A ﬂ uoride-selective electrode (Fse) for the quanti ﬁ cation of ﬂ uoride in lithium-ion battery (Lib) electrolytes

In this work, a ﬂ uoride-selective electrode (FSE) was applied with regard to the analysis of ﬂ uoride in lithium hexa ﬂ uorophosphate-based lithium-ion battery (LIB) electrolytes. The in ﬂ uence of linear organic carbonate solvents dimethyl carbonate (DMC), ethyl methyl carbonate (EMC) and diethyl carbonate (DEC) which are used as co-solvents in battery electrolytes was investigated. The developed FSE method for the analysis of battery electrolytes was comprehensively validated in view of the (1) trueness and recovery rates (nominal vs. actual comparison; in ﬂ uence of di ﬀ erent amounts of electrolytes on the performance of the electrode; recovery rates of de ﬁ ned di ﬀ erences in concentration), (2) precision (intra-day precision and inter-day precision), (3) selectivity (in ﬂ uence of the carbonate solvents on di ﬀ erent ﬂ uoride concentrations; interferents) and (4) linearity and range. Statistical analysis was performed to evaluate the data and to characterize the reproducibility of the method. The determination of the commercially available LP30 (1 mol LiPF 6 and ethylene carbonate/dimethyl carbonate (EC : DMC, 50 : 50 wt%)) electrolyte stored over 47 days and at 80 (cid:1) C, by the FSE technique was compared to the ﬂ uoride analysis by ion chromatography (IC). While interferences in the IC method resulted in false-high concentrations, the FSE operated free from interferences, selective and speci ﬁ c. The validation of the method was successfully carried out and enables new areas of application.


