USING PRESSURE DATA FOR ACTIVATION ENERGY CALCULATIONS IN ACCELERATING RATE CALORIMETRY
E. Zinigrada, J.S. Gnanaraja, L. Asrafa, H.E. Gottlieba, M. Sprechera, D. Aurbacha,,
M. Schmidtb
aDepartment of Chemistry, Bar-Ilan University Ramat-Gan 52900, Israel
bMerck KGaA, D-64293 Darmstadt, Germany
ABSTRACT.Thermal behavior of the commercially used in Li-ion batteries EC-DMC-DEC/LiPF6 solutions was studied by accelerating rate calorimeter(ARC).It was shown thatARC pressure data can be used for calculation of activation energy and order of simple reactions with gas evolution in the case of compression factor is close to 1. This application is very important for endothermic reactions study by ARC.
INTRODUCTION
Accelerating rate calorimetery (ARC) and the related program for interpretation of experimental data allows some thermodynamic and kinetic parameters of chemical reactions to be determined. These parameters are the heat of exothermic reactions, activation energy and the order of the exothermic reactions. According to [1, 2] all mathematical relations are based on the main assumption that concentration can be represented by temperature changes.
The remarkable mathematical relations [1, 2] do not permit calculation of kinetic parameters of endothermic reactions with ARC data. In this paper, we discuss a possibility of using ARC pressure data for the calculation of activation energy and order of such reactions. Studies of the thermal behavior of the commercially used in Li-ion batteries EC-DMC-DEC/LiPF6 solutions which are widely used in commercial Li-ion batteries, were chosen for illustration of this opportunity.
THEORY
We consider a reaction in which one of the products is gas. Using pressure instead of concentration seems to be more convenient when dealing with reactions where one or more reagents or products are gases. We obtained the following equation between initial concentration of reagent C0 and pressure P of gas evolution:
C / C0= (PF-P) / ΔP, (1)
where C is the current concentration of reagent, PF is the final pressure at the end of reaction, ΔP= PF-P0 is the change of pressure as a result of the reaction, P0 is the pressure at the onset point of reaction. This equation is similar to that appeared in [1,2].
Expression (1) is valid if a proportional dependence between pressure and number of gas moles fulfills (PV=nRT, where n is number of gas moles). However, real gases show deviations from perfect gas low. The compression factor Z can be used for correction in the case of high pressure or for gases with big size molecules:
Z=PVm/RT (2)
where Vm is molar volume.
Using one of the versions of virial equation of state:
, (3)
where B and C are the second and the third virial coefficient, valid pressure value can be calculated. In many cases C/Vm2<B/Vm and hence, the virial equation has only two terms. The virial coefficients depend on temperature.
Combining expression for the rate of reaction (dC / dt) from (1)
(4)
with the general equation known from formal kinetics of chemical reactions:
dC / dt = -k CN, (5)
where k is the rate constant and t is time, we obtained the expression for pseudo rate constant k* similar to that given in [1,2]:
(6)
(7)
wherep is the rate of pressure increase (pressure development rate PDR), p=dP/dt,
is the extent of conversion.
It should be noted that k* depends on temperature in the same way as k (i. e. an Arrhenius relation is expected):
(8)
This allows to calculate an activation energy of reaction Ea from the plot of ln k* vs 1/T.
EXPERIMETAL
1 M LiPF6 solutions in mixture of ethylene carbonate (EC), diethyl carbonate (DEC), and dimethyl carbonate (DMC) (2:1:2 v/v/v) were obtained from Merck KgaA (highly pure, Li battery grade).
Both an accelerating rate calorimeter (ARC, Arthur D Little Inc. Model 2000) and a differential scanning calorimeter (DSC, Mettler Toledo Inc. Model DSC 25) were used.
In the ARC tests the solutions were heated between 40 and 350 0C with 5 0C increments at the rate of 2 0C/min in the search for self-heating at the sensitivity threshold of 0.02 0C/min. The controller was programmed to wait 15 min for the sample and calorimeter temperatures to equilibrate, and then to search 20 min for a temperature increase of 0.02 0C/min. After ARC experiments the bomb was cooled with liquid nitrogen till the pressure was slightly above the atmospheric pressure. The gas was released through a high-pressure valve, specially designed for this purpose. We have used 1H, 13C, 31P and 19F NMR, FTIR and GCMS to analyze the reaction products at different reaction stages. Two milliliters of a solvent mixture or a Li salt solution were placed in a titanium spherical bomb (8 ml volume) in an argon filled glove box and were transferred to the ARC under a highly pure Ar atmosphere.
