Customized Optical Fiber Birefringent Sensors to Multipoint and Simultaneous Temperature and Radial Strain Tracking of Lithium‐Ion Batteries

Batteries are seen as a vital piece for actual carbon‐neutral world needs. However, as they basically operate through extremely exothermic electrochemical events, special attention must be paid to their thermal and volumetric constraints, where continuous and accurate monitoring is of great importance. Considering it, customized optical sensors, based on fiber Bragg gratings recorded in birefringent PANDA fibers (FBG‐PANDA), are developed and instrumented in a coiled configuration into a cylindrical Li‐ion battery (LiB) to simultaneously track temperature and radial strain during galvanostatic cycles, in three different battery locations, for the first time. The maximum temperature and radial strain variations are achieved in the middle and at the end of the discharge steps. This thermal behavior is correlated with the internal heat generation and transfer of thermal energy processes, with a tendency to accumulate in the LiB central zone.Good feasibility and reproducibility are observed in the optical sensor's performance and demonstrated that by operating as a multiparameter decouple system, they can decrease the complexity and intrusiveness in batteries, by using only one optical fiber line. The reported results are in accordance with the literature, indicating that such sensors could be consistently used for future applications regarding battery safety parameters sensing.


Introduction
The European Green Deal was approved in December 2019, and this initiative aims to transform the European Union economy toward a more sustainable future by reducing the emission of greenhouse gases (CO 2 ) and combating climate change. [1][2][3] BAT-TERY 2030+ is a research initiative financed by European Union, DOI: 10.1002/adsr.202200046 it aims to contribute to carbon neutrality in the European Union by developing more sustainable batteries for the future, reducing the actual society's dependence on fossil fuel energy. INSTABAT project is a member of this initiative and aims to research smart batteries and develop new methodologies to sense critical parameters within the battery cells. [4][5][6] Li-ion batteries (LiBs) are, nowadays, the most mature, used, and scalable recharging battery in the market. During a LiB operation, a high heat generation rate is originated from the exothermic chemical reactions within the battery cell. Therefore, is important to manage such heat generation and temperature variation to guarantee an upper battery performance and to improve the safety of the entire battery cells. Once the strain variation is interconnected to the temperature variation due to the thermal expansion of their intrinsic materials, two of the most important critical parameters to be studied in batteries are temperature and strain behaviors during their operation. [7,8] When subjected to abusive charge/discharge procedures, a LiB may achieve high internal temperatures and then damage the solid electrolyte interface (SEI) layer, which represents a crucial component for the control of chemical reactions between the anode-lithium and the electrolyte. [9] Depending on the damage degree or accumulation of dendrites, the SEI layer degradation may lead to an uncontrolled exothermal reaction chain, an event called thermal runaway, leading to combustion or explosion, which will compromise the safety of the battery and its surrounding components. [10,11] Currently, electronic sensors such as thermocouples and thermistors have been used for temperature monitoring in LiBs, being placed on the surface and within the batteries for measurements in their several regions. However, despite being low cost (in the order of tens of Euros), these sensors do not have small dimensions (≈1 cm), are susceptible to corrosion, and are electrically active, not being the best choice to be introduced within the battery cells, still, they present lower spatial monitoring, as only one point can be monitored per sensor location. [12] Strain is another parameter of utmost importance to be studied and monitored in batteries, as it is possible to avoid the appearance of cracks in their internal materials, abnormal swellings due to the production of unusual gases, or even to correlate with the movement/transport of ions throughout the charge and discharge processes. Strain gauges are usually used to track strain in the surface of the battery cells. These devices consist of a resistance that changes its impedance accordingly with expansion and generates a signal that is amplified and converted into strain values. With this sensor, it is also possible to verify the state of deterioration that the battery has throughout the charge and discharge cycles, evaluating the strain values over the life of the batteries; however, they also present larger dimensions (≈1 cm), more than 3 samples are needed to compensation issues in the data acquired, and are unable to be internally instrumented in battery cells due to their electrochemical environment. [13] Alternatively, optical fiber sensors (OFS), as they are electrical insulators, immune to electromagnetic interference, present low power of intrusiveness due to their reduced dimensions (125 m or less), and also present multipoint and multiparameter characteristics, where it is possible to get a network of OFS in only one fiber line, are very promising tools to proceed with measurements of physical quantities in batteries, allowing to track temperature, strain, refractive index, pressure, among other parameters. These sensors allow high sensitivity in a simultaneous measurement of several parameters in different locations of the fiber, being able to be characterized by variations of wavelength, frequency, time, and polarization. [14][15][16][17][18] Among the most used OFS for measuring temperature and strain, fiber Bragg gratings (FBG) are the most commonly used. [8] In recent years, this type of sensor has been applied to batteries to monitor temperature and strain in real-time and under different battery operating conditions. However, to perform such simultaneous monitoring, it is necessary to use different approaches or fiber sensing configurations to discriminate both parameters, as both influence the sensor response, such as by using chirped FBGs, hybrid configuration based on FBGs and Fabry-Perot interferometers, and sawtooth stressor-assisted highly birefringent FBG. [7,10,[17][18][19][20][21][22][23][24] The most used approach has been the use of two optical fibers placed side by side, where the location of the FBG sensors is very close, but in different fibers, one of the fibers being fixed, the FBG being influenced by variations in temperature and strain, and the another is loose, being only subject to temperature variations. During their operation, batteries simultaneously heat up and expand/contract, alternative solutions must be developed to perform better and practical monitoring of these both parameters simultaneously. In this way, FBG sensors recorded in polarizationmaintaining (PM) optical fibers, such as PANDA fibers, have been used in the literature as a solution to be a discrimination element of multiple parameters using only one optical fiber line, due to their properties. [25,26] However, its application as a discrimination sensor element of temperature and radial strain in rechargeable LiBs has never been reported in the literature before.
This work aims to develop a network of FBG sensors inscribed in a section of PM optical fibers to simultaneously discriminate temperature and radial strain variations at different locations on the surface (negative terminal, middle, and positive terminal) of a rechargeable cylindrical LiB. The developed OFS will monitor The directional stress proportioned by the stress rods submits the light traveling within the 6 m core to different refraction indices, depending on its polarization, an effect known as birefringence. Therefore, two propagation modes are induced, the slow mode, in the direction of the stress axis, and the fast mode, in the stress-free axis.
the battery during its operation at abusive rates of 1.9 C charge, and 2.5 and 3.5 C discharge cycles over time.

Fiber Bragg Gratings-PANDA Sensors
The sensors used in this experiment were FBG sensors inscribed in a PANDA fiber (FBG-PANDA), with a physical length of ≈8 mm. This type of sensor is similar to a conventional FBG, however, due to the different stress conditions on the x and y-axis in the PANDA fiber, the light traveling within the fiber is submitted to different refractive index, a phenomenon known as birefringence, inducing two propagations modes, therefore a dual Bragg wavelength reflection appears in their spectral response instead of only one.
Polarization-maintaining high birefringence (PMHB) fibers are optical fibers that maintain their linear polarization throughout propagation, making it difficult for light to cross between the two propagation modes, thus they are used for sensing and for optical communications as well. PANDA fibers are an example of a PMHB fiber. They have only one core with approximately 6 m diameter and a cladding of 125 m. Their geometry presents two stress rods (35 m) along its length, which cause directed stress in the core, creating two modes of propagation along the fiber, the fast and slow modes, according to a fast axis, represented by the YY's axis, and a slow axis, represented by the XX's axis, as shown in Figure 1. [26] The FBG sensors are manufactured by modulating the refractive index of the core, a process performed by using a UV laser through the phase mask method (Figure 2a) (the inscription system used is fully described in Figure S1, Supporting Information). In addition to single-mode photosensitive fibers, FBG sensors can be also recorded on PM fibers if their core is susceptible to the periodic modulation caused by the UV beam. To provide such property, the PM fibers must be subjected to a hydrogena- tion process, which consists of doping the optical fiber core with H 2 and making it more photosensitive to the UV beam. The FBG-PANDA sensors are characterized by the appearance of two reflection peaks, the slow and fast peaks, as shown in Figure 2b.
