Enhanced Lithium-Ion Mobility Induced by the Local Piezoelectric

Transcription

1 Supporting Information to Silicon/Carbon Nanotube/BaTiO 3 Nanocomposite Anode: Evidence for Enhanced Lithium-Ion Mobility Induced by the Local Piezoelectric Potential Byoung-Sun Lee a, Jihyun Yoon b, Changhoon Jung c, Dong Young Kim a, Seung-Yeol Jeon b, Ki-Hong Kim c, Jun-Ho Park a, Hosang Park a, Kang Hee Lee a, Yoon-Sok Kang a, Jin-Hwan Park a, Heechul Jung a,*, Woong-Ryeol Yu b,*, and Seok-Gwang Doo a a Energy Material Laboratory, Samsung Advanced Institute of Technology, 130 Samsung-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do, Korea b Nano & Smart Composite Materials Laboratory, Department of Materials Science and Engineering and Research Institute of Advanced Materials, Seoul National University, 1 Gwanangno, Gwanak-gu, Seoul, Korea c Analytical Engineering Group, Samsung Advanced Institute of Technology, 130 Samsung-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do, Korea * Corresponding author: Heechul Jung (hc0509.jung@samsung.com) and Woong-Ryeol Yu (woongryu@snu.ac.kr) 1

2 1. Morphologies of Si/CNT/BTO nanocomposites (a) (b) 2

3 (c) Figure S1. (a), (b) Scanning electron microscope (SEM) images, and (c) particle size distribution of the prepared Si/CNT/BTO nanocomposites. Figure S2. Raman spectrum of the pristine CNTs. 3

4 2. In situ XRD coin-cell test For the in situ XRD analyses, coin-cells were assembled as shown in Fig. S3 (a). A 5- mm-diameter hole was punched on the bottom of 2032-type coin-cell. The anode slurry (i.e., Si/CNT/BTO nanocomposite and Li-PAA binder, with a nanocomposite-to-binder mass ratio of 9:1) was screen-printed onto the Cu-deposited Al foils, which were 15 mm in diameter. Epoxy resin was pasted onto the surface of the Al foil to prevent leakage of the electrolyte. Sample preparation was carried out in a dry environment. Lithium foil was used as both the counter and reference electrodes. 1.3-M LiPF 6 in EC:DEC:FEC (with a EC:DEC:FEC volume ratio of 2:6:2, Panax Etec) was used as the electrolyte, and polyethylene film (Star 20, Asahi Kasei) was used as the separator. The crystal structure of the Si/CNT/BTO nanocomposite was investigated using powder X-ray diffraction (XRD) (Xʹpert, PANalytical) with a Mo K α source (λ = nm) at angles in the range θ The coin-cells were galvanostatically cycled at voltages in the range V at a rate of 0.1C using a potentiostat (Biologics, VSP-300). Fig. S3 (b) shows the resulting voltage profile. 4

5 (a) (b) Figure S3. (a) Schematic diagram of the coin-cell used for in situ XRD characterization. (b) Voltage time profile during in situ XRD measurements. 5

6 (a) (b) Figure S4. Changes to the BTO (110) peak centre and the FWHM during (a) the first charge and (b) the second discharge. 6

7 3. Electrical conductivity of Si/CNT/BTO composites Si/CNT nanocomposites without BTO were prepared to investigate the role of BTO. Although the density of the Si/CNT/BTO nanocomposite was lower than that of the Si/CNT nanocomposite without BTO, the conductivity was higher than that of the Si/CNT composites, as shown in Fig. S5. It follows that the piezoelectricity of the BTO contributed to the enhanced conductivity of the nanocomposites more significantly than the ferroelectricity of BTO. (Note that BTO nanoparticles are not only piezoelectric, but also ferroelectric. 1 ) (a) (b) Figure S5. Changes in (a) the density and (b) the conductivity of the nanocomposites as a function of the applied pressure. 7

