Activation energy barriers for Na migration in Na12A zeolite: The main contribution to ionic current via doubly occupied NaII site?

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Highlights

  • NaIII+ diffusion via doubly occupied SII site is allowed in Na12A zeolite.

  • Na ionic current is assigned to its diffusion with lower activation energy process.

  • Cl or Br anions and water decrease the activation energy of Na+ diffusion.

  • Maximal decrease of activation energy due to water is achieved at immobile water.

Abstract

The activation barriers for Na jumps between the cationic sites NaI, NaII, and NaIII are calculated using VASP in the presence of anions (Cl, Br) or H2O as well as for the empty Na12A zeolite model. The inter-cage cationic NaIII→NaII’→NaIII′ path, where NaIII′ is located in the neighbor α–cage, was modeled via an intermediate state (NaII′) corresponding to two NaII cations in one 8R window. This NaII′ point can also serve as an intermediate for the second type of intra-cage Na drift, i.e., to a NaIII site in the same cage. Reasonable agreement with experimental activation energy was achieved for NaII’→NaIII′, NaII→NaIII, and NaIII→NaIII jumps. The lower activation energy is obtained for the NaII’→NaIII' jump than for NaII→NaIII, which indicates the possible role of the doubly occupied 8R window as an intermediate state in the Na transfer with high frequency and lower activation energy related to ionic current (inter-cage transfer) in Na12A.

Graphical abstract

PBE, PBE-D2, PBE-D3 approaches for parallel NaIII + H2O diffusion in Na12A.

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Introduction

The charge transfer by cations in various batteries is one of the important processes, the understanding of which is necessary for the development of a new generation of current sources. This complex task often requires theoretical pre-selection between diffusion profiles in the crystalline media with the spatial symmetry that changes during the cation transfer [[1], [2], [3]]. The best electrode candidate can be selected on the basis of tiny differences of 0.1–0.2 eV in calculated barriers of Na-diffusion [2]. The accuracy of the computational approach has not been profoundly tested. The verification of computational tools can pass through a solution for simpler systems, which are also important for understanding the catalytic activity of alkali cations. Because of the lower cation coordination at the sites with lower binding energies, its reactivity is enhanced at least for some reactions in zeolites. As an example, cationic diffusion was demonstrated as the reason of poisoning effect on cracking reactions [4]. The domination of alkali cations in the concurrence for framework oxygen atoms (relative to protons) leads to a lower rate at the limiting step of extra framework aluminum formation assigned to the transformation between the AlOH2+ and Al(OH)2+ in zeolites [4].

Stimulated drift of cations in zeolites was thoroughly studied experimentally [[5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]]. In the absence of adsorbed molecules and anions (or when the anions are fixed) it allowed assigning separate dielectric losses in alternating current experiments to cationic transitions between definite sites [5,21]. For these Na jumps two processes with activation energies from 0.46 [16] to 0.61 eV [15] for the high frequency peak and from 0.62 ± 0.02 [21] to 0.90 ± 0.02 eV [5] for the low frequency peak were observed, respectively (more data presented in Table 1). Understanding of the two types of the high and low dielectric spectroscopy frequency processes (HF and LF) with lower and higher activation energies, respectively, is a general problem of cationic conductivity in the zeolites. They were measured in many cationic forms using impedance spectroscopy [10,14,17,21], mono-frequency dielectric measurements [[5], [6], [7], [8], [9],13,15,16,22,23]. Both transitions are connected with cationic movement, but it is difficult to assign one of the transitions to ionic conductivity [22]. For the case of NaX and NaY zeolites, only analogous LF drift of Na was considered as the main contribution to the ionic current [10,24]. Some possible influences on the processes were already distinguished such as a minor role of the grain boundary effects [12]. Despite of tentative assignment of the cationic SII–SIII–SIII′-SII′ movements (as HF peak, with SII and SII′ in the same cage) and SII–SIII–SII′ movements (as LF peak, with SII and SII′ in the neighbor cages) in faujasites, to definite both HF and LF processes, respectively [10,12,13,23], such results were not interpreted at the microscopic level for either NaA, NaX or NaY to our best knowledge. Fundamental importance of respective explanation originates from the correct presentation of the zeolite charge distribution and its reaction on the cationic drift.

Any assignment becomes more complicated in the presence of particles, which can form stable complexes with cations and thus can change the parameters of ionic migration processes. Different influences of neutral molecules were estimated for cation's drift with NH3 [6,9], SO2 [9], C6H6 [18], (CH3)2CO [18], and CO2 [9] on Na12A (or simply NaA below) [6], Ca4Na4A [9] and LiX [18]. Experimental data for the transitions in zeolites allow us to define the role of adsorbed neutral species for the cation's migration.