Therefore, two Bragg wavelengths can be calculated as follows in Equation (1): where f is the Bragg wavelength for the fast mode, s , for the slow mode, n f,s is the effective refraction index of the fast axis (YY's) and the slow axis (XX's) respectively, and Λ is the period of the gratings. Once the refraction is different for each mode, they will originate different Bragg wavelength reflections. The birefringence of this type of fiber is calculated through the difference in refraction index between two propagation modes, where B is the birefringence value. [25] Through the different sensitivity obtained by both peaks to the several parameters, is possible to simultaneous decouple the influence of two physical quantities in the same location using only one optical fiber line, in this case, radial strain and temperature variations were decoupled, using the following matrixial method: where, K represents the sensitivity coefficients to temperature, K Tf for the fast axis and K Ts for the slow axis, or to strain, K f and K s for the fast and slow axes, respectively. Δ f,s represents the wavelength variation of the fast and slow modes, respectively, Δ and ΔT are the strain and temperature variations, respectively, and D is the K matrix determinant. [25] The strain variation is detected by the FBG-PANDA due to the photo-elastic effect that will make the sensor elongate, changing their effective refractive index, n eff . Thermal expansion of the fiber material and the temperature dependence on n eff induces the sensibility of FBG sensors to temperature variation. In this way, the Bragg wavelength changes with temperature and strain is characterized by the following expression: where P 11 and P 12 represent the Pockel coefficients, , the Poisson ratio, , the thermal expansion coefficient. [25] Assuming that the temperature and strain responses in the two propagation modes are independent, accordingly to the above expression, the elements of the matrix K are given by the following equations: [25]

Results and Discussion
In this experiment, a FBG-PANDA sensors network was fabricated and attached in a rolled configuration into a rechargeable commercial INR18650 MH1 3200mAh LiB (18 × 65 mm), manufactured by LG Chem company, with a nominal and cut-off voltage of 3.63 and 2.5 V, respectively, which the anode is composed by graphite and the cathode by lithium nickel manganese cobalt.   To proceed with the simultaneous multipoint temperature and radial strain discrimination, only one optical fiber line was used.
The LiB was always kept within the climatic chamber, in a 20.0 ± 0.1°C constant environment, and operated in the horizontal orientation, as shown in Figure 3 (the picture of the real experiment is shown in Figure S2, Supporting Information). The optical interrogator provided the data acquisition of the Bragg wavelength of the FBG-PANDA sensors, and the DAQ (USB6008, National Instruments), the voltage data of the LiB terminals. For the galvanostatic cycling processes, a charger and different ceramic resistors to operate at different C-rates were used.  ] From these equations, derive the cross-matrix presented in Figure 4 (sensors output). The resolution of the PANDA-FBG sensors was determined when the sensing head was subject to strain and temperature shifts with ranges of ≈1400 and 25.0°C, respectively. The spread of the data in this figure shows root mean square deviations of ±0.5°C and ±27 for temperature and strain measurements from the simultaneously discrimination for all PM-FBGs sensors used, respectively. For these calculations and in order to increase the measurement accuracy, precise signal processing tolls based on data treatment FFT filters were also used and the resolution of the interrogation device on the PANDA-FBG peaks detection was also improved based on the tools "x55 HYPERION Custom Peak Detection Configuration v1.1.0.9" and the "ENLIGHT Sensing Analysis" software's from LUNA company.
Aiming to obtain greater thermal and radial variations of the battery, the galvanostatic cycles were executed at high charge and discharge rates. In total, 8 cycles were performed, all on the same battery, the first 4 of them were performed with a 2.5 C discharge rate and the other 4 with a 3.5 C discharge rate. Aiming to achieve thermal and volumetric stabilization of the battery, a rest time of 15 and 20 min was established after charging or discharging processes, respectively. To better visualize temperature and radial strain behavior during the battery operation, different thermal and radial strain color maps were developed for the moments of the end of charge and discharge steps through the MATLAB software.
