dimensional positively charged layers linked by interlayer charge-compensating anions (Fig.1). Its general formula is [Dx Ty (OH)2(x+y) ]y+ (An− )y/n · mH2 O, where D and T are the divalent and trivalent metallic cations like Mg2+ and Al3+ , respectively, and An− is an anion of charge n like OH− and Cl− . Physical and chemical characteristics of LDHs are

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Figure 1: Scheme of a layered double hydroxide in which the interlayer charge-compesating anion is the hydroxide ion. Color code, gray H atoms, red O atoms, green divalent metallic cations, blue trivalent metallic cations. modulated varying the nature of layer cations, the interlayer anions, and the relative proportion of D cations respect to the T ones (R = x/y). Some of the LDH applications, like in anion exchange 2,3 supercapacitors and batteries, 1 rely on the ionic conductivity capacity of LDHs. 4 Still little it is know about the mechanism controlling interlayer ionic diffusion in these materials; 5 i. e. how the R proportion and the ions nature modulate diffusion is not fully understood. In this work it is investigated the intrinsic ionic diffusion properties (i. e. without the presence of water) of a series of LDHs. The aim is to advance our understanding on the connection between the LDH composition and its physicochemical properties. Therefore we study the effect of the anion and cations nature on the anion intrinsic diffusion coefficient. For that diffusion coefficients are estimated simulating diffusion with a kinetic monte carlo (KMC) algorithm, on the potential energy surface (PES) associated to the dry interlayer anion (Fig. 1). Density functional theory (DFT) is used for calculating the PES and the energy barriers between minima. Intrinsic diffusion coefficients are estimated for the OH− and Cl− anions in variuos LDHs with D = Mg2+ , Zn2+ and T = Al3+ , Ga3+ in the temperature range from 298 K to 773 K. It is experimentally known that LDHs decompose at temperatures above 473 K, nevertheless we considered the hypothetical case in which the laminar structure of LDHs is preserved beyond that temperature to investigate if diffusion trends, i. e. the ordering of the values of diffusion coefficients, can be altered as the temperature is increased. 3



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The ratio of D respect to T cations is chosen to be R = 3, as it has been observed that anions in LDHs with that composition presents high mobility. 6,7 The OH− and Cl− are chosen because they present different ionic conductivity 8 and anion-exchange capabilities. 9 The formulas per unit cell of the investigated systems are [Mg3 Al(OH)8 ]+ OH− , [Mg3 Al(OH)8 ]+ Cl− , [Mg3 Ga(OH)8 ]+ OH− , [Zn3 Al(OH)8 ]+ OH− and [Zn3 Ga(OH)8 ]+ OH− , thereafter referred as MgAl-OH, MgAl-Cl, MgGa-OH, ZnAl-OH and ZnGa-OH, respectively. KMC is a non-equilibrium method that describes the time evolution of the events of interest, which are previously identified as well as their associated occurrence rates. 10 Each KMC step consists of one randomly determined event, and the time increment of a step is related to the total event occurrence rates. It is found that the ionic diffusion capability of LDHs increases as the difference between the electronegativity of D and T gets larger. Moreover diffusion is also affected by the nature of the anion-layer, i. e. we found that Cl− is significantly slower than OH− owing to its reduced capability for forming hydrogen bonds (hbs). Furthermore it is shown that diffusion is not solely dictated by the high of the transition barriers, diffusion coefficients change about one order of magnitude when the extension of the PES basins is taken into account in the KMC algorithm, which leads to a better agreement between theoretical and experimental diffusion coefficients.

Theory Ionic diffusion is consider to occur as a hopping process from a given PES basin to a neighbor one. In this process ions move through a transition state, that is the point of maximum energy along the minimum energy pathway connecting both basins. According to the transition state theory the probability of a diffusion jump per unit time (hopping rates) is given by: 10,11 Qt e Q

k(Eb , T ) = k0

4

−Eb kB T

,


(1)

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where k0 = 2kB T h−1 is the jump frequency, Q and Qt the partition functions in the initial and transition state, respectively, Eb the energy barrier for crossing along the transition state, T the temperature, and kB and h the Boltzmann and Planck constants, respectively. In many diffusion events the energy associated to vibrational excitations promoting hopping is of the same order of magnitude that the thermal energy, hence kB T h−1 Qt Q−1 ≈ 1013 s−1 (the lattice-gas model of diffusion). For a system with Nions independent ions, and an ion PES in which each basin has Nnei neighbor basins, the total rate of all diffusion events is defined as the addition of all individual rates:

Rtot =

N Nnei ions X X

ki,m (Eb , T ) ,

(2)

i=1 m=1

where ki,m is the hopping rate of the i-th ion jumping towards the m-th neighbor basin. In the KMC algorithm hopping events to happen are selected randomly. For that, random numbers s are drawn (s is a random number uniformly distributed in [0,1]), then the quantity sRtot indicates which of the events listed in a cumulative way (see Fig. 2), is picked up. For each hopping event time (t) is advanced by the amount of:

∆t = −

ln(s) . Rtot

(3)

Next, ki,m and Rtot are recalculated according to the new ion positions and the barriers to be crossed to transit to the new neighbor basins, a new s value is drawn to move ions to the next positions. According to the Einstein-Smoluchowsky equation the mean square displacement (< r(t)2 >) is proportional to the diffusion coeficient (D), to the number of dimensions through which jumping trajectories evolve (d) and to t; i. e.: 12

< r(t)2 >= 2dDt.

5


(4)


Figure 2: Scheme of a table of events used for selecting movements in a kinetic-montecarlo algorithm. From a cumulative list of hopping rates an event is chosen in terms of a random number s and the total rate of all diffusion events Rtot . As ion diffusion in LDHs can be considered to happen in two dimensions, d = 2, hence diffusion coefficients can be estimated as one-fourth of the slope of the graph of < r(t)2 > against t.

Computational methods The PES associated to the interlaminar anion in MgGa-OH, ZnAl-OH and ZnGa-OH with R = 3, is calculated using DFT in its Kohn-Sham formulation and periodic boundary conditions. We have used the Perdew-Burke-Ernzerhof (PBE) approximation to the exchangecorrelation functional, 13 plane waves as basis set and the projector augmented waves method 14 as implemented in the VASP code. 15,16 PBE has been successfully used by several groups to investigate the structure and dynamical properties of LDH materials. 9,17–23 Moreover we use PBE to be able to compare the MgGa-OH, ZnAl-OH and ZnGa-OH PES against those for MgAl-OH and MgAl-Cl, that were already calculated with PBE and reported elsewhere. 24

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Calculations have been performed with a cutoff of 650 eV and a k-point mesh of 3 × 3 × 3 for sampling the first Brillouin zone. LDH models are built with one layer of material per unit cell leading to the so called 1H layer stacking (see e.g Ref. 24). The relative position of trivalent cations respect to divalent ones along the layers is chosen to be the same found for MgAl-OH in our previous work. 24 In that work we had thoroughly investigated cation distribution in MgAl-OH with the R proportion equal to 2, 3 and 3.5. Actually the cation distribution found to minimize the energy in the LDH with R = 2 matched with the one elucidated using nuclear magnetic resonance spectroscopy for that system. 25 The latter give us confidence in the cation distribution used for building the LDH models here investigated. To get the reference bulk geometry and energy for each system, the interlaminar anion is located between the T and D cations along the a-lattice. This anion position is chosen because it was found in a previous work to lead to the lowest bulk energy for the MgAl-OH system. 24 Optimized bulk geometries are obtained fully relaxing all the lattices parameters and all the internal degrees of freedom. The PES is calculated starting from the optimized bulk geometries but locating the anion in interlayer positions equivalent to the ones used for getting the MgAl-OH and MgAl-Cl PES (see Fig. 3 in Ref. 24). These positions are: a) onto the D and T cations, b) in between the D and T, and c) in between hydroxyl groups. At each of these positions hydroxide is oriented such that the hydrogen is in the farthest position respect to the closest T cation. To determine the diffusion coefficients using the KMC method it is considered an independent single anion per unit cell, i.e. Nions = 1 in eq. 2, diffusing following the PES calculated as described above. The latter ensures that basins neighboring the one hosting the anion are always empty. For purposes of the KMC algorithm, PES basins are considered as distributed in an infinite square lattice with lattice points separated a distance equivalent to the average basin separation. Therefore each lattice site has four nearest neighbors; i.e. Nnei = 4 in eq. 2. The basin separation is taken as the distance between the bottom of neighbor basins. The barriers to evolve from one lattice site to the next one, are those

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estimated from the PES calculated here and those reported in Ref. 24.

