Non-Equilibrium Thermodynamics in Porous Media: Battery Degradation, and Sorption and Transport in Porous Materials by Matthew Bede Pinson PhB, The Australian National University (2008) Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2015 ○c Massachusetts Institute of Technology 2015. All rights reserved. Author................................................................ Department of Physics December 22, 2014 Certified by. Martin Z. Bazant Professor of Chemical Engineering and Professor of Mathematics Thesis Supervisor Certified by. Mehran Kardar Francis Friedman Professor of Physics Thesis Supervisor Accepted by........................................................... Krishna Rajagopal Associate Department Head for Education 2 Non-Equilibrium Thermodynamics in Porous Media: Battery Degradation, and Sorption and Transport in Porous Materials by Matthew Bede Pinson Submitted to the Department of Physics on December 22, 2014, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Porous media offer many interesting problems in physics and engineering due tothe interaction of phase transitions, surface effects and transport. In this thesis I exam- ine two such problems: the degradation of lithium-ion batteries, and sorption and transport of fluids in porous materials. The dominant capacity fade mechanism in many lithium-ion batteries is the loss of cyclable lithium to a solid-electrolyte interphase layer on the surface of the negative electrode. I develop a single-particle model of this fade mechanism, based on diffusion of the reacting species through the growing layer and reaction at the surface of the active material. This analytical model is justified by comparison with a computational porous electrode model. Temperature is identified as the most important variable influencing the capacity fade rate, and the model is able to make predictions for accelerated aging tests as well as the effect of mismatched internal resistances in battery packs. The quantity of a fluid taken up by a porous material as a function of the partial pressure of the fluid relative to saturation can be used to measure the pore sizedis- tribution of the material. However, hysteresis between the wetting and drying paths complicates the interpretation of experimental results. I present a unified model of hysteresis that accounts for both single-pore and network effects, enabling the cal- culation of not only the pore size distribution but also a parameter measuring the connectivity between large and small pores. I then use the ideas of the model to examine drying shrinkage in hardened cement paste, demonstrating that the hys- teresis in this shrinkage is primarily due to water inserted between molecular layers in calcium-silicate-hydrate. Finally, I outline a model of transport of a sorbing fluid with hysteresis, and suggest possible extensions to allow quantitative comparison with experimental results. Thesis Supervisor: Martin Z. Bazant Title: Professor of Chemical Engineering and Professor of Mathematics Thesis Supervisor: Mehran Kardar Title: Francis Friedman Professor of Physics 3 4 Acknowledgments I am very grateful to many people who have supported me during my graduate studies, including: ∙ Anna, Patrick and other friends who sometimes made me feel like I never left Australia, ∙ My fellow music-lovers in the MIT Gilbert and Sullivan Players, who helped me keep my horizons broad while at MIT, ∙ All my friends among the Tech Catholic Community, for the fun, food and faith that we have shared, ∙ Prof. David Williams, who first urged me to consider MIT and continues to help me in my academic career, ∙ The Bazant research group, for their friendly faces each day and useful tips whenever I needed them, ∙ Prof. Hamlin Jennings, Enrico and the rest of the Dome collaboration and Radu, for interesting collaborations leading to the results in this thesis, ∙ My friends in the MIT physics program, for many hours of productive study and enjoyable socializing, ∙ Jordan and Patrick and the many visitors who made PPP Junction feel like a true home, ∙ My thesis committee, Profs Mehran Kardar, Leonid Levitov and Robert Jaffe, for insightful questions and suggestions that helped guide my work, ∙ My family, who encouraged me to make the most of the opportunities that came my way and whose Skype calls have been the highlight of many weekends, and ∙ My supervisor, Prof. Martin Bazant, for finding the right projects for me and never failing to offer suggestions and help. 5 6 Contents 1 Introduction 15 2 Degradation of lithium-ion batteries 17 2.1 Lithium-ion batteries . 17 2.2 Degradation mechanisms . 18 2.2.1 Solid-electrolyte interphase formation . 18 2.2.2 Other degradation mechanisms . 