Vice versa, the distribution of the Na cations is often of prime importance for the passage of adsorbed species [25]. The authors of ref. [25] considered the situation when two types (Na and K) alkali cations populate the cell. The possibility of gas passage is explained by a better K trapping at available SII and SIII sites so that it does not allow the passage of adsorbed molecules in the selected cationic configurations (K cations occupy the 8R window and nearest 4R sites which prevent cationic motion and gas passage through the 8R) [25]. In another work [26], it was concluded that the interaction of cations with CO2 molecules plays a key role for gas penetration through 8R windows in narrow pore zeolites. Otherwise, some computational attempts to check the diffusion profiles at fixed coordinates of a part of the system were undertaken to estimate the extent of the pore opening in narrow pore zeolites [27]. The use of frozen coordinates makes the obtained data rather arbitrary and less reliable. A stimulation of the pore opening owing to the interaction of a cation with carbonate or hydrocarbonate anions was later shown using both static models [28] and AIMD in the NaKA zeolite [29]. The authors of ref. [29] demonstrated the drift of K+ cation from the II site in 8R window and hence the ease of cationic jumps. The local minimum for K+-CO32−complex was previously found outside the 8R plane in narrow pore NaKA by “static” optimizations [28], thus confirming long cationic drifts obtained in narrow pore [[28], [29], [30]] and wide pore [[31], [32], [33], [34]] zeolites. Facilitation of the heavier cation diffusion in wide pore Y zeolites allowed explaining the most intensive IR spectra of CsY together with the specific dependency of the heat of CO2 adsorption in CsY [32]. But in all these works [[25], [26], [27], [28], [29],33,34] no diffusion barrier of the alkali cation was calculated to be compared with available experimental data.

Herein, the barriers of Na diffusion will be calculated in sodium form of Linde type A (LTA) or NaA zeolite (Si/Al = 1) in the presence of the anions (Cl, Br) and H2O molecule. Water remains a candidate for safe and cheap media for electrolyte in future Na-batteries [35,36]. After presenting the computational method and models (part 2), the cationic transitions will be analyzed below (part 3.1), then the barriers will be calculated including the route to new intermediate state which is important for both inter- and intra-cage Na diffusion (part 3.2) considering the addition of NaCl or NaBr salts (part 3.3) and water (part 3.4). The main result of the work is interpreted in the first part of Discussions (part 4).

Section snippets

Computational details

Pseudo-unit 2-α-cage cell (Fig. 1a,b) of fully dehydrated Na12A with the total content Na24Al24Si24O96 (pseudo-NaA) was first induced for KNa23Al24Si24O96 zeolite [28] and later used in some works [27,28,37]. This model allows to replace the full correct Na96Al96Si96O384 model containing 8 α-cages [38] (Fig. 1c) and, thus, reduce computational costs.1

Assignment of the transitions

First, we select cationic transitions that should be calculated as the most probable for comparison with the experiment. For this, we address to the dielectric losses in two close Na12A and Ca1Na10A zeolites [5]. Absence of the NaIII cations in the Ca1Na10A case led to disappearance of the HF transition with lower activation energy (~48 kJ/mol = 0.5 eV), while the transition with higher activation energy (87 kJ/mol = 0.90 eV) remains in Ca1Na10A corresponding to the similar bands observed for

Discussion

The stable NaII′ state closely to the 8R plane offers us a route for ionic conductivity with Na transfer between neighbor α-cages. The second (larger) barrier of 0.56–0.66 eV (Table 1) at the NaIII–NaIII direction corresponds to the process, when NaIII remains in the same α-cage. It describes local Na motions within one cage which do not contribute to measured ionic current. But its first step could lead to the NaII′ intermediate state before passage to a neighbor α-cage. Then the two-step

Conclusions

The route for inter-cage Na transfer is proposed using the stable intermediate site at which two non-equivalent NaII” and NaII′ cations occupy one 8R window as was first proposed by Ohgushi. The first stage of two-step NaIII–NaII′-NaIII′ process in NaA, where NaIII′ is in another α-cage compared to the initial NaIII site, is characterized by a small activation E# = 0.13–0.37 eV. This first step leads to the location of NaII” and NaII′ cations in a doubly occupied 8R window being both

CRediT authorship contribution statement

A.A. Rybakov: Investigation, Software, Writing - review & editing. D.N. Trubnikov: Conceptualization, Project administration, Resources, Writing - review & editing. A.V. Larin: Investigation, Validation, Visualization, Writing - original draft.

Declaration of competing interest

The authors declare that there is no conflict of interests.

Acknowledgement

The authors thank the Russian Foundation for Basic Research within the grant 17-53-18026-Bolg_а. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University [71].

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