Effect of electrolyte composition on lithium dendrite growth

Article abstract of DOI:10.1149/1.2969424

Lithium deposition is observed in situ using a microfluidic test cell. The microfluidic device rapidly sets up a steady concentration gradient and minimizes ohmic potential loss, minimizes electrolyte usage, and shows good repeatability. Dendrite growth is observed at different current densities for electrolytes containing lithium hexafluorophosphate or lithium bis(trifluoromethane sulfonyl) imide (LiTFSI) in mixtures of propylene carbonate (PC) and dimethyl carbonate. Dendrites are formed at shorter times in electrolytes containing LiTFSI and high amounts of PC. The time to first observed dendrites increases linearly (for all electrolyte compositions) with a resistance given by the Tafel slope of the lithium reduction polarization curve.

Full text of DOI:10.1149/1.2969424

A806
Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
0013-4651/2008/155͑11͒/A806/6/$23.00 © The Electrochemical Society
Effect of Electrolyte Composition on Lithium Dendrite Growth
,z
*
**
Owen Crowther and Alan C. West
Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
Lithium deposition is observed in situ using a microfluidic test cell. The microfluidic device rapidly sets up a steady concentration
gradient and minimizes ohmic potential loss, minimizes electrolyte usage, and shows good repeatability. Dendrite growth is
observed at different current densities for electrolytes containing lithium hexafluorophosphate or lithium bis͑trifluoromethane
sulfonyl͒ imide ͑LiTFSI͒ in mixtures of propylene carbonate ͑PC͒ and dimethyl carbonate. Dendrites are formed at shorter times
in electrolytes containing LiTFSI and high amounts of PC. The time to first observed dendrites increases linearly ͑for all
electrolyte compositions͒ with a resistance given by the Tafel slope of the lithium reduction polarization curve.
© 2008 The Electrochemical Society. ͓DOI: 10.1149/1.2969424͔ All rights reserved.
Manuscript submitted April 24, 2008; revised manuscript received June 19, 2008. Published September 5, 2008.
Lithium metal is an ideal negative electrode material because it is
Polymer electrolytes are known to inhibit dendrite formation due
to the mechanical strength of the separator, but they require an op-
erating temperature around 90°C to obtain conductivities necessary
for good battery performance.1 They are also inherently safer than
liquid electrolytes because their lack of volatility slows the reaction
between the polymer and Li preventing thermal runaway.8 Hybrid-
gel electrolytes that attempt to combine the high conductivity of
liquid electrolytes with the mechanical strength of solid polymer
electrolytes have also been shown to delay the onset of dendrites.14
However, these also exhibit the poor safety performance common
with liquid electrolytes.1 Additives are also commonly used to form
a good SEI layer that restricts dendrite formation and propagation.12
Other methods used to control dendrites are increasing stack
pressure,11,15 stirring the electrolyte,16 and using pulse plating.17
Epelboin et al.18 first directly observed dendrites using transmis-
sion electron microscopy in 1980. Yamaki and co-workers19 ob-
served in situ Li deposition from a liquid electrolyte using optical
microscopy in 1993. They found the amount of needle-like Li de-
posits decreased and cycle life increased with decreasing current
density. Osaka et al.20 used a similar method and discovered that
adding a second electrolyte component to propylene carbonate, in
this case dimethyl ether, provided for better cycling efficiency and
smoother deposits.20 Brissot et al.21 published a series of papers that
used in situ optical microscopy observations of Li deposition using a
solid polymer electrolyte at 80°C. They observed needle shaped
dendrites approximately 10 ␮m in width at 0.1 mA cm−2 and attrib-
uted their formation to a nonuniform SEI. Bush-shaped dendrites,
200 ␮m across, were observed at 0.7 mA cm−2. They attributed the
formation of these dendrites to a low local concentration of Li near
the dendrite. Dendrites were also observed at 0.05 mA cm−2 after
38 h that shorted the 1 mm wide cell after 100 h.21 The experimen-
tal setup used earlier that combines an optical cell with a microscope
to record Li deposition is used for many different liquid and solid
electrolytes in the literature.
the lightest metal and very electronegative ͑−3.04 V vs the standard
hydrogen electrode͒. These properties lead to a battery system with
a high energy density that is attractive for powering electric
vehicles.1 Lithium metal batteries consist of lithium ͑Li͒ negative
electrode, a liquid, solid polymer, or hybrid-gel electrolyte, and a Li
insertion compound positive electrode, usually a Li metal oxide.
