Fast and Accurate Measurement of Entropy Profiles of Commercial Lithium-Ion Cells

1

Fast and Accurate Measurement of Entropy

Profiles of Commercial Lithium-Ion Cells Patrick J. Osswald

1,2, Manuel del Rosario

1, Jürgen Garche

3, Andreas Jossen

2, Harry E. Hoster

4,*

1 Technische Universität München, TUM CREATE, Singapore

2 Technische Universität München, Institute for Electrical Energy Storage Technology, Germany

3 Fuel Cell and Battery Consulting - FCBAT Ulm, Germany

4 Lancaster University, Department of Chemistry, United Kingdom

*[email protected]

____________________________________________________________________________________

Abstract

We report on an effective approach to speed up the measurement of thermodynamic characterization curves (entropy of

reaction ΔrS(x)) of rechargeable batteries, in particular commercial 18650 lithium ion cells. We propose and demonstrate

a measurement and data processing protocol that reduces the time required to record entropy profiles from time scales of

weeks to time scales of hours - without loss in accuracy. For time consuming studies such as investigations on ageing of

battery cells, entropy profile measurements thus become as feasible as conventional electrochemical characterisation

techniques like dV/dQ or cyclic voltammetry. We demonstrate this at the examples of two ageing protocols applied to a

commercial high power and a commercial high energy cell, respectively: (i) accelerated calendric aging by storing cells at

100% state of charge at 60°C and (ii) continuous cycling with a 1C current at 25°C.

____________________________________________________________________________________

Keywords: lithium ion battery; thermodynamics; entropy; 18650 cell; battery ageing;

Introduction

Improvement in materials and fabrication processes continuously increased power and energy density of lithium

ion batteries over the past years. As these improvements have almost been stretched out to their maximum, new

developments of anode and cathode materials are needed to satisfy the increasing global need for energy storage

devices[1] . Applications from consumer electronics over plug-in electric vehicles (PEV) up to full battery electric

vehicles (BEV) require, besides a high power and energy density, a stable cycle life and must guarantee a safe use

during their span of life. Optimization of the operational strategy demands fundamental understanding of

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electrochemical processes within the cell during charge and discharge is crucial. Non-destructive measurement

techniques are a central pre-requisite for such a deeper understanding.

In a typical lithium ion battery, using graphite as the anode and a metal oxide as the cathode, the lithium contents

in anode and cathode linearly follow the advancement of the overall cell reaction, denoted as x.

𝐿𝑖0.5𝑀𝑂2 + 𝐿𝑖𝐶6 ⟶ 𝐿𝑖(0.5+0.5𝑥)𝑀𝑂2 + 𝐿𝑖(1−𝑥)𝐶6 (1)

M is a placeholder for one or a combination of the following elements: Mn, Co, Ni, Al. Here, we report on

Li0.5+0.5xNi1/3Mn1/3Co1/3O2 (NMC) and Li0.5+0.5xNi0.8Co0.15Al0.05O2 (NCA). The advancement x of the overall cell

reaction is in this special case equal to the amount of Li extracted from LixC6. Varying Li contents in anode and

cathode imply changes of their electrochemical potentials, in turn resulting in variations of the system enthalpy H

and entropy S. In this context, the “system” involves the overall cell.

According to textbooks of electrochemistry, the cell’s electromotive force EEMF is related to the Gibbs free

energy G via

𝐸𝐸𝑀𝐹(𝑥) = −

∆𝑟𝐺(𝑥)

𝑛𝐹

(2)

where F is the Faraday constant and n the number of electrons involved in the reaction. The Gibbs free energy

can be expressed by the enthalpy H, the entropy S and the temperature T

𝐺(𝑥) = 𝐻(𝑥) − 𝑇 𝑆(𝑥) (3)

Combining equations (2) and (3) leads to

𝐸𝐸𝑀𝐹(𝑥) = −

∆𝑟𝐻(𝑥) − 𝑇 ∆𝑟𝑆(𝑥)

