FRONTIERS ARTICLE
Direct in situ measurements of Li transport in Li-ion battery negative electrodes
Stephen J.Harris a,*,Adam Timmons a ,Daniel R.Baker a ,Charles Monroe b
a Electrochemical Energy Research Lab,General Motors R&D Center,Mail Code 480-102-000,Warren,MI 48090,United States b
Department of Chemical Engineering,University of Michigan,Ann Arbor,MI 48109,United States
a r t i c l e i n f o Article history:
Received 14November 2009In final form 10December 2009Available online 22December 2009
a b s t r a c t
We describe the first direct in situ measurements of Li transport in an operating cell.Motion of the lith-iation front in the graphite electrode suggests that transport could be controlled by liquid-phase diffu-sion.The electrochemical (current–voltage)data are successfully modeled with a diffusion equati
on that contains no material or microstructural information.The model is only qualitatively successful in predicting observed Li transport rate data,suggesting that microstructural information is required and that the actual process is more complex than simply diffusion.The technique can provide data for study-ing Li plating and Li dendrite growth,both of which can cause battery degradation.
Ó2009Elsevier B.V.All rights reserved.
1.Introduction
Because of their high energy density and long cycle life,Li-ion batteries are used today in many practical devices including cell phones and laptop computers,and they are now being contem-plated for mass-produced hybrid and electric vehicles [1].A typical Li-ion battery is shown schematically in Fig.1a and as an SEM in Fig.1b.As the battery is charged and discharged,Li,originally pres-ent in the electrolyte and in the positive electrode*,chemically re-acts with the negative electrode,inserting or intercalating into the bulk material.This lithiation process changes the chemistry of the electrode particles,so the properties of the Li-ion battery depend critically on the chemical nature of the electrode material.Since,by definition,Li is thermodynamically more stable in the positive electrode,a power supply is required to detach Li from the positive electrode (usually a transition metal oxide or
phosphate)to form Li +ions and then to push them into the negative electrode*(almost always a form of graphite or carbon)for charging,as illustrated in Fig.1a.Because lithium reacts with practically everything,the number of potential lithium-ion battery electrode materials—and,therefore,the number of potential lithium-ion battery types—is al-most limitless.
Li-ion batteries are generally analyzed using the macro-homo-geneous porous electrode model developed by Newman and co-workers [2,3].The model consists of equations for:(1)electronic charge balance in the solid phase (Ohm’s law);(2)electrolyte charge and mass balance for Li +using concentrated electrolyte the-ory;(3)diffusion of lithium in the electrode particles (Fick’s law);(4)Butler–Volmer*charge transfer kinetics at the electrolyte-solid
phase boundary;(5)and associated boundary conditions.The model requires as input no microstructural information beyond particle radius,electrode thickness,and electrode porosity.Other-wise,it assumes that the microstructure can be described as an iso-tropic,homogeneous,1-dimensional porous material made up from monodisperse non-porous isotropic spherical particles that are small compared to the electrode thickness.
Of course,none of these assumptions and approximations can be truly correct.For example,significa
nt inhomogeneity in the electrodes and in the state of lithiation within an electrode that should be at equilibrium has been observed [4–6].The charge transfer step is modeled as a single global chemical reaction in which Li +ions in the electrolyte solution de-solvate,transport through a $1–10nm thick solid electrolyte interphase (SEI)layer [7–12]consisting of various degradation products,and react with the electrode material.Remarkably little is known about the de-tailed chemistry of the Butler–Volmer step [12–14],even though it is involved in many proposed degradation mechanisms [11,15,16].Diffusion of lithium in the solid phase active particles is treated with a shrinking core diffusion model [17,18]although its validity is at best uncertain for many commonly used elec-trodes,and although it has been shown to be invalid for at least one material [19].Properties of the conductive carbon and binder,while of considerable importance to battery performance,are ab-sorbed into other parameters.
