Solid State Reaction Mechanisms of the LiMnPO4 Formation Using

Article pubs.acs.org/IECR

Solid State Reaction Mechanisms of the LiMnPO4 Formation Using Special Function and Thermodynamic Studies Chuchai Sronsri,† Pittayagorn Noisong,‡ and Chanaiporn Danvirutai*,† †

Materials Chemistry Research Center, Department of Chemistry and Center of Excellence for Innovation in Chemistry, Faculty of Science, Advanced Functional Material Research Cluster, Khon Kaen University, Khon Kaen 40002, Thailand ‡ Materials Chemistry Research Center, Department of Chemistry, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand ABSTRACT: LiMnPO4 was successfully synthesized via thermal decomposition processes of the synthesized MnHPO4·3H2O precursor. Thermogravimetry/differential thermal gravimetry/differential thermal analysis, Fourier transform infrared, atomic absorption spectrophotometry, X-ray diffraction, and scanning electron microscopy techniques were employed for the characterization of the samples. Three thermal decomposition steps in the sequence of dehydration, polycondensation, and decarbonization were observed. The iterative Kissinger−Akahira−Sunose method was used to calculate the exact Eα values. Regions I and II of the first, second, and final steps were confirmed to be single-step kinetic processes with the unique kinetic triplets. The most probable mechanism functions were found to be R3, R2, A2, and P4 corresponding to contracting sphere, contracting cylinder, assumed random nucleation (its subsequent growth), and nucleation processes, respectively. The preexponential factors, A, were calculated using Eα and g(α). The thermodynamic functions of the transition-state complexes were evaluated from the pre-exponential factors. The kinetic triplets, reaction mechanisms, and calculated thermodynamic functions of the formation of LiMnPO4 are reported for the first time.

1. INTRODUCTION Olivine structure phosphates, LiMIIPO4 (MII = Fe, Mn, Co, Ni), have attracted considerable attention because of their being nontoxic, environmentally friendly, and having excellent thermal stability.1−4 The first olivine structure LiFePO4 was reported in 1997 to be used as a cathode material for Li-ion battery by Padhi et al.2 It has been substantially investigated and successfully commercialized due to its excellent rate capacity, stable cycling performance, and low cost in that period of time.1−4 After that, the isostructural LiMnPO4 was considered as the next promising cathode material because of its higher operating voltage (4.1 V) and theoretical capacity (170 mAh g−1) than those of LiFePO4.5,6 Besides, the higher operating voltage is also well within the typical electrolyte stability window.7 In the previous works,8,9 the lithium singleand binary-metals of LiMIIPO4 (MII = Mn, Mg, Mn0.5Mg0.5, and Co0.5Mg0.5) were synthesized via their hydrate precursors (NH4MIIPO4·H2O) and compared between two different Li sources of LiOH·H2O and Li2CO3 and found that Li2CO3 exhibited smaller particle size. In addition, the nonisothermal kinetic triplets including activation energy Eα, pre-exponential factor A, and the reaction mechanism functions f(α) or g(α) from the formation processes of LiMnPO4 from NH4MnPO4· H2O precursor were studied and reported using Ozawa− Flynn−Wall (OFW), Kissinger−Akahira−Sunose (KAS), Coat−Redfern, and multiple heating scan rates methods.8,9 The related thermodynamic functions (ΔH‡, ΔS‡, and ΔG‡) of the transition state complexes are also evaluated and reported. Our recent work10 reported the isoconversional kinetics, reaction model, and thermodynamic studies of NH4Co0.8Zn0.1Mn0.1PO4·H2O using the iterative method of KAS equation to determine the exact Eα values. The thermal © 2015 American Chemical Society

decomposition reaction mechanisms were determined by comparison between the experimental and reaction model plots. The benefits of kinetic analyses in both practical and theoretical applications are the prediction of the process rates, material lifetimes, and interpretation of experimentally determined kinetic triplets,11 which is needed to provide a mathematical description of the thermal decomposition or formation processes. In addition, knowledge of the thermodynamic properties such as ΔH‡, ΔS‡, and ΔG‡ is an important requirement to understand the chemical reaction process. The thermal analysis study such as thermogravimetry/differential thermal gravimetry/differential thermal analysis (TG/DTG/ DTA) is an excellent method and widely used for the measurements of kinetic and thermodynamic properties from the thermal process of the synthesized compounds.11 Therefore, the purpose of this work is to study the isoconversional kinetics, reaction mechanism, and thermodynamic functions of the formation of LiMnPO4 from the solid-state reaction between the synthesized MnHPO4·3H2O precursor and a Li source of Li2CO3. The samples were characterized by TG/ DTG/DTA, Fourier transform infrared spectroscopy (FTIR), and atomic absorption/emission spectrophotometry (AAS/ AES). The structures and morphologies of samples were investigated by X-ray powder diffraction (XRD) and scanning electron microscopy (SEM), respectively. The exact Eα values were determined by iterative KAS method. The reaction Received: Revised: Accepted: Published: 7083

