Multipulse techniques

A wide variety of ID and wD NMR techniques are available. In many applications of ID NMR spectroscopy, the modification of the spin Hamiltonian plays an essential role. Standard techniques are double resonance for spin decoupling, multipulse techniques, pulsed-field gradients, selective pulsing, sample spinning, etc. Manipulation of the Hamiltonian requires an external perturbation of the system, which may either be time-independent or time-dependent. Time-independent... 

One-dimensional111 and 13C NMR experiments usually provide sufficient information for the assignment and identification of additives. Multidimensional NMR techniques and other multipulse techniques (e.g. distortionless enhancement of polarisation transfer, DEPT) can be used, mainly to analyse complicated structures [186]. 

Mach-Zehnder interferometer, 144 Medical applications, 153 Metal-insulator transitions, 52 Monte Carlo procedure, 135 Multi-energy X-ray imaging, 131 Multilayer targets, 131 Multiphoton absorption, 85 Multiphoton ionization, 82 Multiple filamentation, 91, 92 Multipulse techniques, 152... 

First, various advanced multipulse techniques have been developed since the mid-1970s, and nowadays are routinely applicable on spectrometers of the latest generation. Particularly innovative and ingenious among these methods are two-dimensional NMR techniques (506-508) and double quantum transition measurements (INADEQUATE) (507-509), which allow one to determine connectivities between carbon atoms within a molecule. 

However, it is important to take into account that the influence of the charging current depends on the potential perturbation (for a more detailed discussion concerning multipulse techniques, see Sect. 5.2.3.4). 

However, in the electrochemical literature the terms pulse techniques and multipulse techniques are well established and commonly used to define a set of potential-controlled techniques. In order to maintain this nomenclature, the definition of pulse referred to the potential perturbation should be considered as equivalent to that given for a step potential, i.e., without any restriction on the duration of the perturbation and the return to a given resting potential. This will be the criterion followed throughout this book. 

In conclusion, in Pulse and Multipulse techniques the perturbation is given as an arbitrary sequence of constant potentials without any a priori restriction on the duration of each individual potential of the sequence or on the particular waveform employed, and the current is sampled at a pre-fixed time. 

A complete comprehension of Single Pulse electrochemical techniques is fundamental for the study of more complex techniques that will be analyzed in the following chapters. Hence, the concept of half-wave potential, for example, will be defined here and then characterized in all electrochemical techniques [1, 3, 8]. Moreover, when very small electrodes are used, a stationary current-potential response is reached. This is independent of the conditions of the system prior to each potential step and even of the way the current-potential was obtained (i.e., by means of a controlled potential technique or a controlled current one) [9, 10]. So, the stationary solutions deduced in this chapter for the current-potential curves for single potential step techniques are applicable to any multipotential step or sweep technique such as Staircase Voltammetry or Cyclic Voltammetry. Moreover, many of the functional dependences shown in this chapter for different diffusion fields are maintained in the following chapters when multipulse techniques are described if the superposition principle can be applied. 

They are applicable to electrodes of any shape and size and are extensively employed in electroanalysis due to their high sensitivity, good definition of signals, and minimization of double layer and background currents. In these techniques, both the theoretical treatments and the interpretation of the experimental results are easier than those corresponding to the multipulse techniques treated in the following chapters. Four double potential pulse techniques are analyzed in this chapter Double Pulse Chronoamperometry (DPC), Reverse Pulse Voltammetry (RPV), Differential Double Pulse Voltammetry (DDPV), and a variant of this called Additive Differential Double Pulse Voltammetry (ADDPV). A brief introduction to two triple pulse techniques (Reverse Differential Pulse Voltammetry, RDPV, and Double Differential Triple Pulse Voltammetry, DDTPV) is also given in Sect. 4.6. 

In Multipulse techniques, the potential waveform consists of a sequence of potential pulses Ei, E2, , Ep, and the initial conditions of the system are only regained after the application of the last potential step [1-6]. When the potential waveform is a staircase of constant pulse amplitude AE, the perturbation includes as a limiting... 

The simplest case of a multipulse technique corresponds to the record of the current time (chronoamperometry) or the charge time (chronocoulometry) curves obtained when a given sequence of successive potential pulses Eu E2,. .Ep is applied for times 0 < tn < t , with n= 1, 2,. .., p, as shown in Scheme 5.1. 

As can be seen in this figure, the combined effect of ohmic drop and double-layer capacitance is much more serious in the case of CV. The increase of the scan rate (and therefore of the current) causes a shift of the peak potentials which is 50 mV for the direct peak in the case of the CV with v = 100 V s 1 with respect to a situation with Ru = 0 (this shift can be erroneously attributed to a non-reversible character of the charge transfer process see Sect. 5.3.1). Under the same conditions the shift in the peak potential observed in SCV is 25 mV. Concerning the increase of the current observed, in the case of CV the peak current has a value 26 % higher than that in the absence of the charging current for v = 100 Vs 1, whereas in SCV this increase is 11 %. In view of these results, it is evident that these undesirable effects in the current are much less severe in the case of multipulse techniques, due to the discrete nature of the recorded current. The CV response can be greatly distorted by the charging and double-layer contributions (see the CV response for v = 500 V s-1) and their minimization is advisable where possible. 

In Sects. 2.3 and 4.2.4.1, the electrochemical response corresponding to ion transfer processes through liquid membranes in single potential pulse and double potential pulse techniques has been discussed. In this section, these processes are analyzed with multipulse techniques, mostly with Staircase Voltammetry and Cyclic Voltammetry. 

