PDF Publication Title:
Text from PDF Page: 007
PCCP Paper balance, causing an equivalent current to be drawn in from the external circuit and into the electrode during the squeezing phase. This equilibration of charge happens very quickly com- pared to the double layer’s self-oscillation, and it directs the flow of electrons in the external circuit. During expansion, the interior of the double layer is replenished with positive ions and the electrode is replenished with electrons by the oxidation reaction that consumes the battery’s ‘‘chemical fuel’’ in a thermodynamically irreversible way. This sets up the double layer for the next pumping cycle. The full process is illustrated in Fig. 5. Note that if the positive ions are injected by the oxidation reaction when the double layer is expanded (so that Vd, and therefore the chemical potential m for the ions, is high) and ballistically expelled when the double layer is contracted (so that m = qVd is low), eqn (22) implies that a net positive work can be done to pump the current I. An analogous pumping may occur in the other half-cell. Note, however, that pumping at only one of the half-cells may be sufficient to produce an emf. Further details on the pumping dynamics probably depend on the specific battery configu- ration being considered. From a microphysical point of view, this active transport of charges in an asymmetric potential subjected to a coherent, periodic modulation, is similar to the mathematical model of an artificial Brownian motor.42 In the battery, it is the mechanical self-oscillation of the double layer that produces the periodic modulation of the potential for the ions. Thermodynamically speaking, that modulation is the external work that drives the pumping and which is converted into the electrostatic energy of battery’s charged terminals, minus some internal dissipation. There is ample experimental evidence from ‘‘sonoelectro- chemistry’’ that the application of ultrasound to an electrochemical double layer can significantly enhance the electrical current through that layer.43 This effect has usually been explained as resulting from the ultrasonic driving causing the Nernst diffusion layer at the electrode–electrolyte interface to become thinner, but in our view it may more plausibly be interpreted as resulting from the Fig. 5 In an ordinary capacitor, electrical charge comes out (qr/qt o 0) of the positively-charged plate at potential f+, while charge enters (qr/qt 4 0) the negatively-charged plate at potential f. The instantaneous power is therefore P = VI 4 0, (25) where V = f+ f and I is the integral of |qr/qt| over the complete volume of either plate. A similar analysis applies to the discharging of the two double layers in the supercapacitor. The case of the battery is more subtle, because it can generate P 4 0 without appreciable accumulation or depletion of charge anywhere in the circuit. Purcell argued that this apparent contradiction is resolved by the fact that the battery’s operation involves chemical reactions, which must be described in terms of quantum mechanics.6 Indeed, the average flow of matter inside the battery can be described in terms of dischar- ging chemical potentials,39 which represent an underlying quan- tum physics. But the details of how this chemical energy is converted into electrical work, in a thermodynamically irrever- sible way and without contradicting the laws of classical electro- dynamics, have not been adequately clarified in the literature. It is well known that charges can be accelerated by periodic oscillations of f and qr/qt, as is done in a modern particle accelerator.40 As we shall see, the self-oscillation of the double layer described in Section III modulates qr/qt in phase with f, allowing net electrical work to be performed over a complete period of the oscillation. : When the double layer contracts (i.e., X o 0), the Helmholtz layer is moving towards the electrode, and therefore along a direction of decreasing potential f. The value of qr/qt is negative in the region that the Helmholtz layer is moving out of (where the voltage is higher) and positive in the region that the Helmholtz layer is moving into (where the voltage is lower). Eqn (24) therefore implies that P 4 0 during the contraction phase. This reflects the fact that the ion plane is moving along the internal electric field, and is therefore being accelerated by it. : On the other hand, when the double layer expands (i.e., X 4 0), the ion plane is moving into a region that is screened from the internal electric field. Thus, the region where qr/qt is negative is at a voltage only slightly lower than the region in which it is positive. This allows the net work (i.e., the integral of P in eqn (24) over a full period of the double layer’s self-oscillation) to come out positive, which corresponds to a sustained pumping of the current. Intuitively, we may describe the pumping at the negatively charged terminal in the following terms: During the contrac- tion phase, the positive ions in the double layer are ‘‘squeezed’’, giving them a ballistic motion that allows some of them to pass through the Helmholtz layer and escape into the neutral bulk of the electrolyte, thus generating an active discharge current. The current is rectified because the ions can pass through the Helmholtz layer but not penetrate the solid electrode. The generation of a net current by this oscillation is similar to the operation of a ‘‘valveless pulsejet’’ engine.41 The Coulomb interaction between the positive ions in the electrolyte and the electrons in the electrode enforces charge On the left: during the compression of the double layer, positive ions are squeezed out of the double layer and into the bulk of the electrolyte, giving them ballistic rather than diffusive motion. The Coulomb interaction then drives free electrons away from the interface and into the conducting terminal, maintaining charge balance. On the right: no pumping of current occurs during the expansion of the double layer. The ions and electrons pumped away during the compression phase are replenished by the oxidation reaction. View Article Online 9434 | Phys. Chem. Chem. Phys., 2021, 23, 9428–9439 This journal is © the Owner Societies 2021 Open Access Article. Published on 23 March 2021. Downloaded on 6/26/2022 1:50:45 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.PDF Image | Dynamic theory battery electromotive force
PDF Search Title:
Dynamic theory battery electromotive forceOriginal File Name Searched:
d1cp00196e.pdfDIY PDF Search: Google It | Yahoo | Bing
Sulfur Deposition on Carbon Nanofibers using Supercritical CO2 Sulfur Deposition on Carbon Nanofibers using Supercritical CO2. Gamma sulfur also known as mother of pearl sulfur and nacreous sulfur... More Info
CO2 Organic Rankine Cycle Experimenter Platform The supercritical CO2 phase change system is both a heat pump and organic rankine cycle which can be used for those purposes and as a supercritical extractor for advanced subcritical and supercritical extraction technology. Uses include producing nanoparticles, precious metal CO2 extraction, lithium battery recycling, and other applications... More Info
CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com (Standard Web Page)