April 2, 2015 June 24, 2015 June 30, 2015 July 13, 2015 DOI: 10.1021/acs.iecr.5b01246 Ind. Eng. Chem. Res. 2015, 54, 7083−7093

Article

Industrial & Engineering Chemistry Research

where λ is the wavelength of X-ray radiation, k is a constant taken as 0.89, θ is the diffraction angle, and β is the full width at half-maximum.14 The morphologies of the samples were investigated by using SEM technique (LEO SEM VP1450) after gold coating. 2.3. Isoconversional Kinetics. The TG/DTG/DTA experiments of the mixture between the synthesized MnHPO4·3H2O hydrate precursor and Li2CO3 were carried out at four heating rates of 5, 10, 15, and 20 °C min−1 from 50 up to 900 °C in air atmosphere with the air flow rate of 100 mL min−1. An accurate sample mass of 8 mg was filled into an alumina pan without pressing, and TG/DTG/DTA curves were recorded by using α-Al2O3 as the reference material.

mechanism of the formation of the title compound was determined by comparison between the experimental and model plot results established by the Málek method.11−13 The A value was calculated using Eα and g(α). The related thermodynamic functions of the transition state complexes were estimated from the kinetic parameters. The kinetic parameters, reaction mechanisms, and thermodynamic functions of the formation of LiMnPO4 from MnHPO4·3H2O precursor were evaluated and reported for the first time.

2. EXPERIMENTAL SECTION 2.1. Preparation. MnHPO4·3H2O was prepared through direct precipitation. In a typical synthesis, 25 mL of 0.2 M MnCl2·4H2O solution was added into 25 mL of 0.2 M H3PO4 solution with the mole ratio Mn/P of 1:1. The pH of the reaction mixture was adjusted to be 7 by the addition of 25 mL of 0.4 M NaOH, and then the pale pink precipitates were obtained. The precipitates were filtered, washed with deionized (DI) water several times, and dried in a desiccator. After that, the title synthesized hydrate was converted to LiMnPO4 by the thermal solid state reaction with Li2CO3. The stoichiometric mole ratio of MnHPO4·3H2O/Li2CO3 of 2:1 was finely ground by hand in a alumina mortar for 45 min. After 2 h of the calcination in alumina crucibles, LiMnPO4 samples were obtained and washed with DI water several times, dried at 110 °C for overnight, and kept in the desiccator for further investigations. Preparation of MnHPO4·3H2O and LiMnPO4 was carried out according to the following equation. Direct−precipitate reaction,

3. THEORETICAL Isoconversional procedure,15−22 the thermal decomposition kinetic investigation of the single crystalline compounds, is a solid-state reaction of the type: A(solid) → B(solid) + C(gas)23−29 as well as the solid-state reaction of two or more solids can be described as the type of ∑Ai(solid) → ∑Bj(solid) + ∑Ck(gas).8,9,18 The nonisothermal (isoconversional) kinetic model is a model-free method, which involves measuring temperatures (T) corresponding to the fixed value of extent of conversion (α) at different heating rates (β, β = (dT/dt)/°C min−1, t is time/min). The α-values from thermogravimetric analysis may be defined as the ratio of actual mass loss to the total mass loss corresponding to the investigated process: α=

MnCl 2· 4H 2O(aq) + H3PO4 (aq) + 2NaOH(aq) → MnHPO4 · 3H 2O(s) + 2NaCl(aq) + 3H 2O(l)

2MnHPO4 ·3H 2O(s) + Li 2CO3(s) (2)

dα = Af (α)e−E / RT dt

2.2. Characterization. Water content in MnHPO4·3H2O crystalline hydrate was determined by TG/DTG/DTA methods on a Pyris Diamond Perkin-Elmer. Mn2+ contents of the title compounds were determined by AAS method (PerkinElmer, Analyst 100), while the Li+ content of LiMnPO4 was determined by AES method, which is coupled with the AAS instrument. The FTIR spectra were recorded in the wavenumber range of 4000−370 cm−1 using KBr pellet technique (KBr, Merck, spectroscopy grade) on a PerkinElmer spectrum GX FTIR/FT Raman spectrophotometer with 32 scans and the resolution of 4 cm−1. The structures were determined by using XRD method and compared with the standard Powder Diffraction File (PDF) database of International Center for Diffraction Data (ICDD). The two theta angles are 5° < 2θ < 70° with 0.02° inclement and 1 s step−1 scan speed using a D8 advanced powder diffractometer (Bruker AXS, Karlsruhe, Germany) with Cu-Kα radiation, λ = 0.15406 Å. The lattice parameters and cell volumes can be obtained from a least-squares refinement of the XRD data with the aid of a computer program corrected for systematic experimental errors. The crystallite size (D) can be calculated using the Scherrer equation:

D=

kλ β cos θ

(4)

where mt is the mass of the sample at time t, and m0 and mf are the masses of the sample at beginning and end of the mass loss in the TG curve reaction results, respectively. According to the isoconversional kinetic theory, thermal decomposition kinetic equation of solid-state reaction is assumed to be based on the following equations:30−34

