I. Equivalent Circuit Models Lecture 3: Electrochemical Energy Storage MIT Student In this lecture, we will learn some examples of electrochemical energy storage. A general idea of electrochemical energy storage is shown in Figure 1. When the electrochemical energy system is connected to an external source (connect OB in Figure 1), it is charged by the source and a finite charge Q is stored. So the system converts the electric energy into the stored chemical energy in charging process. When the system is connected to an external resistive circuit (connect OA in Figure 1), it releases the finite Q and drives a current through the external circuit. The system converts the stored chemical energy into electric energy in discharging process.Stored chemical energy (finite Q) O B Discharging Charging I A A simple example of energy storage is capacitor. Figure 2 shows the basic circuit for capacitor discharge. Here we talk about the integral capacitance. The capacitance is defined as a constant The current is (1) (2) 1 Figure 1: Electrochemical Energy StorageLecture 3: Electrochemical energy storage 10.626 (2011) Bazant The voltage applied to the external resistance is (3) Plug (1) and (2) into (3) and use the total resistance , then we get (4) Apply the initial condition , we can solve the equation (5) The relation between stored charge and time is shown in Figure 3, where is called decay time. C Rint e -I -Q +Q Cell Rext Q Time Q0 Figure 2: Basic Circuit for Capacitor Discharge0 τ = RCFigure 3: Stored Charge vs. Time for Capacitor2Lecture 3: Electrochemical energy storage 10.626 (2011) Bazant In the following sections, we will introduce some practical examples of electrochemical energy storage. 1. Supercapacitors A supercapacitor (or ultracapacitor) is an electrochemical capacitor that has an unusually high energy density when compared to common capacitors, typically on the order of thousands of times greater than a high capacity electrolytic capacitor. In general, supercapacitors improve storage density through the use of a nano porous material, as shown in Figure 4. Two very high surface area porous electrodes are soaked in electrolyte. The charge is stored in electrochemical double layers. e tylortcelECarbon aerogel Doubleer layElectrolyte Vext A O Rext B rdx Figure 4: Basic Structure of SupercapacitorΦ=0 Metal cdx Separator Φ(x) Pores Figure 5: Equivalent Circuit of Supercapacitor3Lecture 3: Electrochemical energy storage 10.626 (2011) Bazant A supercapacitor can be modeled as an RC transmission line, shown in Figure 5. Assume a symmetric situation of two identical porous electrodes of thickness L, and thus focus on only one, in the region 0 < x < L. The electrolyte-filled pore space has a constant volume-averaged resistance per length r and constant capacitance per unit length c. Neglect any resistance in the porous electrode or the thin gap between the electrodes. The mean potential in the pores satisfies a linear diffusion equation (6) If we apply a sudden change of voltage V for t>0 at x=0, the current response can be estimated as . 2. Primary Batteries A primary cell is any kind of battery in which the electrochemical reaction is not reversible. Primary batteries can produce current immediately on assembly. A primary cell is not rechargeable because the chemical reactions are not reversible and active materials may not return to their original forms. Leclanche cell is a typical primary battery. The modern commercial Leclanche cell packaging and the basic structure are shown in Figure 6. The detailed reactions are Anode (oxidation reaction, produces electrons): Cathode (reduction reaction, consumes electrons): Net reaction: 4Lecture 3: Electrochemical energy storage 10.626 (2011) Bazant e Anode Cathode Zn ZnO Mn2O3 MnO2 OH -Electrolyte - Rext 3. Secondary Batteries Secondary batteries are also known as rechargeable batteries because their electrochemical reactions are electrically reversible. Li-ion battery shown in Figure 7 is a typical example of secondary battery. Li ions move from the negative electrode to the positive electrode during discharge, and reversely when charging. During discharge the negative electrode is the anode where oxidation takes place and during charge it turns into the cathode where reduction takes place. The half-reactions of discharging are Anode (oxidation reaction, produces electrons): Cathode (reduction reaction, consumes electrons): 5 Image by MIT OpenCourseWare.Figure 6: Basic Structure and Packaging [1] of LeClanche CellLecture 3: Electrochemical energy storage 10.626 (2011) Bazant LiyCoO2 LiyCoO2 e -Electrolyte Li+ Anode Cathode Carbon powder LixC6 Rext Discharging and charging of a simple secondary battery can be modeled as Figure 8. 1) Discharging (connect OA in Figure 8): 2) Charging (connect OB in Figure 8): where R is the total resistance . 6 Figure 7: Basic Structure of Li-ion BatteryLecture 3: Electrochemical energy storage 10.626 (2011) Bazant CaV0 0aRint Vc Cc -Qa +Qa Rext A O B Vext The relation between V and Q of Li-ion battery is often highly nonlinear, as shown in Figure 9. The detail will be discussed in Lecture 9. V 0 Qmax Q I<0, charging I>0, discharging V 0 Qmax Q I<0, charging I>0, discharging I=0 Figure 8: Equivalent Circuit of Rechargeable BatteryI=0 (a) LixCoO2 (b) LixFePO4 Figure 9: Nonlinear V vs. Q Relation of Li-ion Batteries7MIT OpenCourseWarehttp://ocw.mit.edu 10.626 / 10.462 Electrochemical Energy Systems Spring 2011 For information about citing these materials or our Terms of Use, visit: