University of South Carolina Scholar Commons Faculty Publications Chemical Engineering, Department of 1989 A Mathematical Model of a Lithium/Thionyl Chloride Primary Cell T. I. Evans Texas A & M University - College Station T. V. Nguyen Texas A & M University - College Station Ralph E. White University of South Carolina - Columbia, [email protected] Follow this and additional works at: https://scholarcommons.sc.edu/eche_facpub Part of the Chemical Engineering Commons Publication Info Journal of the Electrochemical Society, 1989, pages 328-339. © The Electrochemical Society, Inc. 1989. All rights reserved. Except as provided under U.S. copyright law, this work may not be reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society (ECS). The ra chival version of this work was published in the Journal of the Electrochemical Society. http://www.electrochem.org/ DOI: 10.1149/1.2096630 http://dx.doi.org/10.1149/1.2096630 This Article is brought to you by the Chemical Engineering, Department of at Scholar Commons. It has been accepted for inclusion in Faculty Publications by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. 328 J. Electrochem. Soc., Vol. 136, No. 2, February 1989 The Electrochemical Society, Inc. Table A-I. Concentration, density, and mole fraction of LiAICI4-SOCI2 (p +_ 0.0001) = (0.594484 • 0.000934). XLjAlCI4 solutions at 25~ based on the experiment of Venkatasetty and Saathoff (5) + (1.64388 --+ 0.00004) (R 2 = 0.99997) These lines are valid in the range 0 < XLIA~C14< 0.11, 0 < C Concentration Density < 1.50 mol/liter and 1.64 < p < 1.71 g/cm ~ and at 25~ At (mol/liter) (g/cm~) XLiAIC14a higher concentrations linear extrapolation cannot be done with confidence. Therefore the concentrations in Table II 0.00249 1.6438 0.00018 are shown with few digits. 0.00997 1.6443 0.00072 It should be noted that the equation for the density does 0.03046 1.6451 0.00220 0.04985 1.64599 0.00360 not extrapolate to the generally accepted room tempera- 0.0997 1.64820 0.00722 ture value 1.629 g/cm 3 for SOC12 (17). 0.200 1.6525 0.01450 0.35 1.65903 0.02540 REFERENCES 0.50 1.66555 0.03633 1. "Lithium Battery Technology", H. V. Venkatasetty, 0.65 1.67206 0.04729 Editor, The Electrochemical Society and John Wiley 0.75 1.6764 0.054395 & Sons, Inc., New York (1984). 0.90 1.68293 0.06561 1.00 1.68727 0.07296 2. J. J. Auborn, K. W. French, S. I. Lieberman, C. K. 1.50 1,7090 0.109895 Shah, and A. Heller, This Journal, 120, 1613 (1973). 3. M. Solomon, ibid., 128, 233 (1981). aCalculated by iteration as explained in the text. 4. H. V. Venkatasetty and W. B. Ebner, in Proceedings of the 29th Power Sources Conference, Atlantic City, N J, June 9-12, 1980, The Electrochemical Society, Inc., p. 122 (1981). Ib Henriksens Fond are thanked for providing the finan- 5. H. V. Venkatasetty and D. J. Saathoff, This Journal~ cial basis of this work. 128, 773 (1981). Manuscript submitted Nov. 30, 1987; revised manuscript 6. H. V. Venkatasetty and S. Szpak, J. Chem. Eng. Data, received June 28, t988. 28, 47 (1983). 7. S.Szpak and H. V. Venkatasetty, This Journal, 131, 961 Note added in proof: Recent measurements (16) agree (1984). well with our measurements also at high concentrations. 8. A. N. Dey and J. Miller, ibid., 126, 1445 (1979). 9. R. W. Berg, H. A. Hjuler, and N. J. Bjerrum, Inorg. Chem., 23, 557 (1984). APPENDIX 10. F. W. Poulsen and N. J. Bjerrum, J. Phys. Chem., 79, To facilitate comparisons with the literature, data given 1610 (1975). by Venkatasetty and Saathoff (5) for the density of the 11. G. Jones and B. C. Bradshaw, J. Am. Chem. Soc., 55, SOC12 solution vs. the molar LiA1C14 concentration have 1789 (1933). been used to estimate approximate concentrations. The 12. J. O. Besenhard and G. Eichinger, J. Electroanal. calculations were based on their data points (see Table Chem., 68, 1 (1976). A-I), using an iterative method. We assumed p grams of 13. F. Birkeneder, R. W. Berg, H. A. Hjuler, and N.J. LiA1C14 per mole of SOC12. Thus, p = C. 175.732 (118.9894 + Bjerrum, Z. Anorg. AUg. Chem., Accepted. p)/1000 p, where C is the molar LiA1C14 concentration, p is 14. Statistical Analysis System, Procedures GLM, the density, and the numbers shown are the molar masses RSQUARE CP, and G3D, SAS Institute Inc., Cary, of LiA1C14 and SOC12. From p values calculated iteratively, NC 27511. the molar fraction of LiA1Ch is easily obtained for each of 15. P.A. Mosier-Boss, J, J. Smith, and S. Szpak, Paper 496, the given concentrations. Then the C and p data were p. 711, The Electrochemical Society Extended Ab- stracts, Vol. 87-1, Philadelphia, PA, May 10-15, 1987. treated by regression vs. XLiAIC]4 to give linear de- pendencies 16. J.W. Boyd and G. E. Blomgren, Abs. 9, p. 14, The Elec- trochemical Society Extended Abstracts, Vol. 88-1, (C • 0.0025) = (13.7007 • 0.0143) XLiAlC14 (R ~ = 0.999987) Atlanta, GA, May 15-20, 1988. 