Molecular Dynamics Simulations of Nitrate/MgO Interfaces and Understanding Metastability of Thermochemical Materials.

We explore the role of molten nitrate interfaces on MgO surface treatment for improving the reversibility of thermochemical energy storage via sorption and desorption of water or CO2. Our molecular dynamics simulations focus on melts of LiNO3, NaNO3, KNO3, and the triple eutectic mixture Li0.38Na0.18K0.44NO3 on the surface of MgO to provide atomic scale details of adsorbed layers and to rationalize interface energies. On this basis, a thermodynamic model is elaborated to characterize the effect of nitrate melts on the dehydration of Mg(OH)2 and to quantitatively explain the difference in dehydration temperatures of intact and LiNO3-doped Mg(OH)2.

Introduction

Efficient and sustainable energy systems are unimaginable without means of reliable and inexpensive energy storage.[1] Harnessing solar power[2] or utilization of industrial waste heat on a large scale[3−5] calls for scalable thermal energy storage at 200–600 °C to harmonize energy production and consumption in space and time.

Currently, the use of reversible chemical reactions for thermal energy storage—also known as thermochemical energy storage (TCES)—is attracting attention due to potentially high heat storage density and versatility of chemical heat batteries.[6−8] Advent of this technology in the past decade incites fundamental research on materials reactivity with the goal to enhance the kinetic performance.[9]

One of the promising materials for TCES is MgO which can reversibly absorb water yielding magnesium hydroxide:

The MgO-based thermal batteries are charged by dehydration of Mg(OH)2 consuming heat (Figure ). During this process, the material transforms to MgO while releasing H2O. The consumed heat is hence stored in the form of the lattice energy of MgO. When needed, the system may be discharged in a controlled manner triggering heat release by the addition of water vapor, hence hydrating back to the “discharged” state. A similar cycle can be realized with CO2 instead of H2O and MgCO3 instead of Mg(OH)2, respectively, by the help of sophisticated catalysts.[10]

Figure 1

Operation principle of a thermochemical heat battery based on the transformation of Mg(OH)2 to MgO for energy storage (charging) and its reverse reaction for energy release (discharging), respectively. Charging driven by solar heat (upper left arrow) is accompanied by the decomposition of Mg(OH)2 with simultaneous release of water (upper right arrow). Discharging driven by absorption of water (lower right arrow) is accompanied by emission of useful heat (lower left arrow).

One of the challenges hindering the industrial application of this scheme is the low reactivity in both charging and release processes. This leads to extended metastability zones such that in order to decompose Mg(OH)2 or MgCO3 one has to overheat[17] or undercool[11] considerably (Figure ).

Figure 2

Phase diagram illustrating the equilibrium (black line) and the metastable behavior (red dashed lines) of the Mg(OH)2–MgO transformation based on a literature survey.[11−16]

Such metastable behavior is caused by the high energy barrier of the underlying structural transformations. To boost these processes, ongoing efforts are dedicated to the explorative search for suitable catalysts. Along this line, some inorganic salts (nitrates, chlorides, and acetates of Li, Na, and K) were experimentally shown to be promising for the catalysis of de- and rehydration Mg(OH)2, as well as carbonation of MgO.[11,18−20] Indeed, dramatic differences in the reactivity of MgO with various nitrates still remain to be fully understood.[16,18,21] The fastest progress in understanding is achieved for carbonation of nitrate-doped MgCO3, for which numerous combinations of nitrate dopants were studied,[10,22] a dissolution/crystallization mechanism was established,[23] and the crucial role of the interface was found.[24]

The pronounced liquid/solid interface plays an important role in these systems.[22] It was hypothesized that the reactivity enhancement could be explained quantitatively by accounting for the interfacial energy of molten salt/solid MgO in reaction thermodynamics.[18,25] While the MD simulations for nitrates on MgO were performed,[26] it is yet unclear how the nitrate/MgO interfaces looks like, what are the interface energies, and how they change with composition of the nitrate melt, especially for the most relevant nitrates such as LiNO3, or eutectic mixtures. This knowledge is crucial for the in-depth understanding of the metastability in nitrate/MgO with respect to charging and discharging reactions (Figure ). The molecular dynamics (MD) modeling could clarify these questions. While the ab initio MD is able to capture subtle features of the interfaces[27] and rearrangement of chemical bonds, its high computational cost and sensibility to the basis[28] make this option less attractive in comparison with traditional MD with experimentally verified interatomic potentials.