Results and discussion In Table 1 are listed the optimized crystal lattice parameters of the reference bulk unit cells (see the computational methods section) for the MgAl-OH, MgGa-OH, ZnAl-OH and ZnGaOH systems. Also experimental values for the a-lattice are listed in Table 1. Comparing these theoretical and experimental values we find a very good agreement between them, with differences of 1.5% at most. No further information about the experimental lattice parameters for these systems was found, except for MgAl-OH. A full comparison between the theoretical and experimental MgAl-OH lattice parameters was presented elsewhere. 24 As one should expect, the MgGa-OH, ZnAl-OH and ZnGa-OH lattice parameters vary little with respect to those for MgAl-OH, owing to the similarity in size of divalent and trivalent cations in MgAl-OH with respect to the ones composing the former LDHs. Therefore unit cells for these LDHs are similar, with differences of 2% in lengths and 1% in angles, at most. Yet the PES associated to the anion in MgGa-OH presents significant differences respect to those for the anions in ZnAl-OH and ZnGa-OH (Fig. 3), but looks like the one for the anion in MgAl-OH (see Fig. 5 in Ref 24). These results indicate that divalent cations have Table 1: Optimized lattice parameters in Å and degrees a

a exp. 6.07b 6.17c 6.18d

b

c

α

β

γ

MgAl-OH 6.16a 6.19a 6.88 80.8 90.0 119.8 MgGa-OH 6.24 6.26 6.84 80.4 90.0 119.8 ZnAl-OH 6.20 6.27 6.71 79.7 90.0 119.5 ZnGa-OH 6.26 6.33 6.73 79.6 90.0 119.5 a Values estimated from results presented in Ref. 24. b Value estimated from results presented in Ref. 26. c Value estimated from results presented in Ref. 27. d Value estimated from results presented in Ref. 28. larger influence than trivalent ones on the PES shape; e. g. the width of basins is similar in ZnAl-OH and ZnGa-OH PES, but shorter than the width of basins in MgGa-OH and 8


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Figure 3: Potential energy surface (PES), in kcal mol−1 , associated to the interlaminar anion in MgGa-OH, ZnAl-OH and ZnGa-OH. The size of the depicted PES corresponds to that of a 3×3 unit cell. The zero energy reference is taken to be the lowest energy conformation for each case MgAl-OH PES. Further PES differences at basin centers, which are located on top of the trivalent cations, are noticeable. Energy in these positions is between 2.5 kcal mol−1 and 5 kcal mol−1 higher than the lowest energy conformation in ZnAl-OH and ZnGa-OH LDHs, however is almost degenerate in MgGa-OH and MgAl-OH LDHs (see Fig. 3 and Fig. 5 in Ref 24). Changing OH− by Cl− also affects significantly the PES, likely due to a less number of hbs formed by Cl− than by OH− , particularly at the top of the energetic barriers, as it is discussed elsewhere. 24 To estimate diffusion coefficients for OH− and Cl− along the interlaminar region in MgAlOH, MgAl-Cl, MgGa-OH, ZnAl-OH and ZnGa-OH, we determine the lowest energy barriers along the corresponding PES (Fig. 3 and Fig. 5 of Ref. 24), for escaping from one basin to the next one. These barriers are listed in Table 2. According to these results MgGa-OH presents the lowest barriers for jumping from a basin to another along any of the four possible escaping paths. Therefore one can anticipate that anions in this LDH will present the largest diffusion coefficient. In Table 3 are listed the diffusion coefficients at different temperatures estimated using the KMC procedure described above, and the lattice-gas model of diffusion.

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It is found that MgGa-OH is the LDH with the largest diffusion coefficient, as expected, at Table 2: Energy barriers, in kcal mol−1 , to escape from a basina path 1 path 2 path 3 path 4 MgAl-OH 2.1 3.0 3.9 4.8 b MgAl-Cl 4.8 6.0 6.9 9.9 MgGa-OH 1.2 2.1 3.0 3.9 ZnAl-OH 4.8 6.0 6.9 7.8 ZnGa-OH 3.0 3.9 4.8 6.0 a Path 1 goes along the a-lattice vector direction, path 2 goes along the (−a)-lattice vector direction, path 3 goes along the b-lattice vector direction, path 4 goes along the (−b)-lattice vector direction. b Values estimated from the potential energy surfaces presented in Ref. 24. b

