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Numerical Calculations on Lithium-ion Batteries Group 16 By: Albert Ho, Eric Vavra, Mitchell Gee, Justin Matson, Michelle Empleo faster-charging-batteries/ battery-design-thats-2000-times-more-powerful-recharges times-faster blogspot.com/2010/06/deadly- lithium-batteries.html develop-way-to-triple-battery-life-in-electronics/ 1

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Introduction: Charging Lithium ion batteries are a type of rechargeable battery that is charged by lithium ions moving from the cathode to the anode when charging and from anode to cathode when discharging. 2

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Introduction: Application Lithium-Ion batteries are common in portable electronic devices. These batteries are also being used in some electric cars as well as numerous military purposes. They are known for having a good balance of energy density and power density. 3 package/portable-electronic-devices-for-work Flashlight-Use-By-Cr123a-Li-ion-Batteries.html

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Introduction: Energy Density Energy density is the amount of energy that a battery can store, which is decided by the chemistry of the cell. Lithium ion batteries are becoming very popular for having higher energy density than other batteries with around 115 Wh/kg. 4

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Introduction: Power Density Power density is the rate at which energy can be delivered from the battery to the device. The amount of this is determined by the cell design and kinetics. Lithium ion’s good balance between energy density and power density can be seen on the chart below. 5 tech/lithium-ion-battery.htm computing/ new- lithium-ion-battery-design- thats-2000-times-more- powerful-recharges times-faster

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Method 1: Gibb’s Free Energy A major challenge in battery development is to maximize the energy density. Energy density is a major concern in cell phones. The energy density of a battery is the product of the cell’s voltage and specific capacity. The voltage corresponding to a given-transfer reaction can be related to the Gibb’s free energy. Gibb’s Free Energy is a thermodynamic potential that measures the “usefulness” or process- initiating work obtainable from a thermodynamic system at constant temperature and volume. Gibb’s Free Energy can be determined from the equation: ΔG = -nFE° ΔG = Gibb’s Free Energy n = Number of electrons involved in the reaction = 2 e - F = Faraday’s constant = coulomb/mole (C/mol) E° = Cell Voltage (V) 6

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Table 1 This is a table that we took from our article. It is basically just a list of different electrochemical materials that are used in battery electrodes (referenced to a hydrogen electrode. The reactions of each element and their respective cell voltages.We excluded the oxygen and lithium parts of this table because we wanted to hold n as a constant of 2 electrons and these two elements and 4 and 2 electrons involved in the reaction respectively. 7 Spotnitz, Robert, “Lithium-Ion Batteries: The Basics”, Journal, AIChE, October, 2013, online, 11/20/2013

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Results Element usedΔG, Gibb’s Free Energy F 2, Fluorine Cl 2, Chlorine PbO 2, Lead Oxide Ag, Silver H 2, Hydrogen0 Pb, Lead Cd, Cadmium Zn, Zinc Zn(OH) 2, Zinc Hydroxide

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Numerical Optimization of Gibb’s Free Energy Direct plotting of ΔG vs. E° cell with constant n allows us to find the local minimum value for ΔG analytically and thus to find the most spontaneous cell. The MATLAB script is written as follows: %create values of x in a vector x=[2.87, 1.36, 1.685, 0.342, 0, -0.13, -.43, -.76, ] %function for Gibb's free energy change defined: y=-2*96487.*x %create plot of y vs. x plot(x,y,'o') hold on plot(x,y) xlabel ('Cell Voltage (V)') ylabel ('Free Energy (C*V/mol)') title ('Free Energy vs. Voltage') grid hold off 9

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.m Script and Graph From the plot, we can observe a minimum value of (C*V/mol) for ΔG occurs at a value of for E° cell. 10

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Optimization in MATLAB Cont. We can confirm the answer from the previous slide using MATLAB’s fminbnd function fminbnd uses the golden section search as well as parabolic interpolation to find the minimum value of our function on our given interval We can employ the following MATLAB script to accomplish this task: -2*96487*x; format longg [x,min]=fminbnd(f,-3.05,2.7) 11

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fminbnd Results 12

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Method 2: Mass- Transfer- Limited Current Density, i d Two main categories limit the power of batteries: 1. Voltage loss associated with charge transport 2. Mass- Transfer- Limited Current Density battery-how-li-ion-works/ designing-faster-charging-batteries/ 13

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Current Density Definition The effect of mass transport on the charge (or discharge) rate Equation: i d = mass transfer limited current density (A/m 2 ) D eff = effective diffusion coefficient (m 2 /s) c = concentration of lithium salt in the electrolyte (mol/m 3 ) δ = diffusion length (m) ll/srep01946.html 14