Introduction
The uoride-selective electrode (FSE) came up in the 1960s by Frant & Ross and was successfully applied for uoride analysis in aqueous solutions. 1 The investigation of aging processes in lithium-ion batteries (LIB) is a key point for the further development of rechargeable batteries in the context of research on renewable energies. Therefore, investigations on the changes of the electrolyte composition contribute to the understanding of aging processes that still limit the battery cycling performance. Identication and quantication of compounds and their decomposition products formed in aging processes gain a precise understanding of the aging processes themselves and their inuencing factors. Due to the cross-dependence of aging phenomena, they are very complicated to characterize. 2 Analysis of electrolytes as the connecting media to all cell compounds (cathode, anode, and separator) provides information about interactions between battery components. Electrolytes based on LiPF 6 dissolved in mixtures of organic carbonates such as ethylene carbonate-dimethyl carbonate (EC-DMC), ethylene carbonate-ethyl methyl carbonate (EC-EMC) or ethylene carbonate-diethyl carbonate (EC-DEC) are used most frequently in LIBs. 3 The degradation of LiPF 6 in organic electrolytes has been investigated intensively. 4-6 Campion et al. (2004) proposed a mechanism for the autocatalytic decomposition of LiPF 6 in carbonates due to the presence of protic impurities such as traces of alcohol and water. 7 In thermally aged electrolytes, the formation of HF was also observed. 5,8 The reaction of PF 5 with alcohol and water, respectively, forms phosphoryl triuoride (POF 3 ) and hydrouoric acid (HF). HF for its part is a weak acid and may catalyze the decomposition reaction of LiPF 6 as a further protic compound. The formation of acidic compounds such as HF is known to have negative effects on the stability of the solid electrolyte interphase (SEI) on the anode. 9,10 Moreover, Vetter et al. (2005) reported a disproportionation reaction of lithium manganese spinel used as the cathode material. HF dissolved Mn(III) from LiMn 2 O 4 yielding l-Mn 2 O 4 (Mn IV), Mn 2+ (Mn II) and LiF. Mn 2+ leaves the spinel and gets dissolved in the electrolyte. 4 Mn 2+ may be re-precipitated on the cathode as for example, Mn x O y , MnF 2 or MnCO 3 . Alternatively, Mn 2+ might migrate to the negative electrode and will deposit there. However, while oen damaging effects of HF in the context of the electrodes and electrolyte were reported, HF also stabilizes Al current collectors. HF was found to passivate Al used as the current collector due to the formation of chemically stable AlF 3 or AlO x F y on the surface. 11,34 Overall, the presence of HF has turned out to be decisive for battery life and cyclization performance.
Until now, decomposition products of LiPF 6 -based organic electrolytes were investigated by means of IC as well as ICelectrospray ionization mass spectrometry (IC-ESI-MS), [12][13][14][15][16] by electrospray ionization-high resolution mass spectrometry (ESI-HRMS), 17 by liquid chromatography-tandem quadrupole mass spectrometry (LC/ESI-MS/MS) 18 and by gas chromatographymass spectrometry (GC-MS). 15,[19][20][21][22] Terborg et al. achieved a baseline separation of the dissociation products by IC of dissolved LiPF 6 in water as well as of the components and dissociation products of a commercially available battery electrolyte (1 M LiPF 6 in EC : DEC (3 : 7 w/w)). 12   monitored the uoride formation during aging using the IC technique. 15 Co-elution of the uoride peak with the arising ionic organophosphates was observed caused by the low retention of these compounds on a column with a hydrophilic character. Organophosphates are formed unavoidably from the organic carbonates during cyclization of LIBs and indicate aging processes. With increasing cyclization, amounts of organophosphates increase, too. Thus, besides the interesting uoride concentrations, further aging products arise during ongoing charge and discharge processes impeding the detection of the uoride. It was noted that uoride contents of samples with a higher degree in degradation might have given false-high values due to co-elution. A high selectivity in regard to uoride and organophosphates was achieved on a column with hydrophobic character. However, the analysis time was extremely high caused by a strong interaction of hexa-uorophosphate with the stationary phase. 14 Furthermore, the two-dimensional IC yielded a successful separation of organophosphates but could not separate uoride. 16 Especially in the case of samples of a higher degree of degradation, the IC analysis capability in terms of uoride is limited. So far, there is no method reported which can access the uoride quantication in aged LIB electrolytes. Furthermore, to the best of our knowledge, FSE has not been reported for uoride quantication in LiPF 6 -based LIB electrolytes until now. In addition, an analytical validation for the determination of uoride in this matrix assessing the suitability of the method in this context was not reported in the literature.
Using spectroscopic and chromatographic methods for the quantication of uoride is challenging due to uoride's heavy excitation because of its high electronegativity and its low retention on ion-exchange columns resulting in co-elution with other compounds having the same chromatographic behavior. A highly element-selective and specic analysis tool was developed by Frant & Ross in 1966. 1 A single-crystal of a rare earth uoride, such as LaF 3 , NdF 3 or PrF 3 , was used as the electrode-type sensor giving a Nernstian response over several decades of uoride ion activity. The response of the LaF 3 electrode to the concentration of uoride ions was reported several times to start at 10 À6 mol L À1 upwards. 1,33 The ISE was applied in the past for uoride determinations in water, wastewater, pure salts aer pre-concentration, electroplating baths, milk, minerals and rocks, plants, phosphoric acid topaz, bones, urine, aliphatic amine solutions, dental tissues, samples containing boron, organic compounds, tea, biological materials, hair and D 2 O. 23 In the present work, the FSE was investigated for its applicability of uoride analysis in organic electrolytes. Due to the complexity of battery electrolytes, particular attention was paid to the possible adverse reactions of matrix compounds with an FSE. The method was successfully validated considering the following points: (1) trueness (deviation of the measured value due to systematic errors) and recovery rates investigating (a) a nominal actual comparison, (b) the inuence of the organic carbonates in various compositions and volumes on uoride detection and (c) the recovery of dened differences in uoride concentrations in solutions spiked with different concentrations of a uoride standard; (2) precision (deviation of analysis values due to random errors) investigated (a) as inter-day precision and intra-day precision; (3) selectivity as (a) a comparison of the analyte in standard solutions with the analyte in the matrix of real samples and (b) the application of TISAB solution for prevention of interferences and achievement of pH stability; (4) linearity and range as a comparison of the linear calibration function with the function of the 2 nd degree as well as consideration of the Nernst slope; (5) limits of detection and quantication. Aer validation, the FSE method was applied to the characterization of thermally aged LiPF 6 -based LIB electrolytes. The results were compared to the results obtained by analysis using IC.