Table 3: Diffusion coefficients estimated at different temperatures and considering the lattice-gas model D ×10−8 (m2 s−1 ) T (K) MgAl-OH MgGa-OH MgAl-Cl ZnAl-OH 298 2.44 12.27 0.02 0.01 373 7.11 25.05 0.14 0.12 473 18.38 49.61 0.90 0.82 773 90.29 166.60 13.35 14.03

ZnGa-OH 0.44 2.12 6.90 49.62

any temperature. Also it is found comparable diffusion coefficients for anions in MgAl-Cl and ZnAl-OH, in concordance with the similar energy barriers found for these LDHs. The latter two LDHs also present the largest energy barriers for jumping from one basin to another along any of the four escaping paths. Consequently we get the smallest diffusion coefficients at any temperature for these LDHs (Table 3). Typical diffusion coefficients in an aqueous solution are in the range of 10−10 to 10−9 m2 s−1 at room temperature; e. g. the experimental diffusion coefficient of OH− at infinite dilution is 5.03×10−9 m2 s−1 at 298 K. 29 Our estimated OH− diffusion coefficients in MgAl-OH and MgGa-OH at 298 K are one or two orders of magnitude lager than the experimental value for OH− at infinite aqueous dilution. Further, one should expect smaller diffusion coefficients for especies confined in the interlayer space than in the bulk of a liquid, e.g. it has been experimentally determined that the diffusion coefficient of H2 into the two-dimesional pores 10


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of sparingly hydrated Ca-laponite clay, is one order of magnitude smaller than in bulk liquid H2 . 30 Therefore improvements in our methodology must be made in order to predict reliable diffusion coefficients. One can go beyond the lattice-gas model considering that a particle can translate and/or rotate in a lattice site before it attempts a jump. That will increase the residence time in a lattice point, hence slow diffusion. Following the latter and considering that the bottom of basins in the investigated PES is quite flat and wide, we recalculate the hopping rates taking into account the translational motion of the anion inside the basin. For that it is assumed free motion along a two-dimensional space of square shape. Thus hopping rates are given by: 31 1 k(Eb , T ) = 2L

k0 πm

12

e

−Eb kB T

,

(5)

where L is the distance that the anion translates from one side of the square to the opposite one, and m is the anion mass. In Table 4 are listed the diffusion coefficients at different temperatures estimated using the KMC procedure, and the recalculated hopping rates (eq. 5) that account for translational motion. The L value in eq. 5 is approximated as the width of the bottom of the basin (the blue region), measured between the most distant escaping points. To that distance it is subtracted the diameter of the green/red spot in the center of the basin for the case of ZnAl-OH and ZnGa-OH. Diffusion coefficients thus estimated are one order of magnitude, and in some cases even two orders of magnitude, smaller than those listed in Table 3. These results indicate that accounting for translational motion inside basins leads to more realistic diffusion coefficients. Values thus obtained are within the range of those observed for diffusion in aqueous solution. Certainly including solvent in the calculation of the PES will alter the shape of basins and barrier heights, consequently diffusion coefficients. Still diffusion coefficients listed in Table 4 clearly illustrate the influence of layer composition and anion nature on the LDH transport properties as discussed below. Considering the rotational motion of the anion inside the basin might also alter hopping rates, hence diffusion coefficients. However one should expect less influence of rotational motion on diffusion coefficient trends than translational motion; the former motion likely 11



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Table 4: Diffusion coefficients estimated at different temperatures and considering translational motion inside a basina D ×10−9 (m2 s−1 ) T (K) MgAl-OH MgGa-OH MgAl-Cl ZnAl-OH ZnGa-OH 298 1.1 5.8 0.03 0.02 0.80 373 3.0 10.5 0.16 0.20 3.60 473 6.9 18.6 0.90 1.20 10.40 773 26.5 48.9 10.48 16.50 58.50 a For calculating the hopping rates used in the kinetic montecarlo estimation of the diffusion coefficients, the next values for the L parameter (see eq. 5) were used: 2.74, 2.73, 0.68, 0.66 and 1.03 in Å for MgAl-OH, MgGa-OH, ZnAl-OH, ZnGa-OH and MgAl-Cl, respectively. contribute equally to all systems with the same anion (i.e. in our case all but one), while the latter one differ in each case due to differences in the width of basins. Influence of rotations and solvent on diffusion coefficients are topics out of the scope of this work that nevertheless deserve further investigations. Diffusion coefficients usually obey an exponential Arrhenius relation:

D = D0 e

−Ediff RT

,

(6)

where D0 is a pre-exponential factor, R the ideal gas constant and Ediff an activation energy of diffusion. In Fig. 4 it is shown that diffusion coefficients listed in Tables 3 and 4 fit to an Arrhenius exponential relation. In Table 5 are listed the corresponding values of D0 and Ediff . Fig. 4 also reveals that including translational motion in the calculation of hopping rates affects diffusion coefficient trends; e. g. the ZnGa-OH diffusion coefficient is smaller than those for MgAl-OH and MgGa-OH, as it happens if translational motions is neglected, however at ∼ 350 K it gets larger than the diffusion coefficient for MgAl-OH (see inset in Fig. 4), and around 650 K becomes the largest diffusion coefficient, even though the ZnGa-OH activation energy of diffusion is two times larger than the smallest one (Table 5). The latter is consequence of the pre-exponential factor of ZnGa-OH, which is four times larger than that of MgGa-OH, the system with the smallest activation energy of diffusion (Table 5). Without considering translational motion the pre-exponential factor of ZnGa-OH 12


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is only 1.2 times larger than that of MgGa-OH. Clearly inclusion of translational motion affects primarily pre-exponential factors reducing its values more than ten times, likely due

Figure 4: Change of diffusion coefficients with respect to temperature. Dots stands for the diffusion coefficient values listed in Table 3 (upper panel) and in Table 4 (lower panel). Solid lines stand for the exponential Arrhenius relation (eq. 6) with the D0 and Ediff values listed in Table 5. Color code: black MgAl-OH, blue MgGa-OH, green MgAl-Cl, red ZnAl-OH, cyan ZnGa-OH. Inset shows the amplification of the lower left part of the lower panel graph. to the increment in time of residence in a lattice point prior hopping. Certainly LDHs will decompose before reaching the temperature of 650 K, yet these results serve as an illustration of the intimate connection between diffusion and the underlying potentials; i.e. whereas the LDH structure do not change significantly the full shape of the PES, not only the energy barriers, will increasingly influence diffusion as temperature is augmented.

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Table 5: Pre-exponential factors and activation energies of diffusion D0 × 10−7 (m2 s−1 ) a Ediff (kcal mol−1 ) a MgAl-OH 81.24 1.87 3.48 3.06 MgGa-OH 79.63 1.77 2.50 2.06 MgAl-Cl 75.75 3.96 6.29 5.68 ZnAl-OH 133.94 11.33 6.96 6.45 ZnGa-OH 91.60 8.48 4.53 4.10 a Left entry, values obtained fitting diffusion coefficients listed in Table 3 to a exponential Arrhenius relation (eq. 6). Right entry, values obtained fitting diffusion coefficients listed in Table 4 to a exponential Arrhenius relation (eq. 6). Under experimental conditions LDHs contain interlaminar water molecules. These water molecules will certainly alter diffusion, moreover it is hard to estimate whether its presence will slow down or speed up diffusion without explicitly taking into account aqueous solvent in the models. Yet one may expect solvent influences the same way diffusion in all the investigate LHDs as result of similar interlaminar spacing; i. e. the amount of water molecules that could harbor each of them should be similar, hence its influence on diffusion. Therefore Investigating intrinsic diffusion coefficients, i.e. in the absence of water, help us to elucidate the influence of layer composition on the LDH transport properties; e. g. comparing LDHs with the same interlaminar anion, and considering that Pauling electronegativity values for Mg, Zn, Al and Ga are 1.31, 1.65, 1.61 and 1.81 in Pauling units, 32 respectively, it is noteworthy that at room temperature LDH diffusion coefficients increase as the difference in the electronegativity between the metallic atoms grows. The latter holds even comparing values from other electronegativity scales, for example the Allen electronegativity values that are 1.29, 1.59, 1.61 and 1.76 in Pauling units for Mg, Zn, Al and Ga, 33 respectively. Likely these differences in electronegativity influence hydrogen bonding in the material, particularly the hbs between hydroxyl groups attached to the trivalent cation and the anion. That could be the origen of a lower layer-anion interaction energy on Al and Ga in ZnAl-OH and ZnGaOH, respectively, noticeable in the corresponding PES (see Fig. 3). Also it is worth noting that the Cl− diffusion coefficient is around two orders of magnitude smaller than that of OH− , e.g. compare the diffusion coefficients for MgAl-OH and MgAl-Cl in Table 4, likely 14


