MIT10_626S11_lec37 - IV Transport Phenomena Lecture 37...

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IV. Transport Phenomena Lecture 37: Pseudocapacitors and batteries 1. Pseudocapacitance In this lecture, we will discuss pseudocapacitors and batteries, which store energy in two ways: (i) By capacitive charging of the double layers of the electrodes, energy is stored electrostatically in proportion to the area density of double layers, and (ii) via the products of Faradaic reactions, energy is stored electrochemically. First let us define the pseudocapacitance. Assume we have an electron transfer reaction MIT Student (and MZB) Fig. 1 Two types of capacitance at the interface between electrolyte and metal phase with a double layer lying in between. There are two types of charge storage that can occur at the interface: pseudocapacitance and double layer capacitance. For example, if the electrode is a carbon nanotube with some functional groups on it or nanoparticles that allow interecalation of Li ions, then electron transfer reaction (Faradaic reaction) occurs at the surface of the electrode, and this type of capacitance is called ‘pseudocapacitance’. If no Faradaic reaction is allowed, charges can only be physically absorbed in to the double layer without any electron transfers. In this latter case we only have purely electrostatic double-layer capacitance. When we view the electrode/electrolyte interface as a black box, we only see that ions and electrons enter and are stored at a given voltage, and it is difficult to distinguish whether charge is stored capacitively or Faradaically. The time scales and nonlinear response of each process is very different, however, so it is possible to separate these processes from experimental data using suitable mathematical models.
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10.626 (2011) Bazant Recall the Nernst equation: For example, if R is the solid reactant, then for every reaction at the cathode, charge of –ne is stored, which can be recovered by reversing the reaction. Let c R be the concentration of species R. The Faradaic reaction corresponds to a differential pseudocapacitance (per volume) is: 1.1 Dilute solid solution Fig. 2 Concentration distributions inside particle and in the electrolyte close to the particle. Particle has a typical length scale . If we assume the solid solution is dilute, a R =c R , (O is ion in electrolyte at constant activity R is dilute solid solution), and reactions are fast (R F =0), we have and is almost uniform inside the particle with a typical length scale . There will be no transport of reduced state R on the CNT surface (not true in Li battery case). Then there is an effective ‘pseudocapacitance’ C F Following dilute solid solution approximation, we have We can plot and C F as a function of voltage drop across the double layer (Fig.3). 2
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MIT10_626S11_lec37 - IV Transport Phenomena Lecture 37...

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