Exploring Different Binders for a LiFePO₄ Battery, Battery Testing, Modeling and Simulations

Abstract

This paper focuses on the LiFePO₄ (LFP) battery, a classical and one of the safest Li-ion battery technologies. To facilitate and make the cathode manufacture more sustainable, two Kynar^® binders (Arkema, France) are investigated which are soluble in solvents with lower boiling points than the usual solvent for the classical PVDF binder. Li-LFP and graphite-Li half cells and graphite-LFP full cells are fabricated and tested in electrochemical impedance spectroscopy, cyclic voltammetry (CV) and galvanostatic charge-discharge cycling. The diffusion coefficients are determined from the CV plots, employing the Rendles-Shevchik equation, for the LFP electrodes with the three investigated binders and the graphite anode, and used as input data in simulations based on the single-particle model. Microstructural and surface composition characterization is performed on the LFP cathodes, pre-cycling and after 25 cycles, revealing the aging effects of SEI formation, loss of active lithium, surface cracking and fragmentation. In simulations of battery cycling, the single particle model is compared with an equivalent circuit model, concluding that the latter is more accurate to predict “future” cycles and the lifetime of the LFP battery by easily adjusting some of the model parameters as a function of the number of cycles on the basis of historical data of cell cycling.

1. Introduction

LiFePO₄ (LFP) batteries consist of a LiFePO₄-based cathode and graphite-based anode and are one of the safest types of Li-ion battery [1]. Safety is of particular concern for transport applications, namely electric vehicles and hybrid electric aircraft or space vehicles [2]. Given the low power density of LFP batteries, especially in charge, hybridization with supercapacitors [3,4,5,6,7,8,9,10] makes possible to raise the power while shifting the high rate burden to the supercapacitor [3]. The aging of the Li-ion batteries starts with the formation of the solid-electrolyte interface (SEI) at the electrodes-electrolyte interface, in fact from the first cycle, which controls the Li⁺ ion diffusion [11] while further pore clogging diminishes diffusion and ultimately leads to capacity reduction. Many cycles of Li⁺ ion intercalation and deintercalation strain the battery materials [12] and may cause cracking in the electrodes, which reduces conductivity while more SEI is formed in the newly formed crack surface, both reducing the amount of active material [11]. Heat generation is substantial especially at high operating currents and accelerates battery aging, sometimes also leading to thermal runaway [13,14]. Electrode thickness further controls the performance of Li-ion batteries, where while a thick electrode provides a large amount of active material, it also reduces overall Li⁺ ion diffusion which lowers battery rate performance and, consequently, power density [15]. LFP cathodes combined directly with a Li foil anode exhibit high performance but are under the additional risk of dendritic growth on the Li anode, accelerated at high currents [16,17].

Materials processing and manufacturing of electrode coatings is highly dependent on the binder material which determines the solvent to be used in the process of slurry formation and coating. Polyvinylidene fluoride (PVDF) is the standard, high performance binder used for Li-ion batteries and supercapacitors including an organic or lithium-ion electrolyte [1,6]. However, the solvent employed, N-methyl-2-pyrrolidone (NMP), is highly toxic and has a high boiling point at 203 °C. Water-soluble or water-dispersed binders [18] such as gums [19], SBR (styrene-butadiene rubber) [4,20] or PEDOT:PSS [21] can be used in supercapacitors or the graphite anode in Li-ion batteries [22], where after coating they can be thoroughly dried under vacuum and heat so the electrodes contain no moisture when used in the electrochemical device. However, aqueous slurries are not advised for the LFP unless the LFP particles are protected with a coating shell [23]. Alternatively, Jeong et al. [24] used an ionic liquid solvent for natural cellulose used as a binder in LFP electrodes. In this study, we are investigating two PVDF-copolymer binders that are soluble in a wide range of organic solvents, some of them of a low boiling point. These binders have been used in the electrospinning [25,26,27] of mats on separators for Li-ion batteries, hence, they have proven compatible with Li-ion electrolytes.

Our study involves the fabrication and comprehensive characterization of half and full battery cells, including electrochemical testing of these cells, microstructural examination and surface analysis of their electrodes pre-cycling and postmortem after the cells have been cycled. Furthermore, battery simulation is performed to predict battery cycling. Two types of models have been traditionally used for batteries. Physicochemical process models and equivalent electric circuit models. Our group have developed comprehensive physicochemical models for supercapacitors [28,29,30] and lithium-sulfur batteries [30,31,32,33,34] that take into account the pore size distribution of the electrodes in the ion transport. However, unlike supercapacitors and lithium-sulfur batteries, ion transport in LFP batteries is dominated by the diffusion through the solid LFP particles in the cathode and graphite particles in the anode, with free and easy transport through the large interparticle space. If SEI formation and pore clogging reduces significantly this interparticle distance, this would affect the value of the diffusion coefficient. Hence, the Newman’s single particle model (SPM) is a popular model for Li-ion batteries [35,36,37,38], where Li⁺ ion diffusion is simulated through a phenomenological anode particle and a phenomenological cathode particle with the redox reactions taking place at the particle surface, at the electrode-electrolyte interface, following the Butler-Volmer equation expressing the overpotential. In recent papers, variation of the phenomenological particle diameter is allowed [38] to simulate graded electrodes, for example. Equivalent electric circuit models (EECM) with fits of the open circuit potential from experimental data [39,40] are popular for the energy and power management, offering the advantage of rapid runs and easy integration with control algorithms in the s-domain (after the Laplace transform from the time t-domain). Both SPM and EECM are employed and evaluated in this study. Furthermore, we are using the cyclic voltammetry of half cells at different scan rates to determine the diffusion coefficient of the Li⁺ ions in the anode and cathode, and these values are inputted as property data in the SPM simulations.

2. LFP Battery Models

Two types of models are presented in this study. The first is the classical single particle (SP) model, considering the diffusion and electrochemical processes, and the second is an equivalent electric circuit (EEC) model at system level.

