Understanding the different diffusion mechanisms of hydrated protons

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Understanding the different diffusion mechanisms of hydrated protons and potassium ions in titanium carbide MXene Jing Wen, Qishan Fu, Wanying Wu, Hong Gao, Xitian Zhang, and Bin Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b21117 • Publication Date (Web): 24 Jan 2019 Downloaded from http://pubs.acs.org on January 24, 2019

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ACS Applied Materials & Interfaces

Understanding the different diffusion mechanisms of hydrated protons and potassium ions in titanium carbide MXene Jing Wen1,2, Qishan Fu1, Wanying Wu1, Hong Gao1, Xitian Zhang*,1, Bin Wang*,2 1Key

Laboratory for Photonic and Electronic Bandgap Materials, Ministry of Education, School of Physics and Electronic Engineering, Harbin Normal University, Harbin 150025, P. R. China 2School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, OK 73019, USA ABSTRACT: The high intercalation capacitance of MXenes is attractive, but their performance as electrodes in supercapacitors is limited by mass transport when increasing the thickness and mass loading of the electrodes. Here, we report a combined experimental and computational study, through which we reveal the diffusion of hydrated ionic species at the interlayer spaces. We find that the cyclic voltammetry curves for the delaminated Ti3C2Tx exhibit distinct features in acid (H2SO4) and alkaline (KOH) electrolytes. The DFT-calculated migration profile of K+ and H+, in the presence and absence of water, suggests that the intercalated water molecules stabilize the charged ions, facilitating their diffusion from two dimension to three dimension manifested by the reduced activation barriers and movement pathways. In addition, we show that the diffusion of low and high concentrations of protons is significantly different. That is, protons of high concentrations can adsorb at both sides of the interlayer spaces, and water drives frequent proton hopping between stable adsorption sites as shown in the ab initio molecular dynamics simulations. The calculations can thus explain the varied capacitance and distorted CV curves when the experiments are conducted in acid and alkaline electrolytes. These results can provide the guidance to improve the fast transport of ions and electrons in MXenes with high mass loading.

KEYWORDS: MXene, diffusion mechanism, DFT calculations, cyclic voltammetry

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1. INTRODUCTION Over the past decade, much effort has been devoted to develop efficient electrode materials for high-performance energy storage.1-2 The energy and power densities of the electrode materials depend strongly on the charge storage processes.3-5 Intercalation capacitance, as a highly efficient charge storage process, has attracted much attention.6 It combines two elementary steps – intercalation and surface adsorption – through fast ion diffusion and bulk redox reactions. Some representative materials, such as T-Nb2O57 and MoS28, have been discovered. Among these materials, a large family of 2D transition metal carbides and carbonitrides, so-called MXenes, are particularly promising electrode materials for application in supercapacitors because of their high intercalation capacitance.9-14 MXenes can be generally formulated as Mn+1XnTx (n=1, 2, 3), where M is an early transition metal, X is C and/or N, and T represents the surface functional groups. Ti3C2Tx, the first synthesized and the most studied member in the MXenes family, has shown ultrahigh volumetric capacitance of 900~1500 F/cm3 under the thin-film condition.11,

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This

value is comparable with the volumetric capacitance of noble metal oxides, such as the state-of-the-art mesoporous RuO2.16 Furthermore, the ability of spontaneous intercalations of a variety of alkali metal and multivalent cations in the MXenes broaden their application in non-Li ion energy storage.17-19 The large volumetric capacitance of MXenes suggests that the redox reactions occur not only at the surface like MnO2,3 but also involving the bulk active sites. As a more direct evidence of the bulk redox reactions, in situ X-ray absorption spectroscopy measurements have shown that the charge storage of Ti3C2Tx is accompanied by continuous changes of the titanium oxidation state during cycling in sulfuric acid20 or during lithiation/delithiation in Li-ion batteries,21 suggesting that bulk material is indeed involved during the charge storage. This process is thus referred as the intercalation pseudocapacitance. The electrochemical performance improves when the thickness of the electrodes reduces.11, 15 Note increasing mass loading and thickness of

