Delithiation by Ferrocene-Based

Article pubs.acs.org/JPCC

Kinetics of LixFePO4 Lithiation/Delithiation by Ferrocene-Based Redox Mediators: An Electrochemical Approach James Robert Jennings,*,† Qizhao Huang,‡ and Qing Wang*,‡ †

Faculty of Science and Centre for Advanced Material and Energy Sciences, Universiti Brunei Darussalam, Jalan Tungku Link, Gadong BE1410, Brunei Darussalam ‡ Department of Materials Science and Engineering, Faculty of Engineering, NUSNNI-Nanocore, National University of Singapore, Singapore 117576, Singapore

Downloaded by CENTRAL MICHIGAN UNIV on September 14, 2015 | http://pubs.acs.org Publication Date (Web): July 23, 2015 | doi: 10.1021/acs.jpcc.5b03561

S Supporting Information *

ABSTRACT: An electrochemical approach for studying the kinetics of reactions between redox mediators and Li-ion battery electrode materials has been developed. The approach is based on a simple diffusion-reaction model, similar to that used to describe the classical catalytic electrochemical−chemical (EC′) reaction mechanism. Using this approach it is possible to determine the diffusion length of redox mediators in a porous film made from a Li-ion battery electrode material. The rate constant for reaction between redox species and the porous electrode may then be calculated. The approach is applied to determine rate constants for the disappearance of ferrocene and dibromoferrocenium due to reaction with excess pristine and carbon-coated LixFePO4 (0 ≤ x ≤ 1) nanoparticulate films (porosity ∼0.63, BET surface area 20−30 m2 g−1) and excess Li+ (0.1 M), which are of relevance to the operation of the recently introduced redox-flow Li-ion battery. Pseudofirst-order volumetric rate constants in the range 1−6 s−1 were obtained, corresponding to apparent heterogeneous rate constants in the range 2.2 × 10−6 − 4.4 × 10−6 cm s−1, which we show are fast enough not to limit the charge/discharge rate of redox flow Li-ion batteries constructed from these materials.

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INTRODUCTION Energy storage systems are the focus of recent research and development efforts due to increasing demand from the smart grid and sustainable energy source sectors.1,2 The redox flow battery (RFB) has an edge over its competitors thanks to its quick response time, flexible design, safety, and good cycle life.3,4 To improve the energy density of RFBs, the redox flow lithium-ion battery (RFLB) was invented, in which energy is stored in condensed phases in contrast to the liquid phase for conventional RFBs. As a result, the energy density of RFLBs could be ∼10 times higher than the latter (e.g., vanadium flow batteries).5,6 The RFLB (Figure 1a) inherits safety features intrinsic to RFBs in general, that is, the separation of the power and capacity. Besides having a high energy density, a viable energy storage system must have high power density. Therefore, it is worthwhile to investigate the power output of this new system. The peak power output of the RFLB depends on many factors, such as the concentration of the redox species, electrolyte flow rate, ionic conductivity of the ion-selective membrane, the kinetics of redox reactions on the electrodes, the diffusion coefficients of the redox species, and the reaction rate between redox species and the active materials (i.e., solid Li-storage materials) in the energy storage tanks. The chemical reaction between redox species and the active materials either reduces or oxidizes the active materials and causes lithiation or © 2015 American Chemical Society

delithiation. These redox reactions are important steps in the operation of the RFLB as they facilitate the transfer of electrons between the electrodes and the active materials;5 if these reactions are slow, it could potentially limit the power output of the battery. To isolate the chemical reaction steps from the complicated RFLB system for investigation, we need to establish a practical protocol. Here, we introduce an electrochemical approach for determining the reaction rate between LixFePO4 (0 ≤ x ≤ 1) nanoparticulate films and two different redox species, namely, ferrocene (Fc) and dibromoferrocenium (FcBr2+). Our approach involves electrochemically generating, at a planar, Pt-coated fluorine-doped tin oxide (FTO) electrode, the oxidized (reduced) form of a redox mediator with a formal potential suitable for oxidizing (reducing) LixFePO4 (Figure 1b). The experiments discussed herein utilized dibromoferrocenium (FcBr2+) and ferrocene (Fc), but in principle the approach is applicable to a wide range of redox species. Attached to the electrode, via an insulating porous Al2O3 film, is a thick, porous, nanoparticulate film of LixFePO4. The Al2O3 layer is required to avoid direct electrical contact between the Received: April 13, 2015 Revised: July 8, 2015 Published: July 13, 2015 17522