Liquid electrolytes consist of a Li salt, such as lithium hexafluoro-
phosphate ͑LiPF6͒, in polar aprotic liquid solvent containing ethers
and/or alkyl carbonates. Polymer electrolytes consist of a Li salt in a
polymer matrix like polyethylene oxide. A hybrid-gel electrolyte
consists of both solid polymer and a liquid polar aprotic electrolyte.
A passivating layer, called the solid-electrolyte interphase ͑SEI͒,
forms immediately on the negative electrode when Li is contacted
with the electrolyte. The SEI prevents Li corrosion because Li is
thermodynamically unstable with all organic solvents.2 The SEI
consists of reduction products of the electrolyte and has a major
impact on most areas of battery performance, including power den-
sity, cycle efficiency and life, and safety.3
At the negative electrode Li is deposited via the following reac-
tion as the battery charges
charge
Li+ + e− —— Li
͓1͔
→
All attempts to commercialize rechargeable lithium metal batteries
since they were first proposed in the early 1970s have failed due to
poor cycling and safety performance caused by rough Li deposits
formed on the negative electrode during cell charging.4-6 These de-
posits often take branch or bush like morphologies referred to as
dendrites. Dendrites are common during electrodeposition of most
metals, e.g., copper, only as the current density approaches the lim-
iting current density.7 However, dendrites form and spread during Li
deposition during any polarization after a given time.8,9 The exact
reason for the propensity of Li to assume dendritic morphology is
unclear. It is known that local variations of SEI composition and
thickness will lead to an uneven current distribution and thus un-
smooth deposits.10 The condition of the Li electrode substrate is also
known to play a large role in the initiation of dendrites.11
Dendrites grow larger with successive charge/discharge cycles
and can eventually lead to active material becoming “free” or
“dead.” Uneven dissolution often leaves tips that are not in contact
with the electrode.12 The Li in the tip of such a dendrite is now
electrochemically inactive, decreasing the amount of available Li
and the cycling efficiency. This free Li is extremely active chemi-
cally because of its large surface area.12 Dendrites can also traverse
the separator and cause the battery to short circuit. A short may
cause current to rapidly pass through the battery, producing heat that
causes thermal runaway, leading possibly to battery explosion.13
Dolle et al.22 used in situ SEM to obtain live observations of the
Li/polymer interface. These are the best observations of Li dendrites
due to the high resolution ͑ϳ1 ␮m͒ and three-dimensional nature of
the pictures. They observed longer and thicker dendrites at
0.5 mA cm−2 than the small “mossy-like” deposits found at
0.22 mA cm−2. Dendrite growth was observed not only from the tip
but also from the base. Further, they also observed a short circuit.
Most of the current passed through the dendrite at the time of the
short. As a result, Li in the dendrite melted and the polymer burned,
stopping dendrite growth.22
Microfluidic devices, with flow channel dimensions usually of
10–1000 ␮m, are common in the fields of medical analysis, envi-
ronmental monitoring, biochemical analysis, and microchemistry.23
This work uses a microfluidic device, where Li is deposited on
copper ͑Cu͒ electrodes with an area of 2 ϫ 10−4 cm2. Genders et
al.24 showed experimental data of Li deposition on 5 ϫ 10−5 cm2
Cu electrodes was free of ohmic effects. Flow systems with a high
Pećlet number ͑Pe͒ and a low Reynolds number ͑Re͒ are known to
*
Electrochemical Society Student Member.
Electrochemical Society Active Member.
