ORIGINAL PAPER

Electrochemical features of ball-milled lithium manganatespinel for rapid-charge cathodes of lithium ion batteries

Daniel Crain & Jianping Zheng & Christopher Sulyma &

Corina Goia & Dan Goia & Dipankar Roy

Received: 13 December 2011 /Revised: 30 January 2012 /Accepted: 3 February 2012 /Published online: 22 February 2012# Springer-Verlag 2012

Abstract Lithium manganese oxide (LMO), mechano-chemically modified by ball-milling, is a potentially usefulactive material for high-power-density cathodes of lithiumion batteries. The present work investigates the electrochem-ical characteristic of a cathode prepared from a controlledmixture of nano- and micrometric LMO particles processedin this approach. The nanoparticles in the mixture supportsurface-localized insertion/extraction of Li and thus increasethe cathode charge/discharge rates. The LMO micro-particles promote cathode cyclability by stabilizing thecoexisting nanoparticles against segregation and strong elec-trolyte reactions. The underlying mechanisms of theseeffects are studied here using voltammetry, galvanostaticcycling, Ragone plot construction, and electrochemical im-pedance spectroscopy. The relative timescales of chargetransfer and diffusion of Li+ within the LMO lattice aredetermined, and the criteria for material utilization duringrapid charge–discharge are examined.

Keywords Ball-milling . Lithium ion battery . Lithiummanganese oxide . Nanomaterial . Ragone plot

Introduction

Lithium ion batteries designed for pulse-power applicationsrequire that the electrode materials be capable of supporting

fast intercalation/de-intercalation of Li+. A widely practicedapproach to achieving this goal is to use nano-sized particlesof active materials, where the lithium insertion/extractionsteps are accelerated by reducing the diffusion length of Li+

within the host lattice [1]. Because intercalation/de-interca-lation occurs primarily as “surface” (rather than bulk) reac-tions in such cases, the Li-host nanoparticles experiencereduced volumetric stress of lattice deformation; this servesto increase both the cycle-life and the coulombic efficiencyof the battery. However, while the increased specific areaimproves the rate capability and cyclability of electrodeparticles, this also makes the electrode more susceptible tosegregation and/or modification by Faradaic reactions ofelectrolytes/impurities [2].

A viable option for boosting the power density, withoutsacrificing the electrochemical stability of an electrode, is toincorporate strategically designed mixtures of nanometricand micrometric active particles in the electrode film [3].The micro-particles in such a mixture “protect” the nano-particles from electrolyte induced degradation, while thesmaller particles promote fast charge/discharge. Mechano-chemical processing via ball-milling of micrometric par-ticles offers a broadly reported effective method to achiev-ing such controlled size distributions of active particles [4].Mechanical pulverization by ball-milling allows for particlesize reduction of commercially obtained or chemically syn-thesized micro-structured materials. Ball-milling can alsosupport mechano-chemically induced reactions on continu-ously renewed surfaces, leading to material modification atthe nanoscale. These mechano-chemical reactions, dictatedby a combination of milling variables, control particle sizedistributions, as well as the processes of alloying and newphase formation [5, 6].

Focusing particularly on the considerations for fastcharge/discharge Li ion batteries, the present work

D. Crain : J. Zheng : C. Sulyma :D. Roy (*)Department of Physics, Clarkson University,Potsdam, NY 13699-5820, USAe-mail: samoy@clarkson.edu

C. Goia :D. GoiaDepartment of Chemistry, Clarkson University,Potsdam, NY 13699-5810, USA

J Solid State Electrochem (2012) 16:2605–2615DOI 10.1007/s10008-012-1677-8

investigates certain electrochemical attributes of the ball-milled form of a cathode material, lithium manganese oxide(LMO, LiMn2O4). LMO has an adequate charge capacityand coulombic efficiency, as well as good rate capabilityand environmental compatibility [7–9]. Ball-milling hasbeen shown to further improve several aspects of this mate-rial’s cathode performance [4, 10]. Various structural prop-erties and the main charge–discharge characteristics of ball-milled (BM)–LMO cathodes have been studied by otherauthors [5, 6, 11–13]. In a recent work, we have examinedcertain kinetic aspects of accelerated charge–discharge ofLMO cathodes fabricated from BM particles [10]. In thepresent investigation, we extend our previously reportedexperimental strategy to study the relative times of thekinetically controlled and diffusion limited steps of Li inter-calation/de-intercalation in BM–LMO. Using Ragone plotsof energy–power correlation, we also examine here how theamount (effective thickness) of the utilized active materialchanges with variations in the charge/discharge rates (C-rates) and active particle sizes.

The cathode films are electrochemically characterized inhalf-cells using Li anodes in electrolytes of LiBF4 (knownfor suppressing Mn dissolution [14]) in a mixture of ethyl-ene carbonate (EC) and diethyl carbonate (DEC). The syn-ergistic effects of different particle sizes in the BM materialare probed with slow-scan cyclic voltammetry (SSCV),galvanosatic charge–discharge, and electrochemical imped-ance spectroscopy (EIS). The criteria for material utilizationduring fast charge/discharge are examined using Ragoneplots of energy and power densities. EIS results are analyzedusing the complex non-linear least square (CNLS) methodto determine the voltage-dependent kinetic parameters of Litransport in the LMO cathodes. The relative timescales ofcharge transfer and Li+ diffusion are determined from theseEIS data.

