Modeling and synthesis of carbon-coated LiMnPO 4 cathode material: Experimental investigation and optimization using response surface methodology

25, 2022 Abstract Nanostructured LiMnPO 4 cathode materials for lithium-ion batteries (LIBs) have been successfully prepared by a modified solvothermal method under controlled conditions. Polyethylene glycol (PEG-10000) was used as a solvent to optimize the particle size/mor-phology and as a carbon conductive matrix. In order to investigate the effect of synthesis parameters such as concentration of PEG-10000, reaction time and reaction temperature on the LiMnPO 4 phase purity, Response surface methodology was carried out to find variations in purity results across the composition. The purity of all materials was checked using HighScore software by comparing the matched lines score to ones of reference data. As a result, it has been found that the pure phospho-olivine material LiMnPO 4 can be synthesized using the following optimum conditions: PEG concentration = 0.1 mol l -1 , reaction time = 180 min, and reaction temperature = 250 °C. The as-prepared LiMnPO 4 under optimum conditions delivered an initial discharge capacity of 128.8 mAh g -1 at 0.05 C-rate. The present work provides insights and suggestions for optimizing synthesis conditions of this material, which has been considered the next promising cathode candidate for high-energy


Introduction
Rechargeable lithium-ion batteries (LIBs) with high-energy, high power density, durability, and lightweight have become the most requested energy source in order to meet future society's needs in many renewable energy storage systems, starting from laptops, cell phones to electric vehicles. With the increasing demand for higher capacity and improved safety, many efforts have been made to further develop the next generation of LIBs with high volumetric/gravimetric energy density. Most commercial LIBs are currently based on LiCoO2 layered structure as a cathode material. Therefore, one of the main challenges is to replace the commercialized layered structure cathode (which exhibits a theoretical specific capacity of 274 mAh g -1 ) with other promising and efficient cathode materials.
LiMPO4 (M = Fe, Mn, Co, Ni) olivine-based high-performance cathodes are the recommended alternative cathode materials to replace traditional ones (LiCoO2) due to their low cost, non-toxicity, high thermal and cyclic stability, and environmental impact [1][2][3][4][5]. Compared to the first commercialized cathode, which is LiFePO4, LiMnPO4 is considered as the most promising cathode material in the next generation of lithium-ion batteries due to the high theoretical energy density (701 Wh/kg), which is higher than that of LiFePO4 (586 Wh kg -1 ) [6,7]. Moreover, the low voltage (4.1 V vs Li/Li + ) of LiMnPO4, which is positioned within the stable window of the most commercialized electrolytes, makes it the best candidate material compared to LiCoPO4 and LiNiPO4, which have higher potentials, being respectively 4.8 and 5.1 V vs. Li/Li + [8][9][10].
The synthesis process was also considered a direct approach to achieving desired performances. For this reason, several methods have been applied to prepare LiMnPO4 with high purity, such as spray-pyrolysis [22,27], sol-gel method [28,29], hydrothermal synthesis [30][31][32][33], precipitation method [34,35] and solution combustion process [36,37]. Among all these methods, some selected ones offer more advantages such as morphology control, better homogeneity, submicron-sized particles, and larger specific surface area with increased electrochemical performances [38,39]. The solvothermal technique has significant assets compared to other methods such as simplicity to handle, short reaction time, moderate reaction temperature, good crystallinity and high purity [40,41]. The process is widely used for preparing various micro and nanostructured materials such as cathodes/anodes, oxides, semiconductors, ceramics, etc. However, morphology and particle size are difficult to control since they are determined by many factors such as precursor types, additives or surfactants, pH, reaction time/temperature, and physico-chemical properties of the used solvent. Polyethylene glycol (PEG) is an organic solvent that can be easily adsorbed on the crystal's surface by hydrogen bonding, consequently influencing nucleation and crystallite growth.
Based on these advantages of PEG, we report in this work the synthesis of LiMnPO4 cathode material under solvothermal conditions, using the PEG-10000 as a solvent to optimize particle size/morphology and as a carbon-coated source. To the best of our knowledge and after a thorough literature review, no study is presented on optimizing the synthesis parameters of LiMnPO4 using the Response Surface Method (RSM). Figure 1 is a schematic representation of LiMnPO4 synthesis and analysis performed in this work.

