In situ hydrodynamic spectroscopy for structure characterization of porous energy storage electrodes

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NMAT4577 In situ hydrodynamic spectroscopy for structure characterization of porous energy storage electrodes Netanel Shpigel, 1 Mikhael D. Levi, *,1 Sergey Sigalov, 1 Olga Girshevitz, 1 Doron Aurbach, *,1 Leonid Daikhin, 2 Piret Pikma, 3 Margus Marandi, 3,4 Alar Jänes, 3 Enn Lust, 3 Nicolas Jäckel, 5,6 Volker Presser 5, Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat Aviv, 69978, Israel Institute of Chemistry, University of Tartu, Ravila 14A, Tartu, Estonia Institute of Physics, University of Tartu, Ravila 14C, Tartu, Estonia INM - Leibniz Institute for New Materials, Saarbrücken, Germany Department of Materials Science and Engineering, Saarland University, Saarbrücken, Germany NATURE MATERIALS 1

2 Conventional gravimetric EQCM probe versus a more general EQCM-D probe: Quartz crystal microbalance (QCM) data with simultaneous recording of frequency shift, Δf and, resonance width, ΔW A brief background about the in situ techniques and the physical terms that we are using for the data analysis are provided in this section. In QCM-based techniques, we measure piezo-electric responses of oscillating thin quartz crystals. Electrochemical QCM (i.e., EQCM) refers to parallel measurements of the QCM-active behavior of thin quartz crystals and the electrochemical response of the electrodes deposited on them. In fact, alternating voltage at different frequencies is applied to the thin quartz-crystal (QC) and a corresponding current response is measured (affected by the oscillating crystal). The transfer function between these voltage and current changes is the impedance and its reciprocal term is called admittance. The response has to be treated in terms of complex numbers and is usually presented as the real and imaginary components of the admittance (called conductance and susceptance, respectively) as a function of frequency (Fig. S1). An AT-cut (35 15' angle from the crystallographic c-axis) QC thickness-shear resonators in their unloaded and loaded (e.g., by an electrode coating) states are characterized by two parameters: (i) the resonance frequency (f) and (ii) the width of the resonance peak of the oscillating QC (W). The latter accounts for dissipation of oscillation energy of the coated QC. f corresponds to the peak value of the real part of QC-admittance spectrum (i.e., conductivity), whereas W is the width at halfmaximum of the peak which marks the entire frequency response of the QC. W is also related to the separation between the maximum and the minimum of the imaginary part of the admittance spectrum (i.e., susceptibility) and reflects various dissipation processes in the system (see Fig. S1). [1] Note that the full complex electrical admittance of a 5 MHz quartz crystal shown in this figure was measured using network analyzer technique. [1-2] Other accessible research facilities of QCM and EQCM techniques such as Maxtek RQCM (QCM Research System) and QCM-D (QCM with dissipation monitoring, Q-sense, Sweden) present slightly different output characteristics, namely, the resonance frequency, f, and motional resistance, R, and the resonance frequency, f, and dissipation factor, D. QCM-D systems can measure the QC response at several overtone orders (or multiple harmonics) of its resonance frequency, adding a unique capability for performing in-situ hydrodynamic spectroscopy of electrode coatings. The two quantities R and D are linked to the width of the frequency response and the dissipation factor is defined as the ratio D=W/f. Typical values of D for 5 MHz crystals when measured in air are around , that is, W=40 Hz for the fundamental overtone n=1. 2

3 Figure S1. Components of quartz-crystal admittance measured for 5 MHz QC in air: resonance frequency, f, corresponds to the conductance peak, whereas the full-width at half-maximum (W) characterizes the dissipation of oscillation energy. When a neat crystal or an electrode-coated crystal are immersed in a liquid (in particular, electrolyte solution), its resonance frequency f decreases and the resonance peak width, W, increases as a result of viscous solid-liquid hydrodynamic interactions. [1] In other words, the peak of conductance shown in Fig. S1 becomes broader and shifts to the left towards lower resonance frequency values. Note that the position of the resonance peak width of a crystal in liquid environment at open circuit or under electrode polarization can be directly monitored using a network analyzer by direct sweeping of frequency. Oscillatory Maxtek RQCM or QCM-D systems report only resonance frequency (f), R and D values, respectively. Admittance analysis using a network analyzer is very useful for visualization the shape of the resonance peak width. When an external polarization is applied to an electrode coating on a crystal surface, the resonance peak may behave in two principally different modes. The polarization results in changes of the electrode mass due to insertion/extraction or adsorption/desorption of ions in a way that resonance peak shifts without change of its width; thus the change of the electrode mass occurs without change in the dissipation factor. Significant changes of the dissipation factor occur in addition to the change of the resonance frequency, which generally indicate that in addition to mass change, the electrode layer is subjected to deformation (expansion/contraction). This should modify the solid-liquid hydrodynamic interactions, and or accompanied by changes of the elastic properties of composite electrodes (e.g. electrodes containing ions inserting particles and polymeric binder). 3