Experimental

Cathode fabrication and test cell assembly

A slurry initially consisting of 10 g of LMO powder (SigmaAldrich), 15 ml of 2-propanol (reagent-grade), and cerium-stabilized zirconium oxide beads of 1.2–1.4 mm diameter(Union Process) was ball-milled for 13.5 h at various ratesto obtain a bimodal distribution of particles with 300 nm and1.3 μm average diameters. Milling was performed using avertical shaft-driven model HD-01 Attritor, and the resultingslurry was dried for 12 h in a vacuum oven at 80 C. Particlesize distributions were monitored using aMalvernMastersizer2,000 analyzer. The cathode composite paste contained80:13:7 weight percents of LiMn2O4/acetylene black/polyvinylidene fluoride in a base of N-methylpyrrolidone.

Alumina substrates were coated with Au (~1 μm thickness,served as a current collector) in a Denton cold sputter coater. A“doctor’s blade” was used to coat the Au film with the LMOcomposite paste [2]. The resulting electrodes were dried in avacuum oven for 24 h at 100 °C. The final electrodes typicallycontained about 0.7 mg cm−2 of active material. Micrographsof electrode samples were taken using a JEOL-JSM 6300scanning electron microscope (SEM). The cathode film thick-nesses were ~15 μm, as determined using SEM.

Electrochemical characterization

All electrochemical measurements used a three-electrodeconfiguration with Li foils for the counter and referenceelectrodes and a working electrode of LMO. The Li saltwas dried for 12 h at 70 °C in a vacuum oven, and theelectrolyte, 1 M LiBF4 in 1:1 (by volume) of EC/DEC wasprepared with Fisher reagent-grade chemicals. The mixedelectrolyte was dehydrated in a flask with dried 4 A molec-ular sieves (alumina–silicate, Fisher) for at least 12 h beforeuse. The electrochemical test cell was assembled in a TerraUniversal glove box with a Nitro Watch™ purging system,and the atmosphere inside the glove box was prepared bypumping dry air, followed by dry Ar, through a series ofdesiccator tubes containing activated molecular sievesand silica gel [15]. The experimental electrolyte waspurged with ultra-high purity Ar for 30 min before electrodeinsertion.

Electrochemical measurements were carried out withfreshly prepared electrodes and using a PAR-VersaSTAT3potentiostat/galvanostat (for SSCV) or a 1287A Potentiostat(for galvanostatic and EIS experiments). Ragone plots wereconstructed using galvanostatic data recorded at a fixed 1-Crate of charge and variable rates of discharge. Each freshcathode was discharged to 3.4 V to ensure a staring state ofcharge (SoC) of zero, and then galvanostatic charge/dis-charge measurements were performed at different rates be-tween 3.4 and 4.2 V. In some of these experiments, theupper voltage limit was extended to 4.3 V to check thecut-off voltage necessary for complete cathode-charging.For EIS measurements, the cathode was subjected to inter-mittent galvanostatic charging (3.4–4.2 V) at a rate of (1/3)-C, and Nyquist spectra were recorded at several intermediateopen circuit potentials (OCPs) after the electrode currentcompletely dropped to zero. EIS was performed using a15 mV rms AC perturbation voltage of frequencies rangingfrom 0.01 Hz to 100 kHz. The EIS data were validated bycomparing the input and output frequency spectra andCNLS-analyzed using ZsimpWin™ to obtain electrodeequivalent circuit (EEC) models. The calculated value ofeach EEC element had an uncertainty of <5% and, forreporting, was normalized with respect to the cathode’sactive material mass.

2606 J Solid State Electrochem (2012) 16:2605–2615

Results and discussion

Mechano-chemical processing of LMO powder

The distribution of particle sizes, monitored in terms of aver-age particle diameters (d) at different stages of milling, areshown in Fig. 1. The initial size distribution was broad andcentered at ~6 μm. Successively recorded size distributionsshow that, in 1.5 h, the peak of particle sizes narrowed toaround 1.5 μm. After 4 h of milling, the particles had reachedan average size of about 1.3 μm. Subsequent milling duringthe next 9.5 h was done at a nearly doubled speed of shaftrotation, which eventually resulted in a bimodal distributioncentered at ~1.3 μm and ~300 nm. The shifting of sizedistributions after sonication indicated some degree of initialagglomeration, which was not present in the final dried pow-der. Sequentially taken SEM images, shown in Fig. 2, indi-cated how the particle morphologies evolved from relativelylarge and irregular to smaller, more uniform structures.

