Highly Flexible Hydrogen Boride Monolayer as Potassium-ion Battery

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Highly Flexible Hydrogen Boride Monolayer as Potassium-ion Battery Anodes for Wearable Electronics Pan Xiang, Xianfei Chen, Beibei Xiao, and Zhiming M. Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b22214 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 5, 2019

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ACS Applied Materials & Interfaces

Highly Flexible Hydrogen Boride Monolayer as Potassiumion Battery Anodes for Wearable Electronics Pan Xianga,b, Xianfei Chena*, Beibei Xiaoc, Zhiming M. Wangb* a

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology,

Chengdu 610059, China b

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology

of China, Chengdu 610054, China c

School of Energy and Power Engineering, Jiangsu University of Science and Technology,

Zhenjiang 212003, China

 Abstract The rapid development of wearable electronics has revealed an urgent need of lowcost, high-flexible, and high-capacity power sources. In this sense, emerging rechargeable potassium-ion batteries (KIBs) are promising candidate owing to their abundant resources, low-cost and lower redox potential in non-aqueous electrolytes compared to lithium-ion batteries. However, the fabrication of flexible KIBs remains highly challenging because of the lack of high-performance flexible electrode materials. In this work, we investigated the mechanical properties and electrochemical performance of recently developed hydrogen boride (BH) monolayer as a highperformance anode material based on density functional theory (DFT) formalism. We demonstrated that (i) BH presents ultra-low out-of-plane bending stiffness, rivaling that of graphene, which endows it with better flexibility to accommodate the repeat bending, rolling and folding on wearable device operation; (ii) high in-plane stiffness (157 N/m along armchair and 109 N/m along zigzag) in BH makes the electrode stable against pulverization upon external and internal strains. More importantly, BH electrode delivers low voltage of ~0.24 eV in addition to desired K-ion affinity and hopping

*

Corresponding author. Email: [email protected]; [email protected] 1

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resistance which remains very stable with the bending curvature. Emerged H vacancies in electrode were found to improve both the K-ion intercalation and K-ion hopping, yielding a high theoretical capacity (1138 mAh/g), which was among the highest reported values in the literature for K-ion anode materials. All the presented results suggested that a BH electrode could be used as a brand-new flexible and lightweight KIB anode with high capacity, low voltage, and desired rate performance.

Keywords: potassium-ion batteries, flexible anode material, 2D hydrogen boride, firstprinciples calculations

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 Introduction Wearable electronics, a kind of portable devices that could be placed on the body or integrated in clothes and fixings, are enriching our lives and perceptions and becoming more important in our daily life.1-3 Apart from its miniature, lightweight, flexible, foldable, and stretchable characteristics, these devices can be also considered “intelligent” apparatuses, since they can be interconnected through direct data communication or cloud interactions via wireless network.4 Accordingly, numerous functions including physiological sensing and monitoring, sports data analyzing, sleep monitoring, and intelligent navigation could be integrated into smaller devices. Nevertheless, the lack of suitable energy supply systems hinders the applications of these devices. These energy supply systems must meet stringent low-size, lightweight, and high-flexibility characteristics as a result of the operation conditions of wearable devices. Rechargeable lithium-ion batteries (LIBs) are being widely used as power sources, spurring the rapid development of portable electronics to some degree. However, there are concerns on whether global Li reserves (ca. 14 million tons) could meet the increasing market. These concerns have spurred extensive research efforts in searching alternatives to LIBs such as potassium-ion batteries (KIBs). Unlike LIBs, KIBs are more appealing for powering wearable electronics owing to their low cost, wide geographical distribution of their components, and, especially, the lower redox potential in non-aqueous electrolytes to deliver high cell voltage compared to Li.5-7 However, the high energy consumption of wearable devices poses some requirements on these batteries (e.g., high capacity, low volume, and light weight) to increase their endurance time and to reduce the recharging time. To address these issues, joint theoretical and experimental efforts are urgently required to develop new KIB electrode materials with low cost, light weight, high theoretical capacity, fast ion hopping, and high flexibility. Compared with cathodes, the development of appropriate anode materials for 3