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Linear Regression Solid-phase diffusion coefficients (D eff ) are typically about m 2 /s We can use the numerical method linear regression in order to find a value for D eff for a lithium-ion battery given a table with the current densities vs. the concentration of lithium: 0-breaking-world-record-on- charger-by-using-lithium-ion- battery.html 15

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Linear Regression Calculations Given the info for a monolithic nonporous electrode: F = Faraday’s Constant (96,487 C/mol) δ = 30 * m Since F and δ are constants, we can plot i d vs. c in order to find the slope. With the slope, we can find D eff. This can be done in matlab with the program on the next slide. We can calculate D eff : Spotnitz, Robert, “Lithium-Ion Batteries: The Basics”, Journal, AIChE, October, 2013, online, 11/20/

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Matlab Program function [s, r] = regression(c, id) % input: % c = concentration (mol/m^3) % id = mass transfer limited current density (A/m^2) % output: % s = vector of the slope s(1) and intercept s(2) % r = coefficient of determination n = length(c); if length(id) ~=n, error(‘c and id must be same length’); end c = c(:); id= id(:); sc = sum(c); sid = sum(id); sc2 = sum(c.*c); scid = sum(c.*id); sid2 = sum(id.*id); s(1) = (n*scid-sc*sid)/(n*sc2-sc^2); s(2) = sid/n-s(1)*sc/n; r = ((n*scid-sc*sid)/sqrt(n*sc2-sc^2)/sqrt(n*sid2-sid^2))^2; -programming-who-is-teaching-our-children-to-code.html 17

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Matlab Program cont. % Plot of the data and best fit line cp = linspace(min(c),max(c),2); idp = s(1)*cp+s(2); plot(c,id,’o’,cp,idp) grid on tions-for-use/step-4/ 18

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Matlab Calculations Using the matlab function, the slope of the line is * Plugging this slope into the formula gives you a D eff of * m 2 /sec, which is close to the approximate value of m 2 /s. 19

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Conclusion Numerical methods can be applied to find the Gibb’s free energy of different elements used in batteries. Determining the Gibb’s free energy value can tell us which element(s) are most efficient when creating the optimal performance battery. With the data found we determined that the zinc hydroxide would perform the best based on its Gibb’s free energy change precipitate-andrew-lambert-photography.html 20

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Conclusion (cont.) We can use numerical methods in order to find a value for D eff for a lithium-ion battery given a table with the current densities vs. the concentration of lithium We can use the D eff to determine what diffusion coefficient produces the highest current density amongst lithium ion batteries. 21

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Future Work Separators Separators prevent electronic contact between electrodes while allowing ionic transport nanofiber-based polymeric battery separator Developed by DuPont Increases power up to 30 % Increases battery life up to 20 % Added thermal stability 22

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Future Works Supercapacitors Supercapacitors are capacitors which have low energy density. The organic electrolyte used in supercapacitors allows for fast energy discharge of which is more rapid than that of a battery. A team of researchers at UCLA discovered a way to create graphene-based supercapacitors. Operate three times faster than lithium batteries A Maxwell Technologies supercapacitor cell and two different multi-cell modules UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors. develop-new-technique aspx develop-new-technique aspx 23

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Future Works The lithium-air battery Oxidizes lithium at the anode and reduces oxygen at the cathode which causes current flow. High energy density Energy density (per kilo) comparable to the energy density of gasoline per kilo. Do not store an oxidizer internally since oxygen is used from air 24

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Future Works Liquid-Based Batteries Most traditional battery research has focused on solid-state chemistry and physics principles that have been used for the past two centuries Liquid batteries remove some of the conventional restrictions associated with solid-state batteries. You can store charge in a liquid that you can pump through the battery and then you can recharge the battery by reversing the flow of the pump m/mcontent.gif?v=1&s=db2f5d12c daddec d18d62deb0d 25

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Works Cited Articles: 1Spotnitz, Robert, “Lithium-Ion Batteries: The Basics”, Journal, AIChE, October, 2013, online, 11/20/2013 2Pikul, James H., et. al., “High-power lithium ion microbatteries from interdigitated three-dimensional bicontinuous nanoporous electrodes”, Nat Commun. 2013/04/16/online 11/23/ Reddy,T.,ed., “Linden’s Handbook of Batteries,” 4 th ed., McGraw-Hill, New York, NY (2011) online, 11/23/ Newman, J., and K.E. Thomas-Alyea, “Electrochemical Systems,” 3 rd ed., Wiley, Hoboken, NJ (2004) online, 11/23/ OF-BATTERIES-9-DAVID-LINDEN-THOMAS-B- REDDY-HARDCOVER-NEW- / ?pt=US_Texbook_Education&has h=item2c7685b43a

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References Images: recharges-1000-times-faster recharges-1000-times-faster batteries/ 27

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