(1)

Thermal solid state reaction,

→ 2LiMnPO4 (s) + 7H 2O(g) + CO2 (g)

m 0 − mt m0 − mf

(5)

Eq 5 can be modified to be β

dα = Af (α)e−E / RT dT

(6)

Consequently, eq 6 can be rearranged to be dα A = e−E / RT dT f (α ) β

(7)

where E is the activation energy, A is the pre-exponential factor, R is the gas constant (8.134 J mol−1 K−1), T is the absolute temperature (K), and f(α) is the mechanism function or conversion function in the differential form. The left-hand side solution of eq 7, g(α) = ∫ α0 ((dα)/( f(α)) is the integral form of the f(α). Various scientists suggested different ways of solving eq 7. Thus, the kinetics of solid-state reactions can be described by various equations depending on their mechanisms. The solution of the integral in eq 7 depends on the explicit expression of f(α) function. 3.1. Exact E-Values Determination. The iterative KAS method,35−37 usually regarded as reliable, was used to calculate the exact E-values according to the following equation:

(3) 7084

DOI: 10.1021/acs.iecr.5b01246 Ind. Eng. Chem. Res. 2015, 54, 7083−7093

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Industrial & Engineering Chemistry Research Table 1. Algebraic Expressions of Functions g(α), f(α) and Its Corresponding Mechanism44−49 no.

symbol

g(α)

f(α)

rate-determining mechanism

(1) Chemical Process or Mechanism Noninvoking Equations 1 F1/3 1 − (1 − α)2/3 3/2(1 − α)1/3 2 F3/4 1 − (1 − α)1/4 4(1 − α)3/4 3 F3/2 (1 − α)−1/2 − 1 2(1 − α)3/2 4 F2 (1 − α)−1 − 1 (1 − α)2 −2 5 F3 (1 − α) − 1 1/2(1 − α)3 6 F4 (1 − α)−3 − 1 1/3(1 − α)4 7 G1 1 − (1 − α)2 1/2(1 − α) 8 G2 1 − (1 − α)3 1/3(1 − α)2 4 9 G3 1 − (1 − α) 1/4(1 − α)3 (2) Acceleratory Rate Equations 10 P2/3 α3/2 (2/3)α−1/2 1/2 11 P2 α 2α1/2 1/3 12 P3 α 3α2/3 13 P4 α1/4 4α3/4 14 E1 α ln α (3) Sigmoid Rate Equations or Random Nucleation and Subsequent Growth 15 A1, F1 −ln(1 − α) 1−α 16 A3/2 [−ln(1 − α)]2/3 3/2(1 − α)[−ln(1 − α)]1/3 1/2 17 A2 [−ln(1 − α)] 2(1 − α)[−ln(1 − α)]1/2 1/3 18 A3 [−ln(1 − α)] 3(1 − α)[−ln(1 − α)]2/3 19 A4 [−ln(1 − α)]1/4 4(1 − α)[−ln(1 − α)]3/4 20 G4 [−ln(1 − α)]2 1/2(1 − α)[−ln(1 − α)]−1 3 21 G5 [−ln(1 − α)] 1/3(1 − α)[−ln(1 − α)]−2 4 22 G6 [−ln(1 − α)] 1/4(1 − α)[−ln(1 − α)]−4 23 Au (ln α)/(1 − α) α/(1 − α) (4) Deceleratory Rate Equations (4.1) Phase Boundary Reaction 24 R1, F0, P1 α (1 − α)0 25 R2, F1/2 1 − (1 − α)1/2 2(1 − α)1/2 26 R3, F2/3 1 − (1 − α)1/3 3(1 − α)2/3 (4.2) On the Basis of the Diffusion Mechanism 27 D1 α2 1/(2α) 28 G7 [1 − (1 − α)1/2]1/2 4{(1 − α)[1 − (1 − α]1/2}1/2 29 D2 α + (1 − α) ln(1 − α) [−ln(1 − α)]−1 1/3 2 30 D3 [1 − (1 − α) ] 3/2(1 − α)2/3[1 − (1 − α)1/3]−1 31 D4 1 − 2/3α − (1 − α)2/3 3/2[(1 − α)−1/3 − 1−1 32 D5 [(1 − α)−1/3 − 1]2 3/2(1 − α)4/3[1 − α)−1/3 − 1]−1 1/3 2 33 D6 [(1 + α) − 1] 3/2(1 + α)2/3[(1 + α)1/3 − 1]−1 2/3 34 D7 1 + 2/3α − (1 + α) 3/2[(1 + α)−1/3 − 1]−1 35 D8 [(1 + α)−1/3 − 1]2 3/2(1 + α)4/3[(1 + α)−1/3 − 1]−1 36 G8 [1 − (1 − α)1/3]1/2 6(1 − α)2/3[1 − (1 − α)1/3]1/2

ln

β AR E = ln − g (α )E RT h(x)T 2

x 4 + 18x 3 + 86x 2 + 96x x + 20x 3 + 120x 2 + 240x + 120 4

reaction reaction reaction reaction reaction reaction reaction reaction reaction

nucleation nucleation nucleation nucleation nucleation assumed random assumed random assumed random assumed random assumed random assumed random assumed random assumed random branching nuclei

nucleation nucleation nucleation nucleation nucleation nucleation nucleation nucleation

and and and and and and and and

its its its its its its its its

subsequent subsequent subsequent subsequent subsequent subsequent subsequent subsequent

growth growth growth growth growth growth growth growth

contracting disk contracting cylinder (cylindrical symmetry) contracting sphere (spherical symmetry) one−dimensional diffusion two-dimensional diffusion two-dimensional diffusion three-dimensional diffusion, spherical symmetry three-dimensional diffusion, cylindrical symmetry three-dimensional diffusion three-dimensional diffusion three-dimensional diffusion three-dimensional diffusion three-dimensional diffusion

3.2. Mechanism Functions Determination. Málek method11−13 was used to choose an appropriate kinetic model. According to this method, eq 5 can be rearranged to obtain eq 10 for further determination of the special function y(α):

(8)

where x = E/RT and h(x) are expressed by the fourth Senum and Yang38 approximation formula:8,39,40 h(x) =

chemical chemical chemical chemical chemical chemical chemical chemical chemical

y(α) =

(9)

The iterative procedure can be performed according to the following steps: (i) Assume h(x) = 1 to estimate the E1 initial value. The isoconversional methods stop the calculation at this step. (ii) Using E1, calculate a new E2 value from the plot of ln[β/ h(x)T2] versus 1/T. (iii) Repeat step ii, replacing E1 by E2. When Ei − Ei−1 < 0.1 kJ mol−1, the last Ei value was considered to be the exact activation energy value of the reaction.

⎛ dα ⎞ Eα / RT ⎜ ⎟ e = Af (α) ⎝ dt ⎠ α

(10)

The y(α) values are determined directly from experimental data by substituting the calculated Eα into eq 10. Then, for each value of α, one needs to determine the experimental values of (dα/dt)α and the corresponding Tα. The resulting y(α) values are plotted as a function of α and compared against theoretical y(α) master plots. A suitable model is identified as the best match between the experimental and theoretical y(α) master plots. From a series of experimental kinetic curves, (dα/dt)α versus Tα obtained at different β values lead to a series of the 7085


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Figure 1. Thermal decomposition processes between MnHPO4·3H2O and Li2CO3 demonstrated as (a) TG, (b) DTG, and (c) DTA curves.

experimental y(α) plots. The resulting numerical values of y(α) should not demonstrate any significant variation with β giving rise to a single dependence of y(α) on α. As seen from eq 10, the shape of the theoretical y(α) master plots is entirely determined by the shape of the f(α) functions representing the reaction models in Table 1 because A is a constant. However, because the pre-exponential factor is yet unknown, the

experimental and theoretical y(α) plots have to be normalized in a similar manner. For practical reasons, the y(α) plots are normalized by varying from 0−1. This comparison method is an effective method and recommended by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC).11 7086


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Figure 2. FTIR spectra of (a) MnHPO4·3H2O and (b) LiMnPO4 by KBr technique.

3.3. Pre-exponential Factor A Calculation. Under the maximum reaction rate condition, ((d2α)/dt2) of eq 5 is zero:

step exhibiting multiple peaks or shoulders corresponds to the water molecules at the different sites with varying strength of hydrogen bonding in the hydrate crystal structure. The second one corresponds to the polycondensation to give an amorphous phase Mn2P2O7. However, the exothermic DTA peak at about 640 °C (β = 5 °C min−1) can be described as the phase transition from an amorphous Mn2P2O7 to monoclinic phase Mn2P2O7. In addition, the final one corresponds to the elimination of carbon dioxide molecule (decarbonization) to form orthorhombic-phase LiMnPO4. According to the DTG (Figure 1b), the final step reaction between Mn2P2O7 and Li2CO3 (or decarbonization) to form LiMnPO4 started at about 625 °C (around the decomposition temperature of Li2CO3) at the heating rate of 5 °C min−1. The maximum yield of LiMnPO4 will be at around 750 °C at the same heating rate. According to the results from Figure 1, the thermal solid state reaction between MnHPO4·3H2O precursor and Li2CO3 can be suggested as follows. First step (50−350 °C): Dehydration

⎡ βE ⎛ − E 0 ⎞⎤⎡ d α ⎤ d2α 0 =⎢ + Af ′(αmax ) exp⎜ ⎟⎥⎢ ⎥ = 0 2 2 ⎢⎣ RTmax dt ⎝ RTmax ⎠⎥⎦⎣ dt ⎦max (11)

where f ′(α) = ((df(α))/(dα)) is the first derivative modified from ((df(α))/dt) × (dα/dα), and the subscript max in eq 11 denotes the values related to the maximum of the DTG curve obtained at a given heating rate. As the consequence of eq 11, βE 0 RTmax