**
z E-mail: roc2101@columbia.edu
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Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
quickly form a steady diffusion layer.25 Willey and West26 demon-
A807
strated this experimentally in a microfluidic device for Pe between
1200 and 13,000 and Re 1–13. This eliminates mass transfer issues
caused by a growing diffusion layer. Ambiguities caused by the
onset of free convection when studying deposition in a stagnant
electrolyte are also eliminated by this device. Willey et al.27 showed
experimentally for high Wagner numbers ͑Wa͒ the current distribu-
tion is uniform across an electrode in the direction of the flow in a
similar microfluidic device. Therefore, any deposit roughness will
not be caused by a nonuniform current distribution. The microfluidic
device in this work uses a relatively small quantity of electrolyte.
The time that the first lithium dendrite is observed during galvano-
static deposition shows good experimental repeatability.
The present paper systematically describes the effects of current
density, type of electrolyte salt, and electrolyte solvent composition
on dendrite initiation and propagation using in situ optical observa-
tion with standard electrochemical tests. Liquid electrolytes with
“poor” solvents are used to study the worst case scenarios. The hope
is that information learned from these scenarios will apply to better
liquid and gel-hybrid electrolytes.
(a)
flow channel
cut out of 1.6 mm thick
silicon rubber sheet
Experimental
0.2 mm
The experimental setup consisted of a microfluidic flow cell that
contained copper working electrodes ͑WEs͒ which Li was deposited
on. Li was galvanostatically deposited using a Princeton Applied
Research model 273A potentiostat. Li deposition was recorded using
a Carl Zeiss Stemi 2000-C optical microscope equipped with a Pix-
eLink 623-C digital camera. The ͑WE͒ were a Cu wire with a
0.191 mm ͑bare͒ diameter with Teflon insulation. The WEs were
electropolished in o-phosphoric acid ͑Fisher Chemical͒. A new elec-
trode was used for every experiment. The counter electrode ͑CE͒
and reference electrode ͑RE͒ was another Cu wire located down-
stream. The flow channels were cut out of 1.6 mm thick silicone
rubber and were 2 mm wide and 40 mm long. The rubber did not
swell or react with the electrolyte for at least 24 h. The wires were
embedded into the side of the flow channel. In experiments with a
separate RE, like the linear sweep voltammetry used to obtain the Li
reduction polarization curves, a third Cu wire located downstream
from the CE was used as the RE. Lithium was in situ electrodepos-
ited onto the RE using conditions described by Zhou and Notten28 to
produce a reliable Li RE that would be stable for many days.28 Also
for these experiments the CE was always located 0.75 mm down-
stream from the WE. Electrolyte was introduced to the cell using a
New Era Pump Systems NE-500 syringe pump from 1 to 60 mL
Becton-Dickinson syringes at a rate of 5.0 mL h−1. This flow rate
corresponded to a Pe of 4650 and a Re of 1 ϫ 10−5 for 1.0 M LiPF6
in propylene carbonate ͑PC͒ when using the viscosity and diffusion
coefficient reported by Kondo et al.29 The limiting current density
͑discussed below in more detail͒ was between 120 and
162 mA cm−2 for this electrolyte, corresponding to a diffusion layer
thickness of 13 and 10 ␮m. The Wa for this electrolyte was calcu-
lated to be 24–96 ͑depending on the average current density͒ so the
current distribution would be uniform. Figure 1 is a schematic of the
experimental setup. The entire system is contained in an argon ͑Tech
Air UHP grade͒ filled glove box containing under 100 parts per
million water. All electrolytes were purchased from Electrolyte
Ferro and used as received. Each experiment was repeated five times
and the standard deviation was shown by the error bars. A Dell
Optiplex GX620 was used to control the potentiostat, digital camera,
and the syringe pump.
electrolyte
flow
WE
0.75 mm
CE
PTFE insulated Cu wires
(to potentiostat)
2.0 mm
RE located downstream
(b)
Figure 1. ͑Color online͒ Schematic of test station. ͑a͒ The complete test
setup showing all equipment. ͑b͒ Detail of a section of the microfluidic cell.