As in the case of single potential pulse and double potential pulse techniques, from the transposition of the theory of multipulse techniques to the ion transfer processes taking place at macro-ITIES, the theoretical expressions obtained with... 

As discussed in Sects. 3.4 and 4.5, electrode processes coupled with homogeneous chemical reactions are very frequent and their study is of interest in many applied fields, such as organic electrosynthesis, ecotoxicity, biosciences, environmental studies, among others [15-17]. In this section, multipulse techniques (with a special focus on Cyclic Voltammetry) are applied to the study of the reaction kinetics and mechanisms of electrogenerated species. 

Equations (6.130) and (6.131) are applicable for any multipulse technique such as Staircase Voltammetry (SCV) and Square Wave Voltammetry (SWV). 

By inserting the solutions proposed in Eq. (6.189) and condition (6.175) in Eq. (6.185), recurrent expressions for coefficients 8lp) and are deduced [68] and by inserting these expressions into (6.191) the current is calculated. These expressions allow us to obtain limiting cases like the reversible and irreversible ones which have a discrete character which makes them applicable to any multipulse technique by simply changing the potential time waveform, including the continuous limit of Cyclic Voltammetry. Moreover, they are independent of the kinetic formalist considered for the process. 

This technique is of special interest in the case of charge transfer processes at surface-bound molecules since it allows a simple and more effective correction of the non-faradaic components of the response than Cyclic Voltammetry. Moreover, this technique presents an intense peak-shaped signal for fast charge transfer, whereas other multipulse techniques give rise to nonmeasurable currents under these conditions and it is necessary to use short potential pulses to transform the response to quasi-reversible, which is much more difficult to analyze [4, 6, 10]. 

Eq. (4.102). Moreover, the peak potential coincides with the formal one in the case of the multipulse technique, whereas it is shifted toward more positive values in the case of the double pulse one. 

For electron transfer processes with finite kinetics, the time dependence of the surface concentrations does not allow the application of the superposition principle, so it has not been possible to deduce explicit analytical solutions for multipulse techniques. In this case, numerical methods for the simulation of the response need to be used. In the case of SWV, a semi-analytical method based on the use of recursive formulae derived with the aid of the step-function method [26] for solving integral equations has been extensively used [6, 17, 27]. 

Fig. 7.11 Influence of the reversibility on the multipulse techniques DMPV and DNMPV curves corresponding to planar electrodes, (a)...

In this section, the subtractive multipulse techniques DMPV and SWV are applied to reversible ion transfer across different liquid-liquid systems with one or two polarizable interfaces. These electrochemical techniques allow the accurate and easy determination of standard potentials directly from the peak potentials of the current-potential curves since non-faradaic and background currents are minimized [12, 35-40]. 

The electrochemical characterization of multi-electron electrochemical reactions involves the determination of the formal potentials of the different steps, as these indicate the thermodynamic stability of the different oxidation states. For this purpose, subtractive multipulse techniques are very valuable since they combine the advantages of differential pulse techniques and scanning voltammetric ones [6, 19, 45-52]. All these techniques lead to peak-shaped voltammograms, even under steady-state conditions. 

The currents obtained with the multipulse technique SWV in the steady-state situation, which are shown in the box of Fig. 7.30c, are identical to those obtained with double pulse technique DDPV, whenever A DDPV = 27isw (i.e., when E (DDPV) = f(SW) and 2(DDPV) = fq(SW)) [46, 49], so the currents obtained with SWV in microelectrodes have the same characteristic as those shown for this double pulse technique. 

As indicated in Sect. 6.3.2, explicit expressions for the current corresponding to CE and EC mechanisms have not been found in multipulse techniques even when linear diffusion is considered. 

In the last 20 years, a big effort has been made to characterize different reaction schemes taking place at modified electrodes, with special focus on the case of biomolecules in what has been called Protein Film Voltammetry [79-83]. Among the different situations analyzed with multipulse techniques (including Cyclic Voltammetry), it can be cited the surface ECE process [89, 90] and surface reactions preceded by homogeneous chemical reactions [91]. For a more detailed revision of the different mechanisms analyzed in the case of SWV, see [19]. 

Table 4.1. The principal applications of the multipulse techniques described in this chapter...

Nuclear Magnetic Resonance Spectroscopy. Like IR spectroscopy, NMR spectroscopy requires little sample preparation, and provides extremely detailed information on the composition of many resins. The only limitation is that the sample must be soluble in a deuterated solvent (e.g., deuterated chloroform, tetrahydro-furan, dimethylformamide). Commercial pulse Fourier transform NMR spectrometers with superconducting magnets (field strength 4-14 Tesla) allow routine measurement of high-resolution H- and C-NMR spectra. Two-dimensional NMR techniques and other multipulse techniques (e.g., distortionless enhancement of polarization transfer, DEPT) can also be used [10.16]. These methods are employed to analyze complicated structures. C-NMR spectroscopy is particularly suitable for the qualitative analysis of individual resins in binders, quantiative evaluations are more readily obtained by H-NMR spectroscopy. Comprehensive information on NMR measurements and the assignment of the resonance lines are given in the literature, e.g., for branched polyesters [10.17], alkyd resins [10.18], polyacrylates [10.19], polyurethane elastomers [10.20], fatty acids [10.21], cycloaliphatic diisocyanates [10.22], and epoxy resins [10.23]. 

---