FSE instrumentation
The FSE system consisted of an Metrohm 858 Professional Sample Processor, a 905 Titrando connected to an 801 Stirrer, two 800 Dosinos (20 mL for dispensing the sample into the PTFE test vessel and 50 mL for ushing of the PTFE test vessel aer the measurement), the FSE type no. 6.0502.15 and the Ag Ag/Cl reference electrode type no. 6.0750.100. The instrument was controlled by Methrom tiamo™ 2.4 and Metrohm MagIC Net™ 3.1. All devices and the soware were acquired from Metrohm AG (Herisau, Switzerland). For analysis, 10 mL of TISAB IV solution were lled in the PTFE test vessel and 2 mL of the sample were added.

IC instrumentation
The IC system consisted of a Metrohm 889 IC Sample Center for sample introduction and an 850 Professional IC equipped with a chemical suppression module and a conductivity detector. For the anion separation, the column Metrosep A Supp 4 with the dimensions 250 mm length Â 4.0 mm interior diameter and 9 mm particle size was used combined with the matching guard column Metrosep A4/5 guard, 4.0 mm interior diameter. The suppressor applied a 100 mmol L À1 H 2 SO 4 solution for regeneration of the stationary phase of the suppressor. The system was controlled by MagIC Net™ 3.1. All devices and the soware were acquired from Metrohm AG (Herisau, Switzerland). The column oven was operated at 40 C and the ow rate was set to 1 mL min À1 . Anions were separated isocratically over 18 min using an aqueous solution of acetonitrile (24 vol%), sodium carbonate (2.52 mmol L À1 ) and sodium hydrogen carbonate (2.38 mmol L À1 ) as the eluent.

Statistical analysis
For statistical analysis the open source soware R Studio from R Core Team (2015) was used. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
2.6 Trueness and recovery rates 2.6.1 Nominal-actual comparison with a subsequent t-test. A calibration curve consisting of the following concentrations was used for the external calibration: blank, 0. 5 ppm, 1 ppm, 2 ppm, 3 ppm, 4 ppm, 5 ppm, 20 ppm, 30 ppm, 40 ppm, 50 ppm, 60 ppm, 80 ppm, 90 ppm and 100 ppm. Solutions of 10 ppm and 70 ppm were applied as unknown samples. Their concentrations were calculated based on the external calibration. The solutions were analyzed six times each and data values were compared with the expected concentrations using a one sample t-test.
2.6.2 Inuence of electrolytes. The inuence of EC : DMC (50 : 50, wt%), EC : DEC (50 : 50, wt%) and EC : EMC (50 : 50, wt%) was investigated in an aqueous solution containing 10 ppm uoride. 100 mL of the uoride stock solution (1 mg L À1 ) was mixed with 0 mL, 10 mL, 50 mL, 100 mL, 500 mL and 1000 mL of the electrolytes, respectively, and lled up with de-ionized water in a 10 mL vial. The samples were analyzed three times and the average of the detected voltages was used for calculations.
2.6.3 Recovery of dened differences in uoride concentrations. For the addition procedure, 100 mL of LP30 (1 M LiPF 6 in EC : DMC (50 : 50, wt%)) from a freshly opened bottle was spiked with 0 mL, 20 mL, 50 mL, 70 mL and 90 mL of the uoride stock solution (1 mg L À1 ), respectively, and lled up to 10 mL with de-ionized water resulting in nominal uoride concentrations of 0 ppm, 20 ppm, 50 ppm, 70 ppm and 90 ppm.

Precision
For intra-day and inter-day precision, 16 standard solutions of the following uoride concentrations were diluted in de-ionized water from the uoride stock solution (1 g L À1 ): blank, 1 ppm, 2 ppm, 3 ppm, 4 ppm, 5 ppm, 10 ppm, 20 ppm, 30 ppm, 40 ppm, 50 ppm, 60 ppm, 70 ppm, 80 ppm, 90 ppm and 100 ppm. Larger amounts of all concentrations were prepared to use the same stock solutions for all recurring analysis. For intra-day precision, the solutions were analyzed six times successively on the same day. For inter-day analysis precision, the solutions were analyzed for a period of six days consecutively.