2

⎛ − E0 ⎞ + Af ′(αmax ) exp⎜ ⎟=0 ⎝ RTmax ⎠

(12)

After simple rearrangements, eq 12 is transformed, and the pre-exponential factor A values can be estimated according to eq 13:11−13 A=

⎛ E ⎞ exp⎜ 0 ⎟ f ′(αmax ) ⎝ RTmax ⎠

− βE 0 RTmax

2

MnHPO4 ·3H 2O(s) → MnHPO4 (s) + 3H 2O(g)

(13)

Second step (350−625 °C): Elimination of water of constituent (Polycondensation)

The z(α) function is described by ICTAC as

z (α ) = f (α )g (α )

(14)

2MnHPO4 (s) → Mn2P2O7 (s) + H 2O(g)

It should be noted that z(α) plots demonstrate a maximum at a specific value of conversion, αp, under the condition11

g (α)f ′(αmax ) = −1

(16)

(17)

Final step (625−775 °C): Decarbonization

(15)

Mn2P2O7 (s) + Li 2CO3(s) → 2LiMnPO4 (s) + CO2 (g) (18)

4. RESULTS AND DISCUSSION 4.1. Characterization. TG/DTG/DTA curves of the thermal decomposition between the synthesized MnHPO4· 3H2O precursor and Li2CO3 at four heating rates are shown in Figure 1. The mass loss started at about 50 °C and ended up at about 775 °C. The observed total mass loss in the TG curve (β = 5 °C min−1) is 45.04%, which is in good agreement with the theoretical value of 46.15%. The thermal decomposition of the title system below 775 °C occurs in three steps. Mass losses in the first (50−350 °C) and second (350−625 °C) steps were 24.98 and 5.44%, respectively, while the final (625−775 °C) step was 14.26%, which agree very well with the theoretical values of 25.58, 5.73, and 14.62%, respectively. The first one corresponds to the elimination of water molecules (dehydration) to form MnHPO4. The dehydration process in the first

FTIR spectra of the synthesized MnHPO4·3H2O hydrate precursor and its thermal decomposition products LiMnPO4 are shown in Figure 2. The broad bands at 3464 and 3293 cm−1 are assigned to the O−H stretching vibration, while the doublet bands observed in the region of 1800−1600 cm−1 are assigned to two different of O−H bending modes (1698 and 1638 cm−1) of H2O molecule at different sites of the synthesized crystalline hydrate. This result agrees with the TG/DTG/DTGA results indicating that the water molecules at different sites in the crystal structure possessing different strengths of the hydrogen bonds will be eliminated at different temperatures. According to FTIR spectra of MnHPO4·3H2O and LiMnPO4 (Figures 2a,b), the strong bands around 1176−1015 and 1008−931 cm−1 are attributed to asymmetric stretching ν3(F2) and symmetric stretching ν1(A1) modes of PO43−, respectively. However, the 7087


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Figure 3. XRD patterns of (a) MnHPO4·3H2O, (b) LiMnPO4, and (c) Mn2P2O7+Li2CO3.

bands at around 630−510 and 500−375 cm−1 are assigned to the resolved triply ν4(F2) and doubly ν2(E) degenerate stretching and bending modes of PO43−, respectively. The IR spectrum of MnHPO4·3H2O is very similar to that of MgHPO4·3H2O observed by Boonchom et al.41 Vibrational bands of HPO42− are observed in the regions of 3120−2800, 2400−2300, 1200−1000, 1160−900, 930−840, 900−700, and 500−300 cm−1; those are assigned to the asymmetric stretching νOH(HPO42−), symmetric stretching νOH(HPO42−), ν(PO3), δ(POH), ν(PO2(OH)), γ(POH), and δ(PO3),41 respectively. The bands at 3464, 3293 and 1698, 1638 cm−1 disappeared after the calcination, which indicates the elimination of H2O from the synthesized MnHPO4·3H2O to form orthorhombicphase LiMnPO4. XRD patterns of the synthesized MnHPO4·3H2O hydrate precursor and its thermal decomposition product LiMnPO4 are presented in Figure 3. The strong intensity and smooth baseline of diffraction patterns of both compounds indicate their high crystallinity. According to Figure 3, panel a, all diffraction peaks are indexed as the orthorhombic-phase 15 MnHPO4·3H2O with space group Pbca ((D2h , No. 61) according to the PDF #79−0730 (MnHPO4·3H2O), a = 10.400, b = 10.860, and c = 10.192 Å). The calculated cell parameters are a = 10.423, b = 10.851, and c = 10.200 Å with α = β = γ = 90°. The corresponding calculated cell volume and crystallite size are 1153.70 Å3 and 56.8 nm, respectively. A