8 4. Electrochemical performances of Si/CNT/BTO composites The galvanostatic intermittent titration technique (GITT) is an effective means to measure the kinetic parameters of the electrode materials. 2 In this work, GITT was far briefly carried out by employing an interval between the charging and discharging processes to measure the quasi-open circuit voltage (QOCV) (i.e., the circuit was opened when the closedcircuit voltage (CCV) reached 1.5 V during charging) in order to check the kinetics change by the pieozoelectric material effect. The Si/CNT/BTO and Si/CNT nanocomposites exhibited QOCVs of V (0.487 V) and V (0.546 V), respectively, as shown in Fig. S6 (a), where the values in the parenthesis represent the difference between the QOCV and the CCV. The difference between the QOCV and CCV may be attributed to the diffusivity of the Liions; 2,3 therefore the lower value for the Si/CNT/BTO nanocomposites implies an increased diffusivity of the Li-ions, which we believe resulted from the piezoelectricity of the BTO nanoparticles. In contrast, the difference in the plateau voltage during the lithiation and delithiation processes was V for Si/CNT/BTO and V for the Si/CNT nanocomposite. The lower value for Si/CNT/BTO suggests better kinetic processes in the electrode. 4 We plotted dq/dv curves based on the first charging cycle and the tenth cycle, as shown in Fig. S6 (b) (e). The Si delithiation potential of Si/CNT/BTO nanocomposite was V, which barely changed up to the 10th cycle, whereas with the Si/CNT nanocomposite it changed from V to V. (a) 8

9 (b) (c) 9

10 (d) (e) Figure S6. (a) Voltage profiles of the nanocomposites, including the interval during the second cycle, (b) dq/dv curves of the nanocomposites during the first cycle (the inset shows magnified dq/dv curves focusing on the Si lithiation potential), (c) dq/dv curves during the second cycle, (d) fifth cycle, and (e) tenth cycle. 10

11 Figure S7. Cycle performance of Si/CNT/BTO nanocomposites with added graphite. 11

12 (a) (b) Figure S8. (a) Cycle performance and (b) rate capability of the Si/CNT/Al 2 O 3 nanocomposites. 12

13 5. Piezoelectric potential of the BaTiO 3 particles Comsol Multiphysics was used to calculate the piezoelectric potential of the BTO particles, which was induced by the compressive stress resulting from the volume expansion of the silicon nanoparticles during the charging step. Fig. S9 shows the two-dimensional (2D) geometry used in the simulations. The material properties of the BTO particles were taken from the materials database supplied with Comsol Multiphysics. A compressive stress of 1.7 GPa was imposed on the surface of the BTO particles. Fig. S9 (a) (c) show the mechanical boundaries and Fig. S9 (d) and S9 (e) show the electrical boundaries. Fig. S9 (f) shows the calculated negative piezoelectric potential of BTO. Negative piezoelectric potentials of -0.05, -0.10, -0.15, -0.20, and V were used as inputs to the electric potential boundaries of the BTO particles during the charging step. Figure S9. Simulation of a BTO particle when compressed. 13

14 6. Battery simulation Comsol Multiphysics was used to simulate the battery system with the piezoelectric BTO nanoparticles in the anode. The simulations were based on Newman s porous electrode model 5 and a capacity fade model. 6 The electrolyte solution was treated as a binary electrolyte consisting of a single lithium salt and single solvent at an operating temperature of 298 K. Porous electrode theory 7 was used, which models the electrode as an effective medium rather than as a single particle. For simplicity the negative porous active material used as graphite from Comsol Multiphysics database. 6.1 Governing equations Liquid electrolyte domain The Nernst Planck equation describes the material balance of the ionic species as follows: 8 c l, (S1) t + Ñ N = R l ct where c is the concentration of Li-ions in the electrolyte, N is the flux of Li-ions in the l l electrolyte, and R ct is the molar rate of the charge transfer reaction (note that the bold font indicates vector quantities). Assuming that the convection flux can be excluded under normal battery operation conditions, 9 the flux of Li-ions is given by: N l = -D l Ñc l + i l, (S2) F t + where D is the diffusion coefficient of the Li-ions in the electrolyte, is the current l density in the electrolyte, F is the Faraday constant, and is the number of transference number of Li-ions, which represents the fraction of the current carried by the specific ion. t i l 14