2.1. Single Particle Model

The single particle model represents each battery electrode as a single particle on the basis of two key assumptions: the current supplied to the battery is small and the electrolyte conductivity is large [41], so that the electrolyte concentration and current are constant throughout the electrolyte. To determine the concentration of lithium ions in each particle as a function of time and particle radius, Fick’s second law of diffusion is applied:

$$\frac{\partial C_{s,j}}{\partial t}=\frac{D_{s,j}}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial C_{s,j}}{\partial r}\right)$$

(1)

where $C_{s,j}$ is the lithium-ion concentration in solid phase j (subscript $j$ denotes the positive particle electrode $p$ or the negative particle electrode $n$), $t$ is time, $r$ is the radial coordinate in the particle and $D_{s,j}$ is the lithium ion diffusion coefficient in solid phase j. The initial concentration condition $C_{s,int,j}$ in Equation (2) is equal to zero for the graphite anode and 0.02282 mol cm⁻³ for the LFP cathode:

$${C_{s,j}|}_{t=0}=C_{s,int,j}$$

(2)

Boundary conditions include symmetry at $r=0$ of each particle electrode:

$${\frac{\partial C_{s,j}}{\partial r}|}_{r=0}=0$$

(3)

and a boundary condition for the lithium flux at the surface $\left(r=R_j\right)$ of each particle, $J_j$:

$${\frac{\partial C_{s,p}}{\partial r}|}_{r=R_p}=\frac{J_p}{D_{s,p}}$$

(4)

$${\frac{\partial C_{s,n}}{\partial r}|}_{r=R_n}=-\frac{J_n}{D_{s,n}}$$

(5)

The molar flux of lithium ions at the surface of each electrode $J_j$ is calculated by the relation:

$$J_j=\frac{I}{F{A}_j}$$

(6)

where $I$ is the current applied to the cell, $F$ is the Faraday’s constant and $A_j$ is the total electroactive surface area of the electrode, calculated by the following relation:

$$A_j=\frac{3{\epsilon }_j{V}_j}{R_j}$$

(7)

where ${\epsilon }_j$ is the electrode particle volume fraction, $R_j$ is the electrode particle radius and $V_j$ is the total volume of that electrode. The state of charge $x_j$ of the electrodes is given with respect to the maximum lithium concentration of the electrode, $C_{s,j,max}$:

$$x_{j,surf}=\frac{C_{s,j,surf}}{C_{s,j,max}}$$

(8)

The initial state of charge of the electrodes is given by the following equation:

$$x_{int,j}=\frac{C_{s,int,j}}{C_{s,j,max}}$$

(9)

where $C_{s,int,j}$ is the initial concentration of the electrode.

The Butler-Volmer equation is used to calculate the overpotential of the electrodes ${\mathsf{\eta }}_j:$

$$J_j=k_j{C}_{s,j,max}{c}_e^{0.5}{\left(1-x_{j,surf}\right)}^{0.5}{x}_{j,surf}^{0.5}\left[exp\left(\frac{0.5F}{RT}{\mathsf{\eta }}_j\right)-exp\left(-\frac{0.5F}{RT}{\mathsf{\eta }}_j\right)\right]$$

(10)

where $k_j$ is the temperature dependent reaction rate constant, R is the ideal gas constant and $c_e$ is the electrolyte concentration in solution phase. The overpotential ${\mathsf{\eta }}_j$ is expressed as follows:

$${\mathsf{\eta }}_j={\mathsf{\varphi }}_{1,j}-{\mathsf{\varphi }}_{2,j}-U_j$$

(11)

where ${\mathsf{\varphi }}_{1,j}$ is the solid phase potential, ${\mathsf{\varphi }}_{2,j}$ is the solution phase potential and $U_j$ is the open circuit voltage of the electrode which is dependent on the state of charge of the electrode. In this study, empirical relations were used for the U_p of the LFP cathode and the U_n of the graphite anode taken from Schimpe et al. [42] which were fitted to open circuit voltage data from the paper of Safari et al. [43]. The solution phase is simplified as a nonlinear resistor so the potential drop between the positive and negative electrodes in the solution phase is given by the equation:

$${\mathsf{\varphi }}_{2,p}-{\mathsf{\varphi }}_{2,n}=I{R}_{cell}$$

(12)

The cell voltage can be expressed as the difference of solid phase potential between the positive and negative electrodes:

$$V_{cell}={\mathsf{\varphi }}_{1,p}-{\mathsf{\varphi }}_{1,n}$$

(13)

An explicit expression for the cell voltage can be derived from Equations (10)–(13):

$$V_{cell}=U_p-U_n+\frac{2RT}{F}ln\left(\frac{\sqrt{m_p^2+4}+m_p}{2}\right)+\frac{2RT}{F}ln\left(\frac{\sqrt{m_n^2+4}+m_n}{2}\right)+I{R}_{cell}$$

(14)

where:

$$m_p=\frac{I}{F{k}_p{S}_p{C}_{s,p,max}{c}_e^{0.5}{\left(1-x_{p,surf}\right)}^{0.5}{x}_{p,surf}^{0.5}}$$

(15)

$$m_n=\frac{I}{F{k}_n{S}_n{C}_{s,n,max}{c}_e^{0.5}{\left(1-x_{n,surf}\right)}^{0.5}{x}_{n,surf}^{0.5}}$$

(16)

Using Equation (14), the cell voltage can be calculated directly from the state of charge of the positive and negative electrodes. The high reaction constant values of k_p = 1 × 10⁻⁹ m^2.5/mol^0.5 s and k_n = 5 × 10⁻¹¹ m^2.5/mol^0.5 s [44] were used for the LFP cathode and the graphite anode, respectively. An explicit finite volume/finite difference scheme [45,46] has been used for the solution of the diffusion partial differential Equation (1), adjusting the time step, Dt, so that: D_s,j Dt/Dr² ≤ 0.25 to ensure numerical stability (Dr is the spatial interval in the radial direction r of the particle).

2.2. Equivalent Circuit Model

Figure 1 presents the general equivalent electric circuit model created to represent a cycled battery cell. It consists of constant phase elements (CPE) and resistances (R). A CPE is a hybrid capacitor-resistor with the real and imaginary impedance components, Zre_CPE and Zim_CPE, given by the relations:

$$Zr{e}_{CPE}=\frac{1}{Q{\omega }^n}\cos \left(-\frac{n\pi }{2}\right) Zi{m}_{CPE}=\frac{1}{Q{\omega }^n}\sin \left(-\frac{n\pi }{2}\right)$$

(17)

where w is the angular frequency and n and Q are empirical parameters: if n = 1, the CPE is a pure capacitor of capacitance Q; if n = 0, the CPE is a pure resistor of resistance 1/Q.

