Staircasing

Osteryoung J 1991 Square-wave and staircase voltammetry at small electrodes Microelectrodes Theory and Applications (Nate ASI Series) ed M I Montenegro, M A Queiros and J L Daschbach (Dordrecht Kluwer)... 

Potential-excitation signals and voltammograms for (a) normal pulse polarography, (b) differential pulse polarography, (c) staircase polarography, and (d) square-wave polarography. See text for an explanation of the symbols. Current is sampled at the time intervals indicated by the solid circles ( ). 

Figure 7.3 Schematic diagram illustrating that there ate two similar grooves in a helical staircase. Four rungs ate viewed from the top of the staircase in (b).

In 1953, James Watson and Francis Crick made their classic proposal for the secondary structure of DNA. According to the Watson-Crick model, DNA under physiological conditions consists of two polynucleotide strands, running in opposite directions and coiled around each other in a double helix like the handrails on a spiral staircase. The two strands are complementary rather than identical and are held together by hydrogen bonds between specific pairs of... 

The formation of such a staircase structure in the macromolecules of PAN in the process of thioamidation of PAN fibres with aqueous solutions of ammonium sulfide accounts for the significant increase of heat resistance of the modified fibres obtained. 

At Tonic, the generation named Britney walked up and down the steel staircases, balancing their martini glasses with perfect form, gripping them gingerly at the rim. 

We begin by showing that (3-33) holds for the special case where is a staircase function i.e. 

The concluding step in the argument is to note that many can be approximated, as closely as desired, by means of a staircase function. This means that, given such a function , it is possible to find a sequence of staircase functions fa with the property... 

The justification of Eq. (3-119) is similar in every respect to the one presented in the one-dimensional case. One first verifies, by direct calculation, that Eq. (3-119) is valid for n + m dimensional staircase functions—functions that are constant over n + m-dimensional intervals of the form an < xn < bn, cm < ym <, dm—and then argues that, since any function can be approximated as closely as desired by staircase functions, Eq. (3-119) must also hold for all . 

This means that the integral in Eq. (3-239) converges because all the increments of N(t) are, by definition, finite. Moreover, many h(t) of interest can be approximated as closely as desired by a staircase function so, at least for practical purposes, there is little loss of generality in restricting our attention to h(t ) s of the form (3-244). 

FIGURE 3-10 Potential-time wavefonn used in staircase voltammetry. 

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

In particular, considering a ballistic model for the charge transport through a dot, it was possible to demonstrate that the current through it should be represented as a series of equidistant peaks whose positions correspond to the steps in the coulomb staircase. 

All of the theoretical work proposed during the past 10 years forces experimental researchers to develop real systems to observe the described phenomena. In reality, only a year after the very first work of Averim and Likharev, the first measurements of the coulomb blockade and the coulomb staircase phenomena were published. 

A few months later, the observation of the coulomb blockade appeared (Fulton and Dolan 1987). In the case of a coulomb staircase, only one additional mouth was required (Earner and Ruggiero 1987). 

On the other hand, even in particle systems the coulomb blockade (Van Bentum et al. 1988a) and the coulomb staircase (Van Bentum et al. 1988b) were observed, some nonlinear effects were observed in the current-voltage characteristics (Wilkins et al. 1989), and behavior related to the quantized energy levels inside the particles was described (Crom-mie et al. 1993, Dubois et al. 1996). 

However, the main research result from those years was the discovery of the room-temperature single-electron phenomenon. In the 1990s, STM experiments on liquid crystal had shown a very weak staircase (Nejoh 1991) only one year later, the clear observations of the coulomb blockade and the coulomb staircase were demonstrated on gold nanoparticles (Shonenberger et al. 1992a) and the role of system symmetry on the appearance of these two phenomena was outlined (Shonenberger et al. 1992b). 

Finally, it was possible to build up the first stand-alone room-temperature singleelectron junction by depositing a semiconducting particle directly onto the tip of a very sharp electrode, avoiding in this case the use of an STM microscope, and it was possible to observe the coulomb staircase in such a system (Facci et al. 1996). 

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