In the years since the model appeared,a number of papers,some from Newman’s group,have examined the effects of relaxing some of the microstructural assumptions of the original model.For example,Darling and Newman [20]analyzed the effects of multi-ple particle sizes,Yi and Sastry [21]considered particles with ellip-soidal shapes,and Santhanagopalan et al.[22]and Yi et al.[23]looked at extending the model to higher dimensions.These and other efforts notwithstanding,the original macro-homogenous model performs very well and is still widely and successfully used
0009-2614/$-see front matter Ó2009Elsevier B.V.All rights reserved.doi:10.1016/j.cplett.2009.12.033
*Corresponding author.Address:Electrochemical Energy Research Lab,General Motors R&D Center,Mail Code 480-102-000,30500Mound Rd.,Warren,MI 48090-9055,United States.Fax:+15869862244.
E-mail address:stephen.j.harris@gm (S.J.Harris).Chemical Physics Letters 485(2010)
265–274
Contents lists available at ScienceDirect
Chemical Physics Letters
j o ur na l h om e pa ge :w w w.e lse v ie r.c om /lo c at e /c pl et
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[24]for optimizing electrode parameters such as thickness and porosity.It is,in fact,the basis for COMSOL’s commercial Li-ion battery code.
On the other hand,the ability to predict cell degradation re-mains a challenge because so many unaccounted for and seem-ingly unrelated micro-scale degradation mechanisms have been identified or postulated [4,21,25–39].Experimental measurements describing local chemistry,details of the microstructure and trans-port,and an understanding of how these factors evolve are re-quired in order to sort out the issues involved with degradation.At present,analysis of specific degradation
mechanisms can sometimes offer explanations for experimentally observed degra-dation [22,29,40,41],but without additional experimental data
and associated theoretical analysis,cause-and-effect relationships between observation and degradation pathway can be difficult to demonstrate.For example,a widely invoked degradation mecha-nism is loss of internal ‘electrical connectivity.’The loss of connec-tivity has been directly observed by Kostecki and McLarnon [4],and they attributed it to the movement of conductive carbon (‘car-bon retreat’),reducing electron transport within the electrode.But loss of internal electrical connectivity has also been attributed to particle fracture [36,38,42],to precipitation of thick surface films [30,35],to gas generation [43],to loss of contact between active material and the current collector [44]or between the current col-lector and the cell housing [45],and to degradation of the binder [46].As a result,there has not appeared to be any experimental or modeling strategy that elucidates degradation as a general phe-nomenon.Because a lower degradation rate translates directly into lower-cost batteries,the ability to predict,mitigate,and deal with degradation by understanding fundamental chemical and material properties is critical if batteries for transportation are to become economically viable.
In an ideal Li-ion battery,the only process that should occur at the mesoscale (smaller than an electr
ode,larger than a molecule)is transport of lithium ions through the electrolyte and in the active particles,accompanied by reversible reactions of lithium at appro-priate locations within the electrodes.All of the seemingly dispa-rate mechanisms of battery degradation lead in some way to inefficiency or irreversibility of these fundamental transport and associated chemical processes.The present work is predicated on the notion that a general study of degradation can begin with mea-surements of Li transport and insertion into porous electrodes.These measurements could then guide researchers towards other experiments and models that provide fundamental knowledge of degradation.With this goal in mind,we provide here in situ time-dependent Li spatial maps and transport rate measurements at the mesoscale.
2.Experimental
Charging and discharging experiments were carried out in an optical half-cell*.Fig.2shows the optical half cell as seen from the side (schematic)and from above (photograph).The cell was assembled in a glove box under an Ar atmosphere (<1ppm oxygen and water),since even N 2reacts with Li.A brushed piece of Li foil acted as the negative electrode,while a porous graphite electrode cut from an LR1865AH 18650*laptop battery made by Tianjin Lishen Battery Co.served as the positive electrode.The electrode material coated both sides of a copper current collector,as can be seen for a
different electrode in Fig.1b.
Conventionally,electrodes are stacked (or wound)facing each other with a separator keeping them apart so they do not short,as shown in Fig.1a.(Putting electrode material on both sides of the current collector allows this stacking arrangement.)This geom-etry minimizes Li +transport barriers and in-plane gradients.For our system,the electrodes,each roughly 1cm square,were instead placed side-by-side on separate spring-loaded stainless steel sup-ports that were separated by a Teflon spacer,Fig.2.The electrodes and supports were electrically isolated,but they could be con-nected through an external circuit.The electrodes were soaked with electrolyte (1M LiPF 6salt in 1:2volumetric ratio ethylene carbonate:diethyl carbonate solvent),which also filled the gap above the Teflon spacer and between the electrodes.The cell was then covered with a quartz window,sealing it.(Quartz is gradually attacked by lithium.Sapphire is a better choice.)The pressure of the window on the electrodes was approximately 1bar.