4 The first case presents a very important particular case of the gravimetric use of EQCM described by the Sauerbrey s equation [2] : Δf n /n = C m Δm, Eq. S1 where n is the overtone number (e.g., n=1 relates to the fundamental resonance frequency, f 0 ), C m is the sensitivity factor (proportional to f 2 0 ), which depends on the acousto-elastic properties of the quartz-crystal itself rather than on the properties of the electrode coating. For an AT-cut QC with the fundamental frequency f 0 =5 MHz the sensitivity factor is equal to C m =56.7 Hz/µg cm 2. The Maxtek oscillatory circuit RQCM system operates on the fundamental frequency only (n=1) whereas Network analyzer and QCM-D can also follow recording on higher overtones (up to n=13). Eq. S1 clearly shows that identical gravimetric information can be obtained by using any overtone; thus, the use of different overtones is excessive in this particular case. In contrast, when electrodes change their volume upon insertion/extraction of ions, or when the coatings are viscoelastic, recording of frequency and dissipation shifts on different overtones provides an additional extent of freedom, allowing for in situ characterization of intercalationinduced geometric changes in the electrode coatings. From a hydrodynamic point of view, liquids differ from each other by their specific density, ρ, and dynamic viscosity, η. [1, 3] The ratio of these quantities defines an important hydrodynamic parameter of the liquid, characterizing its interaction with solid at different overtone numbers of shear wave, n, called penetration depth, or, equivalently, the velocity decay length, δ n : δ n = [η/(πnf 0 r)] 1/2 Eq. S2 When only the fundamental frequency is being used, variations of δ are possible by using liquids with different viscosity-to-density ratio; measuring the response of surfaces on QC in such different liquid phases enables ex situ spectroscopic probing of rough/porous structures. [4] The different overtone order measurements dramatically increase the hydrodynamic spectroscopic ability of EQCM-D mainly because it allows working with the same electrolyte solution (same density and viscosity) modulating penetration depth by the change of n. This allows for in situ hydrodynamic spectroscopy of electrode coatings in a single solution. 4

5 Hydrodynamic modeling of EQCA responses of intercalation electrodes Detailed presentation of the hydrodynamic model of non-homogeneous solid layers in contact with liquid was given elsewhere. [4] Also, facile application of this model to describe Li-ion insertion/extraction into/from Li x FePO 4 electrodes as a typical representative example for the hydrodynamic response of intercalction electrodes, was recently reported. [5] The frequency response (Δf/n) is presented as a sum of the responses due to pseudo-uniform porous layer (called here film) and particles of large sizes (semi-spherical asperities): f f rδ 0 n 2π 4 f π r = f (1 mπr ) q mr 0 m( r + r) n film 2 rqmq 2 3 rqmq b 2 f 2r 0 1 (1 q) Re( ) rqmq q 0 Eq. S W 2 f (1 ) 0 rδn 2π f (1 ) 0 r 1 = W film mπ r q + mr q Im( ) Eq. S4 n rqmq 2 rqmq q 0 where ρ q and µ q are density and shear modulus of the quartz crystal, n is the overtone order, m is the surface density of the intercalation particles, r is its radius (assuming a semi-spherical shape), ρ b and ρ are bulk density of the particles and bulk liquid, respectively, and η is the dynamic viscosity of the liquid. For thin coatings (films) with small loading mass the surface coverage of the crystal is designated as q. Note that when using Eq. S3 and Eq. S4 for electrodes coating at OCV, there are changes in frequency and resonance width when transferring the coated crystal from air into the electrolyte solution under consideration. However, these equations are used for electrochemicallydriven charging process connected with change in mass due to extracted (inserted) ions; thus, the frequency shift is corrected by the change in mass based on the amount of charge obtained from differential capacity curves as follows. The first Faraday law is used to convert charge into mass changes, then the latter is transformed into inertial contribution to the measured frequency using Sauerbrey s Eq. S1. Δf film /n and ΔW film /n (Eq. S4 and Eq. S4) are the EQCA response of the porous film which depends on the thickness, lateral characteristic length, density and penetration depth. If the semi-sphere is porous, then ρ b includes the mass density of liquid contained in the pores. To obtain the expressions for Re(Δf film /n) and ΔW film /n in Eq. S3 and Eq. S4, we use the results obtained previously for rough surfaces. [1] 5