In Figure 5 it is presented the results of the temperature variations tracked by all the FBG-PANDA sensors at different points of the battery during the 1.9 C charge and 2.5 C discharge cycles over time. A thermal mapping of the mean temperature variation val- Figure 5. Temperature variations of the 18650 LiB while submitted to a 1.9 C charge and 2.5 C discharge processes. The charge processes are represented by a beige color background, the discharge, by blue color, and the rest interval between procedures, by white color background. The higher temperature variations were achieved in the end of the discharge processes and in the middle location, as can be observed in the thermal mapping.
ues registered by the sensors on the end of charge and discharge steps is also presented. An accentuated increase in the temperature variation is achieved when the battery discharges (blue color) up to the lowest voltage (2.0 V), reaching the maximum temperature variation at the minimum battery terminal voltage.
The greatest temperature variations were recorded in the middle location, where a 35.0 ± 0.5°C average temperature variation was achieved, against 30.0 ± 0.5°C in the negative and 25.0 ± 0.5°C in the positive terminals, respectively. The temperature decreases up to 10.0 ± 0.5°C at all points of the battery during the resting time after the discharge steps. The battery temperature does not achieve initial temperature ranges, proving that, for high discharge and abuse rates, the LiB requires more time to stabilize and return to its initial state of temperature, while operating horizontally, in a constant 20.0 ± 0.1°C environment.
During the charging processes (beige color), average ΔT values of 20.0 ± 0.5°C were observed in the negative terminal and in the middle, and 18.0 ± 0.5°C in the positive terminal. It should be noted that these maximum values of temperature variations during charging were achieved when the highest current was applied to the battery. Figure 6 shows the radial strain variations detected by all the sensors at different points of the battery during the 1.9 C charge and 2.5 C discharge cycles over time. A radial strain mapping of the mean radial strain values registered by the OFS on the end of charge and discharge steps is highlighted.
Radial strain tends to decrease with the depth of the discharge. In the negative terminal and in the middle, this contraction is abrupt, reaching an average variation of −168 ± 27 and −235 ± 27 , respectively, throughout all the discharge processes of the 4 cycles, the positive terminal presented a different behavior. A significative decrease of the radial strain values occurred in this location after the discharge processes (during the rest time), reg-istering a mean variation of −100 ± 27 for all cycles. During the rest step after discharge, a mean variation of 125 ± 27 was observed in middle, and 80 ± 27 at the negative terminal. During the charging processes, a double behavior was registered by the sensors, in which a negative variation followed by a positive variation occurs in the middle and negative positions. Curiously, these inversions appear when the voltage slope is more accentuated however, an opposite behavior was detected in the positive terminal, where a positive radial variation was followed by a negative variation. This behavior is in accordance with previous related studies. [27] In the end of the charge steps, mean radial strain values of −93 ± 27 , −106 ± 27 , and −134 ± 27 , in the negative terminal, middle and in positive terminal, respectively. After each charging process, there is a resting time of 15 min, where at all battery locations the radial strain tends to stabilize in direction of the initial values.
The results obtained from the temperature variations detected by the FBG-PANDA sensors at the different locations of the battery during the galvanostatic cycles at 3.5 C discharge and the correspondent thermal mapping at the end of charge and discharge steps, are represented in Figure 7. It was possible to observe similar behavior if compared to the 2.5 C discharge cycles. However, a greater temperature variation is achieved at the end of the discharge processes, detecting mean values of 40.0 ± 0.5°C, 35.0 ± 0.5°C, and 32.0 ± 0.5°C in the middle, negative terminal, and positive terminal, respectively. These greater temperature variations are probably associated with the greater electrochemical performance of the interior of the battery, due to the greater demand and movement of lithium ions, which induces a greater exothermic process and a consequent greater heat generation. Due to the occurrence of diffusion and thermal convection processes existing inside and on the battery surface, respectively, these temperature values tend to accumulate in the middle lo-  cation, registering higher values in the sensor FBG-PANDA 2 in that area, as can be well observed through the correspondent thermal mapping. Figure 8 represents the radial strain variation tracked by all the FBG-PANDA sensors during the galvanostatic cycles at the higher discharge rate and the correspondent radial strain mapping. Regarding the values of Δ detected by the FBG-PANDA sensors, there was a similar variation to the cycles at 2.5 C discharge, that is, averaged of −163 ± 27 , −199 ± 27 , and −117 ± 27 in the negative terminal, medium, and positive terminal, respectively. This indicates that we will probably be close to reaching the contraction limit of the different battery zones. The radial strain values detected by the developed OFS during the galvanostatic tests are in accordance with the literature reports regarding the strain monitorization by strain-gauges sensors. [28] From all the 8 cycles performed in this experiment, we observed a very good feasibility and reproducibility in the FBG-PANDA sensors performance. With that, we can assume that these approaches, by using the optical fiber sensing technology to track and discriminate specific parameters in LiBs, are a reasonable tool to improve the safety of next batteries generation. As future work, it may be the evaluation of the performance and autonomy of this type of battery, with this same configuration (coiled), in different operating conditions, such as different ambient temperatures and/or abusive overload conditions (above 4.20 V).

Conclusion
In this work, fiber Bragg gratings sensors inscribed in a PANDA birefringent optical fiber were designed to real time and simultaneously discriminate temperature and radial strain shifts in an 18650 LiB during their operation. Different spots (positive terminal, middle and negative terminal) were monitored during its operation and in abusive charging and discharging conditions.
The largest temperature variations were detected at the end of the discharge processes (2.0 V), Greater variations were recorded in higher discharge rate and in the middle location (∆T of 40.0 ± 0.5°C). During the charging processes, with a rate of 1.9 C, the largest temperature variations were also recorded for the central position of the battery (ΔT of 20.0 ± 0.5°C), and when the voltage value presents a steeper slope, that is, close to 3.7 V. This thermal behavior can be justified due to the occurrence of processes of generation and transfer of thermal energy which exists inside the batteries (diffusion and convection), with a tendency to accumulate in the central location, because it exposed less area to the external environment and, in this way, being more difficult and slower to heat dissipation.
Regarding the radial strain tracking, similar values of variation were verified along the two different discharge rates, having the FBG-PANDA sensors registered higher values at the negative terminal and center of the battery. These results indicate that we will probably be close to the radial contraction threshold of the bat-tery, and that beyond these values, the battery will be in insecure regimes and possible rupture or crack formation.
The objective of the proposed work was accomplished, that is, the discrimination of temperature and radial strain in a cylindrical LiB by using FBG sensors recorded in PANDA polarizationmaintained birefringent optical fibers. It should also be noted that it was the first time that this type of monitoring technology (FBG-PANDA sensors) was used in this type of application, in a coiled configuration around the surface of cylindrical batteries for measuring radial strain variations.
In a future perspective, PANDA-FBG sensors may be embedded within battery cell materials to track internal temperature and strain variations; however, to provide a simultaneous measurement of temperature and strain within the cell, the optical fiber would have to be allocated during the manufacturing battery process of the jelly roll. However, we believe that such a sensing approach would be more useful when applied during the development stage of new battery designs (laboratory tests), before their commercialization, in order to evaluate their performance and safety limits. Later, it would be possible also to correlate the internal parameters data measured in this laboratory analysis to develop new thermal and stress model algorithms, performing a "virtual sensing", based on machine learning processes.

Experimental Section
Sensor Inscription: To be able to inscribe the FBG sensors on PANDA optical fibers, it began by placing a small portion of this fiber (≈50 cm) in a hydrogenation chamber at a constant pressure of 10 bar for 1 week, allowing the hydrogen to penetrate the fiber and provide a photosensitive characteristic to the core. In the sequence, the fibers were fused to 1.5 m long single mode optical pigtail ( Figure S3A, Supporting Information), in order to acquire their signal in the optical interrogator ( Figure S4, Supporting Information) which was connected to the computer. Signal acquisition was controlled through the Enlight software, which displayed the signal of optical power losses as a function of wavelength. In order to fuse the fiber with the pigtail, it was first necessary to strip the two fiber ends (acrylate removal) and make a cut in the two fiber sections perpendicularly to the propagation axis (90°). Then, the fibers were placed in the two terminals of the fusion machine ( Figure S3B, Supporting Information), and the fusion was performed by an electrical discharge between the electrodes. As the PANDA fiber was doped with hydrogen, in the area where the fusion will be carried out, it was necessary to submit them to a heat treatment, with a soldering iron, to release the hydrogen present in that area, thus avoiding the formation of a hydrogen bubble during the fusion. Then, to record the Bragg gratings on the PANDA fiber, a small section of it was stripped (1 cm) in the areas where the sensors were inscribed. To record the sensors, a UV laser was used ( Figure S1, Supporting Information). In order to inscribe the 3 FBG-PANDA sensors with Bragg peaks at different wavelengths, 3 phase masks (1067, 1072, and 1077 nm) were used. The PANDA fiber was initially placed with some tension on the fiber holders. After that, the phase mask was placed and adjusted with a minimum distance relative to the fiber. The laser beam was aligned to pass through the phase mask and to reach the fiber core, inscribing the Bragg grating. The same procedure was repeated for the remaining phase masks, and by moving the fiber to record the FBG-PANDA sensors in different positions of interest. Figure S4, Supporting Information, presents the final spectrum of all FBG-PANDA sensors.