19 2.2.3 Degradation of silicon anodes . 20 2.3 Degradation modeling . 20 3 Modeling of solid-electrolyte interphase formation 23 3.1 Advantages of a physical model . 23 3.2 A porous electrode model . 24 3.3 Single particle model . 30 3.3.1 Model formulation . 30 3.3.2 Comparison with experiment . 34 3.3.3 Multiple reacting species . 34 3.4 Temperature effects . 35 3.4.1 Accelerated aging . 35 3.4.2 Resistance mismatch in battery packs . 39 3.5 Lifetime prediction and statistics . 46 3.6 Extensions for rapid capacity fade . 47 3.6.1 Fresh surface . 48 7 3.6.2 Unstable SEI . 49 4 Overview of models of sorption in porous materials 53 4.1 Modeling of sorption in a single pore . 53 4.1.1 Surface adsorption . 53 4.1.2 Pore filling . 54 4.2 Modeling of sorption hysteresis in porous materials . 56 4.3 Modeling of transport in porous materials . 58 5 A model of sorption in multiscale porous materials 61 5.1 Single pore hysteresis model . 61 5.1.1 Model . 61 5.1.2 Application to simple porous materials . 63 5.2 Network effects . 63 5.2.1 Model . 66 5.2.2 Insertion within the “solid” . 68 5.2.3 Homogeneous nucleation . 70 5.2.4 Application of the model to experimental data . 72 5.2.5 Scanning isotherms . 76 5.3 Potential for further developments . 78 6 Drying shrinkage in hardened cement paste 81 6.1 Overview of hardened cement paste . 81 6.1.1 Structure . 81 6.1.2 Shrinkage hysteresis . 82 6.2 Classification of water in cement paste . 85 6.2.1 Interlayer water . 85 6.2.2 Gel pore water . 85 6.2.3 Capillary pore water . 85 6.2.4 Surface adsorbed water . 86 6.3 Water sorption isotherm of hardened cement paste . 86 8 6.3.1 Interlayer water . 86 6.3.2 Gel and capillary pore water . 87 6.4 Continuum modeling of reversible drying shrinkage . 87 6.4.1 Macroscopic length change due to Laplace pressure . 89 6.4.2 Macroscopic length change due to surface energy . 89 6.4.3 Macroscopic length change due to loss of interlayer water . 90 6.4.4 Comparison with experiment . 91 6.5 Potential future extensions . 93 7 Modeling of transport with hysteresis in porous materials 95 7.1 Model formulation . 95 7.2 Results . 98 7.2.1 Time-dependent hysteresis curves . 98 7.2.2 Saturation-dependent apparent diffusivity . 101 7.3 Humidity-dependent permeability . 101 7.3.1 Pore size . 103 7.3.2 Pore connectedness . 103 7.4 Inclusion of detailed modeling of hysteresis mechanisms . 104 8 Conclusions and outlook 107 8.1 Battery degradation . 107 8.2 Sorption and transport in porous materials . 108 9 10 List of Figures 2-1 Intercalation (desired) and SEI formation (unwanted) reactions . 18 3-1 Experimental and modeled capacity fade . 27 3-2 Simulated capacity fade depends on time, not on number of cycles. 28 3-3 Voltage-capacity curves with and without SEI resistance . 29 3-4 Spatial variation in SEI formation . 31 3-5 Experimental and modeled capacity fade at several temperatures . 36 3-6 Accelerated aging prediction for a Li-Li cell . 37 3-7 Accelerated aging prediction for a Li−LiCoO2 cell . 38 3-8 Current distribution between parallel-connected cells . 40 3-9 D as a function of C rate, fit to measured capacity fade. 41 3-10 Experimental and model capacity fade for two cells. 42 3-11 Maximum charging current vs excess capacity . 43 3-12 Modeled capacity fade according to Wang et al. [178] . 44 3-13 Experimental and predicted lifetime as a function of resistance mismatch 46 3-14 Lifetime distribution statistics . 47 3-15 Capacity fade of a full cell with a Si anode . 50 3-16 Capacity fade with SEI dissolution or delamination . 52 4-1 Adsorbed layer thickness and example configurations . 55 4-2 Illustration of radial filling and axial emptying . 57 5-1 Experimental and model sorption isotherms in carbon black plugs . 64 5-2 Calculated PSD of carbon black plugs . 65 11 5-3 Hysteresis due to the absence of a liquid-vapor interface . 66 5-4 A network of small and large pores is represented by a Bethe lattice . 68 5-5 Emptying probability vs fraction of pores below emptying pressure . 69 5-6 Example sorption prediction showing single-pore and network hysteresis 73 5-7 Experimental and model isotherms in various porous materials . 74 5-8 Calculated PSD of various porous materials . 75 5-9 Experimental and model scanning isotherms in dental enamel . 77 5-10 Cavitation pressure vs reduced temperature . 80 6-1 Water sorption and shrinkage of cement, clay and Vycor . 83 6-2 Schematic illustration of water sorption in cement paste . 84 6-3 Water sorption in cement divided by location of water . 88 6-4 Experimental and predicted drying shrinkage of cement paste . 92 7-1 Dynamic hysteresis of water content with no resting . 99 7-2 Dynamic hysteresis of water content with resting .