DOI: 10.1021/acs.jpcc.5b03561 J. Phys. Chem. C 2015, 119, 17522−17528

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The Journal of Physical Chemistry C

Figure 1. (a) Schematic representation of a RFLB consisting of an electrochemical cell with the anodic and cathodic compartments separated by a Li+-conducting membrane, two energy storage tanks, and a pump-assisted circulation system. (b) Cyclic voltammograms of the redox mediators used in prototypical RFLBs, Fc and FcBr2, as well as the cathodic Li+-storage material LiFePO4.

active film and the electrode. After electrochemical generation, oxidized (reduced) redox species diffuse through the pores of the Al2O3 into the pores of the LixFePO4 film where they are reduced (oxidized) back to their original form, limiting the growth of the diffusion layer, by a chemical reaction that overall may be represented as either FcBr +2 + LiFePO4 → FcBr2 + FePO4 + Li+

(R1)

Fc + FePO4 + Li+ → Fc+ + LiFePO4

(R2)

small aliquots of the suspension and quantifying Li content by atomic emission spectroscopy. The excess of reductant/Li+ or oxidant used in these experiments ensured that the reactions were not limited by transport in the solution phase or surface reactions. Instead, the reaction rates were thought to be limited by processes occurring within the particles, such as lithium diffusion and/or nucleation and growth of new crystalline phases. Redox shuttles such as ferrocene have also been used to characterize different aspects of lithium-ion battery electrodes, such as the solid-electrolyte interphase.16−18 The new electrochemical approach we present here differs from that of Kuss et al. and LePage et al. in a number of ways. First, when using our approach rapid mixing of liquids is not required for the study of the early stages of reactions or for material combinations exhibiting faster kinetics than those studied in previous work. Another important difference in our approach is that the Li content of the particles remains practically unchanged during the measurement, which means that different aspects of the complicated lithiation/delithiation process are probed in our experiments. A possible criticism of our approach is that the pseudo-first-order rate constants we obtain are only applicable to the particular LixFePO4 film composition with which measurements were performed. As such, the rate constants cannot be used to describe the entire lithiation or delithiation process, and special care must be taken to establish the relevant rate-determining step(s) associated with the rate constant, before making comparisons with previous work or attempting to draw conclusions about the operation of conventional Li-ion batteries or RFLBs. Nevertheless, our methodological approach is novel and is thus interesting from a fundamental point of view; indeed, considering that in our approach different reactants are in excess compared with previous studies of chemical lithiation/ delithiation kinetics, our approach can be viewed as being complementary, as well as providing insight into the operation of RFLBs employing the specific materials studied here.