diffraction pattern of the well-crystalline phase LiMnPO4 (Figure 3b) observed after thermal decomposition of the precursor is indexed as LiMnPO4 (PDF #77−0178), which is in the orthorhombic space group Pnma (D16 2h, No. 62). The standard cell parameters are a = 4.711, b = 10.370, and c = 6.038 Å. In this work, the calculated cell parameters are a = 4.732, b = 10.298, and c = 6.055 Å with α = γ = 90° ≠ β, while the corresponding cell volume and crystallite size are 295.11 Å3 and 38.5 nm, respectively. Figure 3, panel c presents the XRD pattern of the thermal solid state reaction between MnHPO4· 3H2O precursor and Li2CO3 at 625 °C after the completion of the second step (350−625 °C) reaction. This step corresponds to the elimination of water of constituent or polycondensation. The chemical reaction equation is 2MnHPO 4 (s) → Mn2P2O7(s) + H2O(g). The existence of two components, namely Mn2P2O7(s) and Li2CO3(s), was confirmed by the XRD patterns according the standard PDF file #77−1243 and #87− 0729, respectively, before the decarbonization step started. The XRD pattern of the thermal solid state reaction between hydrate precursor and Li source under air atmosphere at 750 °C (Figure 3b) represents the major product of LiMnPO4; however, the trace amount of impurities was also with very low XRD intensity compared with that of the sample. This method (under air atmosphere) is the simple and economical route. We present the simple alternative pathway to prepare the target compound. 7088


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Industrial & Engineering Chemistry Research SEM micrographs of the synthesized MnHPO4·3H2O hydrate precursor in Figure 4, panel a illustrate the plate-like

major concern because those parameters can be affected greatly by possible minor errors in baseline determination.11 The Eα−α relations of the first, second, and final steps are shown in Figure 5. If Eα values are roughly constant over the entire conversion range and if no shoulders are observed in the reaction rate curve, it is likely that a process is dominated by a single-step reaction and can be adequately described by a single-step model.11,43,44 However, it is more common that the reaction parameters vary significantly with the conversion. If the reaction rate curve has multiple peaks or shoulders, the Eα and ln A values at appropriate levels of conversion can be used for input to multi-step model fitting computations.11,23,43−45 In addition, it can be considered as the single step if the Eα values are independent of α, by which the changes of the maximum or minimum Eα values from the average one must be less than 20%.10,11,41 The average exact Eα values of the first, second, and final thermal decomposition processes were determined to be 84.14, 128.07, and 196.04 kJ mol−1 with the corresponding average correlation coefficient r2 from the plots in iterative KAS equation (ln(β/(h(x)T2)) versus 1/T) of 0.9985, 0.9898, and 0.9995, respectively. Eα values of this system are found to increase in the sequence of the first, second, and final steps, respectively (Figure 5). The Eα−α curve displays two regions: Region I α = 0.10−0.56, where the Eα values are invariable. In contrast, Region II (α = 0.58−0.90) exhibits the jump or increasing of Eα values. However, the discontinuous range is α = 0.56−0.58, which represents the change in the reaction mechanism of the thermal decomposition of the title system. These results agree with the TG/DTG/DTA (multiple peaks/ shoulders) and FTIR (two bands of bending mode of H2O) results. Figures 1, 2, and 5 support that the thermal decomposition of the first step is a kinetically complex process and cannot be considered as a single-step reaction. However, each Regions I and II could be considered as single-step process and can be described by a unique kinetic triplet. The average Eα values of the Regions I and II were calculated by the iterative KAS equation and found to be 87.59 and 79.26 kJ mol−1, respectively. The relative errors between the maximum or minimum Eα and the average Eα values of the Regions I and II of the first step as well as the second and final steps are displayed in Figure 5. The calculated maximum relative errors are 10.69, 11.19, 17.50, and 18.08%, respectively, which are less than 20% different from the average Eα value. Therefore, Regions I and II of the first step as well as the second and final

Figure 4. SEM micrographs of (a) MnHPO4·3H2O and (b) LiMnPO4.

crystals having sizes of about 5−7 μm in width and 8−11 μm in length together with the smaller irregular particles of about 1−4 μm. However, its final decomposition product LiMnPO4 shows the irregular shape having sizes of about 0.15−0.20 μm together with the bigger irregular particles of about 0.20−0.50 μm (Figure 4b). LiMnPO4 exhibiting different morphology is suggested to be due to the whole decomposition sequence of types: dehydration, polycondensation, and decarbonization processes, respectively. The mole numbers of the metals per chemical formula of the synthesized hydrate precursor and its final thermal decomposition product were determined by AAS and AES (for Li) methods and the mole number of water from TG/DTG/DTA technique. The results confirmed the formula of the synthesized hydrate precursor to be MnHPO4·3H2O, while its thermal decomposition product is LiMnPO4. 4.2. Kinetics, Mechanisms, and Thermodynamics. 4.2.1. Excat Eα Values. Nonisothermal TG/DTG/DTA results of the thermal decomposition between the synthesized MnHPO4·3H2O hydrate precursor and Li2CO3 at four heating rates β of 5, 10, 15, and 20 °C min−1 are shown in Figure 1. The peak temperature increases as the heating rate increases; this result is attributed to the fact that at a high heating rate, there is not enough time for curing, and thus the TG/DTG/ DTA curves will shifts to a high temperature to compensate for the reduced time.42 The isoconversional iterative KAS equation was used to evaluate the exact Eα values. The Eα values of three thermal decomposition steps corresponding to different α (0.10−0.90 range with 0.02 increments) are obtained. Variation of Eα and A for α < 0.10 and α > 0.90 is not automatically a

Figure 5. Eα dependence on α for three thermal decomposition processes. 7089


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Figure 6. Plots of (dα/dt) versus α for three thermal decomposition processes.