6 2f ρ 1 h 1 1 2q ffilm / n= Re { + [ [cosh( qh 1 ) 1] + sinh( qh 1 )]} Eq. S5 ( mρ) ξ ξ / q q q0 q1 W q1 q1 4f ρ 1 h 1 1 2q Wfilm / n= Im { + [ [cosh( qh 1 ) 1] + sinh( qh 1 )]} ( mρ) ξ ξ / q q q0 q1 W q1 q1 Eq. S6 Here 1/2 q = (2 i πnf ρ / η), q = q0 + ξ H and W=q 1 cosh(q 1 h)+q o sinh(q 1 h), and δ is penetration 0 0 depth. The first terms on the right sides of Eq. S5 and Eq. S6 describe the response of the smooth quartz crystal-liquid interface. The additional terms present the shift and the width of the EQCAresponse caused by the interaction of the liquid phase (the electrolyte solution) with a non-uniform interfacial layer with flat surface. The last terms of Eq. S5 and Eq. S6 take into account the influence of the outer surface roughness of the electrodes. The form of the terms corresponds to the case of a slight roughness with a lateral parameter, which is larger than the decay lengths. Eq. S5 and Eq. S6 are the expressions for Δf film /n and ΔW film /n, respectively. Fabrication of electrode coatings onto quartz-crystal surface by spray pyrolysis. The precursor solution for spray-pyrolysis consisted of 25 mm CH 3 COOLi + 50 mm Mn(NO 3 ) 2 in ethanol. All the chemicals were purchased from Aldrich-Sigma: CH 3 COOLi 2H 2 O ( %), Mn(NO 3 ) 2 4H 2 O (99.99 %), absolute ethanol. For preparation of aqueous solutions of Li 2 SO 4 we used double distilled water and Li 2 SO 4 (Aldrich-Sigma, >99.0%). Spray-pyrolyzed films were fabricated by spraying the precursor solution onto quartz-crystal surface placed on a hot plate at 300 C. The desired thickness of the coating was reached by repeated spraying of the precursor solution onto the crystal surface. After pyrolysis, the coated crystal was kept at this temperature for another 40 min. The coated crystal was measured by QCM-D in air, and the loading mass was obtained by application of the Sauerbrey s equation Eq. S1 to the difference in frequency of the coated and uncoated crystal. The quality of the coating was controlled by SEM. 6

7 Limiting thin-layer behavior As follows from the subsequent hydrodynamic modeling, the dense layer 1 differs from the porous layer 2 by the average pore size, l dens and l pore, with respect to δ n : l dens << δ n and l pore δ n, respectively. For the dense layer, when l dens <<δ n (thin-layer approximation) the following characteristic properties should appear: (i) Such thin electrode layer with relatively flat surface is hydrodynamically inert as it does not provide any additional contribution to the resonance width change compared to that of non-porous, ideally flat surface of Au-coated crystal: their ΔW/n during hydrodynamic spectroscopic test under OCV should be identical. Δf/n may include additional contribution due to the liquid trapped in narrow pores. (ii) We now consider the case when thin-layer electrode is subjected to repeated Li-ion extraction/insertion (see the smallest differential capacity curve marked in green in Fig. 2a). The hydrodynamic contribution to Δf/n and ΔW/n during charging of thin-layer electrode becomes negligibly small (zero), and as a result Δf/n appears to be a function of the electrode potential only due to extracted/inserted Li-ions; simultaneously zero dissipation changes should be observed (ΔW/n = 0: the porous electrode layer is too thin to cause any potential-dependent dissipation change). Hence the necessary and sufficient conditions for implementation of Sauerbrey s equation are fulfilled and the gravimetric limit of thin-layer electrode is reached (further presented in Fig. 5a). 7

