Non-reversing curve

Tgr = the glass transition at the mid-point of the reversing signal A//nr = the area under the non-reversing curve (i.e. the area between the reversing and total curves)... 

The concentration profiles are very sensitive to the kinetics of the electrode reaction. In this context, the determination of the diffusion layer thickness is of great importance in the study of non-reversible charge transfer processes. This magnitude can be defined as the thickness of the region adjacent to the electrode surface where the concentration of electro-active species differs from its bulk value, and it can be accurately calculated from the concentration profiles. In the previous chapter, the extensively used concept of Nemst diffusion layer (8), defined as the distance at which the linear concentration profile (obtained from the straight line tangent to the concentration profile curve at the electrode surface) takes its bulk value, has been explained. In this chapter, we will refer to it as linear diffusion layer since the term Nemst can be misunderstood when non-reversible processes... 

As can be observed from these curves, the rate of variation of linear and real diffusion layer thickness with time increases with k°, being maximum for A° > 0.1 cm s 1. which corresponds to the reversible case. From Fig. 3.1a, it can be seen that for reversible processes the surface concentration is independent of time in agreement with Eq. (2.20) (see also Fig. 2.1 in Sect. 2.2.1). However, for non-reversible processes (Fig. 3.1b and c), the time has an important effect on the surface concentration, such that csQ decreases as I increases, with this behavior being more marked for intermediate k° values (quasi-reversible processes). So, for k° = 10 3 cm s 1. the surface concentration decreases by 19 % from t = 0.1 to 0.4 s, whereas for k° = 10 4 cm s 1 it only varies 7 %. It is also worth noting that for the reversible case (Fig. 3.1a), the diffusion control (cf, > 0) has practically been reached at the selected potential. 

Equations (5.83) and (5.84) and the curves in Fig. 5.12 indicate that both peak current and potential of the CV curves change with the scan rate, a feature which is not observed for the peak potential of reversible processes (see Eq. (5.57)). However, the experimental evidence that for a given system the potential peak of the cathodic CV curves shifts to more negative values with increasing scan rate should be used with caution when assigning a non-reversible behavior to the system since, similar displacements can be observed for Nemstian systems when the ohmic drop has an important effect (see Fig. 5.11). Thus, the shift of the CV peak potential with the scan rate is not always a guarantee of a non-reversible charge transfer process. 

For nonplanar electrodes there are no analytical expressions for the CV or SCV curves corresponding to non-reversible (or even totally irreversible) electrode processes, and numerical simulation methods are used routinely to solve diffusion differential equations. The difficulties in the analysis of the resulting responses are related to the fact that the reversibility degree for a given value of the charge transfer coefficient a depends on the rate constant, the scan rate (as in the case of Nemstian processes) and also on the electrode size. For example, for spherical electrodes the expression of the dimensionless rate constant is... 

Thus, the number of peaks is not merely a function of AEf, as in the reversible case. As an example, the CV curves corresponding to a two-electron non-reversible charge transfer calculated for A Ef = 0 V and Xplane, (=1) and different values of Kpiane2 have been plotted in Fig. 6.4. From these curves, it is clear that the morphology of the voltammograms evolves from a single pair of peaks for the case in which Kplane 1 = Xplane 2 to the appearance of a second pair of peaks which are... 

Moreover, for non-reversible charge transfers, the voltammetric curves corresponding to the direct and reverse scans can become very different, and the number of peaks is no longer fixed only by the value of Abut also by the values of the kinetic constants of steps 1 and 2 in scheme (6.II). Thus, for the CV curves of these figures, the direct response tends to present two peaks as the process becomes more irreversible (an obvious feature for very negative values of AEf1 but not so obvious for zero or even positive ones), and the reverse voltammogram presents only one. 