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KIBs is more difficult because of the larger radius of K compared with Li. Thus, stateof-the-art graphite anodes are not compatible with the KIB technology and provide capacities as low as 87 mAh/g.8 With the aim to reduce the anode weight while maintaining its flexibility, 2D materials including graphene-based materials9, phosphorenes11,

12,

transition-metal dichalcogenides (TMDCs)13,

14,

10,

transition-metal

carbides and carbonitrides (MXenes)15, and boron-based materials16-18 among others, have been widely investigated. These reports have provided important insight into the use of sophisticated anode materials for wearable electronics. Compared with other synthetic 2D materials, borophene is the lightest metalloid and possesses the Lowest-Z element to form extended covalent networks. Thus, borophene holds great potential to be applied in wearable applications. However, borophene suffers from free-standing instability, easy surface oxidation, and difficult transferring from silver substrates, which limit its applications. In this scenario, it is of great importance to develop new simple synthesis methodologies and stable boron-based derivatives to overcome the instability of borophene while maintaining its excellent properties. Recently, Kondo et al.19 successfully fabricated hydrogen boride (BH) monolayer at room temperature by exfoliation and complete ion-exchange between protons and magnesium ions from MgB2. The as-synthesized BH monolayer possessed high stability and, for the first time in boron-based 2D structures, a Dirac ring.20 The low mass density, unique electronic structure, excellent stability, and simple and eco-friendly fabrication process of BH monolayers provide this material with potential for KIB applications, although this potential remains to be investigated. Moreover, limited attention has been paid in previous works to the effects of mechanical bending on the electrochemical performance of flexible electrodes. Since mechanical bending is inevitable during wearable devices operation, this phenomenon must be studied, especially for wearable battery applications. In this work, we systematically investigated the mechanical, electronic, and electrochemical properties of BH monolayer KIB anode materials. The bending and inplane stiffnesses of the BH electrode revealed high flexibility and favorable strength 4


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for this material to endure repetitive folding, rolling, bending, expansion, and shrinking electrode operations. In addition, the BH electrode showed high theoretical capacity, low voltage, and steady performance upon bending in flexible devices. The corresponding intercalation and hopping mechanisms of K-ion on pristine, curved, and defected BH electrode surfaces were revealed. Our results provided a steady path towards the utilization of BH as high-performance KIB anodes.

 Computational Details The calculations were performed based on the dispersion corrected density functional theory (DFT-D2) per Grimme21 as implemented in the Dmol3 module22, 23 with the generalized gradient approximation (GGA) and Perdew–Burke–Ernzerhof (PBE) as the functional. All electrons including some relativistic effects were adopted to treat core electrons with the basis set of double numeric plus polarization (DNP). The convergence criteria of energy, force, and displacement for geometry optimization were set at 1.0 × 10−5 Ha, 0.002 Ha/Å, and 0.005 Å, respectively. For BH single-wall nanotubes, the periodic boundary condition along the tube axis direction was applied. A vacuum layer of 20 Å was used to minimize the artificial interactions because of the employment of periodic boundary conditions. A smearing of 0.002 Ha was used, and the global orbital cutoff was fixed at 5.6 Å for all calculations. The complete linear synchronous transit (LST)/quadratic synchronous transit (QST) search protocol24 assisted by the transition state (TS) confirmation method was used for finding the saddle points and the minimum energy paths (MEPs) with a root-mean-square (RMS) convergence of 0.002 Ha/Å. The stability of the electrode material was investigated by performing ab initio molecular dynamics (AIMD) simulations in canonical ensemble (NVT) at 300 K. Besides, the electron density difference (EDD) and the electron localization function (ELF) were calculated by using the CASTEP module. The open-circuit voltage (OCV) was calculated as: V=―

𝐸𝑥2 ― 𝐸𝑥1 ― (𝑥2 ― 𝑥1)𝑢𝐾 𝑛𝑒 5


(1)


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where Ex2 and Ex1 are the total energies of the substrate covered by x1 and x2 K; uK represents the energy of a single K atom in a body centered cubic (BCC) bulk; and x1 and x2 are the numbers of inserted K. In addition, the specific energy-storage capacity was determined as: C=

𝑥𝑚𝑎𝑥𝑛𝐹

(2)

𝑀𝑠𝑢𝑏

where xmax is the maximum concentration of adsorbed K; n = 1; F is the Faraday constant; and Msub is the weight of substrate. All the capacity data referenced in this paper were converted according to above formula for the sake of comparison.