15 Here, the positive ion is the Li-ion. The governing equation for ionic transport is based on concentrated solution theory; 10 i.e.: eff c eff i t l ( Dl cl ) t A j l il t F F F l s ct, (S3) l where is the volume fraction of electrolyte, is the effective diffusion coefficient of eff D l electrolyte phase, j ct is the current density resulting from the charge transfer at the electrode and electrolyte interface, and eff A s is the specific surface area of the electrode, which is defined as the surface area of the active materials per unit volume of the total electrode; i.e., A 3 r eff s s s, where is the volume fraction and r is the radius of the active particles. s s Making use of: eff i l As jct, (S4) we may rewrite Equation (S3) as follows: eff cl eff i t As jct l ( Dl cl ) l (1 t). (S5) t F F The terms in Equation (S5) describe the diffusion of Li-ions, migration of Li-ions due to electric fields, and Li-ions that leave or enter the electrolyte via the interface of the active particles. Because the electrochemical kinetics occur at the interfaces between the active particles and electrolyte, the interface properties must include the effects of pores. The Bruggeman correction was used to describe the effective transport properties of a porous material; 11 i.e., the effective diffusion coefficient is given by: D i eff = e i g D i (S6) and the ionic conductivity by: 15

16 s i eff = e g i s i. (S7) These terms describe the diffusion coefficient and ionic conductivity of the pure phase i. The Bruggeman coefficient 12 was taken as g = 1.5. The governing equation for charge balance in the electrolyte was modified according to Ohm s law; 10 i.e.: eff eff 2 l RT ln f eff 1 1 t ln c A j F ln c l l l l s ct, (S8) where is the electrolyte potential, R is the universal gas constant, T is the l temperature, and f is the mean molar activity coefficient. 8 Equation (S8) describes an electrolyte consisting of a binary salt using concentrated solution theory Solid electrode domain In the solid electrode domain, Li-ion transport follows Fick s law for diffusion; i.e.: c s, (S9) t = Ñ (-D Ñc ) s s where c s is the concentration of Li-ions. The governing equation for charge balance is Ohm s law; i.e.: i s eff s, (S10) s and the divergence of the current density in the electrode is given by: A j i s eff s ct. (S11) Reaction kinetics (charge transfer) The charge transfer current density over the interfacial area 7 is given by: 16

17 j j j ct rev irr, (S12) where j rev is the contribution from the reversible intercalation reaction and j irr is the contribution from the irreversible solvent reduction reaction or solid electrolyte interphase (SEI) formation reaction. The intercalation reaction is as follows: Li e C LiC, (S13) C f f f where is a free reaction site of the electrode particle. The solvent reduction reaction is: 6 2Li 2e S Li S 2, (S14) S 2 where denotes the solvent and Li S is the irreversible phase. Reversible intercalation and irreversible SEI formation reactions occur on the surface of the porous electrode. The Butler Volmer equation 13 can be used to describe both kinetic reactions; i.e.: j rev afrev cfrev j0, rev exp exp RT RT (S15) and: j irr afirr cfirr ' j0, irr exp exp, (S16) RT RT where rev s irr l Eeq, rev irr s irr l Eeq, irr, j is the local current, density of the charge transfer reaction, j is the exchange current density, and and 0 a c are the anodic and cathodic transfer coefficients. The overpotential is described by the electrode potential, the electrolyte potential, the potential drop due to SEI formation irr s, and the open circuit potential E between electrode and electrolyte material during the reaction. 6 The potential drop can be expressed using Ohm s law; i.e.: eq l 17

18 irr IRirr, (S17) where I is il iedl, iedl is the current density of the electrical double layer, and Rirr is the resistance of SEI layer, which can be expressed as follows: R irr irr irr irr irr, (S18) where and are the resistivity and thickness of the SEI layer, respectively. The increase in the resistance of the SEI layer results in a decrease in the lithium battery capacity over the cycle. The exchange current densities for each intercalation reaction are as follows: a a c a c 0, rev c a s,max s s l l,0 j F( k ) ( k ) ( c c ) c c / c (S19) and: a a c a c 0, irr c a s,max s s l l,0 j F( k ) ( k ) ( c c ) c c / c, (S20) where k is the cathodic rate constant, k is the anodic rate constant, is the c a c s,max maximum concentration of lithium insertion sites, and c l,0 is the initial concentration of Liions. The current density of the SEI layer was assumed to be the limiting current density; i.e., j irr,lim = A/m 2. Therefore, the local current density to form the SEI layer is:. (S21) Using Faraday s law, the thickness of the irreversible interphase at time t is given by: where M is the molar mass of the SEI layer and d is the density of the irreversible phase. irr 1/ 1,lim 1/ ' j j j irr irr irr t ( t) i M / 2Fd d, (S22) irr 0 irr irr irr irr By introducing an electrical double layer capacitance, the change in the potential of the electrochemical system can be made smoother over the cycle. 14 The specific area of the 18