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the electrodes can significantly decrease the volumetric capacitance;11, 22 Elimination of the diffusion limitation to reach the bulk active sites, particularly at high loading and using films of larger thickness, remains as a key challenge for applying Ti3C2Tx in supercapacitors, where the industrial standard of the film thickness is about 100 micrometers. More recent efforts to reduce the diffusion limitation include development of vertically aligned liquid-crystalline MXenes.13 Understanding the diffusion mechanism of charged ions between layers in Ti3C2Tx is thus very valuable not only for providing fundamental insights of the nature of the charge storage process but also for further improving the capacitance of the MXenes family.20-21, 23-35 However, the study about the microscopic processes of hydrated ions diffusion in the interlayer spaces of MXenes is scarce. Previously N. Osti et al. has studied the water diffusion coefficient influenced by the intercalated K ions by experiments.36 The difficulty to understand the mechanisms is partially caused by different kinetic behaviors existing in different electrolytes. In addition, the surface electrode structures are difficult to be well defined: the structures may vary with synthesis methods and treatment processes.37-43 To ambiguously describe the microscopic ion diffusion processes in MXene, a consistent picture remains to be developed. Here we report a combined experimental and computational study, through which we reveal the diffusion properties of the hydrated protons and K ions, at an atomic scale, in the host structure. We find that the measured cyclic voltammetry (CV) profiles of the delaminated Ti3C2Tx paper exhibit significantly different diffusion processes in the H2SO4 and the KOH electrolytes. The Density functional theory (DFT) calculations show three dimensional (3D) diffusion pathways and kinetic processes for the hydrated ions, as compared to the two dimensional (2D) diffusion in the absence of water. The diffusion processes depend on the concentration of the intercalated ions, the diffusion potential surface, and the presence of water molecules. Moreover, the CV curves, measured under different scan rates, can be explained by the ionic dynamics in the ab initio molecular dynamics (AIMD) simulations - that is, the results can be directly correlated to the distinguished diffusion abilities of the ions 3



under different concentrations and hydrated states. These results thus provide a general picture and guidance for improving the fast transport of ions to reach the active sites in MXenes even with high mass loading. 2. EXPERIMENTAL AND COMPUTATIONAL METHODS The delaminated Ti3C2Tx paper was synthesized from Ti3AlC2 by removal of Al using etchant of LiF plus HCl solution. Experimental details on synthesis and characterization of the sample have been described in our previous report.44 Electrochemical experiments were performed under a standard three-electrode configuration with the Pt plate and carbon rod selected as the counter electrodes for the KOH and H2SO4 electrolytes, respectively. The Ag/AgCl was used as the reference electrode. The CV measurements were conducted on the Ti3C2Tx paper electrodes. The current and capacitance can be converted using the formula of

C   idV / ( sV ) , where i is the volumetric current density and s is the scan V

rate, V is the voltage window. The DFT calculations were performed using the VASP code.45 Exchange and correlation potential employed the generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) functional.46 The ion-electron interaction was described using the projector-augmented wave (PAW) method.47 A plane-wave cutoff energy of 400 eV in combination with the 9  9 1 k-point grids were applied to all the unit structure models with two formula units in each cell. Similar grid separations were used for the other supercell structures. Each equilibrium configuration was obtained by relaxing the atomic coordinates under the force criterion of 0.03 eV/Å per atom. The total energies have included the Van der Waals (vdW) correction by using the Grimme’s DFT-D2 method,48 which provides reasonable atomic structures at the interfaces.49 In the AIMD calculations, the time step was set to be 1.5 fs and the temperature was determined by velocity scaling at each step with conserved energy. The calculations were performed at room temperature (300 K) first to simulate the experiment condition, but the migration

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ranges of the ions are too small to be employed to clarify their diffusion properties; thus, the initial temperature was set to 600 K to speed up the ionic diffusion within the simulation period. The relationship between the c-axis value (denoted by c) and the content of intercalated H2O (denoted by m) have been clarified50 as c  21.6  6.653m0.428 based on the formula of Ti3C2O2·mH2O. The c-axis value is 25.8 Å for our delaminated sample, so a simplified structural model of Ti3C2O2·1/3H2O has been adopted for the calculation. The calculated results and conclusions can be generalized to samples with varied concentrations of water as discussed below. To model the fractional portion of water, a 1  3  1 supercell configuration consisting of six formula units has been built to simulate the sample (Figure S1). When evaluate the stability of atomic species intercalated between layers in Ti3C2O2·1/3H2O, the chemical potential was calculated based on the formula given by