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the latter is connected to the observation that Cl− forms less hbs than OH− , particularly at the transition regions where the OH− forms four hbs and Cl− only two. 24 The difference in the diffusion coefficients of Cl− and OH− may be the reason why the former anion is harder to exchange than latter in the LDH anion-exchange experiments. 9

Conclusions In this work we have investigated the anion transport properties of LDH materials using DFT and a KMC method to estimate diffusion coefficients for the interlaminar anion. In conclusion our results indicate that the intrinsic anion transport ability (i.e. in absence of water) of LDHs with OH− as interlaminar anion, correlates with the difference in the electronegativity between the metal atoms forming the LDH layers, the greater the electronegativity difference the larger the diffusion coefficient at room temperature. Thus diffusion coefficients increase in the next order: ZnAl-OH, ZnGa-OH, MgAl-OH and MgGa-OH at room temperature. At higher temperatures ZnGa-OH becomes the system with the largest diffusion coefficient owing to narrow PES basins, which reduces the residence time of the particle in lattice point prior hopping to the next one. These results further our knowledge of the physicochemical principles underlying the LDH properties, which may help to design new LDHs with improved properties.

Acknowledgement G.N acknowledges CONACYT for a posdoctoral scholarship. Authors gratefully acknowledge the computing time granted by LANCAD and CONACYT on the supercomputer Yoltla at the LSVP at UAM-Iztapalapa.

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References (1) Shao, M.; Zhang, R.; Li, Z.; Wei, M.; Evans, D. G.; Duan, X. Layered double hydroxides toward electrochemical energy storage and conversion: design, synthesis and applications. Chem. Commun. 2015, 51, 15880–15893. (2) Israeli, Y.; Taviot-Gueho, T.; Beese, J.; Morel, J.; Morel-Desrosiers, N. Thermodynamics of anion exchange on a chloride-intercalated zinc-aluminum layered double hydroxide: a microcalorimetric study. J. Chem. Soc. Dalton 2000, 791–796. (3) Miyata, S. Anion-exchange properties of hydrotalcite-like compounds. Clay Clay Miner. 1983, 31, 305–311. (4) Jung, H.; Ohashi, H.; Anilkumar, G. M.; Zhang, P.; Yamaguchi, T. Zn2+ substitution effects in layered double hydroxide (Mg(1−x) Znx )2 Al: textural properties, water content and ionic conductivity. J. Mater. Chem. A 2013, 1, 13348–13356. (5) Miyazaki, K.; Asada, Y.; Fukutsuka, T.; Abe, T.; Bendersky, L. A. Structural insights into ion conduction of layered double hydroxides with various proportions of trivalent cations. J. Mater. Chem. A 2013, 1, 14569–14576. (6) Kim, H.-S.; Yamazaki, Y.; Kim, J.-D.; Kudo, T.; Honma, I. High ionic conductivity of Mg-Al layered double hydroxides at intermediate temperature (100-200 o C) under saturated humidity condition (100% RH). Solid State Ion. 2010, 181, 883–888. (7) Tadanaga, K.; Furukawa, Y.; Hayashi, A.; Tatsumisago, M. Effect of Mg/Al ratio on hydroxide ion conductivity for Mg-Al layered double hydroxide and application to direct ethanol fuel cells. J. Electrochem. Soc. 2012, 159, B368–B370. (8) Furukawa, Y.; Tadanaga, K.; Hayashi, A.; Tatsumisago, M. Evaluation of ionic conductivity for Mg-Al layered double hydroxide intercalated with inorganic anions. Solid State Ion. 2011, 192, 185–187. 16


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Page 17 of 20 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


(9) Costa, D. G.; Rocha, A. B.; Souza, W. F.; Chiaro, S. S. X.; Leitao, A. A. Comparative structural, thermodynamic and electronic analyses of Zn-Al-An− hydrotalcite-like − compounds (An− Cl− , F− , Br− , OH− , CO2− 3 or NO3 ): an ab initio study. Appl. Clay