19 double layer area per unit volume of active material was assumed to be as follows: A 3 r edl s neg. (S23) The electrical double layer capacitance was assumed to be density from the electrical double can be expressed as: C edl = 0.2 F/m 2, and the current i ( s l irr ) A C t edl edl edl. (S24) 6.2 Model geometry, boundary conditions, and simulation A simple 2D model of the cell was used, as shown in Fig. S10. The cell was modelled using the 2D geometry shown in Fig. S10 (a), and the following boundary conditions were used. A zero flux boundary was applied at the current collector and the battery boundary, as shown by the blue lines in Fig. S10 (b), indicating that the flux of ionic species was zero; i.e.: n N l = 0, Ñ c l = 0, n i l = 0. (S25) An insulating boundary was imposed where charge transfer reactions cannot occur, as shown by the blue lines in Fig. S10 (c). This boundary can be expressed as follows: n i s = 0, n i l = 0. (S26) app The electric potential around BTO (i.e., ) is shown in Fig. S10 (d). Potentials of -0.05, , -0.15, -0.20, and V were used to investigate the effects of on the electrochemical reactions. Note that an electrical ground was imposed at the negative current collector, and a fixed current density boundary was applied to the positive current collector. The applied current densities at this boundary were I = -24 A/m 2 during charging and I = -24 A/m 2 during discharging. These boundary conditions can be expressed as: app s app (S27) and: 19

20 ni s I. (S28) The initial conditions (i.e., at t 0 ) of the dependent variables,, and c were as follows. For the negative porous electrode and separator domains: 0, (S29) s s l l E ( c c ) l eq, neg s, neg,0 s, neg,max (S30) and: c c l l,0, (S31) and for the positive porous electrode domain: E ( c c ), (S32) s eq, pos s, pos,0 s,max, pos E ( c c ) l eq, neg s, neg,0 s, neg,max (S33) and: c c l l,0, (S34) where the open circuit potentials (OCPs) are a function of the state-of-charge of the battery; 13 i.e.: E ( ) eq, i Eeq, i SOC. (S35) Table S1 lists the maximum concentrations of the inserted particles c si,,max, the initial c si,,0 c l,0 concentration of the inserted particles, and the initial concentration of salt. At the negative porous electrode, the geometry of the active materials was assumed to be spherical. Inside the active materials, transport of Li-ions can occur via diffusion. Charge transfer reactions occur at the solid electrolyte interface; the boundary conditions for this are as follows: cs r r0 0, (S36) 20

21 c ir s m neg Ds r 3 F rr neg m s (S37) and: ict Ns n F, (S38) where the subscript m denotes a reversible or irreversible reaction. The current density is eff described by i A j, and Table S1 lists the radius of the negative active material r, m s m as well as the volume fraction of the solid phase. Table S1 also lists the input parameters required for the simulations. neg The applied piezoelectric potential was much smaller than the evaluated potential (Fig. S9 (f)) considering adverse effects of the electrolytes and the BTO particle is much bigger than the actual particle (D < 100 nm) to simplify the calculation. (a) 21

22 (b) (c) (d) Figure S10. 2D geometry and boundary conditions of the modelled Li-ion battery: (a) The components of the battery model the mass ratio of the active material to BTO was 7:3, (b) zero flux boundary conditions for material transport, (c) insulating boundaries, and (d) electric potential and the current density boundaries. 22

23 Table S1. Input parameters for simulation of a Li-ion battery model. Anode 1.7 Radius of particle ( m ) Cathode 1.7 Volume fraction of solid phase Volume fraction of liquid phase Anode Cathode 0.43 Anode Cathode 0.4 Anode 2.0 Rate coefficient( ms) Cathode Initial electrolyte concentration ( mol m ) Applied current density ( Am ) 24 Equilibrium potential of SEI formation ( V ) Reference current density ( Am ) Conductivity of SEI layer ( Sm) Anode Diffusion coefficient ( m s) 14 Cathode Electrical conductivity ( S/ m ) Anode 100 Cathode 3.8 BaTiO 3 negative current collector positive current collector Initial SEI thickness ( nm ) 0.1 Initial insertion concentration 3 ( mol m ) Maximum insertion concentration 3 ( mol m ) Length ( m) 3 Density of materials ( kg m ) Anode Cathode Anode Cathode negative current collector 7 positive current collector 10 negative electrode 55 positive electrode 55 separator Anode Cathode Separator SEI