𝑛𝐹

(4)

for constant pressure, and cell temperature T. H and S both depend on x and Δr denotes the derivative with respect to

x. Since the crystal structure of anode and cathode often vary significantly with changing x, H(x) and S(x) have non-

linear characteristics and thus sometimes distinctive profiles[2–5]. For this paper, the key formula, derived from

equation (4) is

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(

𝜕𝐸𝐸𝑀𝐹(𝑥)

𝜕𝑇)

𝑝,𝑥

= − 1

𝑛𝐹(

𝜕

𝜕𝑥 𝑆(𝑥))

𝑝,𝑥

= −1

𝑛𝐹∆𝑟𝑆(𝑥)

(5)

which describes that any variation of S as a function of x is reflected in the temperature dependency of EEMF (x). First

comprehensive measurements to determine ΔrS(x) using the temperature dependency of the open circuit voltage

were conducted by A. H. Thompson in 1981 on LixTiS2, using a sinusoidal temperature profile[4]. Later, Baffier et

al. used temperature steps between -20° and 30°C with a relaxation time of 10 hours after each discharge step for

voltage stabilization (±1mmV) to investigate the thermodynamic behaviour of LixMn2O4[5]. Selman et al. used

electrochemical-calorimetric measurements on LiCoO2 based cathodes and full cells respectively[6,7], with every

step lasting 25 hours. The temperature dependency of the open circuit voltage to calculate the entropy profile of

LiCoO2 cathodes and graphite anodes in half cells vs. Li/Li+ metal was investigated intensively by Reynier et

al.[3,8]. The authors could directly relate the measured entropy profiles of LiCoO2 to the phase change mechanisms,

described by Reimers and Dahn[9]. As a compromise between measurement time and measurement accuracy,

approximately 21[3] to 26[5,10] data points, which are equivalent to 5% and 4% changes in the SOC respectively,

were chosen. Depending on the cell’s chemistry[5,10–13], the conducted entropy profile measurements needed

between 10 and 30 hours per state of charge, leading to an overall measurement time of up 600 hours (25 days) per

measurement.

In this paper, we will demonstrate that the measurement time for entropy profiles can be drastically reduced by a

rational re-design of the measurement procedure. Most of the time in entropy measurements is wasted on voltage

relaxation after (dis-)charge steps. We will demonstrate that for an accurate measurement of the 𝜕𝐸𝐸𝑀𝐹(𝑥) 𝜕𝑇⁄

response it is sufficient to measure the temperature response of the open circuit voltage (OCV) even if that potential

is still relaxing towards the equilibrium. The time dependent drift can be automatically determined and subtracted

from the raw data. Kashiwagi et al measured entropy profiles for different kind of metal doping in Mn2-yO4 spinel

structures. Due to the long measurement time of 10h/step, the self-discharge of the half cells was approximated with

a quadratic function to correct the measured results.[14] Thomas et al. followed this basic idea and were able to

reduce the measurement time for entropy profiles to some extent. Their attempt relies on a determination of the drift

background by applying the same charge/discharge programme, but without any temperature variations.[11] This

approach may bear the risk that it relies on an ideal thermodynamic behaviour of the battery. Specifically, such a

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method of background identification can only be relied on if the state of charge of the battery is not influenced by

the temperature variations between the intended charge steps.

Here, we follow an even simpler approach. Similar to Hudak et al. [15], we assume that all information

necessary to eliminate the drift from the temperature-programme response curves is actually contained in those

curves themselves if the temperature programme is chosen carefully. Unlike Pei et al. who recently demonstrated an

elegant extrapolation approach to predict the equilibrated OCV using a second-order RC circuit model,[16] we

postulate that we do not really need to know the equilibrium OCV but can still measure the voltage/temperature

slopes with sufficient accuracy. Waiting periods were trimmed down to the minimum necessary for sufficient

thermal equilibration of the cells (measured by retrofitted thermocouples). That reduces the overall measurement

time by one or more orders of magnitude as compared to all entropy studies reported in the literature so far.