Cyclic voltammetry and Faradaic reactions of surface films

If an intercalation material is subjected to rigorous ball-milling, it is necessary to ensure that the intrinsic ability of

the sample for hosting Li+ ions remains unaffected by themechano-chemical processing conditions applied. This canbe accomplished in a relatively straightforward way by usingSSCV, where the cathode is charged and discharged undervoltage control to probe its expected characteristic features. Aprimary signature of Li+ insertion in LMO is that the reactionis a two-step Faradaic process [16]. The presence of these tworeaction steps generally indicates adequate structural integrityof the host lattice and can be observed as clearly distinguish-able current peaks in SSCV [17]. Slow potential scans used insuch experiments allow for the time necessary to supportsolid-state diffusion of Li+ and minimizes the double-layercurrents. Figure 3a shows the results of SSCV experiments,obtained by applying two consecutive voltage cycles at a rate(v) of 25 μVs−1 to a cathode prepared from the BM–LMOparticles shown in Fig. 2f.

The left vertical axis in Fig. 3a represents the cell current(i) plotted against the applied cell voltage (E) and normal-ized with respect to the cathode’s active material mass. Theintercalation/de-intercalation reactions that lead to this cur-rent have the following general form [18].

h�d þ Liþd� ��! � Liþ þ h0

� �þ e� ð1Þwhere [h0]is the empty host lattice site and e− denoteselectrons; +δ is the partial charge on the intercalated Li+

Fig. 1 Evolution of average particle diameters (d) of LMO powder,sequentially obtained at various stages of ball-milling using differentshaft speeds (RPM). a All-micrometric, AR–LMO. b–c LMO at dif-ferent stages of milling; (d) final dried particle size distribution. Thedashed and solid lines correspond to LMO particles before and aftersonication of the samples, respectively

Fig. 2 a–f SEM images of LMO powder samples considered in thecorresponding panels of Fig. 1

J Solid State Electrochem (2012) 16:2605–2615 2607

and −δ is the opposite charge associated with the intercala-tion site. The left-hand side of Eq. 1 corresponds to a fullycharged LMO cathode and, on the right-hand side, [h0]≡2(λ−MnO2). The two current peaks, marked as P1a and P2a inthe anodic cycle of Fig. 3a show the expected two-stepprocess of Li+ extraction from LMO [17, 19]. The cathodiccounterparts of these current features are labeled as P1c andP2c, respectively.

At voltages below the location of P1, reaction (1) occurswithin a single cubic phase of LMO, where the SoC (x) isless than 0.5. At higher voltages, where 0.5<x<1, the LMOlattice acquires a two-phase structure and gives rise to thesecond current peak P2. In the forward (charge) direction ofreaction (1), the LMO particles have more Li in their coresthan in their surface regions, and the situation is reversedduring the discharge step. These mutually disparate concen-tration profiles of Li+ developed within the LMO particlesduring charge and discharge of the cathode causes a hyster-esis between the forward and backward activations of reac-tion (1) [20]. As a result, the cathodic current peaks inFig. 3a are somewhat shifted toward lower voltages withrespect to their corresponding anodic peaks. These are sig-nature features of Li intercalation/de-intercalation in LMO,and the detection of these features in Fig. 3a confirms that

the LMO after milling retains its usual intercalationcharacteristics.

A relatively small anodic current peak, labeled Pra, isobserved in the first-cycle voltammogram of Fig. 1a. Basedon earlier reported observations [21–23], this peak can beassociated with Faradic reactions of the native cathode surfacefilms (CSFs) [2, 10]. This current most likely comes fromirreversible anodic oxidation of Li–EC complexes containedin the surface films formed on LMO. This CSF reactiondisappears after the first anodic scan and remains absent inall successive cathodic and anodic voltage cycles. Due to thisreason, the total anodic current drops from cycle 1 to cycle 2.As shown previously, the CSF reaction current (ir) can beestimated by writing ir≈(cycle 1)−i (cycle 2). The Faradaicresistance, Rr, of the CSF reaction can be determined from irby using the definition, Rr0(dir/dE)

−1. Voltage-dependent val-ues of [log (Rr)], obtained in this approach using the data ofFig. 3a, are shown in Fig. 3b (symbols) where the dashed lineindicates the overall data-trend.

The plot of Rr in Fig. 3b shows two noticeable dips at thevoltages corresponding to the two steps of Li de-intercalationfrom LMO. This suggests that CSF oxidation occurs at itshighest rate during Li extraction from the cathode and hence,most likely involves the release of Li+ ions. Themechanism ofthis CSF reaction has been proposed previously, suggestingthat the CSF, composed primarily of a Li–EC complex, oxi-dizes with simultaneous releases of C3H4O3 and Li+ in theelectrolyte [15]. The values of Rr measured here for the BM–LMO sample is about an order of magnitude larger than thosemeasured previously under similar conditions using a cathodeof micron-sized LMO particles [2].

