Converted charge

Generally, a continuous recording of electrically available data - for example, current, cell voltage, electrode potentials, temperatures - is beneficial to supervise the proper procedure of each experiment. Especially in case of a failure this will be a valuable help to find the reason. Today, the best way is to use a data acquisition system in a computer that offers the results directly for further calculations, for example, integration of the consumed current (converted charge). For continuously operated experiments the addition of scales, which acquire the weight of input and output reservoirs, will be advantageous in order to supervise the mass balances continuously. 

The time variation of the normalized converted charges for planar, spherical, and disc electrodes can be seen in Fig. 4.3, for which a radius of 10 pm has been assumed for the spherical and disc electrodes. Q is the maximum converted charge for the first potential pulse corresponding to a time t -, and is given by... 

It is clear from Fig. 4.3 that the temporal evolution of the converted charge is electrode-size and shape depending. For spherical and disc electrodes, the evolution... 

Eq. (4.61) and Table 2.3 of Sect. 2.6), whereas for the second potential pulse the amount of converted charge is much smaller than that obtained at a planar electrode (macroelectrode). Indeed, when the electrode radius becomes small enough the converted charge for the second potential pulse is constant and coincides with (for example, from Eq. (4.62) in the limit rs current-time curves. 

Equations (4.54) and (4.55) only consider the faradaic charge, that is, only the converted charge due to the redox conversion of species O and R. The total converted charge should contain also a contribution due to the double layer charging process (Qc) and, if there is adsorption of redox species, an addend which accounts the charge due to the reduction of these immobilized molecules... 

The experimental measurement of the converted charge can be made easily by integrating the recorded current. 

The temporal evolution of the current I and the converted charge Q t have been plotted in Fig. 6.18 for different values of the dimensionless rate constant k°Tj and a = 0.5. Both responses have been written in their dimensionless forms, /n,i = h HQt/ti) and QN I = Q JQ , with QF given by... 

For very small values of k°(i.e., for irreversible processes), very negative potentials are needed to obtain a measurable response and under these conditions red,i kox. i. By introducing this condition in Eqs. (6.115) and (6.116), the expressions of the time-dependent converted charge and current become... 

Equations (6.132) or (6.133) for the converted charge are valid for any electrochemical technique, i.e., the charge/potential response for a reversible process is universal. The Q-E curves given in these equations present a sigmoidal-type feature which allows us to obtain the QP value and, therefore, the total surface excess I, , at sufficiently negative potentials of the cathodic response. 

As stated in Sect. 6.4.1, it has been assumed that the measured experimental currents and converted charges when a potential Ep is applied can be considered as the sum of a pure faradaic contribution, given by Eqs. (6.130) and (6.131), and a non-faradaic one, /pnf and Qpnl. In order to evaluate the impact of these non-faradaic contributions on the total response, analytical expressions have been obtained. If it is assumed that initially the monolayer is at an open circuit potential, rest, and then a sequence of potential pulses , E2, -,Ep is applied, the expression for the non-faradaic charge Qp.nf can be deduced from the analogy between the solution-monolayer interface and an RC circuit [53] (shown in Fig. 6.24), so the following differential equation must be solved ... 

From this result, the converted charge gEE transferred for a di-electronic transfer process is straightforwardly obtained as the sum of charges Qp, and QP 2 for steps 1 and 2, respectively... 

The converted charge can also be obtained by integrating the current ... 

For fast electron transfers, the expression of the converted charge simplifies to... 

A stationary behavior is attained when the condition kc 1 s 1 holds. Under these conditions, the terms 9m become null (see Eqs. (6.200) and (6.201)) and Eqs. (6.202) and (6.205) for the current and converted charge take the following simpler form, whatever the reversible degree of the electrode reaction ... 