24 6.3 Additional results To investigate the effects of BTO weight ratio (with respect to active material) on lithium intercalation reactions, numerical simulations with different BTO contents were carried out. The weight ratios of BTO to active material were set to be 1:9, 3:7, 5:5 and 7:3 as shown in Fig. S11 (a)-(d). The current density profiles and histograms in Fig. S11 showed more intensified current densities as the BTO concentration increased. We also investigated the distribution effect of the BTO by changing the number of BTO particles from 4 to 10, fixing the concentration of BTOs (weight ratio of BTO to active material was fixed 3:7). Although the current density profiles seem to be more uniform as the number of BTO particles increased (see Fig. S12 (a)-(d) below), the median current densities in Fig. S12 (e) were hardly changed and the current densities were more concentrated at about A/m 2. Thus, it can be concluded that the increased BTO concentration resulted in more accelerated charge transfer reaction and more uniform distribution of BTO particles brought about small deviation of the local current density (see Fig. S13). Figure S11. Profiles and distributions of local current density according to different BTO density during charging step. The weight ratios of BTO to active materials were (a) 1:9, (b) 3:7, (c) 5:5, and (d) 7:3. (e) Histograms of local current density distribution. 24

25 Figure S12. Profiles and distribution of the local current density profiles according to different number of BTO particles during the charging step. The BTO concentration (i.e., 30 wt%) was fixed. The numbers of BTO particles are gradually increased: (a) 4, (b) 6, (c) 8, and (d) 10. (e) Histograms of local current density distribution. The inset in (e) shows rescaled histogram of current density distribution.. Figure S13. Average local current densities and their standard deviation according to (a) BTO concentration and (b) BTO distribution during the charging step. Average current densities were represented as absolute value. 25

26 (a) (b) Figure S14. Constant-current discharge curve of the Li-ion battery with a BTO potential of V. Following the constant-current (24 A/m 2 ) step and further charging step at a constant voltage, the batteries were discharged until the voltage reached 3.1 V. (a) Red and black curves represent discharging behaviour with and without the electric potential of the BTO. (b) Magnified view of the discharge curve from s. 26

27 Figure S15. Current density profiles of the battery during the 30th cycle: (a) discharging step at a constant current of I = 24 A/cm 2 until the electrode potential reached 4.1 V; (b) charging step at a constant voltage of 4.1 V until the current density reached I 0.1 A/cm 2 ; (c) charging step at constant current of I = 24 A/cm 2 until the electrode potential reached 3.1 V; (d) charging step at a constant voltage of 3.1 V until the current density reached I 0.1 A/cm 2 ; and (e) open-circuit condition (i.e., I 0 ). 27

28 (a) (b) Figure S16. (a) Intercalation concentration of Li-ions in the anode during discharging and charging. Red and black lines represent the intercalation concentrations of Li in the anode with poled (0.15 V) and nonpoled BTO, respectively. (b) Intercalated lithium ion concentration in anode of nonpoled (left) and -0.05V poled (right) case after 30 cycles. 28

29 Figure S17. Thickness of the solvent layer nanoparticles. irr after 30 cycles with poled BTO Reference 1. Sun, H. Y.; Sohn, H. J.; Yamamoto, O.; Takeda, Y.; Imanishi, N., Enhanced Lithium Ion Transport in PEO Based Composite Polymer Electrolytes with Ferroelectric BaTiO 3. J. Electrochem. Soc. 1999, 146 (5), Weppner, W.; Huggins, R. A., Determination of the Kinetic Parameters of Mixed Conducting Electrodes and Application to the System Li 3 Sb. J. Electrochem. Soc. 1977, 124 (10), Dimov, N.; Kugino, S.; Yoshio, M., Mixed Silicon Graphite Composites as Anode Material for Lithium Ion Batteries: Influence of Preparation Conditions on the Properties of the Material. J. Power Sources 2004, 136 (1), Zhong, K.; Xia, X.; Zhang, B.; Li, H.; Wang, Z.; Chen, L., MnO Powder as Anode Active Materials for Lithium Ion Batteries. J. Power Sources 2010, 195 (10), Doyle, M.; Fuller, T. F.; Newman, J., Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell. J. Electrochem. Soc. 1993, 140 (6),

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