deposited from 1.2 M LiPF6 in ethylene carbonate ͑EC͒:ethyl me-
thyl carbonate ͑EMC͒ ͑3:7 by weight͒ at a rate of 2 mA cm−2 in this
experiment. We can see the first dendrite formed around 180 s. This
time is referred to as the time of first observed dendrite, tFOD. The
dendrite quits growing from the tip at 420 s and starts growing from
the base, a phenomenon also observed by Dolle et al.22 In this ex-
periment, the dendrite grows against the direction of fluid flow.
dendrite
flow
insulated
+
Li
Li
Cu wire
120 s
180 s
420 s
254 microns
Dendrite Initiation Studies
Figure 2 shows side views of the WE obtained during galvano-
static Li deposition. The electrolyte flows past the wire face, from
the top to the bottom of the picture. From this view, we can record
how far a dendrite has grown from the deposit so it is good for
measuring dendrite velocities. However, only a portion of the elec-
trode can be seen from this view so that much of the substrate face
is not visible, only the deposit growing out of it is visible. Lithium is
900 s
1200 s
Figure 2. ͑Color online͒ Sample pictures obtained using the side view cell
setup. Lithium is deposited at a rate of 2 mA cm−2 from 1.2 M LiPF6 in
EC:EMC ͑3:7 by weight͒. The dendrite is first observed at 180 s in this
deposition.
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Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
dendrite
191 microns
z dir.
460 s
480 s
520 s
-2
-2
0.65 C cm
0.25 C cm
680 s
740 s
-2
-2
1.25 C cm
1.00 C cm
Figure 4. Sample pictures of dendrite propagation. Lithium is deposited
from 1.0 M LiPF6 in PC:DMC ͑1:3 by weight͒ at a current density of
4 mA cm−2 in these pictures.
Figure 3. Sample pictures obtained using the electrode view of lithium
deposition. Lithium is being deposited at a rate of 4 mA cm−2 from 1.0 M
LiPF6 in PC:DMC ͑3:1 by weight͒. The charge density at first observed
dendrite, qFOD, is 0.65 C cm−2 in this case.
ity of PC more quickly form dendrites. Also, tFOD increases linearly
with decreasing PC content. The time tFOD increases by a factor of
3–4 when the current density doubles for all electrolyte composi-
tions except for pure DMC.
While dendrites appear to originate at the electrode edge ͑as shown
here͒ in greater than half of the depositions, they also first form in
the center of the electrode a significant portion of the time. Further,
dendrites spread across the electrode regardless of where the first
dendrite forms.
The effect of current density, i, on qFOD and tFOD is shown in Fig.
7 and 8. Figure 7 shows that qFOD increases as i decreases. The
charge at first observed dendrite for the electrolyte salt LiPF6 is
about twice that of lithium bis͑trifluoromethane sulfonyl͒ imide
͑LiN͑SO2CF3͒2, LiTFSI͒. One reason may be that trace water im-
Figure 3 depicts another type of picture that views the whole
electrode. Lithium was deposited from 1.0 M LiPF6 in PC:dimethyl
carbonate ͑DMC͒ ͑3:1 by weight͒ at 4.0 mA cm−2 in this experi-
ment. A small rough spot forms at a charge density of 0.65 C cm−2
.
purities will react with the PF−6 anion to form HF, whereas TFSI−
does not react to form HF. HF is known to result in smooth lithium
deposits.30 However, qFOD levels out at around 2.2 C cm−2 as i de-
creases below 2 mA cm−2 for LiPF6. Such results show more than
deposit thickness must be considered in predicting when dendrites
This charge is called the charge density of first observed dendrite,
qFOD. This rough spot may not have been seen in the top view
pictures shown in Fig. 2. This view was used to determine tFOD and
qFOD because small details are observable at an earlier time.