or

If it is assumed that negligible amounts of LiFePO4, FePO4, and Li+ react during the experiment (which can be achieved in practice by using a very low concentration of redox mediator and limiting the duration of the experiment), the one-electron reduction (oxidation) of the mediator ought to be pseudo-firstorder in mediator concentration. In this case the mechanism is essentially identical to the classical catalytic electrochemical− chemical (EC′) mechanism.7 The average distance electrogenerated redox species can diffuse into the film is the diffusion length of the redox species and can be quantitatively related to the steady-state oxidation (reduction) current flowing under potentiostatic conditions. By also measuring the effective diffusion coefficients of the oxidized and reduced redox species in the porous film, it is possible to calculate the pseudo-firstorder rate constants for the chemical reaction between the mediators and the LixFePO4 nanoparticulate films. Most previous studies of LixFePO4 lithiation/delithiation in the literature utilized an electrochemical approach where direct electrical contact was made between an electrode and the LixFePO4 particles, with conduction facilitated by a carbon additive.8−13 While these studies undoubtedly offer important mechanistic and kinetic information, they are not necessarily directly relevant to chemical lithiation/delithiation of LixFePO4 or the operation of the RFLB. An important exception is the recent work by Kuss et al. and LePage et al., who also studied the kinetics of lithiation/delithiation by chemical reduction/ oxidation.14,15 These authors mixed a suspension of FePO4 or LiFePO4 particles with a large excess of chemical reductant and Li+, or a large excess of oxidant, respectively, and then monitored the reaction progress until completion (i.e., full lithiation or delithiation), either by measuring the suspension absorbance in situ as a function of time or by periodically taking

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THEORY Diffusion-Reaction Model. We consider one-dimensional diffusion of redox species in a pseudohomogeneous porous medium along a direction, x, normal to the plane of the electrode with its origin at the electrode surface. The onedimensional space is divided into two regions (Figure 2), one

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no divergence of the flux of either species at the boundary between regions A and B A Dred

DoxA

d[Red]A (x) dx

d[Ox]A (x) dx

B = Dred x=s

B = Dox x=s

d[Red]B (x) dx

d[Ox]B (x) dx

x=s

x=s

(7)

(8)

and concentrations of reduced and oxidized species far from the electrode surface equal to their initial concentrations (i.e., before application of a potential to the electrode) [Red]B (∞) = [Red]*


[Ox]B (∞) = 0

spanning from x = 0 to x = s that represents a thin, porous, insulating film (A, e.g. Al2O3) and the other spanning from x = s to x = ∞ that represents a thick, porous, redox-active film (B, e.g. LiFePO4). If only the oxidized half of the redox couple reacts with the redox-active film (e.g., the mediator has a much more positive formal potential than the film material) and only the reduced form of the mediator is initially present in solution, the steadystate continuity equations for oxidized (ox) and reduced (red) redox species in the two regions can be written as

B Dox

d 2[Ox]B (x) − kobs[Ox]B (x) = 0 dx 2

(4)

where [i]j(x) and Dji are the concentrations and diffusion coefficients, respectively, of species i in region j, and kobs is the rate constant for the reaction of the oxidized redox mediator with the redox-active film. The same equations can be applied if only the reduced half of the redox couple reacts with the redoxactive film (e.g., the mediator has a much more negative formal potential than the film material) by substituting “red” for “ox” and vice versa. At long times and an electrode potential sufficiently more positive than the formal potential of the redox couple, the concentration of reduced species at the electrode surface will be essentially pinned to zero, leading to the following boundary condition [Red]A (0) = 0

(5)

The other boundary conditions stipulate equal but opposite fluxes of reduced and oxidized species at the electrode surface d[Red]A (x) dx

= −DoxA x=0

d[Ox]A (x) dx

x=0

(11)

Dox kobs

(12)

Analogous expressions to eqs 11 and 12 may be derived for the case of an initially present oxidized redox mediator, the reduced form of which is capable of reducing FePO4, by reversing the sign of the current density and replacing “red” with “ox” and vice versa. Model Assumptions. A number of important model assumptions require justification if diffusion lengths and rate constants extracted using the above model are to be considered meaningful. First, in order for the above 1-dimensional model to be valid it is important that the reaction between the redox mediator and the pore walls be kinetically limited, not under mixed or diffusion control, so that only macroscopic diffusion normal to the substrate need be considered. On the basis of the rate constants derived using eqs 11 and 12, together with numerical modeling of three-dimensional diffusion and reaction in a cylindrical nanopore (Supporting Information), we believe that the one-dimensional model is accurate. Second, it is assumed that a steady state can be achieved on the experimental time scale. It seems reasonable to assume that this is the case if a constant current is observed. Third, the redox-active film is assumed to be infinitely thick. Obviously this is not the case, but it is a reasonable approximation if oxidized (reduced) redox species are unable to reach the edge of the redox-active film without reacting (i.e., redox-active film thickness ≫ Lox). In fact, this is a prerequisite for observing a constant current; if this were not the case one would expect a Cottrell-like decaying current due to growth of the redox species diffusion layers outside of the redox-active film, which is not observed in our experiments. Fourth, in the derivation of eq 11 it is assumed that the diffusion coefficients of the redox