The arrangement shown in Fig.2allows transport of Li +ions from the metal,above the spacer,and into the edge of the
porous
Fig.1.(a)Schematic of a lithium-ion battery being charged.Each electrode is a composite made from $10l m particles (red and green balls,$80%by mass)with which Li +ions react and into which the lithium inserts.By definition,lithium binds strongly with positive electrode*material (low D G ?high voltage)and weakly with negative electrode*material (high D G ?low voltage).The particles are held together and attached to a metal current collector with a minimal amount of binder (light blue,polyvinylidene fluoride PVDF,$10%by mass).In order to ensure that electrons have a low-resistance path for electrons to get from the current collector to active particles,which are often electrical insulators such as LiCoO 2,a minimal amount of conductive carbon (black squiggles,soot or carbon black,$10%by mass)is also added.Electrode porosity is $15%in a laptop battery,but it may be much greater when high power is required;and electrode thickness is 50–100l m.The electrolyte solution—LiPF 6salt in a diethyl carbonate/ethylene carbonate solvent—functions as a filter that passes ions but not electrons.The electrolyte solution fills the pores,but there is no free liquid.Electrodes are prevented from short-circuiting with a 10–20l m thick porous polymeric separator.(Thanks to V.Srinivasan of LBNL for the diagram)(b)SEM cross section of a LiCoO 2(positive)electrode,potted in epoxy,which fills the pores.Electrode material coats both sides of the al
uminum current collector,seen running towards the upper left corner.This double-sided arrangement allows electrodes to be easily stacked in parallel.(a)shows electrode on only 1side.)
266S.J.Harris et al./Chemical Physics Letters 485(2010)265–274
graphite electrode.Within the graphite electrode,Li +ions may either insert into the graphite or diffuse through the electrolyte,which fills the pores between the particles.Although a direct diffu-sion path perpendicular to the lithium and graphite edges is most favorable,other Li pathways were observed.For example,lithium could electrodeposit directly on the stainless steel or travel around the edges of the graphite far from the Teflon spacer.In principle,it could also move through pores that are between the window and the electrode top surface.In order to confirm that such transport was not dominant,we imaged the edge of the electrode during the lithiation step in a separate experiment to determine the lith-iation rate just under the quartz window compared to that for the rest of the electrode.
After assembly,the cell was removed from the glove box and put under an Olympus SZX12optical microscope at 90Âmagnifica-tion.The brushed lithium metal electrode showed no obvious oxi-dation or nitride formation over a time scale of up to a week.
Cells were placed under either current or voltage control using a high precision source/measure unit (Keithley 237)in an external circuit.Current densities,defined with respect to the nominal geo-
metric surface area of the electrode edge,were in the range 1–10mA/cm 2.
Digital micrograph images of the electrodes were recorded every 15min,with the microscope focused near the edge of the graphite electrode closest to the Li metal electrode.Experiments typically ran for a couple of days.Videos,some of which are avail-able online [47],were constructed from the sequence of images.Because of the color change that occurs when graphite is lithiated [48–50],these images provide approximate time-dependent Li concentration maps or spatial profiles in the graphite electrode.(For the images shown in this Letter and on the web [47],we have enhanced the colors using Photoshop.)
Our experimental arrangement (Fig.2)has several advantages for performing studies on Li transport compared to a more conven-tional face-to-face arrangement (Fig.1a).
(1)By placing the electrodes ‘face up’we can take advantage of
graphite’s color changes upon lithiation to measure in situ spatial profiles of intercalated Li.Bazant et
al.[51]used a conceptually similar geometry to follow transport and reac-tion in a copper–chlorine corrosion system.
(2)The side-by-side arrangement leads to large concentration
gradients.While undesirable in a conventional cell,large gradients are useful when the goal is to make transport measurements.