Materials preparation
All chemical precursors are of analytical grade and used without any further purification. The cathode LiMnPO4 was prepared via facile solvothermal reaction using the following raw precursors; Li3PO4, MnSO4.H2O (99 %, Sigma Aldrich) and PEG-10000 (flakes, Sigma Aldrich). Firstly, Li3PO4 intermediate compound was prepared by mixing Li2CO3 (99 %, Honeywell Fluka) with (NH4)2HPO4 (99 %, Merck) and citric acid (2M) (99.5 %, Merck) in appropriate amounts under magnetic stirring and heat at 90 °C for 60 min. The resulted product was filtered, washed with deionized water (DW) and dried overnight. Then, MnSO4 . H2O, Li3PO4, and PEG-10000 (with different concentrations: 0.00, 0.05 and 0.1 M) solvent were mixed under vigorous stirring for 60 min. The suspension was transferred into a 100 ml stainless steel autoclave followed by thermal treatment at different temperatures, i.e., 150, 200 and 250 °C for a certain reaction time ranging from 60 to 180 min. The autoclave was then taken out of the furnace and cooled down to room temperature. The obtained products were washed with distilled water several times, collected by filtration, and finally dried at 80 °C overnight. Surface carbon coating of LiMnPO4@C was activated by sintering the as-prepared products at 700 °C for 6 hours under argon atmosphere with a heating rate of 5 °C min -1 .

Experimental design and statistical analysis
The Box-Behnken design was used for the response methodology to examine the relationship between one or more dependent response variables and a set of quantitative experimental factors (independent variables). A mathematical model, followed by the second polynomial equation, was developed to describe the relationship between the predicted response variable (matching lines score (purity) of the synthesized LiMnPO4) and the independent variables of solvothermal synthesis conditions. It was described by eq. (1) where YLiMnPO 4 is the predicted response variable, Xi, Xj (1 ≤ i, j ≤ 3; i ≠ j) represent the coded independent variables (solvothermal conditions), 0 is the intercept coefficient,  i are linear terms,  ii are squared terms, and  ij are interaction terms.
This study used this design to determine the effect of three factors (PEG concentration, solvothermal reaction time and temperature) on LiMnPO4 phase purity. The ranges and levels of the experimental parameters are depicted in Table 1. The Design-Expert12 software was used to analyze the results of all experiments.

Structural, morphological and electrochemical characterization
Crystalline structure and phase purity of all products were analyzed and evaluated by X-ray diffraction using diffractometer PANalytical's X'Pert PRO, with Cu Kα radiation ( = 1.5418 Å). The surface morphology and the chemical compositions were observed with a scanning electron microscope (FEI QUANTA 200) equipped with EDS for microanalysis of the surface.
The electrochemical tests were performed at room temperature in the potential range between 2.5 and 4.5 V using battery test systems (BaSyTec GmbH, Germany). All experiments were conducted using coin-type cells (CR2032) assembled according to our previous work [25].

Phase and morphology of the intermediate compound Li3PO4
All detectable peaks of the as prepared Li3PO4 are shown in Figure 2, where the peaks are indexed as Li3PO4 according to the standard data PDF # 071-1528. Based on the matching lines score, no impurity-related peaks could be detected, indicating a high level of purity of the as-prepared Li3PO4 material. The prepared sample has an orthorhombic crystal structure with a Pmn21 space group. Figure 3 shows SEM images of the Li3PO4 product at different magnifications, which suggest that the product is of an irregular nanoplate-like structure. The present results are in good agreement with the literature [33,42]. The microstructure of Li3PO4 was studied by energy dispersive spectroscopy (EDS) to obtain the elemental composition. The collected EDS results shown in Figure 3, confirm the presence of only P and O atoms with a high amount of carbon (from the sample holder and citric acid), without the appearance of any other element.