The paper is organized as follows. After a brief description of the experimental setup, we will describe the

background correction approach in some detail. We will then demonstrate that the derived entropy profiles cannot be

distinguished from such obtained in slow measurements with long voltage relaxation times. Furthermore, we will

highlight that a proper treatment of the background drift is necessary even for slow measurements with long voltage

relaxation period. The drift behaviour strongly varies between cell types and for different states of charge, and it is

much more pronounced for aged cells. Finally, as a "real world example", we will show some preliminary results of

how ageing due to repetitive cycling and storage at higher temperature is reflected in the entropy profiles. In this

context, we will discuss to what extent this method can be applied as a standard non-destructive technique for

battery characterization in a laboratory scale and how far applications for mobile battery monitoring are conceivable.

Experimental set-up

For the measurements, we studied commercial 18650 cells with different cathodes; specifically

Ni1/3Co1/3Mn1/3O2 (NMC) and Ni0.8Co0.15Al0.05O2 (NCA). All cells contain a graphite-based anode. The cells were

charged and discharged with a BasyTec CTS battery cycler. To improve the accuracy of voltage and temperature

measurement, an Agilent 39720A with a 34901A 20 channel armature multiplexer was connected to the set-up via a

programmable software interface. The Agilent 39720A was used as a 5 digit multi meter with a maximum voltage

error of 0.0020% of the 10V range as well as 0.0005% for the measured value over a time period of 90 days at room

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temperature. For temperature control, the cells were embedded into a custom-made copper block with a cylindrical

hole, which itself was coupled to a Julabo F12-MA Refrigerated/Heating Circulator with heating and cooling

capacities of 2kW and 0.16kW, respectively. It should be noted that we also achieved good results using a simple

climate chamber for the temperature control, though the larger volume will naturally slow down the heating and

cooling process.

Measurement methodology

The entropy measurements rely on a temperature step programme around a main operating temperature, which

we kept at 30°C. To minimise the overall measurement time, the temperature range ΔT the number of steps within

this range, and the duration of each temperature step were optimised.

Optimising of Temperature range ΔT

The temperature induced voltage changes of the OCV are small (<0.5mV K-1

) compared to the time dependent

voltage drifts. Precise measurements thus call for larger temperature ranges. Lowering the temperature before the

cell achieves constant OCV values causes the kinetic processes within the cell to slow down, delaying the voltage

relaxation. On the opposite side, high temperatures >40°C foster accelerated aging due to side reactions as e.g.

electrolyte decomposition as well as self-discharge of the cell[17]. The aforementioned accurate voltage

measurement of the set-up allowed us to use a small temperature range ΔT of 10K in this measurement, ranging

from 30°C to 20°C. Discharge steps were performed at 30°C for faster relaxation.

Optimising of temperature step duration

The entropy measurements rely on a homogenous temperature distribution in the cell. To track the thermal

equilibration of the cells, we retrofitted prepared two test cells with two type-T thermocouples (accuracy ± 0.5 K),

respectively, mounted at the surface and in the core of the cylinder. The internal thermocouple was introduced

through a hole in the bottom that was drilled into the fully discharged cell. The exposed metal junction of the

thermocouple was insulated using Apiezon® wax to avoid electrical contact as well as chemical contamination of

the cell. The feed through hole was sealed with epoxy glue. All cell modifications were performed in an argon filled

glove box. The modified cells were fully charged and then discharged to 60% SOC. Resting for 60 hours allowed

the cells to achieve quasi-equilibrium conditions, as the voltage relaxation became negligibly small. After inserting

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the cells into the copper block, the heating circulator conducted the programmed temperature profile. Fig. 1 shows

the temperature profile applied for the entropy measurements, including cell surface temperature, cell core

temperature and the corresponding voltage response of the cell. The temperature was kept at 30°C in the beginning

and was then stepped to 25 °C and 20 °C, each step taking 15 min. The circulator is capable to cool the system to the

pre-set temperature of 25°C and 20°C within nine minutes. This is the minimum time achievable and is limited by

the cooling capacity of the used circulator. After these two temperature steps, the cells were heated up to 30°C again

within another 15 minutes. Thanks to the high thermal conductivity of copper, copper block and cell surface follow

the temperature of the circulator’s water bath almost instantly. Due to the low thermal conductivity of the active

material inside the cells, however, a time delay of five minutes is observed until also the core of the cell reaches the

respective temperature. This leads to an overall time of 14 minutes for a homogeneous cell temperature with no

further change of the cell voltage. Based on these measurements, the shortest time per temperature step was chosen

to be 15 minutes. The temperature dependency of the OCV shows linear behaviour with the change of temperature

for the chosen temperature range from 20°C to 30°C. The tests with the thermocouple modified cells confirm that it

is sufficient to measure the temperature of the Cu block as long as all data points during the initial 14 minutes after a

temperature step are discarded.

