# Radial Thermal Conductivity Measurements of Lithium-Ion Battery Cells

Author: Harsh Bhundiya
Mentors: Melany Hunt and Bruce Drolen
Editor: Sherry Wang

## Introduction

In recent years there has been increased scrutiny of lithium-ion batteries, partly because of incidents in which the batteries have been linked to harmful fires. One such incident occurred in September of 2010, when the lithium batteries inside a Boeing 747-400F cargo aircraft near Dubai caught on fire, killing both of the crewmembers inside the airplane. Since 2006, there have been numerous mobile phone fires caused by their small lithium-ion batteries. The much-publicized incidents of the 2016 Samsung Galaxy S7 phones catching fire serve as a recent example.

The cause of these fires is thermal runaway, a term that describes the rapid increase in temperature caused when the energy generated within a cell is larger than that which can be dissipated by the cell. To further complicate the situation, the sudden dissipation of energy in one cell may result in heating of neighboring cells leading to thermal runaway at the battery level, as shown in Figure 1. This propagation of the runaway event can proliferate to all of the cells in the battery, leading to a much more energetic and potentially catastrophic event. To prevent propagation of a cell failure, it is important to understand the thermal pathway from cell-to-cell, which requires an understanding of the transport properties of the cells.

To improve the operation of lithium ion batteries, researchers have developed analytical thermal models of individual lithium-ion cells and the batteries they comprise[1-3]. A key consideration in these models is the effective radial thermal conductivity of a cell. In this study, the radial thermal conductivities of two 18650 and 26650 lithium-ion cells are measured and compared to a thermal model for layered radial geometry. Such batteries are commonly used for consumer products like flashlights and toys. Unlike previous studies, the thermal conductivity measurements are made by directly heating the cell from its center. Though the measurements reported herein are for two specific cell types, the experiments and analysis are expected to be relevant to any similarly constructed lithium ion cell and help us better predict thermal runaway.

## Disassembly and Battery Construction

The thermal conductivity measurements in this study were taken on windings extracted from discharged but otherwise functional cells. Eight Samsung INR18650-25R cells (3.6 volt) and two K2 Energy Solutions LFP26650P (3.2 volt) cells were discharged by connecting the cells to resistors and leaving the cells for several days. After discharging, the top and bottom of each cell were removed using a Dremel tool and vice in a vented fume hood, making sure not to harm the cell’s winding during cutting. For several of the cells, the windings were also removed from their cylindrical metal case. To remove these windings, the external metal can was cut longitudinally being careful to cause minimal damage to the winding itself.

After removing the top and bottom, the cells were placed under a hood. No further effort was made to dry out the cells prior to thermal testing. The time between cell extraction and thermal testing varied from days to weeks. For several of the cells, the windings were used to measure the thicknesses of the constituent layers to support the thermal analyses found in the next section. Figure 2 shows a picture of the windings of a disassembled 18650 cell after the removal of the case. Two 18650 cells and one 26650 cell were unwrapped and the thicknesses of each cathode, anode, and plastic separator layer were measured using a micrometer.

## Experimental Approach

The effective thermal conductivity measurements were made on both the 18650 and the 26650 cells under a variety of conditions. The cells that were used in these measurements were kept intact and not unwrapped or dried in an oven prior to testing. For the conductivity measurements, heat was provided using a nichrome wire of diameter 0.812 mm that was inserted along the centerline of each cell’s winding. Two type K thermocouples of diameter 0.127 mm were also inserted into the center of the windings and two type K thermocouples of diameter 0.812 mm were placed on the outside surface of the cell. A thin layer of SteelStik™ conductive putty was placed around each thermocouple to increase the thermal contact to either the winding or the outer wall. These thermocouples measured the temperature difference between the center and case of the cell when it was heated from inside.

The experimental setup is shown in Figure 3. In each experiment, current was supplied to the wire until the temperature measurements stabilized, indicating the cell had reached a steady state. The power supply was then disconnected and the cell was left to cool in preparation for the next trial. In each case, tests were run at several different power levels to evaluate the consistency of the results.

Figure 4 shows examples of the unsteady temperature variation measured inside (T1) and outside (T2) of an 18650 and a 26650 cell relative to the initial temperature, T1-Ti and T2-Ti, for similar power inputs. The temperature inside the cell rises quickly relative to the outer surface, especially for the 26650 cell. After the sharp interior temperature increase, the heat has penetrated to the outer surface of the cylinder and the cell’s temperature rises uniformly across the thickness of the cell for the remainder of the test.

Using the power input ($\dot Q$), the measured steady-state temperatures, and the cell dimensions, the effective radial thermal conductivity of the cell, $k_{eff}$, can be calculated as follows:

$k_{eff} = \dot Q \ln (\frac{r_2}{r_1}) / [2 \pi L(T_1 - T_2)]$ (1)

Multiple experiments were done on each cell for different power inputs. The power input to the wire ranged from 0.35 W to 1.5 W resulting in temperature differences between the inside and the outside of the cell of 4oC to 38oC. To minimize damage to the windings, the maximum temperature of the cell was kept to temperatures below 65oC. The uncertainty in the measurements was computed using a root-sum-square (RSS) method on all the variables used to calculate $k_{eff}$ in Equation 1.