 RESULTS AND DISCUSSION 3.1 Structure, electronic properties, and flexibility of the BH monolayer BH monolayer consists of a graphene-like skeleton with hydrogen atoms on both sides of two parallel B–B bonds, forming continuous hydrogen chains (Figure 1a). As indicated by the blue dashed rectangle in Figure 1a, the optimized lattice constants of the primitive cell were a = 5.31 Å and b = 3.02 Å, in agreement with previously reported experimental19 and theoretical20, 25-27 results. The length of the B−B bond with (without) H atoms and the distance between two symmetric H atoms were 1.83 Å (1.72 Å) and 1.94 Å, respectively. Since the electronic properties of the electrode determine its rate capability and cyclability,28, 29 the band structure and partial density of state (PDOS) of BH were calculated (Figure 1b). The BH monolayer showed high metallicity with some B−2p orbitals crossing the Fermi level, such that additional conductive additives are not required in the electrode. As in the case of borophene30 and graphene31, the Dirac cone was obtained near the Fermi level, which could facilitate charge transport and, in turn, improve the charging/discharging rate. However, unlike pristine borophene17 and borophane32 in which metallic transport is only observed along certain directions, the BH monolayer showed isotropic metallicity, which is advantageous for electrode applications.

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Figure 1. (a) Top and side views of the optimized structures of BH monolayer, (b) corresponding band structure and partial density of states (PDOS). H1, H2, T1, T2, and B1 correspond to hollow, top, and bridge sites for K adsorption on BH, respectively. The blue dashed rectangle indicated the unite cell, while the orange circle reveals the Dirac cone in BH.

Figure 2. Energy evolution of single BH atom–pair with the radius of: (a) armchair and (b) zigzag BH nanotubes. Diamond symbols and solid lines represent the values obtained from DFT calculations and continuum model, respectively. The illustration provides the configurations of: (a) armchair and (b) zigzag BH nanotubes. Flexibility is a crucial property for any electrode material intended for wearable devices. This flexibility can be characterized by the out-of-plane bending stiffness (BM) of the electrode. Theoretically, BM could be obtained by fitting the energy difference of the BH atom–pair in nanotubes and that in a planar monolayer as a function of the tube radius as follows:33 𝐸𝑡𝑢𝑏𝑒 = 𝐸𝑙𝑎𝑦𝑒𝑟 + 𝑆0𝐵𝑀𝑟 ―2/2

(3)

where r is the radius of the BH nanotubes; Etube and Elayer are the energy per BH atom– 7



pair in tubular and flat BH compounds, respectively; and S0 = 3.96 Å2 is the area of the BH atom pair in a BH monolayer system. To determine BM, a series of BH nanotubes with different diameters were constructed. The fitting curves are shown in Figure 2, while the corresponding structural parameters of the fully relaxed BH nanotubes are provided in Table S1. The calculated BM values for the BH monolayer along the armchair and zigzag directions (0.43 eV (6.89 × 10−20 N·m) and 0.60 eV (9.61 × 10−20 N·m), respectively) revealed a noticeable anisotropy. We note that the BH monolayer showed BM values well above those of well-known flexible electrodes including graphene (1.44 eV)33, phosphorus (5.21 eV)34, and MoS2 (9.33 eV)35. This low BM value provides the BH monolayer with excellent stress relaxation characteristics, thereby preventing electrode performance fade induced by stress-induced crack propagation. In addition, to avoid electrode fracture upon repetitive bending and folding operation, we further estimated the elasticity performance of the BH monolayer by calculating its in-plane stiffness. The corresponding energy curves under uniaxial and biaxial strains are shown in Figure S1a. The mechanical properties of the BH monolayer along the armchair and zigzag directions were anisotropic, with calculated elastic modulus (E) of 157 and 109 N/m, respectively. These values were comparable to those of MoS2 (133 and 133 N/m)36, β12 borophene (123 and 147 N/m)37, and NbS2 (139 and 132 N/m)38. Thus, the BH monolayer showed favorable elastic modulus and low bending stiffness, thereby holding great potential as a flexible anode material.