Measurements of entropy profiles

Comparison of thermodynamic profiles of different cells requires a reliable SOC reference point. Especially for

aged cells, we found that this reference point has to be the fully charged state, given that the trailing parts of the

discharge curves become too flat and are strongly influenced by kinetic hindrances. All entropy profile

measurements thus start with the cells fully charged at 30°C according to the specifications in Table 1. Based on

their nominal capacity CN, the cells were step-wise discharged with 0.1C (discharge current of 150mA (NCA) and

260mA (NMC)) for 15 minutes, resulting in discharge capacity steps of 37.5mAh and 65mAh respectively. This is

equivalent to 2.5% of the nominal capacity CN, leading to 40 discharge steps for a new cell. The 15 minutes

discharge period was followed by a 90 minutes resting period to allow the cell voltage to relax. The temperature was

kept at 30°C for that time and afterwards decreased to 20°C in two 5 K steps, as described before. After these

cooling steps, the cell was heated up again to 30°C for the next discharge step. The overall time for each SOC step

sums up to 150 minutes (2 hours 30 minutes, see also Fig. 3 more below). Fig. 1b shows the voltage response on the

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temperature step programme. For this specific cell at this state of charge, the voltage increases linearly with

decreasing temperature. The voltages at 30°C at the beginning and at the end of the temperature programme are

virtually identical in this specific case, so no drift background subtraction is needed here.

In the following main part of this paper, we will first demonstrate that the relaxation induced voltage drift will in

general not be negligible, strongly depending also on cell type and SOC. We will then demonstrate the working

principle of our background identification and subtraction procedure, and highlight the type of artefacts generated if

background subtraction is omitted.

Results and Discussion

Voltage relaxation

After changing the cell’s state of charge due an applied charge or discharge current, the cell voltage will

approach a new equilibrium. Depending on chemistry and structure of anode and cathode, relaxation can be

observed for hours or even days. As both electrodes undergo certain structural changes[2,3,18,19], the cell’s

relaxation behaviour also depends on the state of charge. The inset in Fig. 2 exemplarily shows this for an NMC cell

at 80 % and 25 % SOC. The main plot in Fig. 2 depicts the voltage difference δV of the cell voltage immediately

after the discharge step and after two hours of relaxation as a function of the depth of discharge (DOD). For the high

power NCA cell, a minor increase of δV can be observed until 40% DOD, thereafter the voltage difference δV drops

by 25 mV from 163 mV to 139 mV and remains nearly constant until 90% DOD, where it slightly increases again. A

possible explanation for the drop at 40% DOD are the structural changes in the anode, described as stage-1 to stage-

2 transformation[20]. At this point, the well-ordered LiC6 phase fades into the well-ordered LiC12 phase, thus

changing the anode’s Li+ diffusivity. Overall, the voltage difference ΔV can be considered as nearly constant for all

state of charges for the high power NCA cell until 90% DOD.

In comparison, the high energy NMC cell shows a slight decrease in δV until 45% DOD and a strong increase

afterwards, reaching from δV = 116 mV up to δV = 796 mV. As the NMC cell is designed as a high energy cell, the

coating thickness of the cathode is 70 µm while the thickness in the high power NCA cell is only 40 µm. Hence, the

diffusion paths in the high energy cathode are significantly longer, causing an increase in the over-potential η

[21,22] during the discharge step and may explain the long relaxation time. This effect is amplified in calendric aged

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and cycled cells due to increasing diffusion resistance caused by the continuous growth of the solid electrolyte

interface (SEI) at the anode [7,8].