Effect of operating conditions on LiMnPO4 phase purity
The design matrix composed of 17 experiences, along with their experimental and predicted responses, are shown in Table 2. The results show good agreement between experimental and predicted responses. The matched lines score with reference data#01-074-0375 (purity) of LiMnPO4 was found to range from 3 to 100 %.
Based on the results presented in Table 2, the coefficients of the developed model in eq. (1) are estimated using multiple regression analysis technique. The polynomial model for the phase purity of LiMnPO4 is represented by eq. (2): YLiMnPO 4 = 74.60 + 43.25X1 -2.50 X2 + 16.50X3 + 0.50X1X2 + 6.50X1X3 - The fit quality of the LiMnPO4 purity model was attested with an analysis of variance (ANOVA) [43]. Generally, the suitability of the model is confirmed by higher Fisher's value (F-value) with probability (p-value) as low as possible (p<0.05) [44]. Table 3 shows the analysis of variance (F-test) and the p-value for this experiment. The p-value of this model is about 0.0002, which indicates that the model was suitable for use in this experiment. The calculated F-value for the regression is higher than 14, much higher than the value from Fisher tables (F3,4 = 6.69, for a 95 % confidence level), confirming that the model is well fitted to the experimental data [45,46].
The determination coefficient (R 2 ) quantitatively evaluates the correlation between the experimental data and the predicted responses [47]. With R 2 = 0.93, we conclude that the predicted values match the experimental values perfectly. The adjusted R 2 ≈ 0.90 is very close to the corresponding R 2 value, which confirms that the model is highly significant [48].
The regression coefficients of eq. (2) and the corresponding p-values are presented in Table 4. From this result, we can conclude that the linear effect of PEG concentration (X1) and reaction time (X3) are the principal determining factors for the response on LiMnPO4 phase purity. The response surface plot as a function of PEG concentration (X1) and reaction time (X3) is presented in Figure 4(a). X1X3 was chosen as the interaction key, which exhibits a low p = 0.1745 compared to others that are not significant (since they exhibit a p-value higher than 0.1) [49,50].