The EECM components represent the following battery characteristics: R1 represents the electrolyte and electrodes resistance, the Voigt circuit elements, VCE1 and VCE2 represent the contact resistance at the anode/current collector and cathode/current collector interfaces, VCE3 and VCE4 represent ion transfer through the pore hierarchy of the solid electrolyte interfaces (SEI) and electrode coating at the anode and the cathode. The parameters of the EECM will be fitted from the Nyquist curve of electrochemical impedance spectroscopy data in this study. The EECM will be then employed to simulate the galvanostatic charge-discharge stages of battery cycling, where the angular frequency, w (in rad s⁻¹), is considered as a function of the charge or discharge time, t_charge and t_discharge, respectively [4,47]:

$$\omega =\frac{\pi }{t_{charge}} or \omega =\frac{\pi }{t_{discharge}}$$

(18)

The total battery voltage is the sum of the EECM voltage and the open circuit voltage, V_OC, according to the relation:

$$V_{TOT}=V_{R1}+V_{VCE1}+V_{VCE2}+V_{VCE3}+V_{VCE4}+V_{CPE7}+V_{OC}$$

(19)

The voltage differences in Equation (19) are calculated as: V_R1 is the product of R1 and the current; V_VCE1, V_VCE2, V_VCE3, V_VCE4, V_VCE7 are calculated as V_CPE1, V_CPE2, V_CPE3, V_CPE5, V_CPE7, where the voltage drop across each CPE is the sum of the product of the real impedance and the current, and the voltage drop related to the reactance (i.e., the capacitive element of CPE).

At every timestep, V_OC is expressed as a sixth order polynomial of the state of charge, SOC, where the empirical polynomial coefficients a_k are fitted against the experimental data at very low C-rate (0.05 C in this study) following regression analysis [39,40]. The SOC is a function of the maximum capacity, Q_max, of the battery which is adjusted with cycling, according to an artificial intelligence function that adjusts Q_max at cycle ic on the basis of the Q_max variation from the previous cycles obtained from historical experimental data.

3. Materials and Methods

2032 coin-cells were fabricated in the form of full (C-LFP) and half battery cells (C-Li and Li-LFP). Each cell was of an area of 1.77 cm². The LFP cathode was a 60 mm thick coating of 80 wt% LFP (Hi Group, Korea), 15 wt% SuperP carbon (particle size d₅₀ = 40 nm, BET = 62 m² g⁻¹, bulk density 160 kg m⁻³, TIMCAL, Belgium) and 5 wt% binder on carbon-coated aluminium foil (MTI, US) as current collector. The C anode was a 30 mm thick coating of 90 wt% graphite (artificial graphite, particle size d₅₀ = 19–23 mm, tap density of ≥990 kg m⁻³, BET ≤ 4.2 m² g⁻¹ MTI, US), 5 wt% acetylene carbon black (average particle size 42 nm, specific surface area, BET = 75 m² g⁻¹, bulk density 170–230 kg m⁻³, Alfa Aesar, UK) and 5 wt% binder on carbon-coated copper foil (MTI, US) as current collector. For the half cells, the Li anode was in the form of foil (Sigma Aldrich, UK). The separator was a bilayer of a glass fiber (GF/F) filter and Celgard 3501. 300 ml of electrolyte 1 M LiPF₆ in ethylene carbonate/dimethyl carbonate EC/DMC 50:50 v/v (Sigma Aldrich, UK) was added in each cell. Three binders were investigated, all supplied in powder form: PVDF of MW = 534,000 (Sigma Aldrich, UK), KynarFlex^® PVDF 2801-00 (Arkema, France) a PVDF copolymer of melting point T_m = 143 °C, and Kynar PowerFlex^® LBG (Arkema, France) a semicrystalline, high molecular weight copolymer of vinyl F₂ of T_m = 154 °C.

Initially, LFP and graphite powders were dried separately in a static oven at 120 °C overnight to remove moisture from the sample. For the LFP electrodes, 12 g LFP powder and 2.25 g SuperP carbon powder were mixed and ground using an Agate mortar and pestle for 45 min. A slurry was prepared adding 55 mL solvent to this powder mixture and kept under magnetic stirring for 1 h [48]. Then the mixture was heated under magnetic stirring to evaporate the excess solvent, where a 10% solution of the required amount of binder was added in the last half-hour of stirring. The formed paste was coated onto the current collector foil using a dogbone-shaped coating tool at 60 mm gap, aiming for a 60 mm thick coating. The solvent was NMP for the PVDF binder and acetone for the two Kynar^® binders. The LFP electrode coatings prepared using NMP as solvent were dried in a static oven at 80 °C overnight. The obtained electrodes were cut into 15 mm discs and dried in a vacuum oven at 120 °C for 2 h before transferring them to a glovebox. LFP electrode coatings prepared using acetone as solvent were dried at room temperature for two days to remove the solvent. Finally, all the prepared LFP electrodes were evacuated in the glovebox antechamber overnight to remove any remaining solvent/moisture from the electrode surface.

The preparation of the graphite electrode coating was similar. Mixtures in two separate glass containers, 9 g graphite added to 25 mL solvent and 0.5 acetylene carbon black added to 25 mL solvent, were prepared. Each mixture was sonicated in a bath for 30 min, followed by magnetic stirring for 30 min. 0.5 g binder was dissolved in 10 mL solvent. The two mixtures and binder solution were mixed and magnetically stirred for 1 h. Then the mixture was heated under magnetic stirring to evaporate the excess solvent and the paste was coated onto the current collector foil with the dogbone coating tool set at 30 mm gap, aiming at 30 mm thick coating. The graphite coatings with the KynarFlex^® PVDF 2801-00 binder and the Kynar PowerFlex^® LBG binder pealed easily off the current collector foil and it was not possible to be used in coin cell fabrication. As a result, anode coatings were investigated only with the PVDF binder.

Furthermore, wet adhesion tests were carried out for accelerated durability testing of the cathode coating with different binders. For each coating, 10 samples of 25 × 25 mm were soaked in the electrolyte solution EC/DMC for 12 h. Next, each sample was removed and cross-cuts were made with a sharp razor blade according to ASTM D3359-02 to create squares of about 7 × 7 mm each. The coatings were left to dry and the cut lines were first observed. Then an adhesive tape was smoothed over each square and was pulled off rapidly. The area portion removed by the adhesive tape in each square was then measured.