Entropy profiles – raw data and background subtraction

Figs. 3a-d show relaxation transients of the NMC cells at different states of charge. After 90 min, T is stepped

down to 25 °C, to 20 °C and back to 30 °C (see shaded area). The cell voltage immediately reacts on the temperature

change, but those variations are of the same amplitude as the superimposed time-dependent relaxation.

The resulting curves can be expressed via

𝐸𝑂𝐶𝑉(𝑥, 𝑡𝑖 , 𝑇𝑗) = 𝐸𝐸𝑀𝐹(𝑥, 𝑡𝑜, 𝑇0) + 𝛿(𝑥, 𝑡𝑖) + 𝐶(𝑥) ∙ (𝑇𝑗 − 𝑇0) (6)

with t as the time, with ti >t0, reference temperature T0, varied temperature Tj, the SOC and time dependent off-

set 𝛿(𝑥, 𝑡) and an entropy related coefficient 𝐶(𝑥) = −1

𝑛𝐹∆𝑟𝑆(𝑥). The latter is the desired output of the

measurement. The influences of side reactions and self-discharge in commercial 18650 cells under room

temperature are very small and are therefore neglected for simplification. In addition, thermal effects such as heat of

mixing during the voltage relaxation period are rather small due to the low current used and the small Lithium

concentration gradient in the electrodes during entropy measurements[23]. We thus assume the superimposed

voltage drift 𝛿(𝑥, 𝑡) to be approximately temperature independent

(

𝜕𝛿(𝑥, 𝑡)

𝜕𝑇)

𝑝,𝑥≅ 0

(7)

The OCV changes remaining after subtraction of δ(x,t) from the curves in Figs. 3a-d just reflect the response on

the temperature steps, allowing to calculate 𝐶(𝑥) = −1

𝑛𝐹∆𝑟𝑆(𝑥) through the slope of a plot (EOCV - vs. T. Here,

we use the data points obtained at 30 °C to identify the background curve δ(x,t). For both cell types studied here,

most of the voltage relaxation occurs during the first 10 minutes. After that period, the voltage relaxation transient is

smooth enough to be approximated by fitting curves. These are shown as dotted red lines in Figs. 3a-d. For the

mathematical modelling, MatLab 2013a with the curve fitting toolbox was used. To bear the differences in the

relaxation behaviour and allow a correct modelling of the relaxation behaviour, suitable function sets were used for

different data sets but without deeper interpretation of those curves themselves.

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Figs. 3e-h show the OCV transients after subtraction of the fitted background curves. The dark grey vertical bars

mark the areas where the voltages are stable enough to provide data points for the E vs. T data sets. Fig. 4 shows the

respective temperature dependency of the cell voltage with and without background subtraction. Fig. 5 shows the

entropy profiles with and without background subtraction of the NMC cells for different waiting times. The

differences between both curves show that even long waiting periods of up to 24 hours per SOC step (Fig 5a) do not

justify omitting background subtraction. With 24h per SOC step and 40 measured SOCs, this measurement needs 6

weeks. In a second measurement, the relaxation time after each discharge steps was reduced to 90mins as stated

before, thus shortening the overall measurement time to 4 days. (If the cell’s entropy profile is known to be

featureless in certain regions, one could in principle skip certain data points and thus further speed up the

measurements). For some of the curves shown here, the number of SOC steps was reduced to 20 without any loss of

information and accuracy. The concomitant drastic reduction of the measurement time brings entropy profile

measurements into a regime similar to that of other characterisation techniques as impedance spectroscopy[19],

cyclic voltammetry, GITT[24] or slow discharge dV/dQ analyses[25,26].