 A  [ E Asite (c )  Ehost (c )  n Aref ] / n, where E Asite (c) and Ehost ( c ) are the total energies of intercalated structure and the optimized host with the consistent c-axis value determined by the content of intercalated water, respectively.50 n is the number of intercalated A element per formula unit and  Aref is the referenced chemical potential of A in the bulk state. 3. RESULTS AND DISCUSSION Figure 1a shows the scanning electron microscopy (SEM) image of the sample. It is generally accepted that the Ti3C2Tx sample is terminated with –O, –OH, and –F functional groups,10, 51 and their ratios and distributions depend on the experimental conditions and processes.52 If the etching process is carried out in the HF solution, the dominated terminations is often the –F groups.52 Substitution of the –F groups by –OH and –O can be realized by thermodynamic fluctuation processes.40 If a mixture of LiF and HCl is used instead of HF, delaminated sheets of Ti3C2Tx can be obtained as shown in Figure 1b. Each sheet consists of a few atomic blocks of Ti3C2Tx unit. 5



Water molecules and hydrated ions can be adsorbed between the sheets. After treating the samples by alkali metal ions,36 the adsorption of the hydrated ions can diminish the separation between layers and make the paper more compact. The presence of –F(–Cl), –OH, –O, –Li, and interlayer water molecules have been found in the interlayer spaces of the sheets as indicated in Figure 1c.44 Different from the samples etched by HF, the more favorable terminations of the delaminated sheets are often the O-containing groups.50,

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In addition, the interlayer distance of the sheets can be

expanded from 9.6 to 12.9 Å due to the intercalations of the H2O molecules and hydrated ions. DFT calculations suggest this expansion is caused by transformation from the H-bonds between layers to the hydrated ions (Figure S2).50 Therefore, a generalized formula for Ti3C2Tx can be expressed as Ti3C2(F[Cl])xOy(OH)zAn·mH2O, where A denotes the intercalated mental element, F[Cl] denotes that a portion of –Cl occupy the equivalent sites of –F as shown in Figure 1c. DFT calculations suggest that it is unstable for the F-containing unit to adsorb K or H, so in the following discussion we don’t take the contribution of –F into account while the electrolyte is chosen as KOH or H2SO4. Figure 2 shows different CV profiles of volumetric capacitance vs. potential curves in 1 M KOH and 1 M H2SO4 electrolytes. The difference under different scan rates becomes more obvious in the plot of the current vs. potential profiles. We find that the capacitance behavior of the sample – a typical square shape in the CV curve – in the H2SO4 electrolyte can not be maintained well under the high scan rates, which is different from the case when the electrolyte is changed to KOH. In addition, the capacitance obtained in H2SO4 is much higher than it in KOH. These significant differences may be ascribed to the inherently different diffusion processes for the protons and K ions at varied scan rate, correspondingly, different ionic concentrations. This clear difference motivated us to explore their microscopic diffusion processes in the host structure. Migration pathways of intercalated ions can be employed to illustrate the microscopic diffusion processes. A preferred trajectory depends on the local minimums of energy and the activation barrier between the two energy minima. Figure 3 shows the 3D energy surfaces of intercalated K ions, which have been calculated based on the adiabatic trajectory method.53 Figure 3a shows the structure model to illustrate the 6


