ARTICLE pubs.acs.org/JPCC
First-Principles Theory of Electrochemical Capacitance of Nanostructured Materials: Dipole-Assisted Subsurface Intercalation of Lithium in Pseudocapacitive TiO2 Anatase Nanosheets Joongoo Kang,*,† Su-Huai Wei,† Kai Zhu,† and Yong-Hyun Kim*,‡ †
Chemical and Materials Science Center, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States ‡ Graduate School of Nanoscience and Technology (WCU) and KAIST Institute for the NanoCentury, KAIST, Daejeon 305-701, Korea ABSTRACT: As the size of the material decreases to the nanoscale, the distinction between batteries and electrochemical capacitors becomes obscured. Here, a first-principles approach is developed to calculate electrochemical capacitance of nanomaterials. Using TiO2 anatase nanosheets interfaced with lithium ion-containing electrolytes as an example, we reveal a microscopic mechanism for lithium intercalation in this system. We demonstrate that a TiO2 nanosheet is a hybrid of supercapacitor and battery, possessing characteristics of both depending on electrode potential. At positive electrode potential above 2.2 V versus Li/Liþ, the system behaves as capacitor with the formation of electric double layers at the surface. As the electrode potential decreases below the threshold, lithium intercalation into the interior takes place, assisted by the surface electric dipole field. Our findings provide a coherent picture of how a transition from pure capacitors to batteries or pseudocapacitors occurs in these nanostructured materials.
1. INTRODUCTION Both batteries and electrochemical double-layer capacitors, or supercapacitors, store electrical energy in materials; the former usually have high energy density and the latter have high-rate discharge capability.1-3 In lithium-ion batteries, electrochemical energy is stored at an anode material during the charge cycle. When discharge occurs, electron and ion arrive at a cathode material through different pathways, i.e., electron-conducting wire and ion-conducting electrolyte, respectively. The charge/discharge of batteries is usually characterized by a voltage plateau, as shown in Figure 1. In contrast, electrochemical double-layer capacitors store energy directly as charge. Unlike in conventional dielectric capacitors, the electric charge is stored in an electric double layer set up by ions at the interface between a high-surface-area electrode (e.g., activated carbon4) and a liquid electrolyte. Then, the charge (Q) is a linear function of voltage (V) with a characteristic slope, i.e., Q = CV (Figure 1), where the classical capacitance C = εε0A/d, ε is the electrolyte dielectric constant, A is the surface area of the electrode, and d is the interlayer distance of the electric double layer. The supercapacitors have ultrahigh capacitances of about 100 F/g, compared to capacitances of traditional dielectric capacitors typically measured in microfarads. In addition to the high surface area, the nanometer-scale charge separation is the main origin4 of the ultrahigh capacitance. Although lithium-ion batteries and supercapacitors are widely deployed and mature at the industrial level, each technology suffers from its own shortcomings.2,3 Batteries typically show a r 2011 American Chemical Society
low power density and a short cycle life compared to high-power and long-lasting supercapacitors. On the other hand, supercapacitors can store only a fraction of the energy that a battery can store for a given volume or weight. To overcome those shortcomings, each technology has adopted nanostructured materials5 as electrodes, as conceptualized in Figure 1. As the battery material shrinks in size to -3.4 V (vs Vfb), the TiO2 nanosheet behaves as a blocking electrode as in supercapacitors, preventing any Li intercalation. This is because the activation energy, ε2(0) - ε1 = 3.4 eV, should be overcome for the Li intercalation (see eq 4b). As the V is lowered from zero to negative potential, the electric charge is stored with the formation of electric double layers. At the same time, the εcap in eq 4 increases due to the increased dipole field at the surface. At the threshold voltage (-3.4 V vs Vfb), εcap = 3.4 eV, because V = -εcap/e for pure supercapacitor. Hence, when sufficient coverage of the Liþ-EC4 ions is adsorbed on the surface to make V < -3.4 V, the capacitive energy level εcap becomes larger than the activation energy (3.4 eV) for the Li
Figure 10. (a) Potential-capacitance plot in Figure 9b is redrawn with the potential V vs V(Li/Liþ). The capacitance is displayed on a logarithmic scale to show the supercapacitor-pseudocapacitor transition in the discharge cycle. In part b, the simulated potential-current plot is shown for the 1.7 nm thick TiO2 nanosheet ( 3 3 3 and —). The measured cyclic voltammogram of TiO2 nanoparticles (—, red; taken from ref 20) is also shown for comparison. The experimental result is for the cathodic (Liþ insertion) sweep and 7 nm particle size. The same sweep rate (0.5 mV/s) was used for the simulation and the experiment. The simulated current density is enlarged by a factor of 6.