Galvanostatic charge/discharge of cathodes

The cyclability and rate capability of the BM–LMO materialwere compared with those of all-micrometric LMO through aseries of galvanostatic charge/discharge experiments performedat different rates between 0.3-C and 10-C. Illustrative results ofthese measurements are presented in Fig. 4, where panels a andb show capacity vs. voltage plots of AR–LMO and BM–LMOfor three successive cycles, maintained at a 0.3-C rate ofelectrode cycling, respectively. In Fig. 4c, the BM sample ischarged/discharged at 10-C. In all three panels, the plotscorresponding to cycles 1, 2, and 3 are labeled accordingly.

The right-most data point on each plot in Fig. 4 representsthe maximum experimentally available capacity, Cm, for thegiven sample under the corresponding experimental conditions.For porous cathode films, Cm0f0CTh, where CTh is the theoret-ical charge capacity of LMO; CTh0(F/M)0148 mAh g−1;F and M are the Faraday constant and the molar mass ofLMO, respectively. The fraction f0 is defined as [24]:

f0 ¼ nhð1� fÞLMðm0Þ�1 ¼ CmðCThÞ�1 < 1; ð2Þ

Fig. 3 a Current (i) and intercalation capacitance (Cint) of a BM–LMOcathode, recorded during the first two SSCV cycles performed at a scanrate of 25 μVs−1 using an electrolyte of 1 M LiBF4 in 1:1 (volume) EC/DEC. The current feature Pra arises from electro-oxidation of cathodesurface films. P1a and P2a represent signature features of phase transi-tion in the host lattice during anodic de-intercalation of Li+. P1c and P2c

are the corresponding cathodic current peaks of Li+ intercalation. bFaradaic reaction resistance Rr of the surface film of LMO

2608 J Solid State Electrochem (2012) 16:2605–2615

where nh is the density of empty host sites [h0] available in thecathode film to support reaction (1); ϕ and L are the porosityfactor and thickness of the cathode film, respectively; m0 is thearea-normalized mass of LMO in the cathode.

According to Fig. 4a, b, at the relatively slow 0.3-C rate ofcycling the AR–LMO cathode exhibits a higher value of Cm.This is expected because mechano-chemical effects tend topartially oxidizeMn and decrease the Li-content of BM–LMO[25]. Thus, the term nh in Eq. 2 acquires a comparativelylower value for the BM sample, which acts to limit themaximum available capacity of the sample [11]. Despite itsinitially constrained values, the capacity of the cathode inFig. 4b fades at a relatively lower rate. In particular, the first-cycle capacity loss, which is associated mostly with CSFreactions, is comparatively less drastic for BM–LMO. This isconsistent with the rather large values of Rr observed in Fig. 3bfor BM–LMO. At increased cycling rates, the charge capacityof the AR–LMO cathode was found to drop noticeably, where-as that of the BM–LMO cathode decreased by lesser amountsunder the same conditions. Sample results for the latter case arepresented in Fig. 4c, showing that, even after a >30-foldincrease in the C-rate, the capacity of the BM–LMO cathoderemains nearly unchanged with respect to its values observedin Fig. 4b. Because the voltage range (3.4–4.2 V) used inFig. 4b was slightly smaller than that (3.4–4.3 V) in Fig. 4c,the capacities measured in the latter case typically exhibited asmall increase (3–5%) in their values. Nevertheless, the generallevel of capacity retention for BM–LMO remained essentiallyunchanged between 0.3-C and 10-C.

The electrochemical performance of BM–LMO observedunder the conditions of rapid charge/discharge is rooted inthe fast transport of Li+ within the nano-metric constituentof this material. To illustrate this point, we note that the netrate of reaction (1) is dictated by the timescale of slow (solidstate) diffusion of Li+ in the LMO matrix. The characteristic

diffusion time, tðoÞd , of Li in an active particle has the form[10, 26]:

tðoÞd ¼ ðldÞ2ðeDÞ�1; ð3Þwhere ld is the Li+ diffusion length, which corresponds to

the dimension of the active particle. D�

is the chemicaldiffusion coefficient of Li+ in LMO. According to Eq. 3,the diffusion time of Li+ is considerably reduced as theLMO particle size is reduced from micro- to nano-scale

[23]. Furthermore, the value of D�

for a nanoparticle hostis larger than that for a micro-particle, because the diffusionchannels are restricted in the former case [1]. These attrib-utes of the nanosized active particles enhance the cathode’scharge/discharge rate capability.

Galvanostatic charge/discharge characteristics of theBM–LMO and AR–LMO cathode samples were also testedunder the conditions of extended cycling, using 50 repeatedcycles at a rate of 3-C (detailed results not included here).Cumulatively, the BM–LMO exhibited a 90% capacity re-tention over 50 cycles in comparison with a 76% retentionfor the all-micrometric sample. However, the coulombicefficiencies, calculated as [Cm (discharge)/Cm (charge)]from the 3-C galvanostatic data, were quite comparablebetween the two samples, with a consistently fixed valueof 99.2% over 50 cycles.

