Nonlinear system voltage-current curves

Abstract Described are the synthetic routes to precisely defined molecular wires which are of discrete length and constitution. They are fully conjugated systems and are expected to have nearly linear current-voltage response curves. Their ends are functionalized with molecular alligator clips, based on chalconides and isonitriles, for adhesion between proximal probes. Both solution and solid-phase approaches have been used to prepare these molecular wires that are based on oligofthiophene ethynylene)s and oligofphe-nylene ethynylene)s. Molecular device syntheses are also described that would be expected to have nonlinear current-voltage responses. 

We saw previously that concentration polarization results in the decrease of solute concentration near the permselective interface (right at the interface in the electro-neutral version) where most of the system s resistance thus concentrates, and where the space charge develops. The system is expected to be sensitive to the minimum concentration value, and because of nonlinearity nontrivial effects, could be anticipated in response to unsteady disturbances of this value (e.g., provided by harmonic modulation superimposed upon a constant voltage applied to the system). Since it is easier to increase the minimal concentration (close to zero at the limiting current) than to decrease it, we might expect a positive rectification effect for the direct current component, counterintuitive ( anomalous ) in the present system with a convex stationary VC curve. Thus the topic of this section is the rectification effects that arise in the stationary concentration polarization in response to a harmonic voltage modulation. 

From Figure 7.20 and file Butler—Volmer Eq. 7.15, it is clear that file DC resistance is strongly dependent on the DC current through the electrode. Wifli an AC superimposed on a DC, the resultant AC is dependent on the incremental resistance/conductance of the DC curve. If excitation is sinusoidal, and the measured AC voltage or current also is sinusoidal, then the system is linear with the amplitudes used. By increasing the amplitude, there will always be a level when nonlinearity is reached. 

The local ohmic behavior is not in contradiction with the fact that Eq. (41) shows a nonlinear variation of 7 with the potential drop A >. At low potentials, fA4> 1, the DBL is practically nonpolarized (i.e. the ionic concentrations take their bulk values throughout the DBL) and the slope of the current-voltage curve is When increasing A, the slope of the current-voltage curve decreases owing to the development of concentration polarization. The effective conductivity varies then with position and this makes the overall system behavior to be nonohmic. 

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