17. S. T. Bowden and A. R. Morgan, Phil. Mag., 29, 367 and (1940). A Mathematical Model of a Lithium/Thionyl Chloride Primary Cell T. I. Evans,* T. V. Nguyen,* and R. E. White** Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843 ABSTRACT A one-dimensional mathematical model for the lithium/thionyl chloride, primary cell has been developed to investi- gate methods of improving its performance and safety. The model includes many of the components of a typical lithium/ thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict one-dimensional, time dependent profiles of concentration, porosity, current, and po- tential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to deter- mine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to estab- lish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided. The lithium/thionyl chloride (Li/SOC12) cell is an attrac- of toxic gases and explosion. A mathematical model of this tive primary energy source because of its high energy den- battery has been developed to investigate the operational sity (1, 2). However, researchers have observed that the and design characteristics which can be adjusted to yield Li/SOCI~ cell is a serious safety hazard under certain con- efficient, yet acceptably safe Li/SOC12 cells. ditions (2). High discharge rates and high temperatures promote thermal runaway which can result in the venting Description of a Li/SOClz Cell The model describes the Li/SOCI~ cell illustrated in *Electrochemical Society Student Member. Fig. 1. The four cell regions are the lithium chloride (LiC1) **Electrochemical Society Active Member. film which forms on the anode surface, the separator (usu- Downloaded 13 Jun 2011 to 129.252.106.20. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp J. Electrochem. Soc., Vol. 136, No. 2, February 1989 The Electrochemical Society, Inc. 329 ally a glass matting), the electrolyte reservoir, and the po- determine the concentration and reaction rate profiles in rous carbon cathode. The anode surface and cathode cur- the cell. Other Li/SOC12 cell models (10-14) are based on rent collector are the boundaries of the model region. The conservation of energy and are used to determine the ther- electrolyte consists of lithium tetrachloroaluminate mal behavior of the cell. (LiA1C14) in thionyl chloride (SOC12). The Li/SOC12 cell is a Tsaur and Pollard (4, 7, 8) present a one-dimensional complex chemical and electrochemical system involving model of the Li/SOC12 cell. They use porous electrode an unknown number of reactions (2). The overall reactions theory (20, 21) and concentrated solution theory (22-24) to which seem most important to include in modeling are: develop this model, and then use their model to predict the oxidation of lithium at the anode concentration profiles, reaction rate distributions in the porous electrode, distributions of LiC1 precipitate in the Li -+ Li + + e- [1] pores of the porous electrode, and cell utilization. How- the reduction of SOC12 at the cathode ever, in their model development Tsaur and Pollard (4, 7, 8) assume that the reservoir is a well mixed solution of con- 2SOC12 + 4e- --+ 4C1- + S02 + S [2] stant concentration, which may not be a valid assumption as shown by Gu et al. (15). Also, they treat the LiC1 film in a and the formation of the LiC1 film on the anode and the simplified manner by ending their finite difference mesh precipitation of LiCI on the pore surfaces of the cathode at the LiC1 film/separator interface. This work shows the during discharge by the following reaction importance of including the film region in the modeling as Li + + C1- ~ LiCl(s) [3] evidenced by the large concentration gradients in the film and the effect of film porosity on cell performance. Due to the low solubility of tiC1 in the SOCI~ + LiAIC14 sol- Several models (10-14) have been presented to describe vent (3), reaction [3] is assumed to occur completely and in- the thermal behavior of Li/SOC12 cells. Parnell and Szpak stantaneously. Thus, reactions [2] and [3] can be combined (10) present a thermal model for the Li/SOC12 cell in one di- to yield one overall reaction representing the processes oc- mension.