3.2 Adsorptions and diffusions of K on pristine BH monolayer The electrode performance can be meticulously estimated by considering the adsorption energies (Ead) and the diffusion energy barriers (Ebar) of a K atom on the electrode surface. With this aim, five feasible symmetric sites (indicated in Figure 1a) were considered to determine the most energetically K adsorption configuration. As shown in Figure 3a, K occupied preferably the hollow site above the B-hexagon, upon which the BH substrate showed a slight bending. Ead was −0.21 eV, which was calculated by: 8


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(4)

𝐸𝑎𝑑 = 𝐸𝑡𝑜𝑡𝑎𝑙 ― 𝐸𝑠𝑢𝑏 ― 𝑢𝐾

where Esub and Etotal are the energies of pristine and metalized BH monolayers, respectively. It is important to note that this calculated Ead was considerably lower than those reported for pristine borophene (−1.45 eV for β12 borophene, −1.43 eV for χ3 borophene, and −1.88 eV for striped borophene)17. This reduced bonding to K-ions in anode is beneficial for the achievement high output voltage when assembling into batteries. This behavior could be partially attributed to the passivation of active B atoms on the boron sheet surface by the covered hydrogen atoms as observed in Li and Na adsorption on C-borophane32 and BH monolayer25, 26. The low Ead might also result from the high flexibility of BH, since energy is consumed via adsorption-induced bending. Moreover, a repulsion interaction between K and H emerged as a result of the large atomic radius of K (Figure 3a). As a result, H atoms are pushed away from their equilibrium positions. The weight of the latter two factors could be obtained by calculating the substrate deformation energy (Ede) (i.e., the energy difference between pristine and deformed BH substrates upon K adsorption). Ede was calculated to be 0.21 eV.

Figure 3. (a) Top and side views of the most energy favorable adsorption configurations of K on BH monolayer. (b) Schematic hopping path for K-ion on BH electrode surface, and (c) corresponding energy profiles. As shown in Figure 3b, three representative migration pathways were considered for the diffusion of a K-ion from one thermodynamic equilibrium site to its nearest one 9



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in light of the BH symmetry. The energy profiles along with their marked Ebar are shown in Figure 3c. Generally, the calculated Ebar along path 2 (0.32 eV) was significantly lower than those calculated for path 1 (0.58 eV) and path 3 (0.58 eV). An intuitively overestimation of the K-ion hopping dynamic could be achieved by considering the diffusion coefficient (D): 𝐷~exp ( ―

𝐸𝑏𝑎𝑟 ) 𝑘𝐵𝑇

(5)

where Ebar and kB are the diffusion activation energy and the Boltzmann’s constant (8.62 × 10−5 eV/K), respectively and T refers to the operation temperature of the battery. At room temperature, the K-ion hopping along path 2 was ca. 2.35 × 104 and 2.30 × 104 times faster than those along path 1 and path 3, respectively, revealing a strong anisotropy. This behavior is quite common in 2D materials (e.g., borophene16, phosphorus39, and penta-graphene40), allowing oriented migration of metal-ions through the electrode. Moreover, the low Ebar (0.32 eV) for K migration was comparable to those of well-known Li electrodes such as graphite (0.4 eV)41, graphene (0.3 eV)42, and MoS2 (0.24 eV)43. However, wearable devices undergo repetitive bending, rolling, and folding. Thus, it is of great concern to consider the adsorption and diffusion performances of K-ion in BH electrodes under different bending conditions.

3.3 Adsorption and hopping of K-ion on curved BH electrodes The effects of mechanical bending on the electrochemical performance of BH anode were considered by investigating the adsorption and diffusion of K on curved electrode surface with different curvature radii. The curved BH surfaces were constructed by wrapping BH monolayer into nanotubes with various diameters. For convenience, we only considered the two typical wrapping directions yielding zigzag and armchair nanotubes, respectively. To avoid the artificial interaction between K atoms produced by the periodic boundary conditions, we considered a 1×3×1 supercell for armchair nanotubes and 1×2×1 supercell for zigzag nanotubes (Figure 4a, b), and these supercells showed adjacent-ion distances of 9.00 and 10.58 Å, respectively. 10


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Besides, each K atom could be adsorbed on both sides of the curved BH surface (i.e., concave and convex sides as labeled in Figure 4 a, b). The calculated results are shown in Figure 4c, d. Interestingly, the most stable adsorption configuration on BH nanotubes was still above the center of hexatomic ring (hollow site), while the calculated Ead vary with the curvature radius and the adsorption modes.

