Modeling and Analysis of Electrochemical Performance of Lithiumsulfur

Modeling and Analysis of Electrochemical Performance of Lithium-sulfur Batteries Aashutosh Mistry and Partha P. Mukherjee Energy and Transport Sciences Laboratory Texas A&M University Jul 11, 2016 Presentation at College on Multiscale Computational Modeling for Energy Applications, International Centre for Theoretical Physics (ICTP), Trieste, Italy

Contents To give a brief overview of models for electrochemical discharge of Li-sulfur cell 1. 2. 3. 4. Mathematical Model Finite Volume Discretization Lumped (0 th Order) Model MATLAB tips 2

1. Mathematical Model 3

1. Mathematical Model 4

1. Mathematical Model 5

1. Mathematical Model Concentration balance: Charge conservation in electrolyte phase: Charge conservation in solid phase: Volume balance for solids: 6

2. Finite Volume Discretization 7

2. Finite Volume Discretization 8

2. Finite Volume Discretization 9

2. Finite Volume Discretization Governing equation (PDE): 10

2. Finite Volume Discretization Governing equation (PDE): 11

2. Finite Volume Discretization Concentration balance: Charge conservation in electrolyte phase: Charge conservation in solid phase: Volume balance for solids: 12

2. Finite Volume Discretization Concentration balance: 13

2. Finite Volume Discretization Charge conservation in electrolyte phase: 14

2. Finite Volume Discretization Charge conservation in solid phase: 15

3. Lumped th (0 Order) Model Concentration balance: Charge conservation in electrolyte phase: Charge conservation in solid phase: Volume balance for solids: 16

3. Lumped th (0 Order) Model Concentration balance: Charge conservation in electrolyte phase: Charge conservation in solid phase: Volume balance for solids: 17

3. Lumped th (0 Order) Model Concentration balance: Charge conservation in electrolyte phase: Charge conservation in solid phase: Volume balance for solids: 18

3. Lumped th (0 Order) Model Concentration balance: Charge conservation Volume balance for solids: 19

4. MATAB tips input() & disp() Syntax: var. Name = input(‘input string’); Syntax: disp(‘output string’); Syntax: disp(var. Name); clear, clc Example: write a script to compute ‘sine’ of a given number – do not modify script file to enter different input value 20

4. MATAB tips linspace() & plot() Syntax: linspace(lower_bound, upper_bound); Syntax: plot(x, y, format_specification); title(), xlabel(), ylabel(), axis() Example: write a script to compute ‘sinh’ of numbers between –π and π, and plot the function y = sin(x) 21

4. MATAB tips save() & load() Syntax: save(filename, variables); Syntax: load(filename, variables); Example: write a script to compute ‘sin(1/x)’ of numbers between – 0. 01 and 0. 01, plot the function y = sin(1/x), save data as a “. mat” file, clear workspace, load data and replot 22

5. Team Projects 1. 2. 3. 4. 5. Effect of porosity on cell performance Effect of mean pore size on cell performance Effect of sulfur loading on cell performance Effect of S 8 dissolution rate Effect of Li 2 S precipitation rate Perform computations at C/10, C/5, C/4, C/3 and C/2 23

5. Team Projects Vcell: cell voltage in V j 2 to j 6: rates of electrochemical reactions r 7 & r 8: rates of chemical reactions time: time of discharge in hr cap: discharge capacity in m. Ah/g of S 8 ES 8 s, ELi 2 Ss, Esep, Ecat: volume fractions a: active area C’s: concentrations 24

Thank You! 25