Backward scans

As a first illustration of the potentialities of the convolution approach, we examine how correction of the ohmic drop may be handled in this manner. Figure 1.11 illustrates the various steps of the procedure. Convolution of the raw current data (solid line in Figure 1.11a) with the function l/y/nt leads to an S-shaped I vs. E curve which is not the same in the forward and backward scans because of ohmic drop (Figure 1.11b). Correction of the potential axis, according to E = E — Rui leads to an ohmic drop-corrected... 

These results suggest that the GaP surface with backward scanning develops an oxidized structure, which is acting as a precursor, or precursors, to the anodic dissolution reactions. 

This assumption is based on three relevant indications. First, this wave results in a limiting-current. This means that steady-state transport phenomena control the rate of this reaction, which is not compatible with a possible oxidation of metallic copper to Cu(I) or Cu(II). If the latter were to be valid, a peak-shaped response should have been obtained because of the limited available amount of metallic copper (initially deposited by reduction of Cu(II) or Cu(I) in the reduction wave). In addition, the second voltammetric oxidation wave in the backward scan direction is actually compatible with such a dissolution reaction. 

In the case of two separate peaks, the difference between the peak potentials coincides with the difference between the formal potentials for AE < —142 mV. Under these conditions, the value of the formal potentials can be extracted from the average value of the peak potentials of the forward and backward scans ... 

Fig. 39 a Topography, b Normal force error signal. Friction for c the forward scan d the backward scan e real part (i.e. conductivity) f imaginary part (i.e. capacity) of the simultaneously measured a.c. current The cantilever is made of silicon coated with diamond. Scan range 11.5x5.1 pm, topography corrugation 121 nm, force and friction in arbitrary units, ohmic current range 0-42 nA, capacitive current —60 pA to +30 pA, excitation 1 V at 16,789 Hz... 

FIG. 13 Effect of phasing on signal shape. The TMS peaks on both forward and backward scans are quite high and narrow, with good ringing and perfect symmetry. Ringing is seen only on CW spectrometers. 

Figure 5.26 Hysteresis effects of a piezoelectric scanner on imaging. The bottom figure illustrates the profile difference between forward and backward scanning. (Reproduced with permission from RC. Braga and D. Ricci (eds), Atomic Force Microscopy, Humana Press. 2004 Humana Press.)...

The convolution technique offers a number of advantages in the treatment of linear sweep data (and perhaps also in other electrochemical techniques). For a reversible reaction in a cyclic voltammetric experiment, the curves of l(t) vs. E for the forward and backward scans superimpose, with l(t) returning to zero at sufficiently positive potentials [where Cr(0, 0 = 0]. This behavior has been verified experimentally (20, 25, 28) (Figure 6.13a). 

Figure 6 shows voltammograms for the transfer of FRTR+ cations across the DCE W interface in the absence and presence of 20 mM decamethylferrocene in DCE [12]. The negative current on the backward scans completely disappeared on addition of decamethylferrocene in DCE. In view of the lipophilicity of decamethylferrocene, this is a good example of the ion-transfer process described by the E Ci mechanism. From the shift of the peak potential, E, with the scan rate, v, the pseudo-first order rate constant, kf, can be estimated using the Nicholson and 8hain s equation for the peak shift in the case of Ej.C mechanism [42] ... 

Data are collected during the forward and backward scan of the mirror. Forward and backward scans are coadded separately, calculated and then added. This mode has less dead time and a better signal-to-noise ratio, but requires twice as much computation time. 

On the Store page (Fig. 10.41) specify the wavenumber range and the spectrum type to be saved. Notice that the calculated spectrum block always is of type Single-Channel In addition, one can also save the Phase spectrum and the Power spectrum, which can be calculated from the parts of the interferogram known from forward and backward scans with the Phase Resolution setting. 

Interferograms recorded in forward/backward mode can be processed using either the scans during the forward or the backward movement of the mirror. If the two directions of the mirror travel should be evaluated, the forward and the backward scan will be transformed separately, followed by a phase correction and calculation of the average spectrum. 

If the data have been recorded in multiplex mode, then the interferogram contains alternating data from two ADCs. With the options even and odd the data from both ADCs can be evaluated separately. There is no such option for backward scans. Therefore, multiplex measurements should be recorded only with pure Forward modes. 

When CV is conducted at stationary microelectrodes with slow V, in both forward and backward scans sigmoidal current-voltage curves are found which are usually coincident, except for processes involving coupled chemical reactions that display more or less marked hystereses. This sigmoidal shape (steady-state current) can be accounted for by considering the radial diffusion to the edges of ultramicroelectrode surfaces that is very important at slow v, so as to make the diffusion rate of analyte molecules to the electrode surface comparable with the charge transfer rate. 

Fig. 6.15a,b Cyclic voltammogram (a) and voltadeflectogram (b) of a PANI film in 1 moldm HCIO4. Scan rate 50mVs Forward scan (full arrow) and backward scan (dotted arrow) are shown. (Reproduced from [144] with the permission of Elsevier Ltd.)... 

Fig. 1.5 Methanol oxidation peak currents as a function of Pt coverage (4 nmol as 2D islands is approximately 0.8 of a monolayer), where If and Ib represent peak currents at forward and backward scans, respectively (a) Pt mass activity for methanol oxidation on commercial PtRu and PtML/Ru electrocatalysts (b) [77] (reproduced with permission from J. Electrochem. Soc. 155, B183 (2008). Copyright 2003, The Electrochemical Society)...

The reversible electron transfer results in anodic peak on the backward scan (curve 3 ). The height of Ip is identical with Curve 4 in Fig. 12B is characteristic for the irreversible electron transfer in the kinetic zone. Both 2- and /I-parameters are low. Forward and backward curves (4 and 4 ) have sigmoidal shape and retrace the same path. For the limiting kinetic current Eqs. (75) and (76) resp. hold as well. 

Fig. 13. Simulated cyclic voltammograms for ECj mechanism for several values of X=kfla. Normalized current functions ij/i vs. nd E = n(E - Ej/2) values of A for backward scans (1) 0.01, (2) 0.1, (3) 10, (4) 500. Curves 1 and 2 in the forward (cathodic) scan coincide backward (anodic) scans are dashed. Adapted from ref. [81].

Figure 1. Topographical and lateral force line scans of 100 nm, recorded with an applied load of 9.5 nN and pH = 4. The mean roughness of the sample is below 0.1 nm. The difference between forward and backward scans in the lateral force scan corresponds to twice the frictional force.

The experimental results in Figure 1 display a single line scan over a range of 100 mn for an applied load of 9.5 nN and a pH of 4. The upper panel shows the topographical signal, while the lower panel shows the signal due to lateral forces. To determine the frictional force, we have calculated the difference between a forward and a backward scan. Since the samples are very smooth (rou ness below 0.1 nm over a scan range of 100 mn),... 

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