Chemomechanical oscillators

There is not always a clear distinction between Type I and Type II systems. Section II of this volume addresses several works with gels. In some cases the nonlinearities of the gel also play a role. The extreme case is the system developed by Siegel. He and his colleagues utilized the hysteresis in a hydrogel s permeability to create autonomous chemomechanical oscillations in a hydrogel/enzyme system driven by glucose 49,50), This is also addressed in chapter 4. 

Figure 1. a) Schematic of glucose-driven chemomechanical oscillator, b) pH oscillations observed in Cell II at varying mole fractions of MAA incorporated into the hydrogel membrane, and varying glucose concentrations in Cell I (Reproduced from reference 10. Copyright American Chemical Society.)... 

Finally, the numerical simulations showed that the frequency of chemical oscillations within the heterogeneous BZ gels depends on whether the gel is responsive or not, and changes upon deformation of the sample. Figure 8.8 shows the oscillation frequency a>o as a function of the stretch X for the responsive (black symbols and Hnes) and nonresponsive (red symbols and Unes) gel having one patch of length Ip = 5Lo at/ = 0.7. The frequency of the chemomechanical oscillations in the responsive gel is seen to be lower than that of the purely chemical oscillations in the nonresponsive gel. In Figure 8.8, the open symbols mark the data obtained... 

Dhanarajan, A.P., Misra, G.P., and Siegel, R.A. (2002) Autonomous chemomechanical oscillations in a hydrogel/enzyme system driven by glucose./. Rhys. Chem., 106, 8835-8838. 

Li, B. and Siegel, R., Global analysis of a model pulsing drug delivery oscillator based on chemomechanical feedback with hysteresis, Chaos, Vol. 10, No. 3, 2000, pp. 682-690. 

A chemomechanical device capable of moving a load up and down automatically and repeatedly is the simplest application of electro-shrinkable gels. Thus, two pieces of water-swollen gel (10-20 g) of AMPS were placed on the two plates of a balance and a DC current (10 V) was applied to one of the pieces. The weight of the gel decreased, bringing the device out of blance. DC was now connected to the other gel and started shrinking it. Thus, the balance could oscillate many times (more than 100 times) until most of the water of the gel was consjimed. 

Boissonade etal. consider the chemoelastodynamics of responsive gels in Chapter 9. This chapter is devoted to the spontaneous generation of mechanical oscillations by a responsive gel immersed in a reactive medium away from equilibrium. Two important cases are considered. In the first case, the chemomechanical instability is mainly driven by a kinetic instabiUty leading to an oscillatory reaction. The approach is applied to the BZ reaction. The second case is a mechanical oscillatory instability that emerges from the cross-coupUng of a reaction-diffusion process and the volume or size responsiveness of the supporting material. In this case, there is no need for an oscillatory reaction. Bistable reactions, namely, the chlorite-tetrathionate (CT) and the bromate-sulfite (BS) reactions, were chosen... 

In the wake of the researches for oscillatory reactions more than a dozen pH-autoactivated reactions were shown to produce bistability when operated in a CSTR [57]. Theoretical calculations and experiments demonstrate that such systems readily give rise to spatial bistability when conducted in an OSFR. They would provide a large choice of reaction systems to test the chemomechanical instabilities theoretically described above. However, in our selection criteria, we have to take into account that many of these reactions can already exhibit kinetic oscillations over more or less wide ranges of feed parameters. Such complication can make it difficult to discriminate between kinetic and chemomechanic oscillatory instabilities. Furthermore, it has also been shown that in the case of proton-autoactivated system the natural faster diffusion of this species can lead to another source of oscillatory instability in an OSFR, the long range activation instability [58]. 

Case B Another limiting case is the one where the entire sample is constrained, that is, where all the faces of the 3D sample are attached to hard walls so that the volume of the sample remains constant. Again, we consider a small sample and neglect diffusion in Equation 3.3. Here, we fix < = st (determined from Equation 3.11), so that the dynamics is described solely by Equations 3.2 and 3.3 with = st-Figure 3.3 shows the stability map for Cases A (solid lines) and B (dashed lines) in terms of the important variables of the BZ reaction, / and s it may be recalled that / characterizes the stoichiometry of the reaction and e is proportional to the concentration of MA. This map indicates the critical values of/ =/, where the stationary solution loses its stability in Cases A and B. The curves are plotted for three values of the parameter x. which characterizes the responsiveness of the gel (x = 0.01, x = 0.05, and x = 0.105 are shown in black, blue, and red, respectively). If the values of /, e lie below the respective solid curves, the sample remains in the steady state, whether or not it is attached to hard walls. If, however, the /, e values are above the respective dashed curves, the sample undergoes oscillations, which are chemomechanical in Case A and purely chemical in Case B since the mechanical oscillations are suppressed by fixing the sample s size. Note that for all the values of x >f increases with increasing e. 

---