Overall, the electrode coatings were examined under the high-resolution scanning electron microscope HR-SEM JEOL-7100 F in SEM and EDX (energy dispersive X-ray analysis) mode before any testing (as prepared) and postmortem after 25 electrochemical test cycles. The cycled cells were disassembled in a glovebox under argon atmosphere, rinsed with dimethyl carbonate three times and then evacuated in the antechamber. Samples for postmortem SEM analysis were transferred in a sealed bag filled with argon gas.

XPS (X-ray photoelectron spectroscopy) was carried out using a Thermo Scientific K-Alpha⁺ XPS instrument. Spectra were obtained in constant analyzer energy mode with pass energies of 200 and 50 eV and a step size of 0.4 and 0.1 eV for survey and high-resolution spectra, respectively. A monochromated Al Kα X-ray source was used with a 400-μm radius spot. For data acquisition and analysis, Thermo Scientific Avantage V5.980 software was used. Transfer of samples from the glovebox to the spectrometer was achieved without exposure to the ambient atmosphere by the use of a Thermo Scientific Vacuum Transfer Module (VTM). This allows the postmortem samples to be prepared and mounted within the argon atmosphere of the glovebox. The VTM is then loaded into the entry lock of the K-Alpha⁺ spectrometer which is then pumped down in the usual manner. Once a high vacuum is achieved, the VTM is opened and the sample(s) are transferred to the analysis chamber for XPS.

The half and full battery cells were subjected to electrochemical testing using a Gamry Interface 1010E potentiostat. The electrochemical tests included electrochemical impedance spectroscopy (EIS) in potentiostatic mode in the frequency range of 10 mHz–1 MHz; cyclic voltammetry (CV) at five different scan rates; and galvanostatic charge-discharge (GCD) cycling at 0.05 C.

4. Results

4.1. Experimental Results

After the cathode coatings with the different binders were prepared, they were first subjected to adhesion testing as a form of accelerated durability test. After they were soaked in the electrolyte solution for 12 h, they were cross-cut with examples of results presented in Figure S1A; the cuts in the coatings with PVDF binder and KynarFlex^® PVDF 2801-00 binder are invisible in the images and in reality they were barely defined on the surface of the coating, never reaching the current collector foil; however, the cuts in the coating with Kynar PowerFlex^® LBG binder are clearly visible all the way to the current collector foil, with a cut width of 0.8 ± 0.2 mm on average for all samples, indicating that the coating with this binder had weak wet scratch resistance. After stage B of the adhesion test (Figure S1B), it was found that the KynarFlex^® PVDF 2801-00 binder induced excellent adhesion strength with only 1.0 ± 0.5% of the coating mass removed by the adhesion tape. This was not the case with the other two binders: the coating with the PVDF binder was the worst with 95 ± 2% of its mass removed, and the coating with the Kynar PowerFlex^® LBG binder had 76 ± 2% of its mass removed by the adhesive tape.

Figure 2 presents the SEM micrographs of the LFP coatings with different binders, as prepared and postmortem after 25 electrochemical cycles of half cells. The images in Figure 2(a1,b1,c1) reveal the microstructure and degree of particle segregation in the LFP coatings, as prepared, which is quantified in the particle size distribution graphs in Figure 2d–f. The high resolution SEM images in Figure S2 reveal that particles of about 200–500 nm size in the coating with the PVDF binder are homogeneously dispersed with some small aggregates of about 1 mm size. Particle segregation is observed for the coating with the Kynar PowerFlex^® LBG binder in Figure S2(c1), with aggregates of up to about 5 mm. The PSDs in Figure 2d–f. show that the coating with the PVDF binder has the greatest number of small particles, up to 10 mm diameter, compared to the other two Kynar copolymer binders. The PSDs also reveal that the coatings with the KynarFlex^® PVDF 2801-00 binder and the Kynar PowerFlex^® LBG binder have 73% and 14% more particles greater than 50 mm, respectively, than the coating with the PVDF binder, indicating particle segregation in the coatings with the Kynar copolymer binders. This is attributed to the sticky nature of the flexible component in the Kynar copolymers, as it was also proven from the adhesion test in which the PVDF binder created the worst adhesion in the coating. Some cracks are observed in the coating with the Kynar PowerFlex^® LBG binder in Figure 2(c1), which can be attributed to the more brittle character of this highly crystalline binder. In fact, pin-holes were visible to the naked eye in this coating.

Postmortem characterization of the LFP coatings after battery cycling show flattened microstructures with original small gaps between particles now totally bridged with the formed SEI. More detail of the formed SEI around small particles in the higher magnification images is seen in Figure S2(A2,B2,C2) (postmortem) against Figure S2(A1,B1,C1) (as prepared). The PSDs in Figure 2d–f show clearly that the number of small microparticles is reduced in all postmortem coatings, as well as the specific surface area, especially for the coatings with the PVDF and the KynarFlex^® PVDF 2801-00 binder. It must be noted that the information available in the PSDs and the SEM micrographs in Figure 2 covers only microparticles. Nanoparticles and cracks of nanosize width would increase the surface area available for the redox battery reactions.

XPS analysis was carried out for each binder with the results presented in Figures S3–S5: PVDF consists of 49.7 at% C (C1s at 286.4 eV), 50.1 at% F (F1s at 688.1 eV) and 0.2 at% O (O1s at 532.7 eV); KynarFlex^® PVDF 2801-00 contains 47.7 at% C (C1 at 286.4 eV), 52 at% F (F1s at 688.2 eV) and 0.3 at% O (O1s at 533.8 eV); Kynar PowerFlex^® LBG binder contains 53.2 at% C (C1s at 285 eV), 13.4 at% F (F1s at 688.5 eV) and 23.6 at% O (O1s at 532.1 eV).