In the present work, we use molecular dynamics simulations of nitrate/MgO interfaces for three nitrates (LiNO3, NaNO3, and KNO3) and the triple nitrate eutectic mixture to provide structural insights into the adsorbed layers, calculate adhesion energies, and relate them to the dehydration/hydration temperature for one of the most promising systems with the smallest metastable zone, namely, LiNO3/Mg(OH)2.[29,30]

Methods

Molecular mechanics models were adopted from the literature with a focus on interaction potentials relying on formal charges for the cations, such that the full range of metal ion mixtures may be addressed. The interaction potentials of MgO (Mg–Mg, Mg–O, and O–O) were adopted from the Lewis–Catlow model with formal charges[31] with parameters from ref (32). The model shows good results for the mechanical properties and the melting point in accordance with our simulations. The interaction potential between all three pairs of atoms consists of Coulombic and Buckingham parts (Table ):

Table 1

Buckingham Parameters for Interactions in MgO[32]

interaction	A/eV	ρ/Å	C/(eV Å6)
Mg2+–O2–	821.6	0.3242	0.0
O2––O2–	22764.0	0.1490	27.88
Mg2+–Mg2+	0		0

The model for XNO3/MgO (X = Na, K) was adopted from the works of Anagnostopoulos et al.[26,33] In order to model the whole set of interactions, these authors adopted the model of Jarayaman et al. with formal charges for cations and anions[34] by approximating the Buckingham potentials with Lennard-Jones potentials and using the Lorentz–Berthelot mixing rules (eqs and 8) to define interatomic potentials for interactions between XNO3 (X = Na, K) and MgO. The Lennard-Jones parameters for Li+ ions were taken from the work of Rushton[35] to extend the model of Anagnostopoulos. It is noteworthy that the parameter mixing approach was experimentally verified by Anagnostopoulos and resulted in correct contact angle for a NaNO3 droplet on MgO slabs.[26]

Thus, all the interatomic interactions except those in Table were modeled by eqs , 3, 6–8, which included mixing rules (Table ):

Table 2

Lennard-Jones Parameters for Interactions X–NO3 and XNO3–MgO[26,33,35]

atom	charge	ε/eV	σ/Å
Li	+1	5.0 × 10–9	6.0707
Na	+1	0.0056373	2.3
K	+1	0.00433641	3.188325
N	+0.95	0.0073719	3.10669
OXNO3	–0.65	0.006938258	3.00939
Mg	+2	2.253319968	1.501
OMgO	–2	0.005020786	3.369

The model for the NO3– ions was also adopted from the work of Jayaraman et al.[34] Therein, the N–O bonds are modeled by harmonic potentials (Table ):

Table 3

Intramolecular Parameters for Nitrate Ions[34]

interaction
bond (N–O)	kb = 525.0 kcal mol–1 Å–2	r0 = 1.2676 Å
angle (O–N–O)	kθ  = 105.0 kcal/mol/rad2	θ0 = 120.0°
improper (NO3)	kψ = 60.00 kcal/mol/rad2	ψ0 = 0.00°

The O–N–O angular interactions were accounted for byin combination with an improper torsion type function that keeps NO3 planar:

Molecular dynamics simulations were carried out by the large-scale atomic/molecular massively parallel simulator (LAMMPS) code.[36] The trajectory of each particle is obtained by integration of Newton’s equations of motion with a 1 fs time step. The cutoff distance for the van der Waals and the real-space part of the Coulombic interactions was set to 11 Å, whereas Ewald summation is applied for the long-range contributions. Visual molecular dynamics software (VMD)[37] was used for simple structural analyses and visualization.