(2)

(3)

A Dred

FDred [Red]* s + Lox

where F is the Faraday constant and Lox is the diffusion length of the oxidized species in the redox-active film

(1)

d 2[Red]B (x) + kobs[Ox]B (x) = 0 dx 2

B Dred

js =

Lox =

d 2[Ox]A (x) =0 dx 2

(10)

where [Red]* is the initial concentration of the reduced half of the mediator. Assuming that DAred = DBred and DAox = DBox (this assumption should be approximately valid if the porosities of A and B are the same, as is the case in the present work), the solution of eqs 1−4 with the above boundary conditions yields the following expression for the steady-state current density at the electrode

Figure 2. Scheme illustrating model geometry and key processes.

d 2[Red]A (x) =0 dx 2

(9)

(6) 17524


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Figure 3. (a) Potential step chronoamperometry of 0.04 mM Fc+ (red) and FcBr2 (blue) solutions (0.1 M LiClO4/propylene carbonate) on bare FTO electrodes (dashed lines) or Al2O3/(Li)FePO4-coated FTO electrodes (solid lines). (b) Cottrell plot of the same data shown in (a), illustrating that the Cottrell equation is not obeyed for the coated electrodes.

Electrode Preparation. A ∼3 μm thick spacer layer of Al2O3 nanoparticles followed by a layer of FePO4, LiFePO4, or partially delithiated LiFePO4 nanoparticles (thickness 36−120 μm) was deposited on fluorine-doped tin oxide (FTO, Pilkington TEC-15) glass by screen printing (Al2O3) and doctor blading (LixFePO4). Before film deposition, the FTO substrate was sonicated sequentially in 5% Decon 90 solution, distilled water, and ethanol for 15 min each. The Al2O3 paste was screen printed on cleaned FTO and dried at 120 °C. The process was repeated until the spacer layer was 3 μm thick. The Al2O3 films were annealed in air on a programmable hot plate: 110 °C for 30 min, 125 °C for 15 min, 325 °C for 5 min, 375 °C for 5 min, 450 °C for 15 min, and 500 °C for 15 min. The Al2O3 electrodes were cooled to room temperature, and then a layer of FePO4 or LiFePO4 was deposited on the Al2O3 film by doctor blading. The thickness of the film was controlled by adjusting the number of layers of tape used during doctor blading. The electrodes were then dried at 105 °C for 24 h under vacuum. Electrochemical Measurements. Voltammetric and chronoamperometric measurements were performed using a computer-controlled potentiostat (Autolab PGSTAT 302N/ FRA2, Ecochemie) and the Nova 1.9 software package. Potential step chronoamperometric measurements were performed with either platinized FTO or platinized FTO coated with a porous Al2O3/LixFePO4 bilayer film as the working electrode, a Pt wire counter electrode, and a Ag/Ag+ (0.01 M AgNO3, 0.1 M TBAP) reference electrode. The electrolyte solution was 0.04 mM in either Fc+ or FcBr2 and 0.1 M in LiClO4, with propylene carbonate as the solvent.

species are the same in both porous media A and B (Al2O3 and LixFePO4 in the case studied here). Since the porosities of our Al2O3 and LixFePO4 films were found to be almost identical, it is unlikely that a significant difference in mediator diffusion coefficients exists between these media. Finally, it is assumed that the redox-active material and lithium ions are in excess so that the rate expression (last term in eqs 3 and 4) is pseudofirst-order in redox species concentration. It was estimated from currents flowing during experiments that only 0.4 mol % of active material was consumed in experiments lasting as long as 200 s; therefore, the pseudo-first-order assumption seems reasonable.