Figure 3, Figure 4 and Figure 5 present the XPS spectra of the surface of the LFP coating with different binders, as prepared (a1) and after 25 cycles of battery testing (a2). Figure 3 presents the XPS spectra of the surface of the LFP coating with the PVDF binder. The main C1s peak at 285 eV denotes the C–C bonds in PVDF and SuperP carbon which reduces substantially after battery cycling, possibly due to the SEI formation on top of the surface of the original LFP coating. There is also a second C1s peak at 291 eV characteristic of CF₂ in PVDF and the O=C–O group [49], which is possibly present in SuperP carbon. A peak around 55.4–55.9 eV in Table S1 represents the combination of the Fe3p and Li1s peaks, hence, it is very difficult to distinguish and determine the lithium concentration in the LFP cathode from XPS. The Fe2p3/2 peak at 713 eV characteristic of FePO₄ is considerably reduced after cycling, attributed to thick SEI formation over the LFP coating, as XPS can detect surface features to very small depth of the order of 10 nm; for this reason, no Fe2p peak fit is produced for the cycled specimen (a2). Figure 3(a1) exhibits both P2p at 134 eV and P2s at 192 eV, which decreases in postmortem after battery cycling in Figure 3(a2) (in fact, the weak P2s peak disappears) due to the formation of the thick SEI layer. Given the dominance of the P2p over the P2s peak, XPS data quantification in Table S1 is based on the P2p peak. Further analysis of the P2p peak in Figure 3 denotes the P2p3/2 peak at 133.4 eV, characteristic of PO₄ in C_xH_y environment, present in coatings both before and after cycling, with the additional peak P2p at 137 eV characteristic of Li_xPF_yO_z in the LFP coating after 25 cycles, denoting a side reaction in the electrolyte with moisture or oxygen traces [50]. The O1s peak at 532 eV, characteristic of PO₄ but also in C–O, does not broaden after cycling as observed in previous studies of Li-LFP cells [51], but increases in intensity due to the oxygen of the electrolyte solvents. The F1s peak around 688 eV, indicating the PVDF binder, remains at the same position before and after cycling with a distinct shoulder at 684.9 eV after cycling, which is assigned to LiF [52]. Hence, the SEI seems to consist of a considerable amount of epoxide groups (C–O–C) and some LixPF_yO_z and LiF.

Similar trends are observed for the LFP coatings with KynarFlex^® PVDF 2801-00 and Kynar PowerFlex^® LBG binders in Figure 4 and Figure 5, respectively. The LFP coating with KynarFlex^® PVDF 2801-00 contains a significant proportion of C–O–C groups before any cycling, as shown in the C1s spectrum in Figure 4, which is reduced after cell cycling. Tables S1–S3 present the XPS quantification data for the coatings with the three binders, demonstrating increased content of lithium (Li1s) and oxygen (O1s) after cell cycling, consistent with a formed SEI containing LiF, C–O–C groups and some LixPF_yO_z. Careful observation of all individual element peaks in Figure 3, Figure 4 and Figure 5 reveals some shifts to lower energies after battery cycling, possibly uncovering the presence of more compounds on the SEI surface. More specifically: the C1s peak is at the same binding energy of 284.98 eV before and after cycling for the two coatings (Figure 3 and Figure 4), but shifts to 284.88 eV postmortem for the coating with the Kynar PowerFlex^® LBG binder in Figure 5; this indicates the addition of C–O–O functionality for this coating after battery cycling which may be attributed to alkyl carbonates (RCO₂OLi) originating from the decomposition of carbonate solvent by ring opening and polymerization. The C1s peak at 291.2 eV related to the CF₂ group in the binders is also shifted to lower energies of 289.9–290 eV after battery cycling for all coatings, which is also attributed to the presence of Li₂CO₃ generated from the decomposition of the carbonate solvents. The F1s peak moves from 688.1–688.8 eV to 687.3–687.8 eV after battery cycling for all coatings, which indicates ionic bonding of F with a metal and is attributed to the formation of LiF. The P2p peak is shifted from 133.88 eV to 133.58 (PVDF and KynarFlex^® PVDF 2801-00 binders)-133.78 eV (Kynar PowerFlex^® LBG binder) after battery cycling, indicating the presence of Li_xPF_y produced from the reduction of the electrolyte salt LiPF₆ to LiF and Li_xPF_y.

Finally, comparing the F1s peak in the coatings with the different binders, Figure 3(a1) and Figure 5(c1) reveal an additional small fitted peak at 690.2 eV and 690.85 eV, respectively, which after extensive search in the NIST XPS database were found to indicate CF₂-CF₂ segments from the binder for the PVDF and the Kynar PowerFlex^® LBG binder; no such peak was fitted for the KynarFlex^® PVDF 2801-00 binder (Figure 4(b1)). After battery cycling, this peak disappears in Figure 5(c2) for the coating with the Kynar PowerFlex^® LBG binder, attributed to the fact that the binder is concealed under the thick SEI layer. However, Figure 3(a2) reveals that for the coating with the PVDF binder, after cycling, new small peaks are fitted at 690.6, 690.1, 688.9 and 687 eV, which correspond to CF₃, CF₂–CF₂, CH₂CHCOOCH₂CH₂(CF₂)_m(CF₃)_n and CHF–CH₂, respectively; the first and the two last groups indicate chemical changes in the PVDF binder in the presence of the electrolyte during the battery cycling.

Figure 6 presents SEM/EDX micrographs of the LFP coatings with different binders, as prepared, and postmortem after 25 electrochemical cycles of half-cells. This technique detects elements not just at the surface but deeper under the surface to about 1–2 mm, depending on element size. As a result, it goes deeper than just the surface microstructure displayed in Figure 2 and the PSDs before and after battery cycling in Figure 2 that indicate particle aggregation due SEI formation on the surface layer. It also goes deeper than the XPS analysis of just a surface layer of about 10 nm, consisting of the SEI after battery cycling. The element mapping from the EDX analysis reveals the microstructure of the LFP particles under the SEI layer, as well as elements from the SEI layer. For the PVDF and KynarFlex^® PVDF 2801-00 binders, it can be seen that in the postmortem micrographs Fe and F from LFP are evenly distributed at the micron level, and O seems more micro-fragmented after 25 cycles of Li⁺ ion intercalation and deintercalation, indicating that LFP particles are expanded possibly due to Li⁺ ion insertion, while the bridging of small interparticle gaps observed in the SEM images of Figure 3 might be due to this LFP particle expansion and filling and covering of the gaps with the SEI layer. Kynar PowerFlex^® LBG binder, involved in particle agglomeration in the as prepared electrode, provides an even distribution of Fe in Figure 3(c1), before any cycling, so it is difficult to observe the cycling effects on the Fe EDX map. However, micro-fragmentation can be observed in the O and F EDX maps of the postmortem sample in Figure 3(c2) for this binder as well.

Figure 7 presents the Nyquist plots from the EIS tests of the Li-LFP battery cells as fabricated and pre-cycled. It is thought that differences between the ESR (equivalent in series resistance) values between the cathodes with different binders are due primarily to the different loading of the LFP coatings. Differences in the electrochemical double layer (EDL) capacitance (1/Zim at the lowest frequency) are also observed between the different LFP coatings, with the LFP coating with the PVDF binder exhibiting the lowest EDL capacitance. It seems that particle aggregation in the LFP coatings with either of the two Kynar^® binders, observed in the SEM images in Figure 2, reduces the micropore size which enhances the EDL capacitance for the small Li⁺ ions [28,29] as it has been established that the highest EDL capacitance is achieved when the micropores are close to the size of the electrolyte ions.

Figure 8 presents the results of the GCD tests for the Li-LFP cells for the three different binders in the LFP coating. All cells present a discharge capacity of 152 ± 1 mAh/g_LFP. The LFP cathode with the PVDF binder exhibits the flattest plateau in both charge and discharge, indicating the lowest resistance in Li⁺ ion diffusion. Apart from the higher ion resistance in the LFP coatings with the other two binders, these also show lower coulombic efficiency between charge and discharge than the LFP coating with the PVDF binder.

CV tests were carried out in half cells at different scan rates and the results were used to determine the diffusion coefficient of Li⁺ ions, D_Li⁺, in the electrode, employing the Rendles-Shevchik equation [53]:

$$I_{peak}=2.69\times {10}^5{n}^{1.5}A{D}_{{Li}^{+}}^{0.5}{r}^{0.5}c$$

(20)

where I_peak is the peak current (A) in the voltammogram, n is the number of electrons in the electrochemical process, A is the electrode area (cm²), r is the CV rate (V s⁻¹) and c is the initial concentration of Li⁺ in the anodic process and of the vacancies in intercalates in the cathodic process (mol cm⁻³). It has been suggested [53] that the specific surface area of LFP particles may be given by the following relation, as a function of the particle radius, R_p, and density r = 3600 kg m⁻³:

$$A_{sp}=\frac{3}{R_p\rho }$$

(21)

A mean LFP particle diameter of 450 nm was estimated from the SEM micrographs in this study, yielding A_sp = 3700 m² kg⁻¹. Figure 9a presents CV graphs for a Li-LFP cell with PVDF binder in the cathode and the linear fits of the Rendles-Shevchik equation to a correlation factor R² = 0.998. Considering the initial concentration of Li⁺ ions in the cathode: c_Li⁺ = 0.02282 mol cm⁻³ and the same A_sp value as cycling progresses, the anodic process fit yields the anodic diffusion coefficient values: D_Li⁺,anodic = 2.02 × 10⁻¹⁴ (6th cycle), 1.98 × 10⁻¹⁴ (7th cycle), 1.92 × 10⁻¹⁴ (8th cycle) cm² s⁻¹, describing the rate of deintercalation of Li⁺ ions from LFP. Assuming the same concentration c = 0.02282 mol cm⁻³, the cathodic process fit yield the cathodic diffusion coefficient values: D_{Li⁺,cathodic} = 1.26 × 10⁻¹⁴ (6th cycle), 1.21 × 10⁻¹⁴ (7th cycle), 1.24 × 10⁻¹⁴ (8th cycle) cm² s⁻¹, which are about 60% of the D_Li⁺,anodic values. Our anodic diffusivity values are in total agreement with Galaguz et al. [53] and our cathodic diffusivity values are higher than theirs, where their D_{Li⁺,cathodic} values are 50% of their D_Li⁺,anodic values [53]. In general, it is evident that our cathodic I_peak values in the intercalation process and the corresponding gradient are 79% lower than our anodic I_peak values and gradient, possibly due to (a) the smaller number of vacancies during intercalation compared to the number of Li⁺ ions in the cathode for deintercalation and (b) lower diffusion coefficient during intercalation compared to the easier deintercalation process. This results in inefficiency between charge and discharge.

The CV results for the Li-LFP half cell with cathode binder KynarFlex^® PVDF 2801-00 binder are presented in Figure 9b. Clearly, the CV displays wide peaks indicating a highly controlled cycle by diffusion, with additional evidence of the higher resistance for this cell with this cathode binder (Figure 7) in the anodic step. The CV plots display a wider difference of anodic-cathodic potential peaks for Li-LFP(2801), DE_o = 0.43 V at 0.03 mV s⁻¹ and 0.85 V at 0.14 mV s⁻¹, compared to DE_o = 0.23 V at 0.03 mV s⁻¹ and 0.40 V at 0.14 mV s⁻¹ for Li-LFP(PVDF), consistent with a more diffusion-controlled process for Li-LFP(2801). The linear fits of the Rendles-Shevchik equation produced lower gradient values for Li-LFP(2801) (correlation factor R² = 0.971) than for Li-LFP(PVDF), which further yielded a much lower diffusion coefficient for Li-LFP(2801): D_Li⁺,anodic = 1.39 × 10⁻¹⁵ cm² s⁻¹ (three cycle average) and D_{Li⁺,cathodic} = 0.88 × 10⁻¹⁵ cm² s⁻¹ (three cycle average), with the cathodic value also about 60% of the anodic value.

Figure 9c presents the CV plots for the Li-LFP half-cell with Kynar PowerFlex^® LBG binder in the cathode. Sharp peaks are encountered with difference of anodic-cathodic potential peaks: DE_o = 0.23 V at 0.03 mV s⁻¹ and 0.41 V at 0.14 mV s⁻¹, similar to that of the Li-LFP(PVDF) half-cell. The determined diffusion coefficients from the linear fits of the Rendles-Shevchik equation (correlation factor R² = 0.993) for the Li-LFP(LBG) half-cell are: D_Li⁺,anodic = 2.65 × 10⁻¹⁴ cm² s⁻¹ (three cycle average) and D_{Li⁺,cathodic} = 1.39 × 10⁻¹⁴ cm² s⁻¹ (three cycle average), with the cathodic value 52% of the anodic value. These diffusion coefficient values for the Li-LFP(LBG) half-cell are higher than those of the Li-LFP(PVDF) half-cell.