The simulation systems were prepared as “sandwich” models, initially consisting of crystalline NaNO3 (8 × 12 × 5 unit cells) on top of a (001) MgO slab (10 × 10 × 10 unit cells). The MgO slab thus was exposed by its (001) surface that is the most relevant for real cubic crystals of MgO. This setup was transformed into a nitrate melt/MgO solid system using several consecutive steps that carefully avoid artificial defect formation (Figure ).

Figure 3

Scheme of simulations for NaNO3/MgO. Other cationic compositions were obtained by substituting Na+ before the third step at 3000 K, followed by additional XNO3 relaxation for 2 ns.

In step 1, the system was allowed to pre-relax at 1 K (time step, 0.1 fs; NVT) to fill the gaps in the nitrate phase due to the lattice mismatch between NaNO3 and MgO. The resulting glassy nitrate phase was then heated up to 3000 K (time step 1 fs) in step 2, using the anisotropic barostat (NpT). At this stage, the MgO atoms are kept frozen to enable full melting and spatial relaxation of the nitrate melt without compromising the MgO crystal. After propagating for 5 ns, good decorrelation from the NaNO3 crystal was ensured. The other nitrate phases were prepared from this state by substituting the Na+ cations with the cation(s) of interest, namely, Li+ or K+, or mixed cationic composition with Li+:Na+:K+ = 0.38:0.18:0.44 corresponding to the triple eutectic mixture.[38] After such substitutions, the system was relaxed for another 2 ns at 3000 K.

In step 3, the systems were cooled from 3000 to 773 K in 1 ns. Next, the MgO atoms were unfixed and each simulation was propagated for 10 ns in the NpT ensemble (1 atm, 773 K) without geometry restraints (Figure ). Periodic boundaries were applied for all directions, and p = 1 atm is applied in the anisotropic barostat. It is noteworthy that, on the basis of the autocorrelation functions, the characteristic times of energy decorrelation for these systems did not exceed 0.01 ns which means that nanoseconds-scale simulations provide hundreds of uncorrelated data points (Figure S1 the Supporting Information).

The resulting “sandwich” systems at 773 K, 1 atm conditions consisted of the (001) MgO slab of 42 × 42 × 42 Å3 and an approximately similar volume of a nitrate melt. Due to the extended ordering in the case of KNO3 the amount of liquid phase was doubled before step 3 to ensure the presence of several nanometers scale bulk liquid in the system.

In order to calculate the adhesion energy, the nitrate/MgO interfaces were compared to isolated phases of MgO and nitrate with and without surface. The relaxed bulk nitrate melts without MgO were sampled from 5 ns simulations in an NpT ensemble at 1 atm and 773 K. Separately, similar systems with flat surfaces were sampled from NVT simulations at 773 K. The same procedure was performed for MgO without nitrate.

All of the energy averages were assessed from Gaussian fits of the corresponding occurrence profiles. The statistical data are provided in the Supporting Information.

Results and Discussion

Structure of Adsorbed Layers

While cooling from 3000 to 773 K (step 3 in Figure ), a static monolayer of adsorbed nitrate is formed on the surface of MgO. The layer contains both nitrate ions and corresponding cations adsorbed in an ordered manner as shown for LiNO3/MgO and (Li,Na,K)NO3/MgO in Figure and for NaNO3 and KNO3 in the Supporting Information (Figure S2).

Figure 4

Structure of adsorbed monolayers of LiNO3 (left) and triple eutectic mixture (Li,Na,K)NO3 (right) on a (001) MgO slab. Both systems are shown from a tilted view direction to illustrate ordering of the adlayers. The picture on the left also illustrates primary adsorption centers for Li+ cation and coordination of nitrate ion to MgO layer as well as main geometric parameters of the nitrate; the distances and the angles are calculated on the basis of coordinates of atomic centers. The inset on the right figure shows the fraction of each cation type in the first adlayer. Colors: Mg, red; O(MgO), blue; Li, green; Na, yellow; K, violet; O(NO), orange; N, black.

The cations (Li+, Na+, and K+) are attracted to the oxygen atoms with average distances d(X) in the range of 2.17–2.84 Å, increasing with the cationic radius in the row Li+–Na+–K+ (Table ). For Li+ the distance almost perfectly matches the Mg–O distance in the MgO crystal due to very close cationic radii.[39] This is in line with the finding that for the mixed nitrate (Li,Na,K)NO3/MgO interface the predominant cation at the contact layer is Li+, thus suggesting higher adsorption energy due to better geometric fitting.

Table 4

Average Geometric Parameters for the Adlayer of XNO3 on a MgO Slaba

system	d(X), Å	d(N), Å	d(OB), Å	αBB, deg	αBL, deg	αT, deg
LiNO3/MgO	2.17	3.17	2.38	119.68	120.16	86.49
NaNO3/MgO	2.28	3.34	2.5	119.30	120.35	89.85
KNO3/MgO	2.84	3.08	2.5	119.50	120.25	87.72
(Li,Na,K)NO3/MgO	2.30	3.18	2.42	119.10	120.45	87.46

Distribution and standard deviations can be found in the Supporting Information (Figures S3 and S4). d(X), average shortest distance between cations in adlayer and MgO slab; d(N), average shortest distance between nitrogen in adlayer and MgO slab; d(OB), average shortest distance between oxygens OB (Figure ) in adlayer and MgO slab; αBB, average angle OB–N–OB in the adlayer; αBL, average angle OB–N–OL in the adlayer; αT, tilt angle between nitrate plane and the MgO slab.

The oxygen atoms from the nitrate are coordinated to pairs of Mg2+ ions adjacent to each other in diagonal direction [110] in the plane (Figure , left inset). The average tilt angle, αT, between the plane of nitrate (OB–N–OB) and the MgO (001) plane is close to 90°, suggesting almost perpendicular orientation of nitrate with respect to the MgO surface. However, the high standard deviation of αT of about 45° (Figure S3) suggests high thermal mobility of adsorbed nitrate with respect to tilting.

For the adsorbed nitrate ions, the distances between nitrogen and surface-bound oxygens from nitrate (N–OB) are equal to the distances between nitrogen and loose oxygen atoms of nitrate (N–OL) for all of the studied systems (1.26 Å, Figure S3). The angles OB–N–OB (αBB) and OB–N–OL (αBL) are also mutually equal: αBB ≈ αBL ≈ 120° (standard deviation ∼ 5°). Thus, the nitrate geometry is not distorted by adsorption.

The distance between bound oxygen atoms OB of nitrates (Figure , left inset) and the closest MgO atoms slightly increases in the row LiNO3–NaNO3–KNO3, with the LiNO3 system exhibiting the closest one to the Mg–O distance in MgO (2.1 Å). Thus, the adsorbed monolayer exhibits geometric parameters that tend to match the ordered structural motifs of MgO, and the best fit is observed for adsorbed the monolayer of LiNO3.

The interface ordering is not limited to the monolayer. The Z-distribution profiles (Figure ) suggest that at least two layers after the first one are partially ordered as there are at least two more peaks of cations and nitrogen before the distribution curve becomes flat corresponding to average numbers of distribution in bulk liquid nitrate at z = 10–12 Å. In the case of KNO3/MgO three additional peaks are observed instead of two, and the ordering is observed up to 15 Å. A possible reason for this is the dominant contribution of Coulombic interactions in the chosen potentials that favor packing of ions. The increase of ionic radii in the row Li–Na–K and its approach to the anion radius make such packing more favorable, which is expressed in the deeper “ordering” for KNO3.

Figure 5

Adsorbed layers and distribution of atoms in them across Z-axis (normal to MgO surface). Colors: Li, green; Na, yellow; K, violet; Mg, red; O(MgO), black; N, orange; O(NO3), orange.

