*3.2. State of Charge Variation*

Although the influence of the relative air humidity is known and can be minimized, the relative air humidity in temperature chamber 2 is kept constant (43.4% ± 0.9%) by using a vessel with a saturated salt solution of potassium carbonate (K2CaO3) for the long-term cyclization experiment. Furthermore, the temperature of the temperature chamber 1 is set to 20 ◦C during the whole time, thus the Bragg sensor is particularly sensitive to changes of the cell's surface strain.

In Figure 7, the result of the cyclic experiment is shown. For a time of 27 days, the lithium-ion cell underwent 25 full charge–discharge cycles with a current of 5 A between 4.2 V and 3.0 V. It can be seen that the reflected wavelength signal, measured by the AWG, is in good agreemen<sup>t</sup> to the signal measured by the OSA in the transmitted spectrum.

**Figure 7.** Result of the cyclization experiment. Over 27 days, 25 cycles are performed. The AWG signal is in good agreemen<sup>t</sup> to the OSA signal at any time and represents the battery status well.

For every time step, the error of the AWG is shown in Figure 8, along with the values for the relative humidity. Even though the maximum error is in the range of 3 × 10−<sup>2</sup> nm during the 16th cycle (at experiment time 390), the total mean error is 6.5 × 10−<sup>4</sup> nm, with a standard deviation of 5.9 × 10−<sup>3</sup> nm. Furthermore, it is evident that the largest deviation between OSA and AWG occur when there are significant variations of the relative humidity, like in hour 240, 408 and 576, respectively.

**Figure 8.** Difference between AWG and OSA signal together with the relative humidity. The largest errors occur when there are grea<sup>t</sup> variations in the humidity.

From this long-term experiment, an estimation of both the accuracy and precision of our system can be derived. At the selected settings, our Yokogawa AQ6373B optical spectrum analyzer features a wavelength accuracy of ±5 × 10−<sup>2</sup> nm and a resolution of 2 × 10−<sup>2</sup> nm. The above-described error between OSA and AWG adds to that, so that the accuracy of our system can be calculated to ±7.59 × 10−<sup>2</sup> nm.

To demonstrate the eligibility of the presented polymeric AWG interrogator as a useful device for the status monitoring of lithium-ion cells, one single cell charge–discharge cycle is shown in detail in Figure 9. The cell charging starts at experiment hour 601 when the cell voltage rises significantly and the first drop in the wavelength takes place. This is caused by a typical temperature decrease at the beginning of the charge process, since endothermic chemical processes are predominant over the Joule heat generation. In the ongoing course, the reflected wavelength begins to rise, as the lithium-ions intercalate to the anode, causing an increase of the cell's volume and therefore of the surface strain. Reference [39] demonstrates the correlation between the graphite anode potential (vs. Li/Li<sup>+</sup>) of a lithium-ion battery and its intercalation stages. This can be seen in Figure 9 by different voltage rates of change that are typical for lithium-ion cells. The optical signal also has a nonlinear course and shows different rates of change, which makes them suitable for the detection of characteristic phase transition points that can be used for status monitoring of lithium-ion batteries, although the exact correlation between voltage signal and volumetric behavior is not fully understood yet.

The charging terminates at the signal peak at experiment hour 609.5, followed by a rest period of 5 h, during which a relaxation of the cell takes place. The voltage signal decreases only slightly but a larger decrease in the strain signal occurs, showing ion diffusion processes on the one side and a temperature approximation to the ambient temperature on the other side. It is known that this behavior can also change with an ongoing degradation of the cell because the open-circuit voltage of a lithium-ion cell is linked to its capacity, what can be used to determine the actual SOC or SOH, for example by performing incremental capacity analysis [40].

The discharge cycle starts at hour 615 and is identifiable by a sudden decrease of the voltage signal and the reflected wavelength. Similar to the charging period, the course of the voltage signal shows again characteristic rate changes at certain points caused by the deintercalation of the lithium-ions from the graphite anode and it can be seen in Figure 9 that the strain course also changes at these points. At the end of the discharge cycle at experiment hour 619, the signal rises again, which is due to a significant temperature rise, caused by a typically increasing internal cell resistance that leads to increased Joule heating. After discharge, the cell rests again and the voltage converges to its open circuit voltage. The strain signal decreases with decreasing cell temperature and converges to its initial value.

**Figure 9.** Exemplary single cycle showing the typical optically measured strain behavior of a lithium-ion cell along with the cell voltage.