From the charge-potential curves in Figures b and d, it is clear that a stationary behavior cannot be reached in any case. From the first scan of these curves, it can be seen that the converted charge is null up to potentials close to E, from which it increases with the potential, with this increase becoming linear for sufficient cathodic values. For the second scan, the charge-potential curves present an opposite behavior, i.e., they increase linearly until they reach a constant value (charge plateau) for enough cathodic potentials. 

From this linear relationship between the charge and the potential, kc is easily deduced from the cathodic slopes of both sweeps. The expression of the reversible cathodic converted charge plateau can also be deduced from Eq. (6.216) by imposing E —> —00 in the second cathodic sweep (see Eq. (6.217)) ... 

In the case of the CVC curves of Fig. 6.32b, the converted charge increases as the scan rate decreases and they show a clear linear region at potentials above 0.20 V. The slope of these linear zones should be equal to (A cGf)/v (see Eqs. (6.214) and (6.218)). The values of the slopes of the linear regression of these zones for different values of v in the range 0.20-100 V s-1 have been plotted vs. the inverse of the sweep rate and from these data (kcQ ) = (11.3 0.2)nA has been obtained. This value is practically coincident with that obtained from the current-potential curves of Fig. 6.32a. 

A common feature of the electrochemical techniques considered in this chapter is that the recorded signal is the difference between the current (or converted charge) sampled at the end of consecutive potential pulses of a given sequence E, E2,..., Ep without the initial conditions being regained. This difference is plotted versus a potential axis, giving a peak-shaped response in all the cases. 

The general features of the potential time perturbations and of the current-potential (or converted charge-potential) responses characteristic of these techniques are ... 

A variant of DSCVC is DSCVC, for which the response is built by subtracting the converted charge measured at the end of each pair of consecutive potential pulses applied [4] ... 

In SWVC, the square wave potential sequence given by Eq. (7.5) is applied to the analysis of the converted charge in an electrochemical reaction between surface-bound molecules in order to obtain the gsw E curves, in line with Eq. (7.8), instead of the usual /sw E curves corresponding to SWV. The <2SW —E curves present an intense signal for reversible processes from which they can be completely characterized [5]. The analytical expression of the SWVC charge-potential is (see Eqs. (6.131) and (7.8)) ... 

It is evident that the square wave charge-potential curves corresponding to surface-bound molecules behave in a similar way to the normalized current-potential ones observed for a soluble solution reversible redox process in SWV when an ultramicroelectrode is used (i.e., when steady-state conditions are attained), providing the analogous role played by 2sw (surface-bound species) and (soluble solution species), and also 2f (Eq- (7.93)) and the steady-state diffusion-limited current (7 css), see Sect. 2.7. This analogy can be made because the normalized converted charge in a surface reversible electrode process is proportional to the difference between the initial surface concentration (I ) and that... 

The analysis of the influence of the non-faradaic component corresponding to the converted charge-potential (Q-E) and current-potential (I-E) curves, is very different. A short discussion of this influence in some of the subtractive techniques analyzed follows. 

From Fig. 7.55c, d, it is clear that the converted charge-potential curves obtained with SWVC are much more sensitive than the SWV ones for quasi-reversible electrode reactions, although the response charge-potential (SWVC curves) is... 

This equation indicates that the peak potential is located at more negative values than E 1 and it moves toward the formal potential as Esw increases. When high values of the square wave pulse amplitude are used, the Q — E curves show a broad plateau which is centered at a potential E Et° — (RT/(2F)) n + c). Another interesting characteristic of the Q, — E curve is the cross potential for which the converted charge is null. For reversible conditions, it is given by (see... 

Converters charging, slag skim, Smoke, fume, S02 Exhaust system, settling chambers,... 

Methods for converting starch into the 90-d.e. liquors already mentioned were known before Newkirk s invention of these crystallization processes. In those conversions, the general procedures are the same as those described previously for the manufacture of com syrups. However, in the 90-d.e. conversions, the starch concentration is 20%, 50% more acid is used per converter charge, and the maximum pressure and time at that pressure are 45 lb. in-2 (3.16 kg. cm-2) and 30 minutes, respectively. 

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