The Li-host nanoparticles experience reduced volumetricstress of lattice deformation, because intercalation/de-inter-calation occurs primarily as surface-localized reactions. Thisserves to improve both the cycle-life and the coulombicefficiency of the electrode. The larger LMO particles includ-ed in the cathode film support chemical and structural sta-bilities of the film by restricting electrolyte reactions andsegregation of smaller particles in the mixture [10]. Thus,the bimodal particle-size distribution of the BM–LMOfound in Fig. 1f plays a major role in improving the ratecapability and cyclability for this sample.

Correlation between energy and power densities

The gravimetric specific energy, εs, of a battery electrode isobtained as a product of the open circuit voltage and thespecific charge capacity of the cell. The average specificpower, Ps, delivered by the battery while charging, orextracted from the battery while discharging the cell is givenby the ratio, εs/Texp. Here, Texp denotes the total charge or

Fig. 4 Charge/discharge plots for LMO cathodes prepared with a all-micrometric and b, c BM materials. The three upper and lower sets ofplots represent charge and discharge steps of the first three galvano-static cycles of fresh samples, respectively. The cycle numbers and C-rates are indicated

J Solid State Electrochem (2012) 16:2605–2615 2609

discharge time experimentally set by the C-rate, which, inthe galvanostatic mode, is done by selecting a predeter-mined value of the electrode-area normalized dischargecurrent, ig. The energy available from the cell at a givenC-rate depends on the relative values of Texp and the netdiffusion time of Li in the capacity-limiting electrode. Thus,the usable charge capacity of the electrode is given asCm(used)0[(igTexp)/m0].

The diffusion time defined in Eq. 3 is based on the consid-erations of a single active particle. To estimate the overall timescale of Li diffusion in the context of material utilization of afull electrode, it is appropriate to generalize the single-particlediffusion length to the following form [24]:

Leff ¼ nhVMð1� fÞL ¼ m0VMCmðFÞ�1; ð4ÞWhere Leff is the effective length that has to be travelled byintercalating ions within the cathode to fully utilize the avail-able host sites; VM is the molar volume of the active material.The condition for full utilization of the energy stored in theelectrode can be written as:

Texp > td ¼ Leffð Þ2eD ; ð5Þ

Where τd is the minimum diffusion time necessary for Litransport to completely charge or discharge the whole elec-trode. This condition places a restriction on the lower limit ofTexp and hence on the upper limit of Ps that is available from anelectrode specified by a given pair of Cm and εs. This correla-tion betweenPs and εs can be examinedwith Ragone plots [27].

Figure 5 shows Ragone plots, recorded using the sameelectrolyte composition, for two electrodes prepared with (a)AR–LMO and (b) BM–LMO particles. In each case, theexperimental cathode was subjected to repeated galvano-static discharge cycles at variable rates between 1-C and30-C following a fixed 1-C rate charging. The specificenergies were determined by numerically integrating E vs.C plots of the discharge cycles. The diagonal lines indicatethe discharge times (Texp) associated with selected datapoints. At low values of Ps, variations in εs for both theBM- and the AR-LMO samples are relatively insensitivewith respect to increasing the power output. In this region, εsfor AR–LMO is somewhat larger than that of BM–LMO,because, as already noted in Fig. 4a, b, the specific capacityfor the former is comparatively larger under the condition ofslow discharge. However, under the conditions of fast dis-charge (log Ps>3 W kg−1), the BM–LMO cathode exhibitsits noteworthy electrochemical performance by providingrelatively high energy densities available for utilization.While a large absolute capacity of the electrode in a Li ionbattery is essential for high-energy-density applications, therate capability serves as a critical electrochemical character-istic of cathodes for high-power-density applications. The

Ragone plots in Fig. 5 illustrate the usefulness of the BMapproach to electrode fabrication in such cases.

At Texp <5 min, plot (a) in Fig. 5 begins to curve downnoticeably, indicating that the condition specified in Eq. 5 isno longer met for this case at such fast rates of powerconsumption. On the other hand, plot (b) for the BM–LMO stays reasonably flat at even lower values of Texp,demonstrating that Eq. 5 continues to hold for this sampleduring increased power delivery by the half-cell. As shown

elsewhere [10], D�

for the BM–LMO is considerably largerthan that of the all-micrometric LMO. This promotes fastcharge/discharge of BM–LMO, while maintaining the con-dition of active material utilization according to Eq. 5.

The relatively smaller volume-specific surface areas ofmicrometric LMO particles can cause a drop in the surfacevoltage as concentration polarization builds up during rapidcharge/discharge. This also contributes to the lowering of εsin the high-power regime of plot (a) in Fig. 5. The nano-particle constituents of BM–LMO, which determine theshape of plot (b) are mostly free of such concentrationpolarization effects. The Ragone plot for the BM–LMOeventually begins to drop in εs when Texp is lowered below1 min. This suggests that τd for the BM sample should be onthe order of this time scale. More details of this specificpoint are addressed later in the present report using EISresults.