RESULTS AND DISCUSSION
A detail analysis of self-heating rate (SHR) and pressure development rate (PDR) vs. temperature profiles obtained by ARC 2000 was done in [3]. Studies of the thermal behavior of the commercially used in Li-ion batteries EC-DMC-DEC/LiPF6 solutions by ARC, detected one endothermic reaction starting about 170 0C, followed by at least 5 exothermic reactions in the temperature range 200-280 0C (Fig.1). Figure 2 shows SHR and PDR vs. T plots for these solutions.
LiPF6 plays a major role in the thermal decomposition of the solution components in both the endothermic and the exothermic reactions. The endothermic process detected by the pressure data is proposed to involve an elimination reaction of EMC and DMC by F- as a base. We found that the P-F bonds of the LiPF6 or PF5 are stable up to 180 0C and completely decompose at 220 0C. Most of the exothermic reactions detected, involve gas evolution and a build up of pressure due to the formation of HF, CO2 and H2O. The proposed nature of these reactions is shown in equations 11-13, where equation 11 is intended to represent also the ring opening of the EC molecules [4].NMR results show that the compounds CH3CH2F, CH3F and traces of polymer are present in the bomb after heating up 180 0C.
LiPF6→ LiF+PF5 (g) (9)
CH3CH2-O-CO-O-CH2CH3 + F -→ CH3CH2-O-CO-O- + HF + CH2 = CH2 (10)
2CH3-O-CO-O-CH3 + 2F -→ 2CH3-O-CO-O- + 2HF + CH2 = CH2 (10a)
CH3-O-CO-O- CH2CH3 + F -→ CH3-O-CO-O- + HF + CH2 = CH2 (10b)
R-O-CO-O-R + F- → R-O-CO-O- + R-F (11)
R-O-CO-O- → R-O- + CO2 (12)
R-O- + PF5 → R-O-PF4 + F- (13)
We suggest that in the third exotherm (2400 C-2900C) accompanied by pressure growth, the major evaluated gas is CO2. The temperature dependence of pseudo rate constant calculated by SHR (Fig. 3) shows better linear behavior for the fist order reaction. The activation energy calculated for the fist order reaction is 62 kJ/mol (111 kJ/mol for second order reaction).
The real gas behavior may be similar to that of a perfect gas if Z→1. This can be valid at low pressure, small virial coefficients or high molar volume (eq. 3). Molar volume is defined by number of gas moles (n) and the bomb’s volume (8 cm3 in our case). We suppose that ethylene gas formed in accordance to equations (10) transforms to polyethylene condense phase at temperatures below 220 0C (70 atm) and the quantity of HF and H2O is negligibly
small. CO2, R-Fand R-O-PF4 are the main gas components at the end of the third
exotherm.
The pressure 77 atm at set point of the third exotherm (240 0C) is defined, as we assume, by R-F compounds.
Possible molar number of R-F defines by solvent amount. In the sample of 2 ml volume the total molar number of EC (M=88.06, n=0.012 moles), DEC (M=118. 3, n=0.0033 moles) and DMC (M=90.08, n=0.0095 moles) is 0.026 moles. We assume that the highest number of moles of R-F for our sample is
nDEC + nDMC =0.0033 + 0.0095 = 0.0138 moles.
For the bomb volume of 8.2 cm3 molar volume is equal 8.2/0.0138=594 cm3/mol. If we suppose that the second virial coefficient B at 513 K is high taking into account the heavy gases, for a example 40, we obtain:
B/Vm=40/594=0.067.
Thus the molar volume of gases is comparatively big in our case. The second term in eq. 3 is negligible, and we approximate that the ARC pressure data can be used for estimation of the rate of the third exothermic reaction. Figure 4 shows the temperature dependence of pseudo rate constant calculated by PDR. As for self-heating rate data in Fig. 3, calculation of the pressure developed rate, gives better results for the fist order reaction in Fig. 3. The activation energy calculated for the fist order reaction is 66 kJ/mol (107 kJ/mol for second order reaction) which is closed to what obtained from the SHR data
CONCLUSION
ARC pressure data can be used for calculation of activation energy and order of simple reactions with gas evolution in the case of compression factor is close to 1 (i.e. perfect gas approximation). This application is very important when endothermic reactions are studying by ARC.
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Monterey, CA Abs. 341, (2002).
4. S. Mori, H. Asahina, H. Suzuki, A. Yonei, E. Yasukawa, J. Power Sources, 68 (1997)
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