Figure S6 presents the results from the EIS and GCD electrochemical tests of the graphite-Li half cells. A discharge capacity of 310 mAh/g_graphite was measured in GCD tests at 0.05 C. Figure S7 presents CV plots for the graphite-Li half cells at different rates. All peaks are below 0.2 V in discharge which means that they correspond to lithium intercalation and SEI formation only, where peaks at higher voltages would indicate SEI formation due to the electrolyte (0.3–0.9 V) or SEI formation due to additives (1–1.4 V) [54]. The CV plot demonstrates multi-stage transitions [55,56,57] during the lithiation and delithiation of graphite that have been grouped to three oxidation (in charge) and three or four (at low voltage scan rate) reduction current peaks (in discharge). Table S4 presents the voltage values of these peaks identified from the voltage plateaus in the GCD curves in Figure S6.

Figure S8 presents the linear fits of the Rendles-Shevchik equation for all anodic and cathodic peaks of the CV plots of the graphite-Li half cells. Figure S8a shows that the fit equation for P_o1 has an intercept that indicates a systematic error in the determination of the baseline for all scan rates for this peak, which is the last peak at the highest voltage during the charge phase. No such issue is encountered for the rest of the oxidation and reduction peaks in Figure S8. Considering Equation (21), a mean graphite particle diameter of 21 mm and the graphite density of 2260 kg m⁻³, a graphite specific area A_sp = 126 m² kg⁻¹ is estimated for the graphite anode. A mean lithium concentration of 0.0314 mol cm⁻³ is assumed in the graphite anode, corresponding to the mean state of LiC₆, to calculate the diffusion coefficient of Li⁺ ions in graphite using the Rendles-Shevchik Equation (20). Table S5 presents the determined values of the diffusion coefficient for the three oxidation (intercalation) peaks and the four reduction (deintercalation) peaks. For peaks 1 and 2, the Li⁺ ion diffusion seems faster during intercalation than in deintercalation, with particularly slow deintercalation for the P_r1 peak.

4.2. Simulation Results

Figure 10a–e present the results of the computer simulations employing the SP model and their comparison with experimental data from the GCD tests. In some preliminary parametric simulation studies, it was observed that the higher are the ion diffusion coefficient and the surface area of the electrode, the higher is the capacity. All the diffusion coefficient values inputted in the simulations were the same as the values derived from the experimental CV data in Section 4.1. Figure 10a–c presents the results for the Li-LFP half cells for different cathode binders. To ensure a good fit between predictions and the experimental data of GCD tests, a 30(charge)–35% (discharge) higher S_p value was inputted in the simulations than what was assumed in Section 4.1 for the Li-LFP half-cell of cathodes with a KynarFlex^® PVDF 2801-00 binder; this is attributed to the fragmentation of LFP cathode during cycling, which, although it would contribute to an increased capacity, might also increase the cathode resistance. A second order relation of cell resistance against SOC (or 1-SOC) was needed to fit the GCD curves at the end of each GCD stage for cathodes with KynarFlex^® PVDF 2801-00 binder and Kynar PowerFlex^® LBG binder. On the other hand, the surface area of the cathode of the Li-LFP(LBG) half-cell had to be reduced by 34 (charge)–42% (discharge) to fit the experimental GCD capacity, which can be attributed to the large degree of aggregates exhibited in the LFP(LBG) coating after preparation (Figure 6(c1)). Similar treatment had to be applied in the simulation of the Li-LFP(PVDF) half-cell, where the surface area of the cathode had to be reduced by 23 (charge)–27% (discharge) to obtain a good fit between predictions and experiment, although the resistance was independent of the SOC for this particular cell that exhibits approximately a flat potential curve during the GCD cycle. Figure 10d presents the results for the graphite-Li half-cell. The value for the graphite area inputted in the simulations was the same as the area value used for the fitting of the CV peaks in Section 4.1. The cathodic values for the four diffusion coefficients covering multistage transitions in the anode and presented in Table S5 were inputted in the simulations for both the charge and discharge phase and yielded the simulation lines presented in Figure 10d, which is in good agreement with the experimental data.

Finally, using the same input parameters for the anode and cathode as those used in the half cells, the GCD cycle of a full graphite-LFP battery cell was simulated employing the SP model, and the results are presented in Figure 10e together with the experimental data of five GCD cycles. It can be seen that the simulated GCD curves have a higher capacity than the experimental curves, apart from the first experimental charge curve which exhibits a long capacity as expected, which is associated with the formation of the SEI layer primarily on the graphite anode. The capacity of the experimental graphite-LFP cell in Figure 10e was limited by the mass of the LFP in the cathode. During discharge, given the limited mass of lithium intercalating the anode, it was considered that no large influx of Li⁺ ions would occur in the cathode and, hence, it was assumed that no fragmentation of the cathode would take place: therefore, the S_p value was not increased in the simulation model for the full cell in Figure 10e (unlikely the simulation model in Figure 10b for the half cell). The lower capacity of the experimental data compared to the SP model predictions in Figure 10e and slow capacity reduction with cycling are attributed to clogging of the pores due to byproducts from electrolyte reactions, reduction of the diffusion coefficients of the electrodes and diminishing of the Li⁺ ion supply. The latter is a serious problem for the graphite-LFP cells, whereas this was not the case for half cells which had an abundant reservoir of pure lithium.

The next step was to proceed with GCD simulations of the graphite-LFP battery cell using the EEC model. Figure 11a,b depict the fitting of the EEC model against the experimental EIS data before cell cycling and after 5 GCD cycles, respectively. It is clear the pre-cycling Nyquist plot presents only the typical contact resistance between electrodes and the current collector, whereas after cycling there is a substantial addition of a shoulder indicating the formed SEI. Table S6 presents the values of the fitted parameters of the EECM, pre-cycling and after 5 GCD cycles. R1 and R3 reduced after cycling, possibly due to better electrolyte wetting and improvement of one of the two electrode/current collector interfaces. R2 remains the same before and after cycling. For VCE3, R4 almost doubles while CPE4 becomes more resistive after cycling, indicating increased resistance to ion diffusion after cycling, while also the pore surface is decreased, reducing the capacitance of CPE3. The new EECM feature after cycling is the emergence of the VCE4, with a huge R5 resistance but also considerable capacitance in CPE5: this new feature is attributed to the formation of SEI on the anode side with large resistance to ion transport but also considerable pore surface area to generate capacitance in CPE5.