Nyquist spectra and impedance parameters

Figure 6 shows Nyquist impedance spectra for a BM–LMOcathode, collected using EIS at various open circuit poten-tials in the main potential region of intercalation/de-interca-lation during the first two cycles of charge and discharge. Z′and Z′′ denote the real and imaginary parts of the cathodeimpedance, respectively. The perturbation frequencies de-crease from left to right along the Z′ axis. Compared with

Fig. 5 Ragone plots of specific energy (εs) vs. specific power (Ps),recorded for a all-micrometric and b BM–LMO cathodes using galva-nostatic charge (1-C rate) and discharge (variable rates between 1 Cand 50 C) experiments performed in LMO|Li cells

2610 J Solid State Electrochem (2012) 16:2605–2615

earlier reported results for all-micrometric LMO [2], theoverall impedance of BM–LMO obtained here is substan-tially reduced, and indicates more efficient Li+ transport inthe latter case. Because the EIS measurements correspond toequilibrium conditions, the data collected during the chargeand discharge cycles are mutually similar. The results arealso similar between the first and second cycles due to therobust cyclability of BM–LMO. Voltage-sensitive variationsin the Warburg impedance of Li diffusion are noticeable inthe low-frequency (10−0.01 Hz) spectra. At the outer edgesof the intercalation voltage region, these diffusion featuresare at their maximum values and are minimized duringintercalation. The high-frequency arcs are due to the CSF.

The lines in Fig. 6 are CNLS calculated fits to the data,which lead to the EEC model shown in Fig. 7a. This EEChas been extensively used to describe surface reactions ofvarious metal oxide cathodes for Li ion batteries [28–30].The uncompensated electrolyte resistance Ru is essentiallyvoltage-independent in the present experiments with anaverage value of 12.1 Ω g. Qf and Rf denote the constantphase element (CPE) and the net resistance of the CSF,respectively. Cdl is the double-layer capacitance of the cath-ode. W is the Warburg element for Li+ diffusion in thecathode, and Rct is the charge transfer resistance for reaction(1); Cint is the intercalation capacitance of LMO.

The impedance of the Warburg element has the form:

Zw ¼ σ 1� jð Þw�1=2, where ω is the angular frequency of AC

perturbation, j ¼ ffiffiffiffiffiffiffi�1p, and σ is a frequency-independent

diffusion parameter [10, 22, 28]: σ ¼ ½VM=ðFffiffiffiffiffiffi2eD

p�jdE=dxj.

In the context of material utilization of electrodes [31], x≈(C/

Cm), so that σ ¼ ðVMCThÞ½Fffiffiffiffiffiffi2eD

pðdC=dEÞ��1 , where C is

the charge capacity of the cathode [2, 10]. Using the defini-tion, Cint0m0(dC/dE), one can express σ as:

σ ¼ VMm0Cm

FCint

ffiffiffiffiffiffi2eD

p ; ð6Þ

where Cint is in its gravimetric unit. The voltage dependence ofσ, plotted in Fig. 7b, is reversible with respect to charge/discharge as well as with respect to repeated cycling of thecathode. In addition, σ displays two dips at 3.95 and 4.15 V,corresponding to the current peaks seen in Fig. 4. Similar resultsfor σ have been previously reported for LMO cathodes [32].

The Cdl vs. E plot in Fig. 8a shows a broad minimumbetween 4.0 and 4.1 V, which probably corresponds to theeffective potential of zero charge of the carbon-containingpart of the electrode. If the charge transfer step of reaction(1) is kinetically controlled, Rct should have its minimumvalues converged around x00.5 (expected at intermediatevoltages) and should acquire larger values at x≈0 and 1, atthe lower and upper voltage limits of the intercalation re-gion, respectively [10]. The plot of Rct in Fig. 8a appears toinclude the lower- and mid-sections of such a plot. Accord-ing to Fig. 4, the maximum SoC for the BM–LMO sampledoes not reach a value of 1, and hence, the expected increaseof Rct in the higher voltage region (at x>0.5) is not observedhere. Nevertheless, the data plotted in Fig. 8 for the separatecharge and discharge cycles are concurrent and demonstratethe highly reversible nature of electrode cycling.

Fig. 6 Nyquist impedanceplots for BM–LMO recorded atdifferent OCPs. The cellvoltage was changedgalvanostatically at a rate of1/3-C, and the electrode wasallowed to equilibrate at theresulting OCP prior to EISmeasurements. The symbolsand the lines denoteexperimental data and CNLSfits to the data, respectively

J Solid State Electrochem (2012) 16:2605–2615 2611

Figure 9a shows the results for Cint obtained from EISmeasurements at intermediate OCPs during the first andsecond galvanostatic charge/discharge cycles of a BM–LMO cathode. The symbols are data points, and the solidline shows the general trend of the data indicating twodistinctly separated peaks. The voltages matching thesepeaks correspond to those of the current peaks observed inFig. 3a and are associated with the two-step intercalation/de-

intercalation of Li in LMO. For comparison with these EISresults, in Fig. 9b, we plot Cint obtained from thesecond SSCV cycle (where ir00) of Fig. 3a. Theselatter data (symbols) represent the cycle-averaged quan-tity, Cint0[(ia/v)+(|ic|/v)]/2, where ia and ic are the an-odic and cathodic currents of SSCV for the charge anddischarge cycles, respectively; v0(dE/dt). The dashedline in Fig. 9b represents the general inclination of Cint

determined from SSCV, which agrees well with thecorresponding EIS results in Fig. 9a.

