Feedback mode

Selzer Y and Manler D 2000 Scanning electrochemical microscopy. Theory of the feedback mode for hemispherical ultramicroelectrodes steady-state and transient behavior Anal. Chem. 72 2383... 

The feedback mode [Fig. 2(a)] is one of the most widely used SECM techniques, applicable to the study of interfacial ET processes. The basic idea is to generate a species at the tip in its oxidized or reduced state [generation of Ox] in Fig. 2(a)], typically at a diffusion-controlled rate, by electrolysis of the other half of a redox couple (Redj). The tip-generated species diffuses from the UME to the target interface. If it undergoes a redox... 

FIG. 2 Principal methods for inducing and monitoring interfacial processes with SECM (a) feedback mode, (b) induced transfer, and (c) double potential step chronoamperometry. 

To extend the applicability of the SECM feedback mode for studying ET processes at ITIES, we have formulated a numerical model that fully treats diffusional mass transfer in the two phases [49]. The model relates to the specific case of an irreversible ET process at the ITIES, i.e., the situation where the potentials of the redox couples in the two phases are widely separated. A further model for the case of quasireversible ET kinetics at the ITIES is currently under development. For the case where the oxidized form of a redox species, Oxi, is electrolytically generated at the tip in phase 1 from the reduced species, Red], the reactions at the tip and the ITIES are ... 

Thus, the problem is similar to the feedback mode case except for the internal boundary condition described by Eqs. (31) and (32), which relate to the first-order process at the target interface. The internal boundary condition describes the net diffusive flux of Red across the interface from phase 2 to phase 1, as the system attempts to reattain equilibrium following the electrolytic depletion of Red] in phase 1. 

In pioneering studies [47], the SECM feedback mode was used to study the ET reaction between ferrocene (Fc), in nitrobenzene (NB), and the aqueous mediator, FcCOO, electrochemically generated at the UME by oxidation of the ferrocenemonocar-boxylate ion, FcCOO. Tetraethylammonium perchlorate (TEAP) was applied in both phases as the partitioning electrolyte. The results of this study indicated that the reaction at the ITIES was limited by the ET process, provided that there was a sufficiently high concentration of TEAP in both phases. 

The ITIES with an adsorbed monolayer of surfactant has been studied as a model system of the interface between microphases in a bicontinuous microemulsion [39]. This latter system has important applications in electrochemical synthesis and catalysis [88-92]. Quantitative measurements of the kinetics of electrochemical processes in microemulsions are difficult to perform directly, due to uncertainties in the area over which the organic and aqueous reactants contact. The SECM feedback mode allowed the rate of catalytic reduction of tra 5-l,2-dibromocyclohexane in benzonitrile by the Co(I) form of vitamin B12, generated electrochemically in an aqueous phase to be measured as a function of interfacial potential drop and adsorbed surfactants [39]. It was found that the reaction at the ITIES could not be interpreted as a simple second-order process. In the absence of surfactant at the ITIES the overall rate of the interfacial reaction was virtually independent of the potential drop across the interface and a similar rate constant was obtained when a cationic surfactant (didodecyldimethylammonium bromide) was adsorbed at the ITIES. In contrast a threefold decrease in the rate constant was observed when an anionic surfactant (dihexadecyl phosphate) was used. 

In scanning electrochemical microscopy (SECM) a microelectrode probe (tip) is used to examine solid-liquid and liquid-liquid interfaces. SECM can provide information about the chemical nature, reactivity, and topography of phase boundaries. The earlier SECM experiments employed microdisk metal electrodes as amperometric probes [29]. This limited the applicability of the SECM to studies of processes involving electroactive (i.e., either oxidizable or reducible) species. One can apply SECM to studies of processes involving electroinactive species by using potentiometric tips [36]. However, potentio-metric tips are suitable only for collection mode measurements, whereas the amperometric feedback mode has been used for most quantitative SECM applications. 

Recently [8b,30], a new IT feedback mode of SECM was introduced, in which the tip process is a simple or assisted ion transfer. In this mode, a micropipette filled with solvent (e.g., aqueous) immiscible with the outer solution (e.g., organic) serves as an SECM tip. 

In Ref. 30, the transfer of tetraethylammonium (TEA ) across nonpolarizable DCE-water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEA+ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both finite quasirever-sible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer films. 