Figure 4. Optimized configurations of armchair (a) and zigzag (b) BH nanotubes. The outer surface is defined as the convex side, while the inside one is denoted as concave side. For convenience, half of the nanotubes are hidden. Calculated Ead (c) and Ebar (d) on convex and concave sides of BH nanotubes with different curvatures. As shown in Figure 4c, the BH monolayer showed larger affinity to K on the convex side, with Ead increasing with the curvature on both bent surfaces. The calculated Ead was lower on the concave side compared to the convex side. This difference increased with the curvature, and difference of ca. 0.36 eV could be achieved upon a big bending. This discrepancy could be rationalized by the steric effect in which different repulsions between K and H exist for the convex and concave sides upon bending. In the convex side, a sparse distribution of H atoms emerged upon bending, providing more room to accommodate large K-ion. In contrast, in the concave side, external bending compressed the H atoms and squeezed the hexagonal center, hindering 11



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K-ion adsorption. We found that the surface activity of the electrode was more sensitive to the bending surface compared to the bending strength. Even if the curvature changed from 5.00 to 11.67 × 10-2/Å, the change in Ead was as low as 0.06 eV. To reveal the effect of bending on the charge/discharge rate, the migration properties of a K-ion through zigzag and armchair BH nanotubes with different curvatures were calculated (Figure 4d). Unlike Ead, a reduced hopping resistance was observed on the concave side, and the opposite trend was observed on the convex side. The hopping dynamic was likely to be related with the Ead of K in the initial states, with high Ead resulting in large Ebar and vice versa (Figure 4c and d). In the concave side, Ebar decreased to 0.17 eV at high curvature. Nevertheless, the Ebar increased only by 0.09 eV over a wide range of curvature, revealing high stability against external stress.

3.4 Effect of hydrogen defects on the electrochemical performance of BH monolayer The BH monolayer was synthesized by a combination of exfoliation and ionexchange methods. This fabricating process inevitably introduces hydrogen defects in the BH system. Besides, lattice vibrations at elevated temperature also leads to the generation of hydrogen defects in BH systems. This motivated us to further consider the effects of hydrogen vacancies on the electrochemical properties of the BH electrode. A defective BH monolayer structure was simulated by removing one hydrogen atom from a 2×3 pristine BH monolayer (vacancy concentration of 2.1 %), yielding a little lattice constriction with optimized lattice constants of 10.47 and 9.00 Å (Figure 5a). Unlike the remarkable structure reconstruction observed for defective phosphorene44, silicene45, 46, and ReS247 systems, the introduction of hydrogen vacancies only resulted in slight bending for the BH monolayer (curvature radius of 21.76 Å along the armchair direction) with a low formation energy (EF). The EF is defined as follows: 𝐸𝐹 = 𝐸𝐷𝐵𝐻 ― 𝐸𝑃𝐵𝐻 + 𝜇𝐻

(6)

where EPBH and EDBH are the total energies of the defective and the corresponding BH 12


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monolayer, respectively, while μH is the chemical potential of a hydrogen atom obtained from a H2 molecule. The EF calculated for hydrogen vacancies (1.06 eV) was similar to that of sulfur vacancies in ReS2 (1.18 eV)47 and lower than those of boron vacancies in β12 (1.93 eV), χ3 (1.65 ~ 3.18 eV) borophene48, tin vacancies in stanene (1.86 eV)49, silicon vacancies in silicene (2.09 ~ 3.77 eV)45, and carbon vacancies in graphene (7.94 ~ 7.98)50. This low value revealed that hydrogen vacancies are easily formed, potentially reaching high equilibrium concentrations at elevated temperatures. Wu et al.49 recently demonstrated that stanene having vacant defects formed a nanomesh structure rather than a porous structure because of vacancy aggregation. To explore this possibility, the mobility of hydrogen vacancies in a defective BH monolayer was estimated by considering the vacancy diffusion resistance. As shown in Figures S2a and b, two elementary migration pathways (paths I & II) were determined for vacancy diffusion, and the calculated Ebar were 1.19 and 1.44 eV, respectively. These high Ebar values suggested that the hydrogen vacancies in BH monolayers have low mobility, thereby favoring the formation of nanohole structures rather than nanomesh structures.