Voltage-dependent values of D�

for Li+ in BM–LMOwere determined by using the formulation of Eq. 6 andcombining the data for σ and Cint from Figs. 7b and 9a,respectively. In the context of EIS-based measurements of

D�, it is customary to take the SoC of the electrode as the

ratio (C/CTh) [31–34]. We use this convention to determine

D�

from σ, which maintains an internally consistent frame-work for comparing the present results with those previous-ly reported using the same approach for similar systems [10,

32]. The values of D�

obtained in this way are presented inFig. 9c, where the different symbols represent the first twocharge and discharge cycles of a fresh cathode. The general

trend of D�, indicated by the solid line, is similar to that

previously observed for BM–LMO in LiClO4/EC/DEC

electrolytes [10]. The two minima observed in the plot of

D�

appear at the voltages corresponding to the two phases ofLi intercalation/de-intercalation that have already been

Fig. 7 a Electrode equivalent circuit model of the BM–LMO cathodesused in this work. b Diffusion impedance parameter σ (denoted bysymbols) of BM–LMO, recorded during the first two charge anddischarge cycles. The line shows the general trend of the data

Fig. 8 a Double-layer capacitance (Cdl) and (b) charge transfer resis-tance (Rct) of a BM–LMO cathode measured during the first twocharge/discharge cycles. The line shows the general trend of the datadenoted by the symbols

Fig. 9 Intercalation capacitance (a and b) and chemical diffusioncoefficient (c) of a BM–LMO cathode measured in the voltage regionof Li intercalation/de-intercalation. EIS results for the first two galva-nostatic charge/discharge cycles are shown in a and c. b Shows SSCVresults, averaged from the positive and negative voltage scans inFig. 3a

2612 J Solid State Electrochem (2012) 16:2605–2615

observed in the results of Figs. 4a and 9a, b. The values of

D�in Fig. 9c are more than an order of magnitude larger than

those previously reported for micrometric AR–LMO par-

ticles [2]. These enhanced values of D�

for the BM–LMOcan be attributed to the largely surface-confined nature ofreaction (1) in the nanometric particles [1].

Figure 10 shows the voltage-dependent impedanceparameters measured for the CSF formed on BM–LMOduring the first two charge/discharge steps of a fresh cath-ode. The lines through the symbols indicate the data-trends.The strong convergence of the different symbols showsonce again the reversible nature of the EIS measurements.The CSF resistance Rf plotted in Fig. 10a represents aparallel combination of the Faradaic resistance Rr, and anonfaradaic resistance Rf0 of the surface complex. The ob-served values of Rf are controlled primarily by those of Rf0,because Rf in Fig. 10a is significantly smaller than Rr plottedin Fig. 3b. Rf0 represents, in essence, an ohmic element,because its value is determined primarily by the thickness/porosity rather than the activity of the Li+-conducting CSFfilm [10]. However, the CSF thickness and hence Rf0

depends on the voltage-dependent reaction resistance Rr. Aconsiderable dip occurs in the plot of Rf in the voltageregion of reaction (1), where the lowest values of Rr alsooccur in Fig. 3. This shows how the CSF acquires its weakeststructural configuration when its Faradaic oxidation occurs ata high rate.

The impedance (ZQ) of Qf has the form ZQ0[Y0(jω)n]−1,

where Y0 and n are the characteristic CPE parameters, with0≤n≤1. If the electrode surface becomes spatially moreinhomogeneous, then n decreases and Y0 increases [35].As the intercalation voltage region is approached from lowervoltages, Li transport through the CSF increases, which,apparently increases the spatial in-homogeneity of the CSFin this region. This is indicated by the increasing values ofY0, coupled with a correspondingly decreasing n along thepositive voltage axis in Fig. 10a. In addition, adsorption ofBF4

− anions from the electrolyte onto preferential sites ofthe CSF can reduce the spatial homogeneity of the latter [2].Since this anion adsorption is expected to increase along thedirection of anodic potentials, such an effect may also con-tribute to the observed voltage dependencies of the CPEvariables.

The CSF parameters from Fig. 10a–c are combined inFig. 10d, where the site-averaged structural relaxation timeτf of the CSF is plotted by using the empirical definition[32], τf0(RfY0)

1/n. With increasing voltages in the intercala-tion region, τf closely follows the trend of Y0. This impliesthat the CSF’s electrical response becomes similar to that ofa weakly charge-leaking capacitance when large numbers ofLi+ ions are transported through the CSF. Nevertheless, thevalues of τf fall mostly in the millisecond regime, represent-ing a surface process significantly faster than Li extraction/insertion (Texp) in the cathode. Therefore, the CSF does nothave major effects on the cathode’s intrinsic charge/dis-charge attributes.