Fig. 7.15 Influence of the dimensionless rate constant Kplane = k° Jr/D on the SWV forward (idashed lines) and reverse (solid lines) currents i//] la"c and i// 3la"e (a) and on the SWV net current (b), corresponding to a non-reversible electrochemical reaction at a planar electrode. sw = 50mV, AEs = 5mV, a = 0.5. The values of Kplane = k°yJr/D appear on the curves...

The non-reversible behavior is plotted in Fig. 7.46, which corresponds to the corrected (Jcv/v) — E curves (dashed lines) and the (QDSCVC/AE) — E ones (symbols) of the system 4-PhenylazoPhenol. From these curves, it can be seen that although the DSCVC curves are perfectly superimposable, the CV ones clearly show smaller peak heights in both scans. This systematic decrease of the CV signals, which cannot be theoretically predicted, is 5-10 %, and it has been reported when the response of electro-active monolayers in CV has been compared with other voltammetric and chronopotentiometric electrochemical techniques [71, 72], Due to the quasi-reversible nature of the charge transfer reduction of the 4-PhenylazoPhenol, no simple equations for the peak parameters are available. So, a numerical comparison between theoretical and experimental curves for different sets of parameters should be made in order to obtain the kinetic and thermodynamic parameters of the system. 

Fig. 7.55 SWV and SWVC curves for a non-reversible surface EE process calculated from Eqs. (6.185) to (6.191) and Eq. (7.5). The values of the dimensionless rate constant Tl and of the difference between formal potentials AE appear on the figures. = 1, cq = a-i = 0.5, ESw = 50mV, AEs = 5mV, T = 298 K...

While the sorption curves are almost linear on a log log scale, the model fits a gentle curve as this is consistent with a bigger body of information (Fig. 9.). At any given level of sorption, the concentration of selenite in solution decreases with time and with increasing temperature. It is this decrease that is modelled as due to diffusive penetration. Selenate differs in that the sorption curves are steeper (as also shown in Fig. 9.) and, importantly, that the effects of time, though detectable, are much smaller. These two species therefore provide a test for the argument that apparent non-reversibility of sorption occurs because of the continuing reaction. 

Cp X heating rate) is termed the reversing heat flow component. The non-reversing part is obtained by subtracting this value from the total heat flow curve. It is important to note that all... 

Mulopo, J.L., D. Hildebrandt, and D. Glasser, Reactive residue curve map topology Continuous distillation column with non reversible kinetics. Computers Chemical Engineering, 2008, 32(3) 622 629. 

MTDSC has become very much the established technique in the study of polymeric materials where its advantages over conventional DSC can be exploited. Figure 8 illustrates the use of MTDSC for the separation of overlapping thermal events in a poly(ethylene terephthalatej-acrylonit-rile butadiene styrene (PET-ABS) blend. The thermal analysis curve for PET alone was shown in Figure 4. The present figure shows the total heat flow for the blend and its separation into the reversing and non-reversing... 

Figure 1.9 shows an example of detecting a glass transition beneath a cold crystallisation exotherm. The total heat flow corresponds to a conventional DSC experiment. It is not possible from inspection of the distorted peak in this curve to conclude that it is formed from an exotherm (from the crystallisation of PET) superimposed on a glass-rubber transition (from the polycarbonate). The additional signals of MTDSC make this interpretation clear. In this case, the crystallisation acts like a chemical reaction once formed the crystals remain as the temperature increases through the peak. Thus, the process is non-reversing. 

Figure 2.13. Quasi-isothermal cure of an unsaturated polyester at 30, 40, and 50°C (a) non-reversing heat flow (b) heat capacity and heat flow phase the heat flow phase curves were shifted vertically to avoid overlap. The symbols (o) denote the points at maximum auto-acceleration in the non-reversing heat flow.

All non-reversible processes are called irreversible. An example of an irreversible process is expansion of a gas into a vacuum during the expansion process the system is in a state of non-equiUbrimn and cannot be described by the usual macroscopic state variables such as temperature T and pressure p. The irreversible expansion of a gas into a vacuum can therefore not be shown as a process curve in a pV diagram. 

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