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EXPERIMENTAL SECTION Chemical Reagents. Ferrocene (Fe(C5H5)2, Sigma-Aldrich, 98%), 1,1′-dibromoferrocene (Fe(C5H4Br)2, SigmaAldrich, 97%), ferrocenium hexafluorophosphate (Fe(C 5 H 5 ) 2 PF 6 , Sigma-Aldrich, 97%), lithium perchlorate (LiClO 4 , Sigma-Aldrich, 99.99%), propylene carbonate (C4H6O3, Sigma-Aldrich, 99.7%), lithium iron phosphate (LiFePO4, Li-Cell, China), acetonitrile (MeCN, Sigma-Aldrich, dried and distilled, >99%), 1-methyl-2-pyrrolidinone (C5H9NO, Sigma-Aldrich, anhydrous, 99.5%), and polyvinylidene fluoride (−(C2H2F2)n−) were used as received. Al2O3 Paste Preparation. Ethanolic solutions (10 wt %) of ethyl cellulose (EC) were prepared from two kinds of pure EC powders. Amounts of 1.8 g of one EC solution (5−15 mPa s, Sigma-Aldrich #46070) and 1.4 g of the other EC solution (30−50 mPa s, Sigma-Aldrich #46080) were added to a glass bottle containing 6 g of pure Al2O3 powder, 26.0 g of terpineol (anhydrous, Acros), and 30 mL of ethanol, resulting in a mixture with a final volume of 105 mL. The mixture was then stirred and sonicated to homogenize and disperse the Al2O3 powder before being concentrated under vacuum at 40 °C using a rotary evaporator until a viscous paste was obtained. Finally, the paste was further homogenized by passing through a three-roll mill. LixFePO4 Paste Preparation. LiFePO4 or FePO4 nanoparticles (90 wt %), either carbon-coated or pure, and polyvinylidene difluoride (10 wt %) were dispersed in Nmethyl-2-pyrrolidone. The mixture was homogenized, and excess solvent was evaporated by stirring for ca. 24 h until a thick paste was obtained.

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RESULTS AND DISCUSSION

Determination of Redox Mediator Diffusion Length and Rate Constant. Chronoamperometric potential step experiments were performed with uncoated and Al2O3/ LixFePO4-coated platinized FTO electrodes in propylene carbonate solutions that were 0.1 M in LiClO4 and 0.04 mM in either FcBr2 or Fc+ (Figure 3a). To impose the boundary condition given by eq 5 (zero surface concentration of the initially present form of the mediator), the electrode potential was stepped from its equilibrium value to a potential several hundred millivolts more positive (negative) than the oxidation (reduction) peak potential identified in quasi-reversible cyclic voltammograms (not shown) of dibromoferrocene (ferrocene) 17525


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Figure 4. Diffusion length (a) and rate constant (b) for reaction of ferrocence (red) or dibromoferrocenium (blue) with pristine (open circles) or carbon-coated (closed circles) LixFePO4 nanoparticle films, derived from steady-state current densities using a one-dimensional diffusion-reaction model (eqs 11 and 12).