(3)Our arrangement,in effect,converts the problem of measur-ing Li transport perpendicular to the current collector through a distance of about 0.1mm,to the problem of mea-suring Li transport parallel to the current collector through a distance of about 10mm,making the measurement easier.
3.Color of lithiated graphite
Graphite possesses a P63/mmc layered structure [52],where layers of graphene composed of hexagonally arranged sp 2hybrid-ized carbon are weakly bonded to each other by van der Waals forces along the c -axis,resulting in 0.34nm-wide galleries be-tween the graphene layers.The layer stacking of lithium-free graphite is A–B–A–B,with layers translated but not twisted rela-tive to each other.In order to allow lithium intercalation into a gal-lery space,the graphene layers slide with respec
t to each other,creating domains with A–A or B–B stacking [53,54].At room tem-perature,electrochemically lithiated graphite at the LiC 18[55]con-centration has Li in every other gallery (‘dilute stage 2’)on average,although the Li is not well ordered within each gallery [53].This phase is dark blue colored.Additional Li inserts in every second gallery through a two-phase transition to the well ordered (‘stage 2’)[50]LiC 12phase,which grows as the LiC 18phase shrinks [53].This phase is red colored.Once LiC 12is reached,additional Li goes into the unoccupied galleries through another two-phase transi-tion with a phase of well ordered lithium in every layer growing as the LiC 12phase shrinks until a fully ordered (‘stage 1’)LiC 6is ob-tained.This phase is gold colored [56].
There are a variety of factors that can lead to color variation be-tween a particle and its neighbors,even if they are all at the same nominal potential.The need for graphene layers to slide with re-spect to one another when Li is intercalating (to form A–A stacking from A–B stacking)means that defects in the graphite structure may prevent full lithiation [57].As a result,the color homogeneity of lithiated graphite held at a given potential can depend on how defect density varies from particle to particle [57].Any variation in the electrical contact of a particle to its neighbor or to the cur-rent collector may also lead to variation in color if the color is ob-served before the family of particles has been given sufficient time to reach equilibrium.A similar logic could explain variation
in
Fig.2.(a)Side view schematic of the optical half-cell.(A)Quartz window.(B)Li foil electrode,0.38mm thick.(C)Graphite electrode showing current collector bisecting it.(D)Teflon spacer.(E)Coin cell springs.(F)Stainless steel supports and cell housings.(G)Keithley 237source/measure unit,external to the cell.(H)Working electrode wire.(I)Reference electrode wire.(J)Counter electrode wire.Optical data are taken with a microscope viewing the quartz window from above.Electrolyte wets the electrodes and also fills cavities between the electrodes and surrounding the Teflon spacer.Cell housing is not shown.(b)Photograph of the graphite electrode positioned about 2mm from a Li metal electrode on electrically separated stainless steel supports.Electrolyte fills the gap between the electrodes (above the Teflon)so that there is an unimpeded pathway for Li +ions to travel between the electrodes.The electrodes are positioned on spring-loaded supports such that they are pressed against the quartz window (pressure about 1bar)that seals the cell.
S.J.Harris et al./Chemical Physics Letters 485(2010)265–274267
color within a single particle[6].As a result,even when the poten-tial is such that all of the graphite should,for example,be LiC12,as measured by the electrical potential,it is likely that some of the grain
s will have a greater lithium concentration and some of the grains will have a lower lithium concentration.However,from the perspective of canonical mesoscopic transport models[2],only a locally averaged graphite color is meaningful;additional micro-scopic details would be needed to rationalize thesefine-grained color variations.
甘远志Conversion of color to Li concentration should be taken as only semi-quantitative.Various attempts have been made to correlate graphite’s color with intermediate lithium contents[48],but color is difficult to calibrate(for example,it depends significantly on ambient lighting conditions[58]).Furthermore,it is difficult to en-sure that electrochemical equilibrium has been reached when esti-mating an electrode’s lithiation state.lalu
4.Model
To model the insertion experiments,it will be assumed that the process of lithium insertion obeys the transient diffusion equation
@c @t ¼D eff
@2c
@x2
;ð1Þ
where c is the(molar)concentration of lithium with respect to a volume element containing both graphite and pore-filling electro-lyte,x is the distance from the electrode’s edge at the electrode/sep-arating electrolyte boundary,and t is time.The effective diffusion coefficient D eff is intended to lump together microscopic processes such as diffusion and migration*of lithium through the liquid phase,solid-phase lithium transport,and electrochemical kinetics by which lithium crosses solid–liquid boundaries in the cell’s interior.