FIG. 13 Schematic illustration of the SECM feedback mode based on a simple ion-transfer reaction. Cations are transferred from the top (organic) phase into the aqueous solution inside the pipette tip. Positive feedback is due to IT from the bottom (aqueous) layer into the organic phase. Electroneutrality in the bottom layer is maintained by reverse transfer of the common ion across the ITIES beyond the close proximity of the pipette where its concentration is depleted. (Reprinted with permission from Ref. 30. Copyright 1998 American Chemical Society.)... 

Fig. 2. Schematic diagrams of alternative force feedback modes. (A) Illustrates noncontact atomic force microscope feedback. (B) Shear-force feedback frequently used in NSOM imaging applications. From Paesler and Moyer (41), with permission.

Figure 6 Schematic of a control system, using a stirred tank as an example. A stream enters the tank at temperature T-. The system is designed to maintain the exit temperature at Tout- In a feedback mode, the exiting temperature is measured and the stream feed is opened or closed as necessary. Tout is known, but the effects of variability are corrected only after they have entered the system. In a feed-forward mode, the incoming temperature is measured and the stream feed is modified to prevent its variability from entering the system. However, OUt is unknown.

Fig. 6.22 Analog circuits for operation of ion-sensitive field-effect transistor (ISFET) (a) in constant applied voltage mode ((6.62) and (6.63)) and (b) in (source-follower) constant current feedback mode ((6.65) and (6.69))...

When two identical transistors, one with the cation-sensitive membrane (+) and the other with the anion-sensitive membrane (-), are operated in the feedback mode the individual responses are given by (6.68), which for the Na+ ISFET is... 

The feedback mode hindered diffusion and mediator recycling... 

For measurements in the feedback mode, the working solution contains one redox form of a quasi-reversible redox couple (R-> O+rce ). For the discussion of the working principle, it is assumed that initially only the reduced form R is present. This compound serves as electron mediator and is added typically in millimolar concentrations to an excess of an inert electrolyte2. The UME is poised at a potential sufficiently large to cause the diffusion-controlled oxidation of R. In solution bulk the... 

The term feedback mode refers to the coupling of heterogeneous reactions at the specimen and the UME and not to an electronic control principle as commonly used in other scanning probe techniques to maintain a constant sample-probe distance. 

Immobilized enzymes can be investigated in the feedback and in the GC mode. In the feedback mode oxidoreductases can be imaged. They use the SECM mediator as electron donor (or acceptor). Table 37.1 gives an overview about the enzymes investigated. 

When the feedback mode is possible (i.e. the enzymes is immobilized on an insulating support, Fig. 37.5a), it provides a much better lateral resolution but has only a very limited sensitivity. Therefore, it can only be applied for very active enzymes or if enzymes are bound in high surface concentrations. Bard et al. [15] gave a quantitative detection limit for this situation ... 

The left side summarizes the enzyme-dependent terms turnover number kcat and surface concentration renz- In case of enzyme-loaded films, renz should be replaced by the product of enzyme volume concentration in the film and the film thickness. The right side summarizes the experimental conditions diffusion coefficient D, concentration c of the mediator, and UME radius rT. The feedback mode always requires an as small as possible working distance d. The smaller the UME the more difficult it will be to detect the activity of the immobilized enzyme. 

In order to quantify the results in the GC mode, the sample must be a microstructure by itself, so that it develops a steady-state diffusion layer. This restriction does not apply to feedback mode experiments. 

Fig. 37.11. Use of an NO microsensor for detection of the NO release from cultured endothelial cells. The sensor is a dual probe microsensor. The small sensor is a bare Pt UME used to position the sensor in the feedback mode. Onto the larger Pt electrode a polymer was deposited from an acrylic resin containing Ni(4-lV-tetramethyl) pyridyl porphyrin and served as amperometric NO sensor, (a) Schematic of the sensor, (b) optical microphotograph of the sensor surface, (c) Response of the NO sensor to the stimulation of the cells with bradykinin at different distances of the sensor to the surface of the cells. Reprinted with permission from Ref. [104], Copyright 2004, American Chemical Society.

The electrical current flows from the source, via the channel, to the drain. However, the channel resistance depends on the electric field perpendicular to the direction of the current and the potential difference over the gate oxide. Should this surface be in contact with an aqueous solution, any interactions between the silicon oxide gate and ions in solution will affect the gate potential. Therefore, the source-drain current is influenced by the potential at the Si02/aqueous solution interface. This results in a change in electron density within the inversion layer and a measurable change in the drain current. This means we have an ion-selective FET (an ISFET), since the drain current can be related to ion concentration. Usually these are operated in feedback mode, so that the drain current is kept constant and the change of potential compared to a reference electrode is measured. 

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