Selectivity
2.8.1 Inuence of the carbonates. Two sample batches differing in terms of the presence or absence of EC : DEC (50 : 50, wt%) containing the following uoride concentrations were prepared: 0.5 ppm, 1 ppm, 2 ppm, 5 ppm, 10 ppm, 15 ppm, 25 ppm, 50 ppm, and 100 ppm. In the rst batch, the samples are just lled up with de-ionized water. In the second batch, 100 mL of EC : DEC (50 : 50, wt%) were added to each solution and prior to lling up with deionized water. Each batch was analyzed three times. The average of the detected voltages for each concentration step was used for calculations.
2.8.2 Interferences: preparation of total ion strength adjustment buffer (TISAB) IV. For the preparation of TISAB IV solution, 58 g of sodium chloride (0.99 mol) was dissolved in 500 mL of de-ionized water. Aerwards 5 g (13.7 mmol) of trans-1,2-diamino-cyclohexane-N,N,N 0 ,N 0 -tetraacetic acid monohydrate (TISAB IV, Complexon IV) were added and dissolved by adding sodium hydroxide solution (8 mol L À1 ) drop by drop. Glacial acetic acid (57 mL, 17.5 mol L À1 ) was added and with sodium hydroxide solution (8 mol L À1 ) adjusted to pH 5.5. Finally, the solution was lled up to 1 L with de-ionized water.

Linearity and range
For investigation of the linearity, data of the calibration curve were used. Linearity was determined by comparing the linear calibration function to a function of the 2 nd degree. The adjustment of the two functions was compared by an F-test.

Sample preparation and hydrolysis stability
Since traces of water or moisture lead to the rapid decomposition of the conducting salt, the electrolytes were handled in a dry room or glovebox to prevent contamination. However, water can be used as a solvent during sample preparation. Terborg et al. showed that lithium hexauorophosphate is stable in aqueous solution for several days. 12 The same was reported by Metrohm who investigated the stability of PF 6 in water as well as the stability of PF 6 in electrolytes when diluted with water. 35 Regarding the hydrolysis of the organophosphates, Kra et al. demonstrated that these compounds are stable against water and therefore water is an appropriate solvent during sample preparation. 16 2.11 Sample preparation for aging experiments of a battery electrolyte at 80 C For the investigation of the formation of uoride in the electrolytes, 2 mL of commercially available LP30 was lled in aluminum vials closed with a screw cap. In total 40 sample containers were stored at 80 C for 47 days. The samples were analyzed on days 1, 3,5,9,14,16,20,28,35 and 47. At each time, four sample vials were analyzed and each sample was analyzed threefold by IC combined with a conductivity detector as well as with a FSE. Before analysis by means of FSE, all samples were diluted 1 : 100 with de-ionized water. For analysis via IC, all samples were diluted further 1 : 1 with de-ionized water. The average of each time was used for calculations.

Sample preparation for aging experiments of a battery electrolyte at several temperatures
For the investigation of uoride formation depending on the temperature, 2 mL of commercially available LP30 was lled in aluminum vials closed with a screw cap. Groups of four samples were stored at À16 C, 6 C, 20 C, 40 C, 60 C and 80 C, respectively, for the duration of 47 days. For analysis by means of FSE, all samples with the exception of the samples stored at À16 C, 6 C and 20 C were diluted 1 : 100 with de-ionized water. The samples stored at À16 C, 6 C and 20 C were diluted 1 : 10 and analyzed in this dilution by FSE as well as by IC due to the expected very low uoride concentrations. For analysis via IC, all remaining samples were subsequently diluted 1 : 1 with de-ionized water. All samples were analyzed threefold by IC as well as by FSE. The average of each temperature was used for calculations.

External calibration for analysis by means of IC and FSE
For external calibration, ten standard solutions of the following uoride concentrations were diluted in de-ionized water from the uoride stock solution (1 g L À1 ): blank, 0. 5 ppm, 1 ppm, 2 ppm, 5 ppm, 10 ppm, 15 ppm, 25 ppm, 50 ppm and 100 ppm. The external calibration was performed daily before sample analyses by FSE and IC. to determine whether or not the data values followed the normal distribution and conrmed in this case a normal distribution of the data values with a critical value of a ¼ 0.05 at 10 ppm (W a¼0.05 < W ¼ 0.796 and p ¼ 0.054) and at 70 ppm (W ¼ 0.927 and p ¼ 0.559). No signicant difference was found between the nominal and the actual concentrations applying a one sample t-test for 10 ppm, t(5) ¼ À1.367 and p ¼ 0.23, and for 70 ppm, t(5) ¼ 0.850 and p ¼ 0.434, respectively. The t-test veried that the nominal values do not differ from the experimental concentrations within a 95% condence level. The deviations for ion selective analysis techniques are usually given by 2-5%. 25 The data for precision obtained here for the uoride selective electrode are in good accordance to the data from the literature.