Although it has been observed that the diffusion coefficient of lithium in graphite electrodes(lithium exists in graphite as nearly ionic,with a positive charge of about0.8[59])varies with lithium concentration[60,61],for the sake of simplicity it will be assumed here that D eff is constant.For extensions of the model,we believe that it would be better to consider that diffusion of lithium in the pore-filling electrolyte and the solid graphite occur in parallel locally,as in Tobias and Newman’s porous-electrode theory[62], rather than to give the effective diffusion coefficient in equation 1a locally variable value.
Although more sophisticated theories applicable to porous insertion electrodes exist[2,63],Eq.(1)could suffice to approxi-mate experimental results if any of the diffusion processes associ-ated with lithium insertion is rate-limiting.Use of Eq.(1)also has the advantage that it is amenable to analytical solution.The ad hoc assumption that diffusion is rate-limiting will be revisited later, but it is consistent with experimental observations shown below and with the common observation that lithium insertion kinetics tends to be fast—i.e.,ion transfer between pore-filling electrolyte and graphite requires a low overpotential*.
To convert the concentration variable into a more meaningful parameter,we introduce the maximum molar lithium content c max. If the quantity of lithium dissolved in the pore-filling electrolyte is negligible,
c
c max
ð2Þ
represents the local fractional lithiation of the porous electrode.
A typical electrochemical experiment begins with a porous graphite electrode that has been drained to a fully de-lithiated state.After a step designed to remove impurities,the experiment then takes place in two steps:
(A)Lithium is inserted into the electrode at constant current for a
period t0,at which time the electrode/liquid boundary has reached lithiation h max(determined by the color at the bound-ary).At this time the voltage has attained a value U0(t0). (B)The cell is held at the constant voltage U0from t=t0onward.
Experimentally,it is observed that this condition maintains a constant lithiation state(gold color)at the electrode/liquid boundary.During this period the current decays over time as the lithiation state(color)gradually becomes uniform throughout the electrode.
Formally,the initial condition of the experiment is
hð0;xÞ¼0:ð3ÞStep A corresponds to the condition
ÀD eff
@h
@x
ðt;0Þ
¼
i0
nFc0
if0<t6t0;ð4Þ
where i0is the current density during the constant-current step(A), F is Faraday’s constant,and n is the number of electrons transferred during an insertion event;typically n=1for lithium insertion.(Note that current density is expressed with respect to the nominal geo-metric surface area of the electrode’s edge.)Assuming that a con-stant voltage maintains constant lithiation state(color)at the electrode/electrolyte boundary,step B is described by the condition hðt;xÞ¼h max if t>t0:ð5ÞThe electrode size is chosen such that
hðt;1Þ¼0;ð6Þthat is,the initial lithiation state is maintained far from the graph-ite/liquid interface(off the top of thefigures).
An analysis of step A shows that the maximum lithium content at the electrode boundary depends on the constant-current pulse duration,effective diffusion coefficient,and maximum inserted-lithium concentration,through
h max¼
2i0
ffiffiffiffiffiffiffiffiffiffiffi
t0
p
eff
r
:
ð7Þ
The solution to Eq.(1)that satisfies initial and boundary condi-tions(3)–(6)can be obtained using a combination of Laplace trans-formation and Duhamel’s superposition integral,which show that
hðg;sÞ
maxFANPN
¼
ffiffiffiffiffiffip
s
p
ierfcðgÞs60;
ffiffiffiffiffiffip
1Às
p
ierfcðgÞÀ
ffiffiffiffiffiffips
1Às
p
ierfcðg=
ffiffiffis p
Þ
þ1
2
ffiffiffiffiffiffi
1Às
p
R1
ffiffiffiffiffiffiffis
1Àu
p
Àsffiffiffiffiffiffiffiffi
1Às u
p
erfc g=
ffiffiffiffiffiffis
u
p
ÀÁ
伯克纳
du
s>0;
8
>><
>>:
ð8Þwhere the integrated error function complement function is defined as
ierfcðgÞ¼
1
ffiffiffiffip
p eÀg2Àg erfcðgÞ¼1ffiffiffiffip
p eÀg2Àg2ffiffiffiffip
p
Z1
g
eÀu2duð9Þ
and the independent variables g and s relate to time,position,and constant current duration through
gðt;xÞ¼x
原子能2
ffiffiffiffiffiffiffiffiffiffi
D eff t
p and sðt;t0Þ¼1Àt0
t
:ð10Þ
Note that0<s<1when t>t0and s<0when t<t0.