Thus, the interface consists of several (3–4) ordered layers of nitrate with the first ordered layer (adlayer) geometrically matching the structure of MgO. The match is the closest for the case of LiNO3, which could be the reason of predominance of Li+ cations in the adlayer for the system with triple eutectics (Li,Na,K)NO3.

Adhesion and Dispersion Energy

Adhesion energy, Ea, by definition[40] is the work required to divide the interface (nitrate/MgO) into the two constituents, thus creating two surfaces (MgO and nitrate):

We furthermore define the “intercalation” energy, Ei, that reflects the insertion of the MgO slab into bulk nitrate melts:

In addition, the surface energy for MgO and individual nitrate melts were defined asFor such set of definitions, it is fulfilled that

The two contributions to Ea can be derived from the conducted set of simulations (Figure ).

Figure 6

Interfacial (Ei), surface (Es), and adhesion (Ea) energies for XNO3/MgO (X = Li, Na, K, and Li + Na + K) systems.

The surface energy Es for MgO per unit surface is 1.15 J/m2, which is in excellent agreement with the literature experimental data.[41,42]

The surface energies, Es, of nitrates (magenta part of Figure ) are overestimated by 0.05–0.1 J/m2 (indicated by the dashed line) in comparison with experimental values from the literature.[43] The origin of this overestimation is likely a systematic error of the interaction potential for the nitrates approximated by Lennard-Jones functions.

Both Ea and Ei values for all of the systems exceed the MgO surface energy which suggests that formation of interfaces is thermodynamically favorable in nitrate/MgO systems, as was experimentally evidenced for other ionic oxides.[44]

Finally, the self-dispersion energy Edisp can be defined as energy required to form bulk nitrate and bulk MgO from the “sandwich” system:

The calculation by using Hess law (Figure ) for LiNO3/MgO yields 0.53 J/(1 m2 of the interface). Similar calculation yields lower values for other nitrates (inset in Figure ) with KNO3 being almost zero. Thus, for the case of KNO3, the weakest interaction with the surface is observed and it is not clear from the present calculation whether the dispersion of KNO3 is thermodynamically favorable.

Figure 7

Calculation of dispersion energy Edisp for the LiNO3/MgO system.

Role of Interface in Metastability of Mg(OH)2

The data concerning interface energetics could be useful for understanding the effect of salt dopants on the metastability of process 1 reported in numerous works.[13,16,17,45,46] One of them[47] reports a decrease of dehydration temperature for LiNO3 (5 wt %)/Mg(OH)2 in comparison with pure Mg(OH)2, which was accompanied by dramatic reduction of the specific surface area of the product from 250 m2/g for pure MgO to 21 m2/g for LiNO3/MgO. This effect may be quantified thermodynamically if one considers the contribution of surfaces and interfaces to the thermodynamics of process 1, namely, to free formation energy of reagents and products.

To illustrate this approach, we consider the equilibrium of bulk solid phases:and compare it to the metastable pseudoequilibrium state with highly disperse MgO originating from bulk Mg(OH)2:

It was experimentally found that due to the metastability, the real dissociation pressure over Mg(OH)2 is less than calculated from thermodynamic parameters of the bulk phases for equilibrium .[48] In other words, equilibrium is observed under milder decomposition conditions (T = 300–350 °C), while equilibrium is attainable only at high temperature and pressures (T > 500 °C; P ∼ 10 bar), allowing for sintering of the product particles.[49]

The difference between the two equilibria may be attributed to extra surface energy increasing the free formation energy of MgO, thus increasing ΔrG(T) for reaction in comparison with reaction . It can be better illustrated in terms of the following formalism. Equilibrium is defined by the equation of free formation energies of reagents (hydroxide) and products (oxide + vapor):

The intersection of left and right parts of equation as functions of temperature corresponds to the equilibrium of bulk phases of Mg(OH)2 and MgO (intersection point A in Figure a). For the case of disperse MgO, the surface energy term ΔsurfG°(MgO) is added to the right part, thus shifting the intersection point to higher temperatures (point B in Figure a):

Figure 8

Diagram ΔfG°–T illustrating bulk and metastable equilibria for dehydration of pure Mg(OH)2 (a) and LiNO3/Mg(OH)2 (b). REA, reagents; BLK, bulk products; DSP1, disperse products without interaction with the LiNO3 additive; DSP2, represents disperse products with interaction with LiNO3 additive.