intercalation. Thus, the Li intercalation becomes energetically possible. (2) The second regime is pseudocapacitor behavior. Due to the dipole-assisted Li intercalation at below the threshold electrode potential (V < -3.4 V vs Vfb), the TiO2 nanosheet behaves as a Li-intercalation host as in pseudocapacitors with dramatically enhanced capacitance. The inset of Figure 9a shows the transition from pure supercapacitor (region I) to pseudocapacitor (region II) at V = -3.4 V; a solid line (blue) and a dotted line (red) represent the total charge Q and the partial charge stored at the electric double layers, respectively. In region II, electrochemical energy is stored in the fast redox process at the electrode subsurface as well as in the capacitive charge separation at the electric double layers. The capacitance increases most sharply at V = -4.1 V, which comes from the plateau region and is due to the redox reaction as shown in Figure 6b. In most experiments, Li metal is used as a counter electrode to study the Liþ insertion/extraction processes in TiO2. In this case, a potential of the TiO2 electrode is measured with respect to the Li/Liþ potential of Li metal. In our calculations, a plateau of Li intercalation voltage is located at 1.5 V versus V(Li/Liþ) (Figure 6b), in good agreement with the experimental results.20-22 When the electrode potential V is referenced to Vfb, however, the corresponding plateau appears at -4.1 V, as shown in Figure 9a. From the two plateau positions, we can determine the V(Li/Liþ) in our potential scale, such that V(Li/Liþ) = -4.1 - 1.5 = -5.6 V versus Vfb.28 Using the relation between the two reference potentials, we plot the V-C curve with the potential V versus V(Li/Liþ), as shown in Figure 10a. For the initial discharge cycle (i.e., Liþ adsorption) at V > 2.2 V vs V(Li/Liþ), the TiO2 nanosheet works as supercapacitor. The supercapacitor-pseudocapacitor transition occurs when the potential drops to 2.2 V, and the TiO2 nanosheet becomes pseudocapacitor for V < 2.2 V with much enhanced capacitance. From the calculated capacitance dQ/dV and sweep rate dV/dt, the current density i of cyclic 4914
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The Journal of Physical Chemistry C voltammogram is calculated by i = dQ/dt = (dQ/dV)(dV/dt). Figure 10b compares the simulated V-i plot of the 1.7 nm thick TiO2 nanosheet with the measured voltammogram of the TiO2 nanoparticles with 7 nm particle size.20 The same sweep rate (0.5 mV/s) was used for the simulation and the experiment. Both V-i plots exhibit a sharp peak associated with the redox reaction at the TiO2 electrode. The potential of the simulated peak agrees reasonably well with that of the measured current density. Although the dipole-assisted intercalation of Li was demonstrated for the 1.7-nm-thick TiO2 nanosheet, this would be a general process regardless of thickness since the energy diagram in Figure 3 will not change qualitatively for thicker TiO2 electrodes. Among anode materials, TiO2 anatase is known to have relatively high potential (1.7 V vs Li/Liþ) and thus large energy gain for Li intercalation. However, our calculations showed that the energy gain in TiO2 is smaller than the energy cost of the desolvation process. This would be true for most anode materials with less positive potentials. So, the Li intercalation should be aided by the dipole field across the electric double layers, except for some cathode materials with sufficiently positive potential that overcomes the Liþ-solvent bindings. Thus, in many anode materials where both surface and bulk contribute to electrical energy storage, there will be transitions from supercapacitor to pseudocapacitor to battery type storage.
4. CONCLUSIONS In conclusion, we have investigated electrochemical Li intercalation across the anatase TiO2/electrolyte from first principles DFT calculations. Here we proposed a new, coherent theoretical approach to calculating electrochemical capacitances of nanosystems as a function of electrode potential (V). Our microscopic calculation shows a supercapacitor-to-pseudocapacitor transition of a 1.7-nm-thick TiO2 nanosheet at a transition potential V = 2.2 V versus Li/Liþ. At V > 2.2 V, the Li-ion adsorption on the surface in a fully solvated form (Liþ-EC4) is energetically more favorable than Li intercalation into the nanosheet. Therefore, the system behaves as pure capacitor with the formation of electric double layers at the surfaces. As the V decreases below the transition potential, the Li intercalation into the subsurface occurs, assisted by the surface electric dipole field of the electric double layers. The first-principles capacitor theory presented here is generally applicable to other electrochemical systems. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (J.K.); yong.hyun.kim@kaist. ac.kr (Y.-H.K.).