Figure 7. Experimental (different symbols) and model plots (solid line) of three thermal decomposition processes for β = 5 °C min−1.

data and exact Eα values obtained from the iterative model-free KAS method eq 8, the variation of dα/dt versus α for the thermal decomposition between MnHPO4·3H2O precursor and Li2CO3 can be determined. Figure 6 illustrates the variation of dα/dt versus α at a heating rate of 5 °C min−1. After that, the mentioned Málek method eq 10 will be also used to generate the experimental plots between normalized y(α) versus α for β = 5 °C min−1. The resulting experimental plots exhibit nonsignificant variation as well as for other three heating rates (10, 15, and 20 °C min−1 ). Subsequently, the determination of the most probable reaction mechanism functions for three thermal decomposition steps are established by comparing between the experimental and reaction model plots. The reaction model plots are obtained from 36 f(α) equations in Table 1,46−51 representing the most probable mechanism functions and are shown in Figure 7 by inserting the values of α from 0−1 with increment of 0.02 in each selected reaction models f(α). According to the comparison results, the most probable mechanism functions for the first (Regions I and II), second, and final thermal decomposition steps are determined, and the best matching mechanism functions are R3, R2, A2, and P4, respectively. The analytical differential or integral forms of the most probable mechanism functions for the first (Regions I and II), second, and final thermal decomposition steps are f(α) = 3(1 − α)2/3 or g(α) = 1 − (1 − α)1/3 (R3), f(α) = 2(1 − α)1/2 or g(α) = 1 − (1 − α)1/2 (R2), f(α) = 2(1 − α)[−ln(1 − α)1/2 or g(α) = [−ln(1 − α)]1/2

steps were considered to be single-reaction processes and can be adequately described by a unique kinetic triplets [Eα, A and f(α) or g(α)]. According to the results from Figures 1, 2, and 5, the thermal decomposition processes between MnHPO4·3H2O and Li2CO3 are suggested as follows. First step (50−350 °C): Region I (single-step process): Dehydration I MnHPO4 ·3H 2O(s) → MnHPO4 ·y H2 O(s) + x H 2O(g) (19)

Region II (single-step process): Dehydration II MnHPO4 ·y H2 O(s) → MnHPO4 (s) + y H2 O(g)

(20)

x + y = 3 mol of water. Second step (350−625 °C, single-step process): Elimination of water of constituent (Polycondensation) 2MnHPO4 (s) → Mn2P2O7 (s) + H 2O(g)

(21)

Final step (625−775 °C, single-step process): Decarbonization Mn2P2O7 (s) + Li 2CO3(s) → 2LiMnPO4 (s) + CO2 (g) (22)

4.2.2. Most Probable Mechanism Function. The reaction mechanism is the most important information to identify the kinetic process. If this is not appropriately selected, the kinetic parameters will be meaningless. According to the experimental 7090


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Industrial & Engineering Chemistry Research (A2), and f(α) = 4α3/4 or g(α) = α1/4 (P4), respectively. R3 and R2 belong to the deceleratory rate equations of phase boundary reaction, while A2 is the sigmoid rate equation or random nucleation and subsequent growth (Avrami−Erofeev), and P4 is the acceleratory rate equations or power law or nucleation reaction. The results indicate that the sequence of the reaction processes is controlled through the decomposition processes including spherical, cylindrical symmetries, assumed random nucleation, and its subsequent growth and nucleation reactions, respectively. It can be concluded that the first thermal decomposition processes occurred as two consecutive reactions mechanisms. In the range of 0.10 < α < 0.56, the conversion is controlled by spherical symmetry, and then it was changed to cylindrical symmetry in the range of 0.58 < α < 0.90. 4.2.3. Pre-exponential Factor A. The A-values of the thermal decomposition processes of the studied system were calculated using eq 13 after selection of the most probable mechanism integral function g(α). All parameters are substituted in eq 13 at heating rate β = 5 °C min−1, Eα = 87.59 and 79.26 kJ mol−1, and reaction integral functions g(α) = 1 − (1 − α)1/3 (R3) and 1 − (1 − α)1/2 (R2) for the Regions I and II of the first step. However, for the second and final steps, the substituted values are Eα = 128.07 and 196.94 kJ mol−1 and g(α) = [− ln(1 − α)1/2 (A2) and α1/4 (P4), respectively. The maximum temperature Tmax obtained from DTG peaks for Regions I and II, second, and final steps are 435.65, 501.43, 806.32, and 1030.57 K, respectively. All mentioned parameters were substituted into eq 13 to calculate the corresponding preexponential factor A. The A-values for Regions I and II, second, and final thermal decomposition steps are 1.73 × 109, 2.24 × 107, 2.69 × 107, and 1.04 × 109 s−1, respectively. Eq 6 is generalized according to each step as follows: ⎛ E ⎞ dαi A = i exp⎜ − i ⎟fi (α) ⎝ RT ⎠ dT β

is related to the pre-exponential factor A (kinetic parameter) as follows:

ΔS‡ = R ln

(24)

(25)

dα3 ⎛ 128.07 ⎞ 2.69 × 107 1/2 ⎟2(1 − α )[ − ln(1 − α )] exp⎜ − = 3 3 ⎝ dT RT ⎠ β (26)

dα4 ⎛ 196.94 ⎞ 3/4 1.04 × 109 ⎟4α = exp⎜ − 4 ⎝ β dT RT ⎠ (Final step)

(29)

ΔG‡ = ΔH ‡ − T0ΔS‡

(30)

5. CONCLUSIONS Thermal decomposition of the solid-state reaction between the synthesized MnHPO4·3H2O and Li2CO3 was observed to appear in three steps as the sequence of dehydration, polycondensation, and decarbonization, respectively. The final product was confirmed to be LiMnPO4. The isoconversional kinetic study of the thermal decomposition was carried out using the iterative KAS method. The calculated Eα values of all thermal decomposition processes indicate that Region I, Region II of the first step, second, and final steps are a single-step kinetic process and can be adequately described by the unique kinetic triplets. The most probable mechanism functions of thermal decomposition were suggested by comparison between experimental and reaction modeled plots. The reaction models for the Regions I and II of the first thermal decomposition step are contracting sphere (R3) and contracting cylinder (R2) reaction models, respectively. However, the second and final steps are Avrami−Erofeev (A 2 ) and nucleation (P 4 ), respectively. The related thermodynamic functions of the transition state complexes of the thermal decomposition processes were calculated through the kinetic parameters and found to agree well with the thermal analysis data.

(23)

dα 2 ⎛ 79.26 ⎞ 2.24 × 107 1/2 ⎟2(1 − α ) = exp⎜ − 2 ⎝ RT ⎠ β dT

(Second step)

ΔH ‡ = E‡ − RT0

The entropy changes ΔS‡ for Regions I and II, second, and final steps are −79.53, −113.84, −119.26, and −90.89 J K−1 mol−1; four corresponding enthalpy changes ΔH‡ are 83.97, 75.09, 121.37, and 188.37 kJ mol−1; and four Gibbs free energy changes ΔG‡ are 118.61, 133.68, 217.53, and 282.04 kJ mol−1, respectively. The negative ΔS‡ values of all thermal decomposition processes reveal that the activated states are less disordered compared to the initial states and suggest a large number of degrees of freedom due to rotation and vibration, which may be interpreted as a “slow” stage.53 The endothermic peaks in DTA curves agree well with the positive sign of ΔH‡. The positive ΔG‡ values confirm that the thermal decomposition reactions are nonspontaneous processes.

dα1 ⎛ 87.59 ⎞ 1.73 × 109 2/3 ⎟3(1 − α ) = exp⎜ − 1 ⎝ RT ⎠ β dT

(First step, Region II)

(28)

where e is the Neper number and equal to 2.7183, χ is transition factor and equal to 1 for monomolecular reaction, kB and h are Boltzmann (1.3806 × 10−23 J K−1) and Planck (6.6261 × 10−34 J s) constants, T0 is peak temperature from DTG curve, which is the same as the previous calculation of A (β = 5 °C min−1), and R is the gas constant. The enthalpy change or heat of activation (ΔH‡) and Gibbs free energy change of the transition state complex (ΔG‡) can be calculated according to eqs 29 and 30, respectively:

All thermal decomposition kinetic equations for the synthesized MnHPO4·3H2O precursor and Li2CO3 are

(First step, Region I)

Ah eχkBT0

■

(27)

where α1 and α2 are the extent of conversions in Regions I and II. α3, α4, and α are the extent of conversions for the second step, final step, and the whole thermal decomposition steps reaction (α = α1 + α2 + α3 + α4), respectively. 4.2.4. Thermodynamic Functions. According to the transition state complex theory of Eyring,44,52 the entropy change of transition state complex or entropy of activation ΔS‡

AUTHOR INFORMATION

Corresponding Author

*Tel.: +66−43−202222 to 9 Ext. 12243. Fax: +66−43−202373. E-mail address: [email protected]. Notes

The authors declare no competing financial interest. 7091


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ACKNOWLEDGMENTS The authors would like to thank the Materials Chemistry Research Center, Department of Chemistry, Center of Excellence for Innovation in Chemistry (PERCH−CIC), Faculty of Science, Khon Kaen University. The support from the National Research University Project through Advanced Functional Material Research Cluster, Office of the Higher Education, is highly acknowledged.

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Solid State Reaction Mechanisms of the LiMnPO4 Formation Using

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