Figure 5. (a) Top and side views of the optimized structures of a defective BH monolayer, (b) corresponding band structure and PDOS. The green circle denotes hydrogen defect sites, while the orange circle indicates the retained Dirac cone in defected BH electrode. The band structure and PDOS of defected BH monolayer were calculated (Figure 5b). Unlike graphene whose conductivity is severely reduced by the formation of defects, the metallic conductivity and Dirac cone of BH remained very stable under the 13



presence of H defects (Figure 5b). Moreover, hybridization between B and H atoms was intense in the defective BH monolayer, with some new overlapped peaks in PDOS produced by local atomic reconstruction. We also considered the mechanical properties of defective BH. The energy curves of this material under uniaxial strains were calculated and illustrated in Figure S1b. The E for defective BH monolayer along the zigzag direction is similar to that of the pristine counterpart (106 vs 109 N/m), whereas that along the armchair direction decreased substantially from 157 to 115 N/m, becoming more isotropic. The thermodynamic stability of the defective BH monolayer was estimated by AIMD simulations. The snapshot of a defective BH sheet monolayer at 3ps is shown in Figure S2c. Although the configuration of the defective BH was more curved compared to the pristine one, the structural integrity was retained. Moreover, as shown in Figure S2d, the energy and bond lengths of B−B and B−H varied within a small range at the given time. All these data indicated that the hydrogen vacancies in the BH monolayer were very stable, and no segregation or structure collapse was observed at typical batteries operation temperatures. The defective BH monolayer also maintained the excellent electrical conductivity and mechanical properties.

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Figure 6. (a, b) Considered absorption sites and calculated Ead for K on defective BH electrode. Partial density of states (PDOS) and slice of electron localization functions (ELFs) for K adsorbed on hollow sites of: (c, e) a pristine BH monolayer and (d, f) A−Concave site of defective BH monolayer. The formation of hydrogen defects in BH broke its symmetry, thus reducing the homogeneity of the adsorption sites for K. To determine the most energetic site for K adsorption on defective BH, 18 adsorption sites on defective BH surface were considered (Figure 6a, A−I sites above both the concave and convex sides). The calculated Ead (Figure 6b) revealed enhanced absorptivity for all the sites of the defective BH material compared with the pristine one. On the convex side, K was only adsorbed in hollow sites similar to those of pristine BH. In contrast, on the concave side, D-concave and B-concave sites appeared as two new adsorption configurations near the vacancy, with Ead of −0.65 and −0.64 eV, respectively. Nevertheless, the most stable adsorption site remained to be the hollow sites. The enhanced adsorptions were found to depend on the distance to the defect: the closer to the defect, the higher Ead. At the A-concave site (the hollow closest to the H vacancy) Ead reached −0.74 eV, 15



revealing a significantly higher affinity to K compared to pristine BH (−0.21 eV). Interestingly, another neighbor defect (E-concave site) was determined to be unstable for K adsorption, with K spontaneously spreading to the B-concave site after optimization. To reveal the origin of this enhanced interaction between K and defective BH, K adsorbed on A-concave site was selectively analyzed. As indicated above, the energy released upon K adsorption on BH substrates was partially used to deform the substrate. K adsorption on defective BH resulted in an Ede as low as 0.10 eV, lower than that calculated for the pristine material (0.21 eV). Thus, H vacancies in BH help alleviate the adsorption-induced substrate deformation. The partial DOS (PDOS) of K adsorbed on A-concave site was calculated and compared with that of hollow site in pristine BH (Figure 6c and d). As expected, only a few overlapped peaks between K and B were observed in Figure 6c, revealing a weak interaction of K with the pristine BH substrate. In contrast, the defective BH showed many new overlapped peaks in the PDOS (Figure 6d), suggesting a more robust bonding between the K atom and the substrate. This enhanced electron interaction of K on defective BH was also demonstrated by ELFS slices. As shown in Figure 6f, except for the electrons aggregating between the K and B atoms, most of the electrons also accumulated between the K atom and the B−B bond, which is absent in the case of K on pristine BH (Figure 6e), demonstrating enhanced interaction between K and the substrate, in line with the above PDOS analysis.