lengths obtained are in all cases shorter than the thickness of the LixFePO4 films used for the measurements. This indicates that the model is self-consistent because a constant current would not be expected if diffusion lengths were longer than the film thickness. Encouraged by the apparent validity of the diffusion-reaction model, we proceeded to calculate kobs for the reaction between the redox mediators and the LixFePO4 films using eq 12 (Figure 4b). The obtained rate constants fall in the range 1−6 s−1, are similar for both oxidation and reduction reactions, and do not vary significantly with Li content. A significant difference in kobs is observed between carbon-coated and uncoated LixFePO4, with kobs being 4−6 times larger than for uncoated LixFePO4. Physical Interpretation of the Observed Rate Constant. The rate constant measured using the approach outlined above is the volumetric rate constant for the rate-determining step (RDS) or steps (if several mechanisms operate in parallel) in the disappearance of the redox mediator under our experimental conditions. Note that the RDS is not necessarily the same as in more conventional electrochemical or chemical lithiation/delithiation experiments (as in, for example, references 8−15) due to different experimental conditions. A number of possibilities exist for the RDS, many of which have been discussed in detail in the literature. The possibilities can be divided into four main categories: (i) redox mediator or Li+ transport in solution (e.g., a solution phase diffusion-limited rate constant), (ii) electron/hole/Li+ transfer across the particle/ solution interface, (iii) electron/hole/Li+ transport within the nanoparticulate f ilm, and (iv) phase transformation within the particles (e.g., transformation from LixFePO4 solid solution to separate LiFePO4 and FePO4 nanocrystals), limited by nucleation or phase boundary reactions. For many of the above RDS possibilities the reaction rate would be proportional to the surface area of the nanoparticles exposed to the solution. It is therefore useful to estimate the apparent heterogeneous rate constant by dividing the volumetric rate constant by the microscopic surface area per unit volume of nanoparticulate film. The surface area per unit volume of our films was estimated from BET measurements (without binder present) and film density measurements to be ∼2.3 × 105 cm−1 and ∼3.6 × 105 cm−1 for FePO4 and LiFePO4 films, respectively, corresponding to heterogeneous rate constants in the range 2.2 × 10−6−4.4 × 10−6 cm s−1 for uncoated films. It is not possible to obtain meaningful

on uncoated platinized FTO. The current density following the potential step continuously decays for uncoated platinized FTO, obeying the Cottrell equation (Figure 3b) as expected and almost reaching zero after 200 s. In contrast, when the platinized FTO is coated with Al2O3/LixFePO4 the current density stabilizes after 1−15 s (depending on electrode and redox mediator) and remains practically constant for hundreds of seconds. The observation of a constant current over such a long time period indicates that for practical purposes a steadystate has been achieved, as predicted by our model. In order to determine diffusion lengths and rate constants from the steady-state current using eqs 11 and 12, the effective diffusion coefficients of oxidized and reduced forms of the redox mediators in the porous film are required. We have estimated all of the required diffusion coefficients using the following procedure. First, diffusion coefficients were determined in fluid solution using voltammetry at an ultramicroelectrode (Supporting Information). Second, the diffusion coefficient of ferrocenium in the porous film was derived from measurement of diffusion-limited currents in an asymmetrical thin layer cell, using a theoretical approach similar to that of Papageorgiou et al. (Supporting Information).19 The ratio of the fluid solution diffusion coefficient to the diffusion coefficient in the porous film was then assumed to be the same for ferrocene, dibromoferrocene, and dibromoferrocenium. This amounts to assuming that only geometric effects cause the reduction in diffusion coefficient in the pores relative to that in fluid solution. This is possible if specific interactions between redox mediators and the pore walls are either negligible or reduce the diffusion coefficient by the same factor for all mediators. This assumption is partially supported by the fact that the measured diffusion coefficient for ferrocenium is close to that calculated using a simple model that only considers geometric effects (Supporting Information),20 implying that mediator−wall interactions have a minor effect on the diffusion coefficient for this mediator. Figure 4a shows diffusion lengths calculated from steadystate currents using eq 11 for various oxidized and reduced mediators in pristine and carbon-coated LixFePO4 films. The stated Li fractions (x = 0, 0.5, and 1) should be considered nominal as they are derived from the number of oxidizing equivalents added when chemically delithiating pure LiFePO4 with Br2 (a large excess was added for x = 0); the actual Li content of the films was not accurately quantified. The diffusion 17526