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diffusion pathways in the representative migration planes. Taking the lower half of the unit for example, the diffusion range in each interlayer space along the c axis, ranged from 0.21c to 0.29c, has been calculated (Note c= 25.8 Å for this sample). The global minimum of K ion in the unit is located at 0.22c (denoted by 0.22c-plane, which is about 2.06 Å from the Ti3C2Tx surface oxygen). The K is located above the carbon in the Ti3C2Tx layer. As shown in Figure 3b, two optimized pathways can be distinguished at the energetically favorable 0.22c-plane: Along the a axis, the energy barrier is 0.13 eV (pink arrow), while it is 0.11 eV along the b axis. There are two local minima along the b axis (black arrow); The migration along this path need overcome a small barrier of 0.10 eV from the site above the C atom to the site above Ti, followed by migration to another unit by overcoming a barrier of 0.11 eV as depicted by the inset in Figure 3e. The asymmetric behaviors along the a- and b-axis directions result from the different concentrations of K ions along the two crystal directions: The concentration along the a axis is equivalent to 1 and that along the b axis equivalent to 1/3 based on the 1  3  1 supercell configuration. The stability of intercalated K ions decreases with the intercalation concentration (Figure S3a); The chemical potential increases from −2.0 eV to −0.5 eV when the K-ion concentration r in Ti3C2O2Kr increases from 1/3 to 1. The diffusion process seems to be easier for the high concentration case (a-axis direction). Instead of diffusing on the most stable 0.22c-plane, K ions have chances to take other diffusion channels. For example, Figure 3c shows that at the 0.25c-plane, which is about 2.84 Å above the top O atom, diffusion has no barrier along the a axis and 0.03 eV along the b axis, leading to nearly thermal movement of K ions. We identify the saddle point for K diffusion along the c axis is located at 0.25c-plane. Diffusion of K ions along the c axis from 0.22c- to 0.25c-plane saddle point needs to overcome a barrier of 0.21 eV as shown in the upper part of Figure 3d, supported by the AIMD simulations (see below). Now we investigate the effect of water on the diffusion of K. The adsorption energy is −0.44 eV for the intercalated H2O with respect to a free H2O molecule. The position at 0.25c-plane above the Ti atom (denoted by the Wyckoff letter of 2b) in the Ti3C2Tx layer is the energy minimum for water adsorption (see Figure S4). We find that the movement of H2O in the interlayer space is nearly barrier-less as shown in Figure S4: the diffusion barrier of H2O is only 0.03 eV in the ab-plane and about 0.01 eV along the c axis. The moderate adsorption energy and marginal diffusion barriers suggest 7



water can adsorb and diffuse almost freely between layers. The intercalated water may significantly affect the dynamics of K. Figure 3d shows the adsorption and diffusion (along the c axis) profile of K with and without a H2O molecule. The chemical potential of K can be lowered by 0.75 eV due to the extra interactions between the ion and the H2O molecule. The diffusion barrier along the c axis is reduced to 0.14 eV in the presence of water, lower than the value of 0.21 eV without water. The diffusion at the 0.22c-plane become also more favorable for the K ion as shown in Figure 3e: the barriers along the a and b axes are decreased from 0.13 to 0.04 eV and from 0.11 to 0.10 eV, respectively. Therefore, the high mobility of H2O and the interaction between water and the K ions can facilitate the diffusion of K ions. If the water amount is rather low in the Ti3C2Tx layer, we expect that the intercalated H2O molecules can move freely in the interlayer spaces, due to the low diffusion barriers, and drag the encountered K ions. It should be noticed that the valences of K show different values at varied positions and with different concentrations as shown in Figure 3d and Figure S3a, which indicate the ionic and covalent bonds coexist between the K and host structure. The change of valence state of Ti during the charging and discharging processes should thus also correlate with the positions and concentrations of the intercalated ions, in line with the previous experiments.21 The co-exiting ionic and covalent bond at the interface cause varied charge redistribution between K and the host material during the K migration, which may further lead to modified migration potential surface; this charge redistribution should have much less pronounced effect than the effect of concentration and the presence of water. If the intercalated ions are protons rather than K ions, such as when the experiments were run in the acid conditions (Figure 2), the diffusion pathways exhibit significant differences. Figure 4a shows that, in the absence of H2O, the energy minima of protons are located at the top of O at 0.18c-plane (or the symmetrical 0.32c-plane). The migration profile at the favorable 0.18c-plane is plotted in Figure 4b; Three minimum energy paths (pinked arrows) can be connected with a small barrier of 0.06 eV, which means that the diffusion of protons at the 0.18c-plane nearly have no hindrance if the surrounding minimum energy sites are available. Once the protons hop from the 0.18c-plane along the c axis to the 0.25c-plane, the migration in the 0.25c-plane is nearly free (Figure 4c): the barrier at this plane is only 0.01 eV. However, it is difficult for the proton to migrate from the 0.18c-plane to the 8


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0.25c-plane because of a large barrier of 2.9 eV along the c axis (Figure 4d). Figure 4d shows the chemical potentials of the hydrogen species with respect to that of H2 along the c axis in the units with and without a H2O molecule. The chemical potential of the isolated H in the middle region (0.25c-plane) is considerably larger than that at the state of H2, and the valence becomes close to 0, so formation of H2 is inevitable while two isolated H encounter in this region. The diffusion of proton is significantly different in the presence of a H2O molecule. The valence of H always remains at the +1 state, indicating that the water molecule helps to stabilize the positive charge. The chemical potential of the proton is decreased by 0.45 eV compared with that in the water-free units at the energy minimum. The water lifts the proton a little bit to the 0.19c-plane. There are no significant changes for the allowable pathways in the ab-plane compared with that in the water-free units. The activation barrier along the c axis, from the 0.19c-plane to the 0.25c-plane, is decreased to 1.46 eV, much lower than the value of 2.9 eV in the absence of water. It can significantly increase the chances of the protons to migrate from the 0.19c-plane into the 0.25c-plane as confirmed by the AIMD simulations below. We find that hydrogen species can also adsorb at both sides of the interlayer space, pointing to each other, which can explain the larger capacitance when the experiments were conducted in the acidic electrolytes than it in the KOH solution. To model this high concentration of protons, a configuration with three adsorbed H and one H2O molecule present in the interlayer space has been explored. Two of the adsorbed H species have been denoted by H1 and H2 shown in Figure 5a. It is less stable for the hydrogen placed at the two opposite sides pointing to each other (H1) than that at only one side (H2) as indicated in Figure S3b. DFT calculations show that their chemical potential can differ by up to 0.11 eV. Caused by this reduced stability and water-mediated diffusion, the diffusion profile of H1 and H2 are significantly different as shown in the AIMD simulations. Figure 5b, 5c 5d give the mean square displacements (MSD) of the hydrogen species projected along the c, a, and b axes, respectively. The diffusion range of H1 along the c axis shown in Figure 5b is significantly enhanced in the presence of the H2O molecule. The H1 proton can hop between water and the surface adsorption site. In addition, the diffusion of the 9



adsorbed H1 and H2 along the a and b directions also illustrate different migration behaviors. H1 shows typical hopping behavior between stable adsorption sites, assisted by the water molecule, while H2’s MSD profile suggests continuous surface diffusion. The water-mediated hopping behavior ensures the exchanges of the ions among their different stable states during the intercalation/deintercalation processes. Now we can turn our attention to the diffusions of K with and without water molecules as shown in Figure 6a. The K ions can hop periodically along the c axis as shown in Figure 6b, in agreement with the marginal activation barrier for vertical diffusion found in the DFT calculations (Figure 3). The presence of water further enhances its diffusion into the different 2D ab-planes. Along the a (Figure 6c) and b (Figure 6d) directions, we observed surface diffusion of K and occasional hopping between stable sites both with and without water. These results confirm that the presence of water can facilitate the 3D movements of the ions at the interlayer spaces due to the reduced activation barriers of the hydrated ions. The experiments were conducted at room temperature, so the calculated MSD along the c axis for the H and K under the conditions of 300 and 600 K have been plotted together in Figure S5 for the comparative purpose. The main movement properties can be identified from the results based on the room temperature condition, which is consistent with the features that obtained from the condition of 600 K. The results from DFT calculations and AIMD simulations can thus be used to explain the experimental finding. Experimentally, we find that the capacitance is higher in H2SO4 than in KOH, and that the capacitance behavior of the sample – the typical square shape CV curve – in the H2SO4 electrolyte can not be maintained very well under the high scan rate, but it becomes better if the electrolyte is changed to KOH. These differences may be attributed to the inherently different adsorption and diffusion processes for the protons and the K ions, which are summarized in Table S1. The K ions can only be located in a single layer configuration in the interlayer spaces while the c-axis value of the sample is no more than 29 Å as confirmed by DFT calculations. If more than a single layer, the chemical potential of K will be positive and unstable.50 This limitation cannot be applied to the protons. The low scan rate makes the proton 10


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experience the high concentration condition. Many units can host two H at the opposite sides of interlayer space just like the configuration shown in Figure 5a and Figure S3b, so they can move more freely with the help of water just like the case of H1. The two-layer configurations can give the higher capacitance for the H2SO4 than KOH, which is consistent with the experimental results. In contrast, the high scan rate can only trigger the migration process under the low concentration condition with single layer population like the case of H2 shown in Figure 5. So the profile of CV curve obtained in H2SO4 can be deformed more significantly, due to the modified proton adsorption and diffusion under the high and low concentrations, than that in KOH. The deformation of the curves should not be inevitable. One strategy is to increase the content of water in the interlayer spaces to increase the diffusion abilities of the intercalated ions as confirmed by the calculated results. The other strategy is to increase the conductivity of the sample. The improved conductivity can directly affect the net accumulation of electrons in the electrode and provide the extra drag force to help the ions to move in the interlayer space. 4. CONCLUSIONS In conclusion, we have studied the diffusion behaviors of hydrated protons and potassium ions in the interlayer spaces of delaminated Ti3C2Tx in the H2SO4 and KOH electrolytes. The diffusion processes of the ions depend on the migration pathways, activation barriers, concentrations, water molecules, and stabilities of the intercalated ions, leading to different charge/discharge behaviors under low and high scan rates in the CV measurement. Different from the 3D diffusion pathways for the K ions regardless of whether the water molecules are present or not, protons diffusion is rather limited to ab-plane at room temperature under the low concentration condition. The existence of water molecules can facilitate the hopping behaviors and 3D multipath movements of the K ions and protons. The different stabilities of the protons under the two layer occupation configuration makes their migration processes easier to be affected by the scan rates, which can lead to more significant deformation