ARTICLE
’ REFERENCES (1) See the U.S. Department of Energy website: http://www.sc.doe. gov/bes/reports/abstracts.html#EES2007. (2) Simon, P.; Gogotsi, Y. Nat. Mater. 2008, 7, 845. (3) Abru~ na, H. D.; Kiya, Y.; Henderson, J. C. Phys. Today 2008, 61, 43. (4) Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Science 2006, 313, 1760. (5) Arico, A. S.; Bruce, P.; Scrosati, B.; Tarascon, J.-M.; van Schalkwijk, W. Nat. Mater. 2005, 4, 366. (6) Okubo, M.; Hosono, E.; Kim, J.; Enomoto, M.; Kojima, N.; Kudo, T.; Zhou, H.; Honma, I. J. Am. Chem. Soc. 2007, 129, 7444. (7) Wu, N.-L. Mater. Chem. Phys. 2002, 75, 6. (8) Brousse, T.; Toupin, M.; Dugas, R.; Athou€el, L.; Crosnier, O.; Belangerb, D. J. Electrochem. Soc. 2006, 153, A2171. (9) Reimers, J. N.; Dahn, J. R. Phys. Rev. B 1993, 47, 2995. (10) Aydinol, M. K.; Kohan, A. F.; Ceder, G.; Cho, K.; Joannopoulos, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, 1354. (11) Ceder, G.; Chiang, Y.-M.; Sadoway, D. R.; Aydinol, M. K.; Jang, Y.-I.; Huang, B. Nature 1998, 392, 694. (12) Wolverton, C.; Zunger, A. Phys. Rev. Lett. 1998, 81, 606. (13) Koudriachova, M. V.; Harrison, N. M.; de Leeuw, S. W. Phys. Rev. Lett. 2001, 86, 1275. (14) Filhol, J.-S.; Neurock, M. Angew. Chem., Int. Ed. 2006, 45, 402. (15) Taylor, C. D.; Wasileski, S. A.; Filhol, J.-S.; Neurock, M. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 165402. (16) Skulason, E.; Karlberg, G. S.; Rossmeisl, J.; Bligaard, T.; Greeley, J.; Jonsson, H.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2007, 9, 3241. (17) Wagemaker, M.; Kentgens, A. P. M.; Mulder, F. M. Nature 2002, 418, 397. (18) Kavan, L.; Kalbac, M.; Zukalova, M.; Exnar, I.; Lorenzen, V.; Nesper, R.; Graetzel, M. Chem. Mater. 2004, 16, 477. (19) Zukalova, M.; Kalbac, M.; Kavan, L.; Exnar, I.; Graetzel, M. Chem. Mater. 2005, 17, 1248. (20) Wang, J.; Polleux, J.; Lim, J.; Dunn, B. J. Phys. Chem. C 2007, 111, 14925. (21) Brezesinski, T.; Wang, J.; Polleux, J.; Dunn, B.; Tolbert, S. H. J. Am. Chem. Soc. 2009, 131, 1802. (22) Zhu, K.; Wang, Q.; Kim, J.-H.; Pesaran, A. A.; Frank, A. J. Unpublished. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (24) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169. (25) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (26) Graetzel, M. Nature 2001, 414, 338. (27) Li, T.; Balbuena, P. B. J. Electrochem. Soc. 1999, 146, 3613. (28) We can also estimate V(Li/Liþ) by using the results of pure supercapacitors. (1) In eq 3, the adsorption energy of a Li-EC4 molecule is ε = -4.8 eV in a dilute limit. (2) The formation energy of a Li-EC4 molecule is -0.4 eV with Li metal and EC solvent molecules as reference systems. Therefore, V(Li/Liþ) ≈ -4.8 - 0.4 = -5.2 V vs Vfb, which is in reasonable agreement with the value (-5.6 V vs Vfb) from a plateau position of the redox reaction in battery.
’ ACKNOWLEDGMENT We thank A. Frank, S.-H. Lee, A. C. Dillon, and J.-H. Kim for encouraging us to study electrochemical energy storage systems. This work was supported by the DOE/NREL LDRD program under Contract DE-AC36-08GO28308. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231. Y.-H.K. was supported by WCU (World Class University) program through the National Research Foundation of Korea (Grant R31-2008-000-10071-0). 4915
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