Sci. 2012, 56, 16–22. (10) Fichthorn, K.; Weinberg, W. Theoretical foundations of dynamic monte-carlo simulations. J. Chem. Phys. 1991, 95, 1090–1096. (11) Eyring, H. The activated complex in chemical reactions. J. Chem. Phys. 1935, 3, 107– 115. (12) Chandrasekhar, S. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 1943, 15, 0001–0089. (13) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (14) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979. (15) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186. (16) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 1999, 59, 1758–1775. (17) Xu, Q.; Ni, Z.-m.; Mao, J.-h. First principles study of microscopic structures and layeranion interactions in layered double hydroxides intercalated various univalent anions. J. Mol. Struc.-theochem 2009, 915, 122–131. (18) Tavares, S. R.; Vaiss, V. S.; Wypych, F.; Leitao, A. A. Similarities between zinc hydroxide chloride nonohydrate and its dehydrated form: a theoretical study of their structures and anionic exchange properties. J. Phys. Chem. C 2014, 118, 19106–19113.

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(19) Galvao, T. L. P.; Neves, C. S.; Caetano, A. P. F.; Maia, F.; Mata, D.; Malheiro, E.; Ferreira, M. J.; Bastos, A. C.; Salak, A. N.; Gomes, J. R. B. et al. Control of crystallite and particle size in the synthesis of layered double hydroxides: macromolecular insights and a complementary modeling tool. J. Colloid Interface Sci. 2016, 468, 86–94. (20) Yan, H.; Wei, M.; Ma, J.; Evans, D. G.; Duan, X. Plane-wave density functional theory study on the structural and energetic properties of cation-disordered Mg-Al layered double hydroxides. J. Phys. Chem. A 2010, 114, 7369–7376. (21) Trave, A.; Selloni, A.; Goursot, A.; Tichit, D.; Weber, J. First principles study of the structure and chemistry of Mg-based hydrotalcite-like anionic clays. J. Phys. Chem. B 2002, 106, 12291–12296. (22) Fraccarollo, A.; Cossi, M.; Marchese, L. DFT simulation of Mg/Al hydrotalcite with different intercalated anions: periodic structure and solvating effects on the iodide/triiodide redox couple. Chem. Phys. Lett. 2010, 494, 274–278. (23) Costa, D. G.; Rocha, A. B.; Diniz, R.; Souza, W. F.; Chiaro, S. S. X.; Leitao, A. A. Structural model proposition and thermodynamic and vibrational analysis of hydrotalcite-like compounds by DFT calculations. J. Phys. Chem. C 2010, 114, 14133–14140. (24) Cuautli, C.; Ireta, J. Theoretical investigations on the layer-anion interaction in MgAl layered double hydroxides: influence of the anion nature and layer composition. J. Chem. Phys. 2015, 142 . (25) 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. (26) Valente, J. S.; Pfeiffer, H.; Lima, E.; Prince, J.; Flores, J. Cyanoethylation of alcohols by activated Mg-Al layered double hydroxides: influence of rehydration conditions and Mg/Al molar ratio on Bronsted basicity. J. Catal 2011, 279, 196–204. 18


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(27) Manohara, G. V.; Kamath, P. V. Synthesis and structure refinement of layered double hydroxides of Co, Mg and Ni with Ga. Bull. Mater. Sci. 2010, 33, 325–331. (28) Evans, D.; Slade, R. In Layered double hydroxides; Duan, X and Evans, DG„ Ed.; Struc. Bond.; 2006; Vol. 119; pp 1–87. (29) Atkins, P.; de Paula, J. Physical chemistry, 9th ed.; W. H. Freeman and Company: 41 Madison Avenue, New York, 2010; p 940. (30) Edge, J. S.; Skipper, N. T.; Fernandez-Alonso, F.; Lovell, A.; Srinivas, G.; Bennington, S. M.; Sakai, V. G.; Youngs, T. G. A. Structure and dynamics of molecular hydrogen in the interlayer pores of a swelling 2:1 clay by neutron scattering. J. Phys. Chem. C 2014, 118, 25740–25747. (31) Jansen, A. P. J. An introduction to kinetic monte carlo simulation of surface reactions; Springer-Verlag: Berlin, Heidelberg, 2012; p 84. (32) Allred, A. Electronegativity values from thermochemical data. J. Inorg. Nucl. Chem. 1961, 17, 215–221. (33) Mann, J.; Meek, T.; Allen, L. Configuration energies of the main group elements. J. Am. Chem. Soc. 2000, 122, 2780–2783.

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Interlaminar Anionic Transport in Layered Double Hydroxides

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