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The electrical characteristics of highly dense SnO 2 ceramic varistors are believed to be caused by the existence of potential barriers at the grain boundary. A complex plane analysis technique ͑to eliminate the influence of trapping activity associated with the conductance term observed via depression angle of a semicircular relaxation in the complex capacitance plane͒, allied with an approached Mott-Schottky model, are used to demonstrate that the potential barriers at the grain boundary are Schottky-type barriers in SnO 2 varistors such as those observed in the traditional ZnO varistor.

Relaxation processes occurring during electroinsertion into pure SnO 2 and electrochromic SnO 2 /Sb were interpreted on the basis of frequency-dependent response models. Within the framework of the classic theory of porous electrodes, the results indicated that, in the case of nanosized particle-based electrodes, the overall kinetic aspects of the insertion process can be controlled by the transport of ionic and electronic species in the liquid and solid phases, respectively. Therefore, if both the electronic and ionic transport are fast in both the solid and liquid phases, or if the state-of-charge is high, a relaxation process corresponding to the insertion of Li + in specific sites inside the nanosized particles is clearly identifiable, as foreseen by the model discussed in part 1. As a result, in the SnO 2 /Sb samples, we have successfully separated the frequency of slow charging of transport effects due to the nonfaradaic capacitance-related process from that of faradaic related capacitances, because these two processes do not overlap and can, in such specific situations, be separated in complex capacitance diagrams. Moreover, our interpretation of the results indicates that the participation of a large amount of inserted charge in the Sb-doped sample is possible due to the "nanoscale factor", which, allied to the high electronic conductivity in the solid phase, causes rapid charging of the faradaic capacitance-related process. In our interpretation, the faradaic capacitance related process is linked to the insertion of Li + into the solid-state phase of nanosized particles and can be interpreted as an ion immobilization or trapping process, as discussed earlier in part 1.

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Within the context of an electron dynamic (time-dependent) perspective and a voltage driving force acting to redistribute electrons between metallic and addressable molecular states, we define here the associated electron admittance and conductance. We specifically present a mesoscopic approach to resolving the electron transfer rate associated with the electrochemistry of a redox active film tethered to metallic leads and immersed in electrolyte. The methodology is centred on aligning the lifetime of the process of electron exchange with associated resistance and capacitance quantities. Notably, however, these are no longer those empirically known as charge transfer resistance and pseudo-capacitance, but are those derived instead from a consideration of the quantum states contained in molecular films and their accessibility through a scattering region existing between them and the metallic probe. The averaged lifetime (τr) associated with the redox site occupancy is specifically dependent on scattering associated with the quantum channels linking them to the underlying metallic continuum and associated with both a quantum resistance (Rq) and an electrochemical (redox) capacitance (Cr). These are related to electron transfer rate through k = 1/τr = (RqCr)−1. The proposed mesoscopic approach is consistent with Marcus’s (electron transfer rate) theory and experimental measurements obtained by capacitance spectroscopy.

The electron exchange between a redox-active molecular film and its underlying electrode can be cleanly tracked, in a frequency-resolved manner, through associated capacitive charging. If acquired data is treated with a classical (non quantum) model, mathematically equivalent to a Nernst distribution for one redox energy level, redox site coverage is both underestimated and environmentally variable. This physically unrealistic model fails to account for the energetic dispersion intrinsically related to the quantized characteristics of coupled redox and electrode states. If one maps this redox capacitive charging as a function of electrode potential one not only reproduces observations made by standard electroanalytical methods but additionally and directly resolves the spread of redox state energies the electrode is communicating with. In treating a population of surface-confined redox states as constituting a density of states, these analyses further resolve the effects of electrolyte dielectric on energetic spread in accordance with the electron-transfer models proposed by Marcus and others. These observations additionally underpin a directly (spectrally) resolved dispersion in electron-transfer kinetics.

Electrochemical immunosensors offer much in the potential translation of a lab based sensing capability to a useful "real world" platform. In previous work we have introduced an impedance-derived electrochemical capacitance spectroscopic analysis as supportive of a reagentless means of reporting on analyte target capture at suitably prepared mixed-component redox-active, antibody-modified interfaces. Herein we directly integrate receptive aptamers into a redox charging peptide support in enabling a label-free low picomolar analytical assay for C-reactive protein with a sensitivity that significantly exceeds that attainable with an analogous antibody interface.