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Figure 7. (a, b) Migration paths and corresponding Ebar values of K-ion on the concave side. (c, d) Migration paths and corresponding energy profiles of K-ion on the convex side. With regard to the hopping dynamic of K-ion on defective BH monolayer, we considered five and three feasible diffusion paths on the concave and convex sides, respectively (Figure 7a and c), and the corresponding Ebar values are shown in Figure 7b and d. Since K at E-concave site is an unstable adsorption configuration, the final state (FS) of path 4 and the initial state (IS) & FS of path 5 were adjusted to B-concave site. As shown in Figure 7b, the enhanced hopping dynamic of K-ion with reduced Ebar (0.03 ~ 0.28 eV) on concave site could be determined compared with that on pristine BH (0.32 eV). Similar to enhanced Ead by H vacancies, the decreasing trend of Ebar also showed a distance effect (i.e., the closer to the defects, the lower Ebar). In particular, Ebar decreased to only 0.03 eV for the diffusion along path 5, indicating ultra-fast diffusion dynamic for this path. With regards to the diffusion of K-ion through the convex side, the minimum energy path (MEP) was the diffusion along path 7 with Ebar of 0.29 eV, which was slightly lower than that of the K-ion diffusion on pristine BH. Generally, apart from improving the interaction between K and substrate, H vacancies also improved the diffusion dynamics of K-ion.

17



3.5 K storage on BH monolayer Having revealed the adsorption and hopping behaviors of K-ion on a defective BH, we examined the open-circuit voltage (OCV) and theoretical specific capacity (TSC). A series of intermediate KxB24H23 products with different stoichiometries (x = 3, 6, 9, and 12) were considered to simulate the charging/discharging process. For each K-ion concentration, several possible intercalation configurations were investigated to identify the most stable one. The maximum capacity was achieved when the OCV became non-positive or convergent. Accordingly, we calculated OCV values at each stage along with the corresponding energetic configurations (Figure 8a). More details about the average adsorption energies (Eave) as a function of the K concentrations are shown in Figure S4.

Figure 8. (a) Calculated open-circuit voltages (OCVs) as a function of storage capacity and the corresponding configurations of K intercalation in BH electrode (inset). (b) Comparison of the capacities between defective BH electrode and other typical anode KIB anode materials reported.10-15, 17, 18, 51-54 * These data were converted by using Formula (2) for comparison, since the mass of embedded K was considered when calculating the capacity in the original texts. At early stages of intercalation, K tended to adsorb on the convex side of defective BH monolayer, while K was evenly distributed on both sides at higher concentrations. In addition, the potential drops at different charging/discharging platforms remained 18


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very smooth, revealing a steady output voltage for the BH electrode. We note that this quite constant potential drop has also been observed in Shukla et al.’s investigation on BH anode for Li-ion battery.26 Previous reports indicated that, for practical application, the ideal potential range of an anode should be within 0.1 – 1.0 V.55 Low OCV values in the anode could produce high output voltages when integrating into a full battery. Benefiting from the enhanced affinity of a defective BH monolayer to K, the average voltage was calculated to be 0.24 V, slightly higher than that of a commercialized Li−graphite system (ca. 0.15 V)56. According to Formula (2), the TSC of K in a defective BH electrode was calculated to be 1138 mAh/g with a chemical component of K12H23B24. Figure 8b shows the comparison of K capacities between BH monolayer and other typical 2D anodes.10-15, 17, 18, 51-54 Noteworthy, if we consider the mass of the adatoms, TSC is numerically lower.