Figure 4 shows how Li, deposited from the 25% PC electrolyte,
propagates over the electrode. The maximum distance is measured
in the normal direction from the substrate to the dendrite tip over
time to obtain the dendrite growth rate normal to the electrode, as a
function of time shown in Fig. 5. The three-dimensional velocity is
not actually going to zero; usually the dendrite branches out in a
new direction parallel to the electrode. The growth rates are on the
order of those predicted by Monroe and Newman,9 as well as those
experimentally observed by Brissot et al.21 Dendrite growth rates
quickly become relatively high, attaining values between 0.5 and
1.0 ␮m s−1. Our image resolution is approximately 5 ␮m, so the
experimental setup is able to observe dendrites shortly after their
formation. It should be noted that the data observed in Fig. 5 is just
for one set of experiments, where one large dendrite is formed.
Often, even under the same conditions, many smaller dendrites are
observed across the electrode surface. Dendrite tip velocity for this
situation is often lower, presumably because of competition among
the tips.
1.0
-2
-4 mA cm
1.0 M LiPF in PC:DMC
6
0.8
0.6
0.4
0.2
0.0
25% PC
75% PC
0
100
200
300
400
Multiple experiments are summarized in Fig. 6 to show the effect
of solvent composition on time of first observed dendrite, tFOD. The
ratio of two common cosolvents, PC and DMC, is varied and results
are shown for two different current densities. The salt concentration
is maintained constant at 1.0 M LiPF6. Solvents containing a major-
time after FOD [s]
Figure 5. ͑Color online͒ Dendrite tip velocity as a function of the time. The
time denoted as zero is the tFOD for the given experiment. The red circles are
the data for the pictures in Fig. 4 where tFOD was 450 s.
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Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
A809
1400
1200
1000
800
600
400
200
0
-
1.0 M LiPF6 in PC:DMC
5 mL h-1
X = PF6
X = TFSI-
-2 mA cm-2
-4 mA cm-2
103
102
101
1.0 M LiX in PC:DMC (1:3)
5 mL h-1
0
20
40
60
80
100
0
2
4
6
8
10
-i [mA cm-2]
weight % PC
Figure 6. ͑Color online͒ Effect of solvent composition on tFOD
.
Figure 8. Effect of i on tFOD for two lithium salts.
are likely. Figure 8 shows that tFOD decreases with increasing i for
both salts. Again the tFOD for LiPF6 is approximately twice that of
LiTFSI.
fusion layer. The flow system demonstrates that dendrites will form
under conditions where mass transfer is not an issue. However, we
cannot definitively say that mass transfer does not play a role in the
lithium dendrite initiation in batteries because it is possible that the
diffusion layer could grow large enough that mass transfer becomes
an issue.
The Tafel equation relates the current density to the overpoten-
tial, ␩, and is valid for high polarizations, typically greater than
50 mV. It is used here to define a resistance that is correlated to
tFOD. The first derivative of the Tafel equation with respect to ␩ is25
Experimental observations show dendrites or other instabilities
will form for most metals, e.g., copper, as i increases above 80% of
the limiting current density, ilim.7 However, we found ilim is not a
good predictor of when Li dendrites will form. In comparison with
common plating systems, dendrites are not expected to form during
any of the experiments in this paper because i never passes 20% of
ilim, which was measured to be between 50 and 150 mA cm−2 de-
pending on the solvent composition. The limiting current density
decreased with increasing amounts of DMC. The results are not
shown here because the electrode surface roughened in electrolytes
containing mostly PC at polarizations before ilim was obtained mak-
ing it difficult to obtain repeatable measurements. If mass transfer
plays a dominant role, it may be expected that tFOD would decrease
with increasing amounts of DMC because ilim increases. However,
tFOD increases with increasing amounts of DMC. These results sug-
gest that the mass transfer of lithium to the electrode might not be
the cause of lithium dendrite initiation.
However, the above statement may only apply to flow systems.