Figure 11c displays the comparison between the predictions of the EECM and the experimental data for the fifth GCD cycle of the graphite-LFP battery cell, where the EECM parameters were the same as those determined from the fit of the Nyquist plot in Figure 11b and the maximum capacity for the fifth cycle was adjusted according to the trend of the historical experimental data for GCD cycles one to four. It can be seen that the agreement between the predictions and the experimental data is much better for the EEC model (Figure 11c) than for the SP model (Figure 10e). Further to this, the experimental GCD cycling of the graphite-LFP battery cells was continued to 100 cycles with the data presented in Figure 11c. The battery capacity values as a function of cycle number were fit to a logarithmic relation up to the 50th cycle, as presented in Figure S9. This relation was then used in the EECM to predict the battery performance for the 100th cycle, while the rest of the parameters of the EEC model were maintained the same as in the fit of Figure 11b, assuming that the SEI does not change much after the fifth cycle. The predictions for the 100th cycle are presented in Figure 11c and are not that far from the corresponding experimental data, apart from the shape of the curve turning to the final voltage towards the end of the charge or discharge cycle indicating increased resistance in final ion diffusion.

5. Discussion and Concluding Remarks

A comprehensive study of LFP batteries has been presented, including electrochemical testing of half and full cells, microstructural images and surface composition maps and overall data for the cathodes for coatings as prepared (pre-cycling) and postmortem after 25 cycles, determination of the diffusion coefficients in the different redox processes in the cathode and anode from CV plots, and battery cell simulations using the SP model and the EEC model.

Three different binders were investigated for the cathode, where the KynarFlex^® PVDF 2801-00 binder and the Kynar PowerFlex^® LBG binder were explored, as they could be dissolved in acetone, which is a solvent with a much lower boiling point than NMP, the usual solvent for the PVDF binder. In an accelerated durability assessment of the cathode coatings via wet adhesion tests it was found that the coating with the KynarFlex^® PVDF 2801-00 binder has excellent adhesion strength, the next best is that with the Kynar PowerFlex^® LBG binder, and the worst is that with the PVDF binder. In terms of scratch resistance, the worst cathode coating is that with the Kynar PowerFlex^® LBG binder, while the other two binders induce excellent scratch resistance. As a result of the adhesion properties, it was found that cathode particle aggregation was easier in cathode fabrication when using either of the two Kynar^® binders compared to PVDF, with the latter exhibiting a large number of nano and small microparticles due to its poor adhesion properties which discourage particle aggregation. On the other hand, EIS and CV tests revealed that the cathode with the KynarFlex^® PVDF 2801-00 binder had the highest resistance and the lowest Li⁺ ion diffusion coefficient attributed to the sticky, insulating copolymer. The cathode with PVDF binder had the highest Li⁺ ion diffusion coefficient attributed to the open channels left free by PVDF, which does not stick so well on the LFP particles as the Kynar copolymers. Hence, it seems that the LFP cathode with the PVDF binder favors ion diffusion and presents the flattest voltage plateau to the end of the change and discharge phase in the GCD cycles of half-cells in the initial cycles. However, in a heavy-duty battery, possibly also with the production of gas after thousands of cycles, the PVDF binder would run the risk of coating delamination from the current collector, increasing the contact resistance and ultimately shortening the battery lifetime.

Postmortem characterization of cathodes revealed the expected phenomena associated with battery aging that was also encountered in previous studies [11,12]: pore clogging due to the formation of SEI (in all cathodes with either of the three binders) including Li_xPF_yO_z due to side reactions of electrolyte with traces of moisture or oxygen, LiF and Li_xPF_y due to the reduction of the electrolyte salt LiPF₆, epoxide groups from RCO₂OLi and Li₂CO₃ due to the decomposition of the carbonate solvents, and surface cracking and fragmentation. Graphite-Li half cells exhibited multistage transitions corresponding to lithium intercalation and SEI formation, which was also observed and analyzed in several studies in the literature [55,56,57]. The full graphite-LFP cell demonstrated lower capacity than the half-cell capacity, which has been attributed to the loss of active Li⁺ material [11] that could not be replaced from a large reservoir, as with the Li electrode reservoir of the half cells.

In modeling the battery cells, at first a simple SP model was employed to study the physicochemical processes in the battery cells, with the emphasis of Li-ion diffusion for which data were provided from the fitting of CV graphs using the Rendles-Shevchik equation for both anode (with PVDF binder) and cathode electrodes with all three binders. The further adjustments of the cathode surface area in the SP model simulations for the predictions to fit the experimental data provide additional insight of pore clogging due to SEI formation (surface area decreased) or particle fragmentation (surface area increased). In this manner, the SP model simulations contribute to the understanding of some aging effects during battery cycling. However, the simple SP model was unable to replicate the GCD curves of the full cell from the input data derived from the half cells. Furthermore, it would be rather complex to adjust the active area of cathode and anode, and the diffusion coefficients as a function of the number of cycles, in order to predict future battery cell behavior and lifetime using the SP model. As a result, the SP model is recommended for the study of specific physicochemical effects and would be easier to fit its parameters for a half cell.

On the other hand, the EEC model proved much easier to adapt, with fewer parameters to adjust as a function of the number of cycles on the basis of historical data of cell testing. This and the good agreement between EECM predictions with the experimental data of a “future” GCD cycle of a full graphite-LFP battery cell offer great promise for the EEC model to be able to forecast future battery behavior and the lifetime of batteries. This is used for batteries in transport applications, the grid, or consumer goods, so that the replacement time of a battery or the remaining time of a recycled battery can be predicted. Furthermore, the EEC model can be employed in the energy management of batteries, for example to establish an optimized schedule for battery charge and operation depending on the predicted battery state-of-health. Still, the modeling approach proposed in this study to predict future behavior and the lifetime of a Li-ion battery is based on the known cycling history of the battery. Therefore, our recommendation is to equip each battery with the memory storage of its operational history.