8 Validation of pseudo-uniform spatial mass distribution for thin non-continuous electrodes coatings of small mass loading. We show below that the estimated parameter q=0.22 (coverage of the crystal surface) for electrodes with a frequency shift in air 0.9 khz does not violate the electrodes coatings uniformity on a scale much smaller than the wavelength of the shear sound, λ. During spray pyrolysis synthesis of the electrode coating on the quartz-crystal surface, the average diameter of a drop of solution (containing mixed salts precursors) is estimated as 20 µm. A simple calculation of the surface coverage with circular spots of the electrode material arranged on a square lattice results in q=0.22 when the circular spots are separated from each other by a distance 26 µm which is smaller than λ for all the overtone orders used (from 3 rd to 11 th ). Calibration of the quartz crystals. The proportionality constant between frequency change and mass change, K in the equation: Δf=-KΔm was combined with the calculated loading mass (Δm) of three vacuum-sputtered Cu films on the crystal surface: Δm=Ahρ (A is surface area of the coating, h is thickness of Cu film measured by profilometer, and ρ is the specific density of Cu). K was found to be equal to 55.5 Hz cm 2 /µg that is 2% less than the theoretical sensitivity factor 56.6 Hz cm 2 /µg. High quality quartz crystals suitable for multi-harmonic hydrodynamic admittance characterization are those which result in perfect straight lines in both normalized frequency and resonance width shifts as a function of the penetration depth δ when a polished crystal with a flat surface of Au or Pt layer are immersed in different liquids and for different overtone orders. Note that not all the commercial crystals providing fair results in liquid on the fundamental frequency, are equally suitable for highquality measurements using multiple overtone orders. 8

9 Further supplementary figures Figure S2. Schematic drawing of rough/porous electrode coating onto oscillating quartz-crystal surface in contact with an electrolyte solution. The dotted lines show viscous decay of the transverse oscillation waves (δ n ) in pores of different potential-dependent size, d(e). In narrow pores (d(e) << δ n (n, η)), where n is the overtone order, and η is the solution s dynamic viscosity, solution is trapped (its velocity of movement is equal to that of the crystal surface) showing no dissipation. In contrast, in wide pores (d(e) >> δ n (n, η)) the solution moves, showing viscous dissipation. 9

10 Figure S3. XRD patterns of spray-pyrolyzed LiMn 2 O 4 film on silicon wafer, prepared in the same way as the films on quartz-crystal surface, which was annealed first at 300 C and then at 800 C. The diffraction peaks of the LiMn 2 O 4 spinel are described by the respective Miller indices. All other peaks are related to the silicon substrate. As can be seen, the sample annealed at 300 C shows only one diffraction peak (111) of spinel (the strongest one) due to low crystallinity of the active material. As expected, crystallinity of the film annealed at 800 C is much higher: The peak (111) becomes much stronger, and three additional (311), (400), and (440) peaks of spinel can be clearly seen on the XRD patterns. Based on the integral intensity of the (111) peak and assuming 100 % of crystalline phase in the material annealed at 800 C, crystallinity of the film annealed at 300 C was estimated as ca. 20 %. 10

11 Figure S4. (a) Three cyclic voltammograms for spray-pyrolyzed LiMn 2 O 4 coating onto surface of a Pt foil measured in mixed solutions of lithium and sodium sulfates of constant ionic strength (composition is indicated); (b) The redox-potential of the second (more positive) peak is presented as a function of the fraction of Li-ions in their mixture with Na-ions (Na 2 SO 4 is the supporting electrolyte with respect to Li 2 SO 4 ). 11

12 200 nm each 100 nm Figure S5. (a) A cyclic voltammogram measured with spray-pyrolyzed LiMn 2 O 4 coating onto Aucoated quartz-crystal surface (scan rate indicated). At the potential 0.45 V (completely lithiated state) and 0.96 V (completely delithiated state) in situ AFM images were obtained (a and b, respectively). The pores sizes significantly decrease upon Li-ions extraction in 3 locations as denoted by the numbered dashed circles and ellipses. The decrease in pore size obtained from AFM is in line with the decrease in the lateral hydrodynamic parameter ξ by 10 nm during Li-ions extraction. The dotted rose-colored ellipse 4 in panel b shows the location of the single electrode particle with the longest size 200 nm. After deintercalation (panel c) two smaller particles appear instead of the single one: the particle shrinks after Li-ion deinsertion. 12

13 References: [1] L. Da ikhin, E. Gileadi, G. Katz, V. Tsionsky, M. Urbakh, D. Zagidulin, Anal. Chem. 2002, 74, [2] A. R. Hillman, J. Solid State Electrochem. 2011, 15, [3] L. Daikhin, M. Urbakh, Langmuir 1996, 12, [4] L. Daikhin, S. Sigalov, M. D. Levi, G. Salitra, D. Aurbach, Anal. Chem. 2011, 83, [5] M. D. Levi, S. Sigalov, G. Salitra, R. Elazari, D. Aurbach, L. Daikhin, V. Presser, J. Phys. Chem. C 2013, 117, [6] M. D. Levi, S. Sigalov, D. Aurbach, L. Daikhin, J. Phys. Chem. C 2013, 117, [7] T. Stefaniuk, P. Wrobel, E. Gorecka, T. Szoplik, Nanoscale Research Letters 2014, 9,