For systems with a stagnant electrolyte, i.e., a battery, the diffusion
layer will continue to grow. The interpretation of stagnant electro-
lytes is also complicated by free convection. We have performed
experiments using the microfluidic device with no flow ͑results not
shown for brevity͒ and dendrite initiation occurs faster in a stagnant
electrolyte than when the electrolyte is flowing. The dendrites also
branch more quickly and more often in a stagnant electrolyte. Our
experimental setup removes the effect of a time-varying Li ion dif-
ץ
ln͉i͉ = ␤
͓2͔
ץ␩
where the Tafel slope, ␤, can be written as
␣F
␤ =
͓3͔
RT
In Eq. 3, ␣ is the apparent charge transfer coefficient, F is Faraday’s
constant, R is the ideal gas constant, and T is the temperature. Tafel
plots, used to estimate ␤, are shown in Fig. 9. The data are obtained
by plating Li to a thickness of 100 nm at 0.1 mA cm−2 on the Cu
WE in the given electrolyte, and then taking the polarization curve
at 25 mV s−1. The values of ␤ range from 4.4 V−1 for 1.0 M LiPF6
in pure DMC to 9.5 V−1 for 1.0 M LiPF6 in pure PC. According to
the previous equations, ␣ varies from 0.11 for pure DMC to 0.24 for
pure PC. Newman notes ␣ values are usually between 0.2 and 2.0
͑Ref. 25͒, whereas Bard and Faulkner say they are between 0.3 and
10
3.0
increasing PC
1.0 M LiX in PC:DMC (1:3)
2.5
5 mL h-1
-
2.0
1.5
1.0
0.5
0.0
X = PF6
1
X = TFSI-
0% PC
50% PC
100% PC
0.1
0.0
-0.2
-0.4
-0.6
-0.8 -1.0
0
2
4
6
8
10
η [V]
-i [mA cm-2]
Figure 9. ͑Color online͒ Lithium reduction polarization curves used to de-
termine ␤. ␩ is the overpotential.
Figure 7. Effect of i on qFOD for two lithium salts.
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Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
4000
3000
2000
1000
0
1000
800
600
400
200
0
400
iavg = -2 mA cm-2
iavg = -4 mA cm-2
300
200
1.0 M LiPF
1.0 M LiPF
1.0 M LiPF
1.0 M LiPF
1.0 M LiPF
1.2 M LiPF
in DMC
0
20
40
60
80
100
6
6
6
6
6
6
in PC:DMC (1:3)
in PC:DMC (1:1)
in PC:DMC (3:1)
in PC
100
0
1.0 M LiPF in PC:DMC (1:3)
6
in EC:EMC (3:7)
in PC:DMC (1:3)
1.0 M LiTFSI
0
100
200
300
0
100
200
300
400
time after FOD [s]
2
R
]
Tafel [Ω cm
Figure 11. ͑Color online͒ Current density at dendrite tip calculated with Eq.
5 as a function of time.
Figure 10. ͑Color online͒ Effect of RTafel on tFOD. The line is fit to the 1.0 M
LiPF6 in PC:DMC data. The inlay is a magnification of the low resistance
data.
limiting current density for a hemisphere in spherical coordinates is
calculated as 164 mA cm−2 for 29 ␮m and 241 mA cm−2 for
20 ␮m. In Fig. 11, the maximum itip is greater than the ilim for both
of these cases. The maximum itip is also greater than ilim calculated
in spherical coordinates for the electrolytes 1.2 M LiPF6 in
EC:EMC ͑3:7 by weight͒ with Li deposited at 2.0 mA cm−2 ͑depo-
sition shown in Fig. 2͒ and 1.0 M LiPF6 in PC:DMC ͑3:1 by
weight͒ with Li deposited at 4.0 mA cm−2 ͑data shown in Fig. 5͒.
These observations lead us to believe that even though dendrite
initiation may not be correlated with fraction of the limiting current
density ͑averaged over the entire surface͒, growth quickly becomes
mass transport controlled.