Results & discussion
3.1.2 Inuence of the electrolyte. For investigation of the inuence of the battery electrolyte composition on the ionselective electrode surface, organic carbonates used as solvent components in electrolytes of batteries were added to an aqueous uoride solution of constant uoride concentration. Between 10 mL (0.1%) and 1000 mL (10%) of EC : DMC, EC : DEC and EC : EMC, each in a ratio of (50 : 50, wt%), were spiked to an aqueous solution containing 10 ppm uoride. All samples were examined by a three-fold determination procedure. For external calibration, electrolyte-free calibration solutions were applied to make the inuence of the electrolytes apparent. An electrolyte-free solution (0; 0%) containing 10 ppm uoride was analyzed as reference. The recovery rates of uoride observed for different contents of carbonates are between 95% and 109% as summarized in Table 1.
A slightly positive trend becomes visible: with the increasing amount of the electrolyte, increasing recovery rates resulted. However, up to the 500 mL (5%) amount of the electrolyte the recovery rates (95-106%) are in good accordance to recovery rates determined by repeated injections of uoride standard solution containing no electrolyte (10 ppm: 97-103% and 70 ppm: 98-103%; Chapter 3.1.1). Therefore, samples containing 10-500 mL (0.1-5%) of the electrolyte, which corresponds to the volume of the electrolyte that is typically recovered from cycled cells, can be analyzed by means of the uoride selective electrode method without any compensation of matrix effects.
3.1.3 Recovery of dened differences in uoride concentrations. Wherever possible the trueness of an analytical method should be estimated by including suitable certied reference materials (CRMs). If these are not available, as is the case here, spiking of samples containing adjusted amounts of the matrix with standard solution is recommended. 26 For investigation of systematic errors, an LP30 electrolyte taken from a freshly opened bottle was spiked with uoride. In a rst step, the uoride concentration of the freshly opened bottle was determined. Furthermore, the electrolyte was spiked with 20 ppm, 50 ppm, 70 ppm and 90 ppm uoride, respectively. Table 2 shows (a) the expected concentrations, (b) the determined concentrations, (c) the expected differences to the previous concentration and (d) the determined differences to the previous concentration.
The uoride concentration in a freshly opened bottle of LP30 has already been determined to be 2.1 ppm. The initial amount was determined in all samples beyond the spiked amount and led to increased uoride concentrations. The calculated theoretical concentrations were recovered plus about 2 ppm. For example, aer spiking 20 ppm uoride, a total content of 21.8 ppm was determined. Differences in uoride concentrations between the samples of about 20 ppm and 30 ppm, caused by spiked uoride concentrations were observed as expected. Differences between samples could be recovered accurately throughout the concentration range.

Precision
The precision, i.e., the accuracy of the measurement, species scattering of analysis values due to random errors. The scattering of analysis values can be expressed as the variation coefficient of repeated analysis. Variation in the analysis value due to the analysis instrument itself is referred to as 'repeatability of the instrument'. It was specied by a sixfold analysis of the same uoride containing standard solutions. Here, the calibration curve consisting of ten concentration points between 1 ppm and 100 ppm was used to observe variations over the whole calibration range.
3.2.1 Intra-day precision (within batches). The sixfold analysis of the standard solutions analyzed successively on the same day yielded variation coefficients between 0.2 and 2.5%. Comparison of variances using Levene's test proved the variance homogeneity of analysis values at each concentration step (e.g. 1 ppm, 2 ppm, ., 100 ppm). Variances of analysis values at each concentration step are equal, F(14, 75) ¼ 0.7064, p > 0.05, the assumption of homoscedasticity is attained and criteria for a linear regression are fullled.

