![]() Using this scheme, the effects of molecule-lead, electron-electron, and hopping interactions are included nonperturbatively, and the charge transport processes can thus be studied in the intermediate parameter range from the Coulomb blockade to the coherent tunneling regimes. In the perturbation treatment, the zeroth-order Hamiltonian of the molecular junction is composed of independent single-impurity Anderson's models, which act as the channels where charges come through or occupy, and the interactions between different channels are treated as the perturbation. ![]() The salt bridge consists of an intermediate compartment filled with a concentrated solution of KCl and fitted with porous barriers at each end.We study charge transport through molecular junctions in the presence of electron-electron interaction using the nonequilibrium Green's function techniques and the renormalized perturbation theory. In the simplest cells, the barrier between the two solutions can be a porous membrane, but for precise measurements, a more complicated arrangement, known as a salt bridge, is used. Since negative ions tend to be larger than positive ions, the latter tend to have higher mobilities and carry the larger fraction of charge. More detailed studies reveal that both processes occur, and that the relative amounts of charge carried through the solution by positive and negative ions depends on their relative mobilities, which express the velocity with which the ions are able to make their way through the solution. Thus an excess of Cu 2 + in the left compartment could be alleviated by the drift of these ions into the right side, or equally well by diffusion of nitrate ions to the left. ![]() This ionic transport involves not only the electroactive species Cu 2 + and Zn 2 +, but also the counterions, which in this example are nitrate, NO 3. This means that we must provide a path for ions to move directly from one cell to the other. In order to sustain the cell reaction, the charge carried by the electrons through the external circuit must be accompanied by a compensating transport of ions between the two cells. These violations of electroneutrality would make it more difficult (require more work) to introduce additional Zn 2 + ions into the positively-charged electrolyte or for electrons to flow into right compartment where they are needed to reduce the Cu 2 + ions, thus effectively stopping the reaction after only a chemically insignificant amount has taken place. Positive charge (in the form of Zn 2 +) is added to the electrolyte in the left compartment, and removed (as Cu 2 +) from the right side, causing the solution in contact with the zinc to acquire a net positive charge, while a net negative charge would build up in the solution on the copper side of the cell. The need for this can be understood by considering what would happen if the two solutions were physically separated. A current of one ampere corresponds to the flow of one coulomb per second.įor the cell to operate, not only must there be an external electrical circuit between the two electrodes, but the two electrolytes (the solutions) must be in contact. When we measure electric current, we are measuring the rate at which electric charge is transported through the circuit. For most purposes, you can simply use 96,500 Coulombs as the value of the faraday. Careful experiments have determined that 1 F = 96467 C. The amount of charge carried by one mole of electrons is known as the Faraday, which we denote by F. By placing an ammeter in the external circuit, we can measure the amount of electric charge that passes through the electrodes, and thus the number of moles of reactants that get transformed into products in the cell reaction.Įlectric charge q is measured in coulombs. By connecting a battery or other source of current to the two electrodes, we can force the reaction to proceed in its non-spontaneous, or reverse direction. If we place a variable resistance in the circuit, we can even control the rate of the net cell reaction by simply turning a knob. The reaction can be started and stopped by connecting or disconnecting the two electrodes. \]īut this time, the oxidation and reduction steps (half reactions) take place in separate locations:Įlectrochemical cells allow measurement and control of a redox reaction
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