Characterization to Strain: To characterize the sensors to strain, the optical fiber with all FBG-PANDA sensors was glued to a fixed support and to a translation stage support with a micrometric screw ( Figure S5, Supporting Information). The micrometer screw was rotated between 0.00 and 0.55 mm with an interval of 0.05 mm, stretching the fiber. For each step, the resulting spectral response was recorded, and the variation of all Bragg peaks as a function of the applied strain was acquired. The strain values ( ) were calculated based on the variation of length (ΔL) and initial length (L 0 ), through the expression: A linear regression of the wavelength as a function of strain was performed and is present in Figure S6, Supporting Information. From all the linear regressions, the respective sensitivities were obtained for each FBG-PANDA sensor. Higher strain sensitivity values were determined in the slow axis.
Characterization to Temperature: To perform the temperature calibration, the fibers were attached to the battery in the 3 pre-defined locations, in a coiled setup ( Figure S2, Supporting Information). The FBG-PANDA 1 was placed near to negative terminal, the FGB-PANDA 2, in the middle, and the FBG-PANDA 3, near the positive terminal. Then, the 18650 battery already instrumented with the sensors, was placed in the thermal chamber ( Figure S7, Supporting Information), where the temperature was increased between 20.0 ± 0.1°C and 40.0 ± 0.1°C with an interval of 5.0 ± 0.1°C, leaving a 20 min stabilization time for each temperature. Throughout this process, the spectral response from the 3 FBG-PANDA sensors was also recorded, and their analysis was later carried out by tracking the double peaks of each sensor. Sequentially, a linear regression was performed for each FBG-PANDA Bragg wavelength variation as a function of temperature variation ( Figure S8, Supporting Information).
Galvanostatic Cycles: To proceed the experimental tests, the battery was charged and discharged during galvanostatic cycles at different Crates. Throughout this process, the battery voltage was acquired by connecting the positive and negative terminals to a DAQ (USB6008, National Instruments), which was connected to a computer running a LabVIEW software interface. The instrumented battery was kept in a 20.0 ± 0.1°C environment, within the climatic chamber. A total of 8 cycles with abusive charge/discharge operations were performed. By using a heat dissipative resistance of 0.47 Ω, 4 cycles were performed at 2.5 C discharge, and another 4 cycles at 3.5C discharge, through another heat dissipative resistance of 0.33 Ω. For the charging processes, a universal charger (Turnigy Accucel-6 balance) with a maximum current of 6.0 Ah (C-rate 1.9 C) was used. After each charge or discharge process, a battery rest time of 15 and 20 min, respectively, was established to battery cell thermal stabilization and relaxation. Aiming to induce high heat generation, the battery was discharged bellow its cut-off voltage (2.5 V), achieving 2.0 V. Regarding the charging steps, the battery was charged until its maximum charge voltage (4.20 V), therefore, the battery operated between 2.0 and 4.20 V. The Bragg peaks of all FBG-PANDA sensors were tracked during all the charge and discharge cycles.
Fiber Bragg Gratings-PANDA Sensors Data Analysis: The data processing of all FBG-PANDA sensors was performed by a MATLAB routine. For these calculations and to increase the measurement accuracy, precise signal processing tools based on data treatment FFT filters were used. For the simultaneous discrimination of both parameters (temperature and radial strain) the matrixial method, as described in Equations (9-11), was applied.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.