Figure 4. 3D response surface (a) and contour plot (b) of LiMnPO4 phase purity for different coded values of X1 (PEG concentration) and X3 (reaction time)
The combined effects of the two factors are positive and statistically significant, as also revealed by the contour lines presented in Figure 4 The synthesized material LiMnPO4 under optimum conditions was characterized by X-Ray diffracttion to confirm the phase purity. Figure 5 shows XRD results of the pure sample before and after calcination. It is clearly seen that the two patterns are very similar, with a difference in the peaks intensity which is much higher for the calcined sample. It is also observed that thermal treatment has not a remarkable effect on the formation process of the LiMnPO4 phase and does not change the purity of the material, which indicates that the reaction has been done in the autoclave under solvothermal/optimum conditions. On the other hand, the main objective of calcination is the conversion of PEG layer adhered on the surface of the particles to the carbon layer, which promotes a higher electronic conductivity and consequently an improvement of the electrochemical performances. The obtained results also confirm that a pure phospho-olivine structure LiMnPO4 can be generated with a PEG-10000 concentration of 0.1 mol l -1 , a reaction temperature of 250 °C and a reaction time of 180 min. This pure phase was indexed as LiMnPO4 crystal structure according to the standard data #01-074-0375, crystallizes in the orthorhombic system with the Pmnb space group.
During the thermal treatment process, most materials are generally subjected to some changes in the crystal structure, i.e., crystallite size and microstrain (such as crystal lattice defects, stacking errors, displacement, etc. [51]). In order to verify these two parameters, both samples before and after calcination were examined by the Williamson -Hall (W-H) method as explained previously [35,36]. The W-H curves for all samples are displayed in Figure 6. According to these results, we can state that the crystallites size after calcination is about 68 ± 19 nm, which is strictly lower than that of the pristine material (150 ± 90 nm). This difference could be due to the thermal process that leads to the coalescence of the polyethylene glycol particles remaining adhered to the LiMnPO4 material surface during the synthesis steps, leading to the formation of smaller, well-carbonated nanocrystallites. The lowest microstrain value of about 0.1 ± 5 % was observed for the calcined sample, while the highest strain value of 0.3 ± 1 % was detected for the pristine one. It can be noticed that crystal lattice defects can be reduced using an optimized PEG-10000 concentration, which can act as a protective matrix during the synthesis process due to the viscous property of this solvent. Figure 7 shows the corresponding SEM images of the obtained products, pristine LiMnPO4 and calcined LiMnPO4@C materials. The surface morphology of the pristine sample seems like particles embedded in a polyethylene glycol matrix. However, the calcined sample image shows irregular secondary particles, with degradation of PEG matrix formed during synthesis steps, which confirms the transformation of PEG particles still adhered on the LiMnPO4 material surface to a thin carbon layer.  The charge-discharge behavior of the calcined LiMnPO4@C obtained under optimum conditions was studied using the "galvanostatic charging-discharging" method in the potential range of 2.5 to 4.5 V. As seen in Figure 8, the charge-discharge curves of the 1 st , 2 nd and 3 rd cycles exhibit clear charge/discharge plateaus around 4.25 and 4.05 V, which is in agreement with the electrochemical de-lithiation/lithiation process, respectively [52]. The initial charge-discharge specific capacities were 164.8 and 128.8 mAh g -1 at 0.05 C-rate, respectively, which can be mainly attributed to the nanostructured crystallite size with the reduced microstrain that promotes good intercalation/disintercalation of lithium ions within LiMnPO4@C material structure [36,53]. Our findings are in good agreement with some previous works, where it was confirmed that LiMnPO4 olivine structure without impurity could generate improved electrochemical performances [54]. However, the initial coulombic efficiency of about 78.2 % is mainly affected by unavoidable passivation phenomena of the electrolyte and the active electrode materials [55].
The as-prepared material under optimum synthesis conditions will be subjected to a wide range of electrochemical characterization in order to fully explain the different reaction mechanisms during the charge-discharge process.

Conclusions
During this study, the intermediate compound Li3PO4 was firstly synthesized by a simple precipitation method. Thereafter, the main material LiMnPO4 was prepared by solvothermal reaction under controlled conditions. The objective of this research was the optimization of solvothermal synthesis parameters using response surface methodology based on Box-Behnken design. Three independent variables were considered in this study, which are the concentration of solvent (PEG), reaction time and reaction temperature. The RSM optimization of operating conditions for the preparation of the pure LiMnPO4 phase was applied. Analysis of variance (ANOVA) confirmed that the proposed regression model is in good agreement with the experimental data, providing a high determination and adjusted determination coefficients.The obtained results confirmed that the optimum conditions for maximum LiMnPO4 phase purity are: cPEG = 0.1 mol l -1 , T = 250 °C and  = 180 min. The material synthesized under optimum conditions was subjected to supplementary characterization techniques to study the crystalline structure and the surface morphology. The results suggested that the used precursors, as well as the synthesis parameters, can directly affect the material purity and the structural properties.
This as-prepared cathode material LiMnPO4@C, can display an initial charge-discharge capacity of 164.8 and 128.8 mAh g −1 at 0.05 C-rate, respectively, with moderated initial coulombic efficiency of about 78.2 %. Further investigations on the prepared material (such as particle size reduction, improved carbon coating, etc.) will be conducted to improve its electrochemical performance.