Inter-day precision (between batches)
. The sixfold analysis of the standard solutions analyzed for a period of six days consecutively led to variation coefficients between 0.5 and 3.8%. Levene's test proved homogeneity of variances, F(14, 75) ¼ 0.391, p > 0.05. Variances of analysis values are equal. Scattering of analysis values are due to random errors and do not show systematic effects.
The intra-day and inter-day precision, moreover, proved process stability, repeatability and comparability of analysis pointing to a high robustness of the method.

Inuence of the carbonates on varying uoride
concentrations. The analysis of standard solutions oen differs from the analysis of real samples containing matrix compounds and interfering substances. Matrix compounds such as the organic carbonates in battery electrolytes may inuence the detection of uoride using the uoride-selective electrode. While the inuence of the carbonates on the recovery rate of uoride has been shown above, here the inuence of the carbonates on the calibration curve shall be evaluated. By adding 100 mL of the electrolyte under the condition "with matrix", the typically recovered volumes of electrolytes from cycled cells are covered. If the carbonates inuence the calibration curve, the calibration solutions would have to be adjusted to the matrix of the real samples. The carbonates contained in the battery electrolyte would have to be added to each standard solution for calibration. A comparison of the method "no matrix" with the method "with matrix" is indicated. Several methods are discussed to evaluate the agreement between the two methods. 27 As suggested by Bland & Altman for the investigation of the agreement the differences between the two methods were plotted. [28][29][30] The differences between the two experimentally determined voltages (D ¼ no matrix À with matrix) are plotted against the average of the determined voltages (Av ¼ [no matrix + with matrix]/2) in a Bland-Altman plot as shown for the EC : DEC mixture in Fig. 1.
The differences follow a normal distribution as conrmed by the Shapiro-Wilk test, W a¼0.05 ¼ 0.829 < W ¼ 0.899 and p ¼ 0.247. The differences are distributed normally around the mean value. Thus, the mean value of the differences (À0.30 mV) gives the constant bias between the two methods "no matrix" and "with matrix". The measured voltage does slightly and constantly increase over the whole concentration range, if standard solutions contain matrix compounds.
Due to the normal distribution, 95% of differences lie between the mean difference d and twice the standard deviation of the differences s. Here, differences are expected between d AE 2s resulting in [À1.54 and 0.94]. These values are referred to as "limits of agreement" and are estimates of values applying to the whole population. To estimate the precision of the limits of agreement, condence intervals (CI) for both limits are calculated. The 95%-CI for the lower limit is [À2.02 and À1.05] and Even though the number of samples was low and, thus, CI are wide, most data points are between the higher limit of the lower limit of agreement [À1.05] as well as the lower limit of the higher limit of agreement [0.45].
The constant bias of À0.30 mV corresponds to a deviation of 0.23% at 1 ppm and 1.79% at 100 ppm. These variations are smaller than the variation due to random errors (intra-day: 2.5%; inter-day: 3.8%) for precision variation and will not be considered any further. Corresponding analysis were performed with EC : DMC and EC : EMC resulting in comparable data.
3.3.2 Interferences. Several challenges in the past were already successfully mastered yielding this method, free of interferences: (1) the ion-selective electrode for uoride analyses is known to show cross-sensitivity with hydroxide ions at pH > 8, 1,31,32 and (2) some metal ions such as aluminum. 33 (3) The electrode responds to the activity of the uoride ions and not simply to the concentration. The requested analytical information is, however, usually the concentration of the analytes and not its activity. Besides, the activity depends on the total ion concentration in the solution and, thus, differs from the concentration. Other ions in solution may inuence the determined activity and therefore negatively inuence the calculation of the concentrations. (4) The electrode responds selectively to uoride and not to any uoride containing compounds. At pH < 5 uoride is protonated yielding HF and HF 2 À . However, these difficulties were eliminated by the introduction of a Total Ion Strength Adjustment Buffer (TISAB). 32 The application of TISAB leads to a constant pH and ionic strength in analysis solution during measurement. In particular here, the application of TISAB IV (trans-1,2-diamino-cyclohexane-N,N,N 0 ,N 0 -tetraacetic acid monohydrate, CDTA, Komplexon IV) buffered the solution at pH 5.5 and so prevents protonation of uoride and cross-sensitivity of the electrode against hydroxide ions. The xed ionic strength allows drawing conclusions on analyte concentrations without further consideration of any ionic activity. Moreover, TISAB IV reacts with metal ions, such as Al 3+ and Fe 3+ , which form complexes with uoride. Due to the reaction of TISAB IV with the metal ions, uoride bound in metal complexes is displaced and misquantication is avoided. 31,32 Thus quantication of uoride is also possible in rechargeable lithium batteries, if the anodic aluminum current collector becomes dissolved in the electrolyte as described by Krämer et al. (2013). 34 Selectivity and accuracy go hand in hand and conrm each other mutually, here. Selectivity is a precondition for accuracy and, thus, an accurate method is automatically selective. 24

Linearity and range
A look on the calibration curve providing the voltage in mV plotted against log(c) in log(ppm) yielding a regression coefficient of R ¼ 0.999 conrms that a linear relation between the electrode response and the uoride concentration is given. However, the examination of linearity is performed for the sake of completeness. As data of the analysis of precision (Chapter 3.2) show homogeneous variances (homoscedasticity), the criteria for linear regression are fullled. The test of linearity is done by comparing the linear calibration function with the calibration function of the 2 nd degree. The reduction of the residual variance resulting due to the regression model of higher order is checked for statistical signicance by an F-test, F(14, 13) ¼ 20 810 and p < 0.01. As expected, data values t perfectly to a linear model. The comparison of linear calibration functions with calibration functions of the 2 nd degree has been proposed by Mandel in the 1930s and is known as Mandel's tting test in the eld of method validation in analytical chemistry. 24 The range for the determination of uoride here is 0.5-100 ppm with a Nernst slope of À58.5 mV at 20 C in ambient air.

Limits of detection and quantication
The response of the LaF 3 electrode to the concentration of uoride ions was reported in the literature several times to start at 10 À6 mol L À1 upwards. 1,33 The working range here was starting at 2.6 Â 10 À2 mol L À1 ¼ 0.5 ppm and, thus, the lowest concentration is clearly above the limits of detection and quantication and was not determined here.

Analysis of a battery electrolyte thermally aged at 80 C
A central issue for the understanding of degradation processes in LIBs is the understanding and monitoring of uoride formation from the conducting salt LiPF 6 . Fluoride formation is inuenced by temperature and/or by the aging process. 1,6,14 Aer validation of the FSE method in the context of battery electrolytes, the newly evaluated FSE method is compared to conventional uoride analysis by means of IC. The commercially available LP30 battery electrolyte was aged at 80 C and analyzed at various times with a maximum of 47 days. Aer dilution the samples were analyzed by means of FSE and IC. The resulting uoride contents are depicted in Fig. 2.
Data from FSE as well as IC analysis show increased uoride concentrations with passing time from the rst day to the 47 th day. In FSE analysis, uoride concentrations increased from 224.6 ppm to 2413.1 ppm with standard deviations (SD) between 35.1 ppm and 295.0 ppm, which corresponds to SD ¼ 3-19%. In IC analysis, uoride concentrations increased from 238.0 ppm to 2639.2 ppm with approximately SD ¼ 3-17%. The standard deviations varied between samples. For most samples, SDs are in a similar range except for the 9 th , the 14 th , 20 th and 47 th day exhibiting a higher SD. In total, SDs of both techniques overlap for the most days. Both techniques led to uoride concentrations with real values in similar ranges.
Even when a similar trend in concentrations was observed, it is noteworthy that concentrations observed by FSE are always lower than the concentrations observed by IC analysis. Fig. 3 shows the ion chromatograms of LP30 analyzed aer the rst day in the oven at 80 C and LP30 aer the 28 th day at 80 C. While aer the 1 st day only one signal according to uoride is visible, the chromatogram shows two signals aer the 28 th day. The second signal and the apparent peak shoulder of the uoride peak can be assigned to organophosphates, a group of electrolyte degradation products that could not be baselineseparated using all conceivable possibilities. Co-eluting the organophosphate compounds does change the results towards "dust" ndings which explains the higher "uoride" concentrations found in IC analysis. False-high values increase with the number of days. The detected difference in concentration between the FSE and IC analysis Dc (F À ) was 13.4 ppm for the rst day with low degradation and is successively increased until the 47 th day with high degradation, revealing a difference of 226.0 ppm. Fluoride analysis by IC does not only determine the analyte of interest and, thus, cannot be considered as a valid technique for this purpose.
The observed co-elution of uoride and organophosphates is in good accordance with previous results reported from our working group. 14,15  identied organophosphates by means of IC-ESI-MS and discussed the inuence of the co-eluting organophosphates. 15 They assumed that the inuence of the co-elution might be negligible if the content of ionic organophosphates is very low. For samples of high degradation degree, co-eluting compounds were expected to lead in false-high values. 14,15 However, data shown here conrmed their assumptions: analysis of battery electrolytes by means of FSE prevents false-high concentrations especially in strongly aged samples.
The inuence of water was proven to have no inuence on the degradation of NaPF 6 and the formation of uoride as shown elsewhere. 12 Compared to LiPF 6 , the dissociation of NaPF 6 is advantageous due to entropic effects. Nevertheless, an aqueous solution (1% EC/DMC, v/v) of NaPF 6 containing 22.5 ppm Na/P and 22.5-135 ppm uoride, respectively, were analyzed repetitively for four hours. About 20 minutes aer NaPF 6 was dissolved, a uoride concentration of 0.3 ppm was detected by means of FSE. Aer four hours, the uoride concentration increased marginally to 0.7 ppm and, thus, the increase in uoride concentration due to hydrolysis of NaPF 6 is negligible. The sample preparation in water was proven to have no inuence on detected uoride concentrations.
To investigate the inuence of different temperatures, commercially available LP30 was stored at À16 C, 6 C, 20 C, 40 C, 60 C and 80 C for 47 days. The samples were analyzed again by means of the FSE and IC techniques. In Fig. 4    With the exception of the sample stored at 20 C, uoride concentrations were higher when samples were analyzed by IC. The differences in detected uoride concentrations Dc (F À ) of FSE and IC analysis yielded again higher differences for samples that were strongly aged. The more a sample was aged and the more LP30 electrolyte degradation products were present, the more results differed for FSE and IC analysis. Especially for strongly aged electrolyte samples the FSE as the uoride selective method was able to provide a precise analysis, free from interferences with matrix compounds.