0.7 for most systems.31 Because these values are on the low end of
the expected range, there may be another resistance that is slowing
Li deposition. This is especially true since the reduction of Li in-
volves only one electron transfer. This resistance may be the trans-
port of current through the SEI via a high field conduction mecha-
nism. Regardless of the physical explanation for the Tafel slope, a
Tafel resistance, RTafel, which is the local slope of the polarization
curve assuming Eq. 2 can be written as
͑1/␤͒
RTafel
=
͓4͔
iavg
Conclusion
Figure 10 shows an increase in tFOD with RTafel. The line in Fig.
10 is fit only to the points from the electrolytes with PC and DMC
solvents. The 1.2 M LiPF6 in EC:EMC ͑3:7͒ and 1.0 M LiTFSI in
PC:DMC ͑1:3͒ data are, however, included and fit well to the trend.
This shows that the type of solvent or salt does not affect the rela-
tionship between tFOD and RTafel. Dendrites are inhibited as the Tafel
resistance increases. Presumably, such an observation may inform
theoretical dendrite studies, which have not, as of yet, explicitly
treated the SEI. For example, this correlation may suggest that the
local SEI may thicken near an incipient dendrite. The effect of re-
sistance on tFOD agrees with recent work by Park et al.32
In this paper we have built a microfluidic test setup that allows
for in situ observations of lithium deposition. The advantages of the
microfluidic device are that it sets up well-defined transport condi-
tions, minimizes electrolyte usage, shows good repeatability, and
possesses the ability to rapidly change electrolytes. Dendrite growth
rates are on the order of other experimental observations and theo-
retical predictions. The initiation of dendrites, shown by an increase
in tFOD, is delayed by decreasing current density and PC solvent
content. Mass transport does not play a large role in dendrite initia-
tion in the presence of fluid flow. After initiation, deposition is rap-
idly mass transfer controlled. The time to first observed dendrite,
tFOD, linearly increases with the Tafel resistance, RTafel. This paper
shows effects of current density, electrolyte salt, and electrolyte sol-
vent composition on dendrite initiation and propagation.
Dendrite Propagation Studies
The dendrite tip velocity, tip, is measured using methods de-
v
scribed previously. The current density at the dendrite tip, itip, can be
Acknowledgments
estimated by
The authors are grateful to the United States Department of En-
ergy for their financial support under contract no. DE-AC02-
05CH11231.
tipF
v
itip
=
͓5͔
Vm
The molar volume of Li is denoted by Vm in Eq. 5. This calculated
current density is even less than the actual current density due to
branching discussed earlier. Figure 11 shows itip for deposition from
1.0 M LiPF6 in PC:DMC͑1:3͒ over a period of 300 s after the time
of first observed dendrite. The calculated current density is similar
for the averaged current densities of 2 and 4 mA cm−2. That the
current density at the dendrite tip only varies slightly when the av-
erage current density is doubled suggests that the deposition may be
mass transfer controlled. The dendrite tip radius, measured in the
same manner described earlier, is observed to be 29 and 20 ␮m
during the 2 and 4 mA cm−2 depositions in 1.0 M LiPF6 in
PC:DMC ͑1:3͒. The dendrite tip radius is measured when the den-
drite tip is easily observed and well defined but before branching
occurs. The dendrite with the smaller radius has the higher maxi-
mum itip. Assuming a diffusion coefficient 5.5 ϫ 10−6 cm2 s−1, the
Columbia University assisted in meeting the publication costs of this
article.
List of Symbols
Faraday’s constant, 96,487 C equiv−1
F
i
ilim
itip
qFOD
R
RTafel
current density, mA cm−2
limiting current density, mA cm−2
current density at the dendrite tip, mA cm−2
charge density at first observed dendrite, C cm−2
ideal gas constant, 8.314 J mol K−1
Tafel resistance, ⍀ cm2
T
t
temperature, K
deposition time, s
tFOD time of first observed dendrite, s
molar volume, 13 cm3 mol−1
Vm
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Journal of The Electrochemical Society, 155 ͑11͒ A806-A811 ͑2008͒
A811
velocity of the dendrite tip, ␮m s−1
apparent charge transfer coefficent
Tafel slope, V−1
͑2005͒.
vtip
␣
␤
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