The first SOC steps at higher states of charge of the cell show similar values as the long term measurements due

to shorter relaxation times and lower relaxation amplitudes as seen in Fig. 5. An increasing difference between the

non-corrected and the corrected entropy profile values can be observed, becoming significant for SOCs below 80%

(A). This is in good agreement with the observation of the increasing voltage difference ΔV and the correlated

increase in relaxation time for lower SOC values as seen in Fig 2. If no background subtraction is applied, the

entropy profiles not only "drift" away from the correct ones. More serious, certain features in the entropy profile’s

topology may largely disappear. An example is the step marked as B in Fig. 5, which reflects the stage1-stage2

transition in the anode. Also the increase starting at C with a local maximum D (-3 Jmol-1

K-1

) becomes less

dominant. After applying the correction on the same data-set, the values of entropy profile coincide closely with the

values from the 24 hours long term measurement. This congruence justifies the subtraction of the fitted background

curve instead of waiting for complete voltage relaxation.

Effects of ageing

Using the described calculated entropy profiles, the influence of cycling and calendric aging was investigated.

Different cells were cycled (one cycle: 1. charge with 1C constant current; 2. 15 min at constant voltage phase; 3.

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discharged with 1C) in a climate chamber at an ambient temperature of 25°C. Every 150 cycles, an entropy profile

was measured. A second batch of cells was used for accelerated calendric aging: cells were fully charged to 100%

SOC, stored at 60°C, and characterized by entropy profiles every two weeks. In addition to entropy profiles, the

0.2C discharge capacities at 25°C ambient temperature of all cells were determined. The results are shown in Figs 6

and 8 for the NMC cell and the NCA cell respectively. For both types of cells and aging respectively, the decreasing

capacities are also reflected in the entropy profiles. In this work, the discharge capacity Qdischarge was chosen as the

designation for the abscissa, as plotting the entropy profile versus the state of charge in % may not reflect the

capacity loss appropriately and can lead to a falsification of the profile.

Changes in the entropy profile for the cycled cells can be seen with increasing number of cycles, where the local

minimum A/A’ disappears. In Fig. 7a, the minimum B/B’ and the maximum C/C’ shift to the left, to higher states of

charge. The capacity fade during the cycling shows a linear behaviour and is rather small. With ongoing electrode

degradation, a shift of the cell balancing between anode and cathode is the most likely reason for the changes in the

entropy profile. While the changes in the cycled cells needed up to 2400 cycles, the entropy profile of the thermally

aged NMC cells presented in Fig. 7b shows significant changes within very short aging time for the capacity range

of Qdischarge > 1300 mAh. The local minimum A/A’ remains nearly unchanged, while the minimum B/B’ nearly

vanishes over time. The change at the local maximum C/C’ is even more obvious, shifting to a higher SOC values as

well as positive entropy values. After the last characterization step, the cell voltage dropped to 0V after additional

three and four days of thermal aging, respectively. Therefore, the original scheduled test program down to 80% of

the nominal capacity could not be completed. Kang et al. recently gave a reasonable explanation for such a cell’s

failure [27]. Due to the high temperature storage, the cathode degradation is strongly enforced, leading to metal ion

dissolution into the electrolyte, causing micro-size short circuits between anode and cathode as well as a strong gas

generation. The remaining capacities for both calendric aged cells were 93%. To verify this assumption, further

investigations need to be conducted.

The NCA-containing cells show a better stability towards the accelerated calendric aging with a remaining

capacity of 80.2% after 224 days of thermal treatment. In Fig. 9a and b, the effects of cycling as well as thermal

aging on the entropy profile of the NCA-containing commercial cell are shown. The decrease of the cell’s capacity

leads to a contraction, causing a certain shift of the profile. Beside these obvious changes, which are not related to

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the thermodynamic properties of the cell, numerous changes can be observed. With increasing days of thermal aging

and number of cycles, the local minimum A/A’ remains stable, while a new maximum B’ appears. The maximum C

vanishes and while the cycled aged cells show linear behaviour after 2400 cycles in this range around C’, the

thermal aged cell shows a new local minimum in C’. Our ageing studies of commercial 18650 cells are still in

progress and currently further enhanced by in-situ X-ray diffraction studies. In forthcoming publications, we will

thus be able to provide deeper insights into the local processes that are responsible for the changes in the entropy

profiles reported here.

Conclusion and Outlook

We demonstrated that entropy profiles can not only be recorded for small laboratory cells but also for larger

format commercial cells, here, cylindrical 18650 ones. In analogy to previous studies, the profiles were determined

from responses of the open circuit voltage on temperature steps. Those profiles exhibit characteristic fingerprints

reflecting phase changes in anode and cathode. We introduce and validate an advanced measurement protocol that

reduces the time required for recording accurate entropy profiles from 6-8 weeks down to 1-4 days. This is a

prerequisite for adding entropy profiles to the toolbox with other electrochemical standard techniques applied on

commercial cells. We demonstrate that the faster measurement does not sacrifice accuracy. In contrast, the described

protocol is even mandatory to avoid (kinetic) artefacts in the thermodynamic analyses of aged cells.

To highlight the level of detailed information attainable through entropy profile measurements, we showed first

results of an ongoing ageing study of commercial NCA and NMC cells. The NCA cells remained comparably stable

during the aging treatments, resulting in only minor changes in the measured entropy profiles. In contrast, the NMC

-based high energy cells aged at elevated temperatures failed during operation after short time. Even though the

capacity loss of the cells is rather small (<6%), significant changes in the entropy profile at SOCs below 50% were

observed. This unfolds the possibility for entropy measurement to be used as an additional data source for a battery’s

state of health determination. Based on concomitant in-situ X-ray diffraction studies and post-mortem analysis of

aged cells that are currently finalized, we will soon publish more detailed interpretations of the various features in

the entropy profiles.

Acknowledgement

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The presented work was supported by the Singapore National Research Foundation (NRF) through its Campus for

Research Excellence and Technological Enterprise (CREATE) programme. We wish to thank Rachid Yazami for

inspiring discussions about thermodynamic measurements at battery cells.

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Table 1: Tested 18650 cells and their respective parameters

Cathode chemistry NCA NCM

Application purpose High power High Energy

Nominal discharge capacity / mAh 1500 2600

Charging voltage / V 4.2 4.2

Nominal voltage / V 3.6 3.7

Charging method CC CV

(0.2 C, I < 0.01C)

CC CV

(0.2 C, I < 0.01C)

Discharging current / A 0.2C 0.2C

Cut-off discharge voltage / V 2.5 2.75

14

Fig. 1 Optimised temperature profile: Temperature of water bath (red), cell surface (black) and cell core (blue) as

well as the cell’s voltage response (green)

Fig 2 Voltage difference after 2 hours of relaxation as function of depth of discharge for a high energy NMC and a

high power NCA cell

15

Fig 3 Relaxation behaviour of the cell voltage for NMC cell a) 100% SOC, b) 87% SOC, c) 57% SOC and d) 20%

SOC including the voltage response of temperature changes to 25°C and 20°C respectively plotted with the

mathematical fitted background. In e-h), the resulting subtraction of the measured voltage and the calculated

relaxation background for the respective state of charge is shown.

16

Fig 4 Voltage vs. temperature dependency for NMC cell at 20% SOC for a) without background subtraction as show

in Fig 3d and b) with background subtraction as shown in Fig. 3h

17

Fig. 5 Comparison of the entropy profiles of a NMC cell a) for duration of 24h per SOC step with and without

background subtraction, b) for duration of 2.5h per SOC step with and without background subtraction and c)

background subtracted data with 24h and 2.5h duration per SOC respectively. The arrows indicate the calculated

values at 20% SOC as shown in Fig 4

18

Fig. 6 Remaining capacity of calendric aged and 1C-cycled NMC cell, measured at 25°C with a 0.2C rate. The

Roman numerals refer to the respective entropy profile shown in Fig 7

Fig. 7 Entropy profile for a commercial 18650 battery with NMC-based cathode a) after cycling at 25°C with 1C

and b) after several days of storage at 100% SOC at 60 °C

19

Fig. 8 Remaining capacity of calendric aged and 1C-cycled NCA cell, measured at 25°C with a 0.2C rate. The

Roman numerals refer to the respective entropy profile shown in Fig 9

Fig. 9 Entropy profile for a commercial 18650 battery with NCA-based cathode a) after cycling at 25°C with 1C

and b) after several days of storage at 100% SOC at 60 °C