## Experimental Results

In total, twenty experiments were conducted using two different 18650 cells (cells 1 and 2) and eight experiments using two 26650 cells (cells 3 and 4). Figure 5 presents the steady-state thermal conductivity as a function of temperature difference using the definition of the effective thermal conductivity as given in Equation 1.  For the 18650 and 22650 cells, average values for the effective thermal conductivity are calculated as 0.43 ± 0.07 W m-1 K-1 and 0.20 ± 0.04 W m-1 K-1, respectively. These thermal conductivity values are lower than some measurements found in previous studies.

## Modelling Effective Properties

To better understand the experimental results, a thermal model of the cells is created. Specifically, the measured thicknesses and properties of each layer are used to calculate effective properties of the windings and the cell.  The effective thermal conductivity is determined by summing the thermal resistance of each of the n layers. Using Fourier’s law for a cylindrical element with inner radius, , outer radius, the length of the cell L, and thermal conductivity kn, the thermal resistance Rn for each conductive layer within a sheet can be computed as follows:

$R_n = \frac{ln(\frac{r_{n2}}{r_{n1}})}{2 \pi k_n L}$ (2)

For one sheet of the winding, the resistance is the sum of the conductive resistance associated with each of the eight layers of the sheet plus the contributions from the contact resistances at both the inner and outer surface of each of the anode (Ra1 and Ra2) and cathode (Rc1 and Rc2) separators:

$R_m = \sum_1^8 R_n + R_{a1} + R_{a2} + R_{c1} + R_{c2}$ (3)

The total resistance for one cell is calculated by summing the resistance for each of the m sheets and additional contact resistances.

Table 1 presents the product of the planar thermal resistance and the surface area for each of the materials and interfaces in a sheet. The table also includes the total cylindrical thermal resistances for each material, calculated using Equation 2 by summing over every layer in the winding.

As shown in the table, the major contributor to the resistance is the contact resistance at the cathode/separator interface (63% and 76% for the 18650 and 26650 cells, respectively). Figure 6 presents the sum of the thermal resistances as a function of dimensionless cell radius, for both the 18650 and 26650 cells using the values found in Table 2. The thin lines show the cumulative resistance that includes the contact resistances, and the thicker lines show the cumulative resistances assuming perfect thermal contact. The effective radial thermal conductivity of the cell is determined using $k_{eff} = ln(\frac{r_2}{r_1}) / (2 \pi R_t L)$, where $r_2$ is the outer radius including the case and outer plastic and $r_1$ is the inner radius of the windings. Using this approach, the predicted thermal conductivity for the cell windings, including interface resistances, is 0.437 W m-1 K-1 for the 18650 cell and 0.199 W m-1 K-1 for the 26650 cell, in agreement with the experimentally measured results in Section 4.

Using the same model and assuming perfect thermal contact from layer to layer within the windings, the effective thermal conductivity of the 18650 cell is estimated as 1.23 W m-1 K-1 and 0.850 W m-1 K-1 for the 26650 cell. These values are significantly higher than found when the contact resistances are included and are in the range of values that Rickman et al. [1], Tanaka[2], and Coman et al.[3] used in their respective studies.  This result highlights the importance of including the various contact resistances within the cell.

## Conclusion

The radial thermal conductivity of lithium ion cells is of critical importance for predicting scenarios in which thermal runaway may occur in portable batteries. Through experiments on 18650 (LiNiMnCoO2) and 26650 (LiFePO4) cells, the radial thermal conductivity was measured as 0.43 ± 0.07 W m-1 K-1 and 0.20 ± 0.04 W m-1 K-1, respectively. These values were determined by heating the cells from the center and for temperature differences across the cells ranging from 10oC to 40oC.

The experimental values are significantly smaller than the values reported with perfect thermal contact between the layers, which suggests that including realistic, non-ideal, contact coefficients from layer-to-layer is important when modeling the radial transport of heat in cylindrical lithium ion battery cells, in agreement with the findings of Vishwakarma, et al.[4].

In summary, this research provides direct measurements of the effective radial thermal conductivities of 18650 and 26650 lithium-ion cells, which should lead to better models of thermal runaway propagation. Possible directions for future work include rerunning the experiment with wet cells or by cutting smaller holes on the sides of the cells to minimize interference from air.

## Acknowledgements

I would like to express my deep gratitude to my mentors, Professor Melany Hunt and Dr. Bruce Drolen, for their guidance through my research. Their help has been invaluable in this research project. I would also like to thank the Tyson family and Caltech’s Student Faculty Program for supporting my undergraduate research at Caltech as a Mr. Howell N. Tyson, Sr. SURF Fellow.

## References

1. S. Rickman, R. Christie, R. White, B. Drolen, M. Navarro, P. Coman, Considerations for the thermal modeling of lithium-ion vells for battery analysis, ICES-2016-9 (2016).
2. N. Tanaka, W.G. Bessler, Numerical investigation of kinetic mechanism for runaway thermo-electrochemistry in lithium ion cells, Solid State Ionics, 262 (2014) 70-73.
3. P.T. Coman, S. Rayman, R.E. White, A lumped model of venting during thermal runaway in a cylindrical lithium cobalt oxide lithium-ion cell, J. Power Sources 307 (2016) 56-62.
4. V. Vishwakarma, C. Waghela, Z. Wei, R. Prasher, S.C. Nagpure, J. Li, F. Liu, C. Daniel, A. Jain, Heat transfer enhancement in a lithium-ion cell through improved material-level thermal transport,  J. Power Sources 300 (2015) 123-131.