Semi-differentiation

The related circuit, shown in Fig. 35, performs semi-differentiation... 

Methods to compute jF (t) values reliably have been discussed extensively by the above-mentioned authors, especially by Oldham who stated that eqn. (99) can be considered as the semi-integral of jF t), generated by the operator d-1/2/df-1/2. Consequently, various rules derived for semiintegration and semi-differentiation can be applied, placing the principle in a more general context [80]. 

Goto, M. Ikenoya, K. Kajihara, M. Ishii, D. Application of semi-differential analysis to anodic stripping voltammetry. Anal. Chim. Acta 1978, 101, 131-138. 

Calculate the resulting semi-differential, and plot the resulting curve, togetherwith i/4iin>as a function of t and of E, respectively. Compare with Fig. 6.11-3. 

In its semi-differentiation mode, the macro instead converts a stationary current-voltage curve into the corresponding linear sweep or cyclic voltammogram. 

The macro uses a simple semi-integration algorithm given by Oldham which is adequate to illustrate the approach. The semi-differential is then found by taking first differences. 

Rorrer GL, Polne-Fuller M, and Zhi C, Development and bioreactor cultivation of a novel semi-differentiated tissue suspension derived from the marine plant Acrosiphonia coalita, Biotechnol. Bioeng. 49, 559, 1996. 

Fig. 11.10 Linear sweep semi-integral and semi-differential curves of 10 SM Cd(II) in 1M NaCI at a DME. Average of 25 scans, (a) Linear sweep curve, (b) Linear extrapolation of background current, (c) Background-corrected linear sweep curve, (d) Semi-integral curve, (e) Least-squares fitted semi-integral curve, (f) Semi-differential curve. (Reproduced from [39] with permission of the American Chemical Society).

Studies made with this instrumentation on other voltammetrlc techniques such as anodic stripping voltammetry allow one to conclude that the optimization of initial d.c. linear sweep or stripping data leads to optimum performance In the semi-integral, semi-differential and derivative approaches and that, under Instrumental equivalent conditions where d.c. experiments have been optimized with respect to electronic noise and background correction, detection limits are not markedly different within the sub-set of related approaches. Obviously, the resolution and ease of use of a method providing a peak-type readout (semi-differential) are superior to those with sigmoidally shaped read- outs (semi-integral). 

The relationship given in Eq. (II. 1.10) can be used directly to derive the theoretical shape of a reversible cyclic voltammogram by applying semi-differentiation... 

Semi-integral and semi-differential voltammetry It can be shown from solution of the diffusion equation that the time-dependent concentration of Red at the electrode surface is expressed by ... 

On the other hand, the first derivative of m(t) and therefore the semi-derivative of I(t) defined by dl/dt = dm/dt = d -I/dt - is recorded in semi-differential voltammetry. The dm/dt vs. potential curve, shown in Fig. 6 for the reversible case, exhibits a symmetrical peak shape. This indicates enhanced resolution and sensitivity of semi-differential voltammetry relative to potential sweep voltammetry. The peak height and the peak potential for the reversible case are given by 0.25n-F AuDJ/-CR/RT and E i2, respectively. Slow heterogeneous kinetics lowers the peak height and shifts the peak potential positively. 

Fig. 6. Semi-integral (b) and semi-differentiated responses (c) of the linear sweep voltam-mogram (a).

The convolution at time t is thus akin to an integral of the current but with a factor decreasing the importance of the current contribution at a given time of measurement u by the square root of the time elapsed since that measurement was made. Indeed if the is similarly convoluted then the result is the charge Q ie. the integral of i(u) hence the terms semi-integration is used for this particular convolution process. The semi-differential or deconvolution is likewise obtained via semi-integration followed by differentiation. 

A conventional 3 electrode system was used for cyclic voltammetry with 1 cm square planar platinum working counter electrodes a reference electrode using the same TBAP (tetrabutyl ammonium perchlorate) electrolyte (normally at 0.1 mol dm ). In dimethyl formamide (DMF) containing solutions the Ag reference electrode was inunersed in a 0.01 mol dm Ag solution in chloromethane solutions the electrolyte was saturated with lithium chloride. An EG G Potentiostat Model 362 was coupled to a computer based data cs ture treatment system. The latter included the ability to software compensate for electrolyte resistance between reference working electrodes to semi-integrate semi-differentiate Ae current responses obtained. 

The cyclic voltammetric currents were normally not the main source of attention but rather the semi-integral Ij of the current was calculated from this the semi-differential or square root of time deconvolution dlj/dt. This dlj/dE were used for the clearest displays of results. The main difference in application of the latter pair depends on whether a potential ramp linear with time is applied at die working electrode surface i.e. hardware compensated at tte potentiostat if necessary for resistance between working counter electrodes. In this case using the linearly varying potential as an axis dlj/dt dl/dE are similar in shape either provides a suitable display. If uncompensated resistance remains then in Nernstian systems I is a function of the appropriate E (E ) suitable compensation via -i.R can be sqiplied post csqiture... 

Different techniques such as linear sweep voltammetry (LSV) with and without semi-differentiation (SD), pulse voltammetry and differ-... 

That Is, the seml-differentlated current measures the differential change in suface concentration of the target species. Hence the semi differentiated voltammogram gives a much narrower pea for each system 100 mV) centred for a reversible system on the E of the substance. The actual operation of semi-differentiation can be achieved by a simple analogue circuit [21]. 

Fig. 19. A typical semi-differentiated voltammogram obtained with a carbon paste electrode in the striatum of an unanaesthetized rat. h = peak height.

According to the electrochemical analyses with semi-integral and semi-differential methods, the reduction process of [Nd(TFSA)5] or [Dy(TFSA)5] proceeded in one step, [Nd(TFSA)5] +3e —>Nd(0)+5[TFSA] , or two steps, [Dy... 

Fig. 6.15 Semi-differential curve obtained from the voltammogram of 0.5 mol dm [Nd(TFSA)5l - in [P2225HTFSA] at 353 K on a Pt electrode with scan rate 10 mV s ...

Dalrymple-Alford P, Goto M, Oldham KB (1977) Peak shapes in semi-differential electroanalysis. Anal Chem 49(9) 1390-1394. doi 10.1021/ac50017a025... 

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