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The Journal of Physical Chemistry C heterogeneous rate constants for the carbon-coated films as we do not know the area occupied by the carbon coating; however, it is worth noting that the BET surface area for carbon-coated LiFePO4 was ∼12% lower than that of uncoated LiFePO4, despite the 4−6 times larger rate constant. The above rate constants are far too small to be limited by diffusion of the redox mediator or Li+ ions in solution to the particle surface, which for particles of radius 50 nm (as present in our films) and a mediator or Li+ ion diffusion coefficient21,22 of ∼10−6 cm2 s−1 leads to a diffusion-limited heterogeneous rate constant for an isolated particle (i.e., D/r) of 0.2 cm s−1. The true diffusion-limited rate constant in our rather densely packed films must be lower than this estimate due to overlap of diffusion layers between adjacent particles, but this could not account for the ∼100,000-fold lower apparent rate constant. In support of this assertion, numerical calculations indicate that diffusion of redox species from a planar electrode into a cylindrical pore of radius 25 nm with highly reactive walls yields a diffusion-limited current density many orders of magnitude larger than that observed in our experiments (Supporting Information). The insensitivity of kobs to film Li content implies that the volume rates of both lithiation and delithiation reactions do not depend strongly on the surface area of exposed LiFePO4 or FePO4 nanocrystals. Although it is possible that the surface areas do not vary with Li content if one phase is always located at the surface of composite particles (i.e., radial lithiation/ delithiation occurs), the available literature suggests that this would not be the case. Rather, partially delithiated films are more likely to exist as mixtures of pure FePO4 and LiFePO4 particles.8,9,12 It is therefore unlikely that the RDS is an interfacial reaction. That the RDS is not an interfacial electron transfer reaction is in fact expected due to the large driving force for the electron transfer and the fact that a fast, oneelectron, outer-sphere redox mediator is employed. For example, Laoire et al. determined a value of 1.3 × 10−3 cm s−1 for the heterogeneous electron transfer rate constant for ferrocene oxidation on a glassy carbon electrode at zero overpotential (k0) in a lithium-ion-containing organic carbonate electrolyte.21 Taking the overpotential for ferrocene oxidation to be the difference between the formal potentials of LiFePO4/ FePO4 and Fc/Fc+ (∼200 mV)5,23 and a transfer coefficient of 0.3,21 we calculate that the electron transfer rate constant for ferrocene oxidation would be as high as 0.3 cm s−1 on glassy carbon for the same overpotential, ∼104−105 times larger than that obtained above for reaction of Fc with carbon-coated and uncoated FePO4. For several of the above RDS possibilities, including solutionphase Li+ diffusion and solid-phase Li+ diffusion from the surface of the nanoparticles into the bulk, the observed rate constant would be expected to depend on solution Li+ concentration. To investigate this possibility, potential step experiments with FePO4 electrodes and the Fc/Fc+ mediator were performed with solution Li+ concentrations of 0.1 and 1 M. No significant dependence of the steady-state current on Li+ concentration was observed (Supporting Information), confirming that Li+ transport in solution is not involved in the RDS for the lithiation reaction and ruling out several RDS possibilities involving Li+ transfer or transport at/near the solution/nanoparticle interface. Considering all of the above observations, it seems most likely that the RDS in both lithiation and delithiation reactions is the transport of electronic carriers (possibly coupled to solid-

phase Li+ transport) from their initial injection site, through the poorly conducting nanoparticulate film, to their eventual reaction site. Evidence in support of this explanation comes from the fact that larger rate constants are observed for carboncoated LixFePO4 films than for pristine films. Since the BET surface area of the carbon-coated LixFePO4 is slightly lower than that of the uncoated LixFePO4, the presence of carbon must either change the RDS or catalyze it in some way. A very plausible explanation is that the carbon coating makes the entire LixFePO4 film electrically addressable, opening up the possibility of lithiation/delithiation occurring at locations distant from the initial electron transfer. This would mean that smaller particles, which are known to react before larger particles in conventional electrochemical delithiation,9 could react before larger particles, regardless of their location in the film. If charge transport to distant small particles was rate determining in uncoated samples, adding the carbon coating would increase the observed rate constant by improving conductivity. The obvious alternative possibility, that the RDS is interfacial electron transfer and the carbon coating catalyzes the electron transfer reaction, is unlikely due to the absolute magnitude of the heterogeneous rate constant and the insensitivity to film Li content, as discussed above. Relevance of Measured Rate Constants to the Operation of RFLBs. The rate constants measured in this study can in principle be used in modeling of the operation of RFLBs. Here, we restrict ourselves to a simple calculation of the maximum possible charge/discharge rate based on the measured rate constants. To do this we assume that (i) the rate constant remains constant throughout the entire charge/ discharge process (this may be valid over the flat portion of the battery charge/discharge curve but not near the beginning or the end) and (ii) suitable electrode area and potential, combined with vigorous pumping/stirring, maintain a constant oxidized/reduced mediator concentration throughout the porous film, equal to the initially added mediator concentration. With these assumptions the maximum possible volumetric current (i.e., current per unit volume of porous active material) is |jV | = qkobs[M]*

(13)

where q is the elementary charge; kobs is the observed rate constant (Figure 4b); and [M]* is the initially present redox mediator concentration. Assuming a moderate mediator concentration of 0.1 M (below the solubility limit) and a rate constant of 1 s−1 (near the bottom of the measured range), we obtain jV = 9.6 A cm−3. The volumetric capacity for our LiFePO4 films, which have a porosity of ∼0.63, is 814 C cm−3 (226 mAh cm−3), thus the previously obtained jV value corresponds to a maximum “C-rate” of 43. This unrealistically large estimate for the maximum charge/discharge rate is not particularly useful for practical purposes (obviously pumping/ stirring cannot be so efficient that eq 13 is valid), but it does imply that the chemical oxidation/reduction step should not limit the rate capability of RFLBs employing these materials.

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CONCLUSION An electrochemical approach based on a one-dimensional diffusion-reaction model has been used to determine rate constants for reactions between Fc-based redox mediators and Li-ion battery electrode materials. Reactions between either Fc or FcBr2+ with excess nanoparticulate LixFePO4 (porosity 17527


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The Journal of Physical Chemistry C ∼0.63, BET surface area 20−30 m2 g−1) and excess Li+ (0.1 M) have pseudo-first-order volumetric rate constants in the range 1−6 s−1. Accounting for the porous film surface area yields apparent heterogeneous rate constants in the range 2.2 × 10−6 to 4.4 × 10−6 cm s−1 for uncoated LixFePO4. The rate constants are insensitive to film Li content and solution Li+ concentration over the composition range studied and are 4−6 times larger for carbon-coated LixFePO4 than for uncoated LixFePO4. These findings suggest that transport of electronic carriers from their initial injection site to the final lithiation/delithiation site is rate-determining in the chemical lithiation/delithiation of uncoated LixFePO4 films. An analysis based on a simplified model of RFLB operation suggests that these reactions should not limit the rate capability of RFLBs based on nanoparticulate LixFePO4 and Fc-based mediators. Moreover, the electrochemical protocol that we have established for assessing rates of reaction between redox mediators and redox-active nanoparticulate films should make the selection process of redox mediators for use in RFLBs easier and may find application in the measurement of heterogeneous rate constants relevant to other systems.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b03561. Determination of redox species diffusion coefficients. Estimation of diffusion-limited current associated with diffusion of redox species into a cylindrical pore with reactive walls. Influence of solution Li+ concentration on observed rate constant for disappearance of Fc (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel.: +673 7107069. *E-mail: [email protected]. Tel.: +65 65167118. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Q.W. acknowledges financial support from the National Research Foundation, Prime Minister’s Office, Singapore, under its Competitive Research Program (CRP Award No. NRF-CRP8-2011-04). J.R.J. acknowledges financial support from Universiti Brunei Darussalam under University Research Grant UBD/PNC2/2/RG/1(313).

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REFERENCES

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Delithiation by Ferrocene-Based

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