Relaxation times for lithium intercalation/de-intercalation

The lithium intercalation/de-intercalation reaction, whichinvolves diffusion of Li+ in the host material, followed bycharge transfer according to Eq. 1, is rate-limited by the

Fig. 10 Impedance parameters of the surface film formed on a BM–LMO cathode. The symbols correspond to the first two charge anddischarge cycles, and the lines show the overall shapes of the plots. Theparameters in a–c are obtained directly from CNLS analysis of exper-imental Nyquist spectra. In (d), τf is evaluated by combining the datafrom a–c

Fig. 11 a Charge transfer and b diffusion times for Li intercalation/de-intercalation measured with EIS at various open circuit voltages ofAR–LMO (shaded bars) and BM–LMO (open bars) cathodes. Theresults shown here correspond to the first discharge cycle of a freshlyprepared cathode

J Solid State Electrochem (2012) 16:2605–2615 2613

diffusion step—that is, by τd defined in Eq. 5. The relativetimescales of these charge transfer and diffusion steps of Litransport in the cathode film can be estimated from the EISmeasured kinetic parameters of the system. The relaxationtime (τct) of charge transfer in intercalation/de-intercalationcan be obtained as τct 0 RctCint. This empirical definition ofτct includes the time associated with the formation of theintercalation capacitance. Similarly, according to Eqs. 4 and

5, td ¼ ½VMm0CmðFffiffiffiffieD

p�1�2 . By combining this expres-

sion with the formula for D in Eq. 6,

td ¼ 2ðm0σCintÞ2; ð7Þwhich appears as the diffusion time considered in the LorenzMöckel treatment of slow interfacial reactions [36].

Experimental values of τct for BM–LMO were obtainedby combining Rct and Cint from Figs. 8b and 9a, respective-ly. The corresponding charge transfer relaxation times for Litransport were also calculated for a cathode of all-micrometric AR–LMO by using EIS data collected in anelectrolyte of the same composition. These results for theAR sample (shaded bars) are plotted with those for the BMsample (open bars) in Fig. 11a. The general voltage-dependent trends for the two sets of these data are mutuallycomparable, but the overall values of τct for the BM–LMOsample are noticeably smaller than those of the AR–LMOsample. This is a result of the large specific area and thedense packing of LMO nanoparticles that are responsible forthe facile kinetic of reaction (1) in the BM cathode.

To obtain τd for the BM–LMO cathode (open bars inFig. 11b), σ from Fig. 7b and Cint from Fig. 9a werecombined in Eq. 7. The values of σ and Cint for the AR–LMO have been measured previously [2] and were usedhere in Eq. 7 to obtain τd for the all-micrometric LMOsample. The considerably larger values of τd found in thelatter case are indicated by the shaded bars in Fig. 11b. Acomparison of Fig. 11a, b indicates how the diffusion step ofLi intercalation/de-intercalation is rate determining for reac-tion (1). The diffusion impedance, as measured in terms of σin Fig. 7b, decreases in the intercalation voltage region [37],and thus, the voltage-dependent inclination of τd is almostopposite that of τct.

As indicated in Eq. 5, full extraction of the energy storedin the Li|LMO half cell remains incomplete if Texp dropsbelow a threshold value, defined as τd. According toFig. 11b, this latter time for the AR–LMO cathode is about17 min through most of the intercalation region. TheRagone plot (a) in Fig. 5 also starts to rapidly drop alongthe specific energy axis, as the discharge duration of thecathode becomes smaller than this value (located betweenthe diagonal lines for 5 and 30 min discharge steps). Simi-larly, the τd of ~30 s (open bars corresponding to 3.8, 4.1,and 4.2 V) for the BM–LMO corresponds well with the

critical discharge time observed in Fig. 5 (between the1 min and 10 s marking lines), where εs begins to decreasewith increasing power densities on Ragone plot (b). Theseobserved correlations between the galvanostatic Ragoneplots and the EIS-measured diffusion times illustrate furtherhow the considerations of material utilization, as noted inEq. 5, govern the power delivery characteristics of the LMOcathodes.

Conclusions

Mechano-chemical modification by ball-milling is a conve-nient and relatively simple method of converting micromet-ric materials for Li ion battery electrodes to controlledmixtures of micro- and nanoparticles. The synergisticactions of this mixture can enhance both the rate capabilityand the cyclability of the processed material. The presentstudy explores the electrochemical considerations of mate-rial utilization for supporting fast charge/discharge of LMOcathodes prepared in this approach. To do this, a phenome-nological framework, adapted from earlier treatments of theproblem [19, 24], is extended here to combine the results ofEIS and galvanostatic measurements. The relative time-scales for diffusion and charge transfer by Li+ in the LMOlattice are determined, and the effects of mechanical millingon these time parameters are examined. The results demon-strate how the nanoparticles in the BM material play acritical role in supporting fast charge/discharge.

Acknowledgment This work was supported by the Army ResearchOffice (Grant no. W911NF-05-1-0339).

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