To eliminate this discrepancy, the TSC were recalculated without consideration of the mass of adatoms. As shown in Figure 8b, the low average atomic mass and excellent affinity to K of B-based anodes provide these materials with inherent capacity advantages for KIBs. Although χ3 borophene possesses the highest K storage capacity among the materials studied herein, its complex and expensive synthesis limits large−scale applications. In contrast, BH monolayer is more stable and could be fabricated by a simple ion-exchange method. Moreover, the BH electrode delivered very high capacity (ca. 6 times larger than that of Ti3C215, 4–5 times higher than those of graphite10 and V2CSi254, and 2–3 times larger than those of black phosphorene12, MoN251, TiS213, VS214, GeS52, and Ti2CSi254. The lattice expansions of the BH electrode in the x−y plane were calculated to be only 1.85 % under full K intercalation, reducing the risk of electrode pulverization. The ultra-high theoretical capacity, appropriate OCV, and affordable voltage expansion upon charging of the defective BH monolayer make this material appropriate for fabricating flexible KIBs.

19



Figure 9 (a) Top and side views of a K-intercalated BH electrode after 2ps AIMD simulation. (b–f) AIMD simulation of the electrode recovery process with fully removed K. Finally, AIMD simulations were conducted to explore the thermal stability of a potassiated defective BH electrode at room temperature. The snapshots of the configurations at a given time (2ps) are shown in Figure 9a. Generally, the overall structures remained intact with K-ion adsorbed separately on the electrode, although structural deformation was clearly observed. To evaluate the reversibility of the electrode, the intercalated K-ion were removed and performed further AIMD simulations on the residual anode (Figure 9b−f). The deformed electrode was fully recovered to its embryonic structure after 0.4 ps at 300 K, indicating good cyclical stability. To this end, we investigated the electronic conductivity of the BH electrode at different intercalation concentrations. As shown in Figure S5, the main contribution of electronic states at the Fermi level shifted from B−2p orbits to the 3p orbital of K upon increasing K concentration. A large number of electrons injected to substrates from K occupied the empty states of the defective BH monolayer, producing an upward of the Fermi level. Thus, the BH electrode provided excellent conductivity upon charge/discharge cycling without the need for extra conductive additive, which is 20


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beneficial to reduce the ohmic heat.32

 CONCLUSIONS The feasibility of BH substrates as flexible KIB anodes for powering wearable electronics was systematically investigated by DFT and AIMD calculations. Both pristine and defective BH monolayer materials showed metallic characteristics, strong in-plane stiffness, and ultrahigh flexibility, holding great potential as flexible KIB anodes. In particular, the calculated bending stiffness of the BH electrode was quite small. These values were significantly lower than those of well-known flexible electrodes such as graphene and MoS2. Moreover, the BH-based electrode showed favorable affinity to K-ion with a satisfied hopping barrier, regardless the external bending. The EF for hydrogen vacancies in BH electrode was as low as 1.06 eV and the generated H defects did not gather together because of the high vacancy migration barrier. The formation of H vacancies in the BH anode enhanced the affinity of the electrode to K and substantially reduced the K-ion hopping barrier. This enhanced electrode activity produced by the H vacancies resulted in high theoretical capacities and OCV values for the K-BH system (1138 mAh/g and 0.24 V, respectively). Besides, the fully intercalated BH electrode showed a volume expansion as low as 1.85 %, showing excellent cycling stability, as further confirmed by AIMD simulations. All the presented results suggested that a BH electrode with a small amount of H vacancies could be used as a flexible and lightweight KIB anode with high capacity, low voltage, and desired rate performance.

 ASSOCIATED CONTENT Supporting Information Details of the optimized BH nanotubes; stress-strain curves for pristine and defective BH; schematic migration pathways of hydrogen vacancy in defective BH 21



monolayer, and the calculated energy profiles and AIMD simulation results; the most energetic configuration of K-ion adsorbed defective BH and the average adsorption energy (Eave) at different K-ion concentration; partial density of states (PDOS) for different K-ion on defective BH.

Notes There are no conflicts of interest to declare.

 ACKNOWLEDGEMENTS Funding: This work was supported by china postdoctoral science foundation (2017M623306XB) and special funding for postdoctoral research projects in Sichuan.

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 TABLE OF CONTENTS

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Highly Flexible Hydrogen Boride Monolayer as Potassium-ion Battery

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