Eq.(8)can be used to determine theflux at the electrode boundary when t>t0(or s>0).Faraday’s law then shows how the current relaxes during step B:
iðt>t0Þ
¼
2
p arccos
ffiffiffiffiffiffiffiffiffiffiffiffi
tÀt0
r!
:ð11Þ
268S.J.Harris et al./Chemical Physics Letters485(2010)265–274
Eq.(8)can also be applied to obtain the position of the moving boundary between colors as a function of time.The gold/red bound-ary position,for instance,corresponds to a given fractional lithia-tion,h g/r .Since the constant-current duration t 0is set experimentally,s (t ,t 0)is known from Eq.(10);moreover,the exper-iment is constructed to set h max =1;that is,t 0is selected such that the electrode/electrolyte boundary is fully lithiated (gold).A master curve for g g/r (s ),the value of the similarity variable that corre-sponds to the transient location of the gold/red boundary,is found by solving the implicit equation h (g g/r ,s )=h g/r for g g/r at each exper-imental dimensionless time s .This curve is determined by the parameters t 0and h g/r alone;no other properties are required.To obtain x (t ),the transient position of the gold/red boundary,Eq.
(10)can be rearranged to the form x ðt Þ¼2g g =r ffiffiffiffiffiffiffiffiffiffi
D eff t p ,which intro-duces the effective diffusion coefficient.Thus the position of the moving boundary depends on the parameters t 0,h max ,h g/r ,and D eff .The first two of these are controlled experimentally and h g/r can be found by auxiliary measurements.The only unknown is D eff ,which can be determined by a best-fit of an experimental measurement of x (t )by the method of nonlinear least squares.5.Results 5.1.Experimental
Fig.3a and b show a pair of images taken about 45min apart during lithiation.The camera angle gives a view of the edge of
the electrode.The gold color rises from the current collector (Fig.3a)toward the top face of the electrode (Fig.3b),where the quartz window sits.The fact that lithiation occurs first at the cur-rent collector and only later at the top of the electrode suggests that the pore space between the top surface of the electrode and the quartz window is not the main transport pathway for Li +ions;rather,Li +ions travel predominantly through the porous electrode.The result suggests that the state of lithiation at the top surface,which we observe,lags by less than an hour that at the bottom sur-face,only a few percent of the duration of the experiment.
Fig.4shows an SEM micrograph of a cross section of the dou-ble-sided graphite electrode after the p
ores have been filled with epoxy and the electrode cut with a microtome blade,which is a de-vice that cuts very thin slices.The $10l m thick copper current collector runs from the top to the bottom,bisecting the electrode,with epoxy filling the balance of the image,including the voids in the electrode.Striations outside the electrode that run from top
to
Fig. 3.A pair of images showing the gold color climbing up the edge of the electrode,indicated by the region between the white dashed lines.(a)Taken earlier,shows the gold color only at the bottom of the edge,near the current collector.(b)Taken about 45min later,shows the gold color covering the entire edge.See Supplementary video
.
Fig.4.Cross section of the graphite electrode made with a microtome and imaged with an SEM.The electrode was filled with epoxy before being microtomed.Vertical scratches made by the microtome are visible on either side of the electrode.The current collector,approximately 10l m thick,runs top-to-bottom,bisecting the electrode.Individual particles are difficult to make
out.
Fig.5.Experimental (dots)and theoretical (solid line)data for the transient current and voltage during the galvanostatic/potentiostatic lithium insertion experiment described in the Model section.The duration of the galvanostatic control was 28694s,around 8h,with I 0=150l A.
S.J.Harris et al./Chemical Physics Letters 485(2010)265–274269
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