Conclusions
For the rst time, a uoride selective electrode (FSE) has been applied for the analysis of uoride in organic carbonates (EC : DEC, EC : EMC, EC : DEC, each (50 : 50, wt%)) as compounds of LiPF 6 -based LIBs electrolytes as well as in LP30 (1 M LiPF 6 in EC : DMC) as a representative of commercially available battery electrolytes. Method validation of FSE for the analysis of uoride in LiPF 6 -based LIB electrolytes was performed: experimentally achieved concentrations were proven not to differ from nominal concentrations within a 95% condence level. Samples containing 0.1-5% of the electrolyte can be analyzed by FSE without further compensation of matrix effects. Dened uoride concentrations spiked to an electrolyte from a freshly opened bottle were recovered as expected over the whole concentration range (0.5-100 ppm). Scattering of analysis values in repeated analysis of samples were proven to be caused by random errors (0.2-2.5% in sixfold analysis on one day; 0.5-3.8% in sixfold analysis for a period of six days consecutively) and are not based on any systematic effects.
Samples containing increasing uoride concentrations and a typical amount of the electrolyte recovered back from cycled battery cells yielding a 1% electrolyte solution showed no substantial differences in detected voltages to samples containing the uoride and no electrolyte. The application of TISAB IV keeps the pH constant avoiding cross-sensitivity with hydroxide ions and uoride loss due to the formation of HF and HF 2 À . The constant ionic strength allows drawing the desired conclusions from the analyte concentration instead of from the analyte ionic activity. Moreover, reactions of uoride with metal ions, such as with Al 3+ , that form complexes, which make analysis more difficult, are avoided. The calibration curve (0.5-100 ppm) yielded a regression coefficient of R ¼ 0.999 and a Nernst slope of À58.5 mV at 20 C. LP30 samples were thermally aged at 80 C for various durations and for 47 days at various temperatures. Fluoride contents were analyzed by means of IC combined with a conductivity detector and by means of FSE. The comparison of the observed uoride contents yielded an overestimation of uoride analyzed by IC in strongly aged electrolytes due to co-elution of aging products with the uoride peak. The FSE method worked free from interferences, selective and specic and thus could be introduced here as a robust tool for uoride analysis in the complex matrix of battery electrolytes.