Bistable species

Typical bistable species are the so-called photochromic compounds molecules that can be reversibly interconverted, with at least one of the reactions being induced by light excitation, between two forms displaying different absorption spectra.17 8 ... 

The simplest photochromic compounds are bistable species that can be interconverted between two forms (X and Y) exhibiting different colors.17 8 211 Most photochromic compounds change their color as a result of photoexcitation and revert more or less slowly to their initial state when kept in the dark (Figure la). Compounds exhibiting this behavior are useless for information storage (or switching purposes), since the written information (switching state) is spontaneously erased (back-converted) after a relatively short time. 

Switching also implies molecular and supramolecular bistability since it resides in the reversible interconversion of a molecular species or supramolecular system between two thermally stable states by sweeping a given external stimulus or field. Bistability in isolated molecules or supermolecules is, for instance, found in optical systems such as photochromic [8.229] or thermochromic substances or devices, in electron transfer or magnetic processes [8.239], in the internal transfer of a bound substrate between the two binding sites of a ditopic receptor (see Section 4.1 see also Fig. 33) [6.77]. Bistability of polymolecular systems is of a supramolecular nature as in a phase transition or a spin transition, both of which involve an assembly of interacting species. 

The quinone-hydroquinone redox couple built into complexes 124 and 125 fulfils the requirements for the design of a bistable electro-photoswitch both the oxidized and reduced forms are isolable and stable the reduced form 125 is luminescent, whereas the oxidized form 124 is quenched the electrochemical interconversion of the two species is reversible [8.256]. 

Positional changes of atoms in a molecule or supermolecule correspond on the molecular scale to mechanical processes at the macroscopic level. One may therefore imagine the engineering of molecular machines that would be thermally, photochem-ically or electrochemically activated [1.7,1.9,8.3,8.109,8.278]. Mechanical switching processes consist of the reversible conversion of a bistable (or multistable) entity between two (or more) structurally or conformationally different states. Hindered internal rotation, configurational changes (for instance, cis-trans isomerization in azobenzene derivatives), intercomponent reorientations in supramolecular species (see Section 4.5) embody mechanical aspects of molecular behaviour. 

Formulating appropriate rate laws for CO adsorption, OH adsorption and the reaction between these two surface species, a set of four coupled ordinary differential equations is obtained, whereby the dependent variables are the average coverages of CO and OH, the concentration of CO in the reaction plane and the electrode potential. In accordance with the experiments, the model describes the S-shaped I/U curve and thus also bistability under potentiostatic control. However, neither oscillatory behavior is found for realistic parameter values (see the discussion above) nor can the nearly current-independent, fluctuating potential be reproduced, which is observed for slow galvanodynamic sweeps (c.f. Fig. 30b). As we shall discuss in Section 4.2.2, this feature might again be the result of a spatial instability. 

In practice this system was put to work by electrochemical action [100]. Oxidation of the starting Cu (4j yielded the Cu (4) species with its typical 670-nm band, as discussed for the previous bistable system. The rearrangements to Cu (5) and to Cu (6) could not be resolved, even if the overall process was rather slow (minutes or hours), and was strongly affected by the presence of coordinating solvents or ions, as previously discussed. The final point of the oxidation reaction, Cu (6), was clearly characterized by spectro- and electrochemical properties. Interestingly, the oxidation step from Cu (4), through the intermediate Cu (5), to could also... 

Reaction fronts and oscillations The kinetic behavior of the model depends strongly on temperature, as shown in Figure 2. Below 350 K, AB production is zero, because the full coverage of one of the species blocks the grid. Under these circumstances, our simulated system represents a bistable medium. The two stable states cire poisoned states, in which either Aads or Bads blocks all surface sites. Strictly speaking, complete A-poisoning cannot occur because of A des-... 

For Co electrodissolution in phosphoric acid, Sazou and Pagit-sasi32 i33 carried out a systematic study of the dynamic behavior in the voltage/extemal resistance parameter plane. The skeleton bifurcation diagram they found is typical for an NDR oscillator that is, bistability between stationary states occurs at high values of ohmic resistance, whereas oscillations are observed at relatively low values of the external resistance. However, from a chemical point of view, Co dissolution seems to be among the most complicated metal electrodissolution reactions because quite a number of different oxide species are involved. Explanations of the dynamics hardly go further than a general statement that the instabihties are due to the formation of a passive film in combination with an IR drop. 

The above process is illustrated in Fig. 13. The mixed-valence state exists in two forms, A and B, species A accessible only by oxidation of the stable fully reduced form, and species B only by reduction of the stable fully oxidized form. The structures of A and B are different from one another. The structure of A is similar to that of A, and B is similar to B. Hence, the A and B species remember their former structures. There is a bistability in the system and which bistable state depends on the direction of an external perturbation, constituting hysteresis at the molecular level. 

We now turn our attention to molecular hysteresis which has two essential factors. One is that a system can be expressed a double square scheme diagram (or ladder scheme diagram ) [5], as shown in Fig. 17a. A, A, A", B, B, and B" are chemical species or states. These series of A and B vary reversibly with one another under an external perturbation such as potential, pH, ion concentration, light, etc. With A and B more stable than B" and A", respectively, A" and B" can be rapidly converted to B and A. Hence we will obtain a scheme as shown in Fig. 17b. The other important thing is that the conversion is slow between A and B. The slow rate produces a bistability, A and B, which depends on the direction of an external perturbation. This is molecular hysteresis. Some binuclear or multinuclear metal complexes with the double square scheme diagram have been reported [31]. However, because they were not designed to exhibit molecular hysteresis, their hysteresis behaviors in redox are insufficient. 

A centre, called the a trap in connection with the study by Haynes and Hornbeck [98], has been reported to be the first TDD species, but without giving data on its ionization energies [159]. The electronic properties of this centre, labelled BTD-a for bistable thermal donor, or alternatively TDDO, have remained elusive for some time and they will be discussed with the metastability properties of the TDDs. To avoid any confusion in the following, the ionization energies of the different TDDs in the neutral and singly-ionized states are listed in Table 6.23. Apparently, no data have been reported for TDDi+ above TDD9. 

The peroxidase reaction provides another prototype for periodic behaviour and chaos in an enzyme reaction. As noted by Steinmetz et al. (1993), in view of its mechanism based on free radical intermediates, this reaction represents an important bridge between chemical oscillations of the Belousov-Zhabotinsky type, and biological oscillators. In view of the above discussion, it is noteworthy that the model proposed by Olsen (1983), and further analysed by Steinmetz et al. (1993), also contains two parallel routes for the autocatalytic production of a key intermediate species in the reaction mechanism. As shown by experiments and accounted for by theoretical studies, the peroxidase reaction possesses a particularly rich repertoire of dynamic behaviour (Barter et al, 1993) ranging from bistability (Degn, 1968 Degn et al, 1979) to periodic oscillations (Yamazaki et al, 1965 Nakamura et al, 1969 ... 

A typical experimental study of bistability requires monitoring the steady state concentration of a particular species as a function of a bifurcation parameter such as reactant flow rate. (Bihircation parameters are described in more detail in a following section.) A convenient species to monitor in the iodate-arsenite reaction is iodide, the autocatalyst. Figure 4 shows the steady state iodide concentration as a function of the reciprocal residence time, kQ. As the flow rate is increased, displacing the system from equilibrium (where the extent of reaction, and iodide concentration, is high), the iodide concentration gradu-... 

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