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in the CV profiles as observed in the experiments. These results can provide the guidance to optimize the configuration of the MXenes for maintaining the capacitive behaviors of the materials with high mass loading and thickness. AUTHOR INFORMATION *Email:

[email protected]; [email protected]

ORCID Bin Wang: 0000-0001-8246-1422 Xitian Zhang: 0000-0001-6111-8844 Jing Wen: 0000-0002-9107-8377 ACKNOWLEDGEMENTS: This work was partially supported by the Natural Science Foundation of China (No. 51772069, 51472066, and 51772070), Doctoral Foundation of Harbin Normal University (XKB201813). BW appreciates funding from the U.S. Department of Energy, Basic Energy Sciences (Grant DE-SC0018284). NOTES: The authors declare no competing financial interest. Supporting Information： Atomic structure model for simulation, the transformed structures of the host with different pillars, calculated chemical potentials of K and H with different concentrations in the host, migration energy surface of water in the host, comparison results of MSD for H and K at 300 and 600 K, and the table to summarize the diffusion properties of K and H.

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Figure 1. Structures of the delaminated Ti3C2Tx sample. (a) SEM image of the sample. (b) Configuration of the Ti3C2Tx sheets stacked along the c axis. (c) Atomic structure of each Ti3C2Tx sheet that consists of few atomic blocks of functionalized Ti3C2Tx and the intercalated groups. 375x117mm (300 x 300 DPI)



Figure 2. Electrochemical performances of the Ti3C2Tx paper electrode. (a) Current density (left) and volumetric capacitance (right) vs. potential curves at different scan rate in 1 M KOH electrolyte. (b) Current density (left) and volumetric capacitance (right) vs. potential curves at different scan rate in 1 M H2SO4 electrolyte. 249x154mm (300 x 300 DPI)


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Figure 3. Energy surfaces and migration pathways of the intercalated K ions in the water-empty and watercontaining units. (a) Structure model of the Ti3C2Tx sample and the representative migration planes denoted by their positions along the c axis, such as 0.22c-plane and 0.25c-plane. (b) Migration energy surface and migration pathways of the K ions in the energetically favorable 0.22c-plane in the water-empty unit. (c) Migration energy surface and migration pathways of the K ions in the 0.25c-plane. (d) Calculated chemical potentials of K along the c axis in the water-empty and water-containing units denoted by Ti3C2O2K1/3 and Ti3C2O2K1/3•1/3H2O. (e) Activation barriers and migration pathways of K located in the 0.22c-plane along the a- and b-axis directions in the water-containing unit denoted by Ti3C2O2K1/3•1/3H2O. 307x167mm (300 x 300 DPI)



Figure 4. (a) Structure model of the unit structure with the favorable migration plane of hydrogen denoted by their positions along the c axis. (b) Migration energy surface and migration pathways of hydrogen in the energetically favorable 0.18c-plane in the water-empty unit. (c) Migration energy surface of hydrogen in the 0.25c-plane. (d) Calculated chemical potentials of hydrogen along the c axis in the water-empty and watercontaining units. 222x195mm (300 x 300 DPI)


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Figure 5. Structural configuration (a) and mean square displacements of the adsorbed hydrogen species projected along the c (b), a (c), and b (d) axes, respectively. 200x111mm (300 x 300 DPI)



Figure 6. Structural configurations of K in the water-containing and water-empty units denoted by K1 and K2 (a) and the mean square displacements of K projected along the c (b), a (c), and b (d) axes. 204x115mm (300 x 300 DPI)


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Understanding the different diffusion mechanisms of hydrated protons

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