This shift to higher temperature may be interpreted as metastability with respect to equilibrium . The surface energy ΔsurfG°(MgO) may be approximated by specific surface energy multiplied by surface of MgO under consideration (e.g., 250 m2/g):

This formalism is applied here to calculate the temperature difference for dehydration of pure Mg(OH)2 and modified with LiNO3. For the latter case the following processes are considered:

We will consider the following states on the ΔfG°–T diagram (Figure b):

REA: reagents of processes –25, i.e., non-interacting bulk Mg(OH)2 and bulk LiNO3

BLK: products of process , i.e., non-interacting bulk MgO and bulk LiNO3

DSP1: products of process , i.e., non-interacting disperse MgO (S1 = 250 m2/g) and bulk LiNO3

DSP2: products of process , i.e., disperse LiNO3/MgO (S2 = 25 m2/g) with pronounced interface between LiNO3 and MgO

The observed temperature difference between dehydration temperatures of pure and LiNO3-doped Mg(OH)2 may be evaluated in this concept as the equilibrium temperature difference between the equilibria REA–DSP2 and REA–DSP1. Both equilibria may be determined from the thermodynamic data for the bulk phases from the literature[50] and specific surface or interface energies as follows:for DSP1 state andfor DSP2 state. Both Es and Edisp were determined by relaxation of the MgO surface or the LiNO3/MgO interface as described above.

Such calculation gives the temperature difference, ΔT, between dehydration temperatures of Mg(OH)2 and LiNO3/Mg(OH)2 (5 wt % LiNO3) of 79 K. This temperature difference is in good agreement with 76 K as found in ref (18) and confirmed later in ref (16). The difference between REA–BLK and REA–DSP2 is only 4.5 K, which suggests that the state DSP2 is thermodynamically very close to the bulk state BLK. Thus, the catalyst almost completely brings the system to the equilibrium of bulk phases.

Conclusions

In this work, we present molecular dynamics simulations of nitrate/MgO sandwich models to characterize the structure of the interfaces, calculate interfacial energies, and discuss how this knowledge helps in understanding the catalysis of Mg(OH)2 dehydration.

The modeling based on experimentally verified potentials allowed highlighting the structural features of the interface. The nitrates form ordered layers (extended over 9–12 Å) next to the MgO surface. Oxygen atoms are the primary adsorption centers for cations, while nitrates are adsorbed to Mg via two coordinating oxygen atoms, the angle between the nitrate plane and the MgO slab is close to 90°. For the triple eutectic mixture Li ions prevail in the adlayer, followed by Na and K ions.

The adsorption of nitrate leads to high adhesion energy, Ea, ranging from 1.3 J/m for KNO3 to 1.8 J/m for NaNO3 to 1.9 J/m2 for LiNO3, which makes creation of such interfaces thermodynamically favorable.

The calculated values help in understanding the difference of equilibrium temperatures for the dehydration of LiNO3/Mg(OH)2 and Mg(OH)2. The developed formalism consists of analysis of thermodynamic data for bulk and dispersed products, using the values of adhesion and dispersion energies from the MD modeling. Our theoretical estimate for this system (79 K) on the basis of the thermodynamic formalism is close to the experimental value (76 K).

In general, the data on specific surfaces of the resultant oxides in combination with knowledge of interfacial energies reported here may be used to thermodynamically quantify how far is a thermochemical system from the bulk equilibrium, thus predicting the potential effect for new nitrate-based dopants.[16] Thus, it may be possible to put this approach in a broader context and apply it to other systems involving MgO and catalytic additives, for instance, NaNO3/hydromagnesite[21] or nitrate mixtures/MgCO3.[22]