A reaction-diffusion memory device.

Any computer consists of processor and memory elements. Patterns and waves in excitable or oscillatory reaction– diffusion media are able to perform such processor tasks as counting, logical operations, signal transformation, and finding the shortest path through a maze. Since the brain may be thought of as a reaction–diffusion system, these capabilities are perhaps not so remarkable, though the simplicity of the systems employed is striking. Kuhnert et al. demonstrated that the photosensitive Belousov–Zhabotinsky (BZ) oscillating chemical reaction is capable of briefly (for a few periods of oscillation, that is, several minutes) storing and smoothing an image as complex as a human face. However, practical applications require the ability to store information for longer periods of time, ideally indefinitely. Localized patterns in reaction–diffusion systems have been suggested as media for memory-storage devices. The BZ system dispersed in a water-in-oil microemulsion (ME) with the surfactant sodium bis(2-ethylhexyl)sulfosuccinate (BZ-AOT system) exhibits a rich variety of pattern formation, including several types of localized structures. Herein we show that a photosensitive BZ-AOT system can store spatial information for up to an hour, even without replenishment of reactants. Simulation of this behavior with simple reaction–diffusion models reveals the likely mechanism of this information-storage capacity. We recently reported the existence of localized stationary and oscillatory patterns in the BZ-AOT system. In a system with tris(2,2’-bipyridine)ruthenium ([Ru(bpy)3] ) catalyst, patterns can be suppressed by sufficiently intense illumination, which leads to photogeneration of bromide, an inhibitor of the reaction. We have found conditions under which this system displays hysteresis and bistability (between a homogeneous steady state and stationary Turing patterns). Turing patterns, which are often invoked as a mechanism for biological morphogenesis, are spatially periodic concentration variations that arise as a result of the interaction between nonlinear reaction kinetics and diffusion. Turing patterns form spontaneously in our system in the dark. If the light intensity (I) is slowly increased, the patterns initially change only slightly, but at a critical intensity (Isc), they suddenly vanish, and a homogeneous steady state (SS) is observed. If we then slowly decrease I, the Turing patterns spontaneously reemerge at a lower intensity (Ic). For Ic< I< Isc, the system is bistable, which is a characteristic feature of subcritical Turing instability. In this bistable range of I, localized patterns generated by a local perturbation can be stable, and Turing patterns cannot emerge spontaneously elsewhere in the medium, since the SS is also stable. First, we attempted to photoimprint an image and maintain it as long as possible for I within the bistable region, and then to develop a model that reproduces this phenomenon. Since our BZ-AOT system is operated in a batch (closed system) mode, we first sought conditions under which stationary Turing patterns can survive for long periods of time (an hour or more) and the system displays significant photosensitivity. These criteria are fulfilled when [MA]0= 0.1m, [H2SO4]0= 0.3m, [NaBrO3]0= 0.25m, [Ru(bpy)3]0= 0.004m, w= 10, and fd= 0.45 (MA is malonic acid, w [H2O]/[AOT] determines the radius of water droplets in the microemulsion, and fd is the volume fraction of the droplets). The radius of the water droplets, measured by dynamic light scattering, is 2 nm, and the microemulsion is below the percolation threshold, as shown by conductivity measurements in the range fd= 0.4–0.7. Under such conditions, the diffusion coefficient of small, oil-soluble molecules, such as the inhibitor Br2, is significantly larger than that of watersoluble molecules, such as the activator HBrO2, that diffuse with entire water droplets. When I is in the bistable region, the image of the mask imprinted in the layer of reactive ME can persist essentially unchanged for approximately 30 min. Since our system is closed, the concentrations of BZ reactants and intermediates evolve, and the photosensitivity, as characterized by, for example, the values of Ic and Isc, also changes with time. To maintain the image of the mask for longer wemust change the light intensity accordingly. This procedure extends the lifetime of the image to more than an hour, which is roughly the lifetime of the reactive ME in our batch configuration. Figure 1 presents snapshots taken from a typical experiment. The image in Figure 1 A, which is taken shortly after decreasing I to within the bistable region, is essentially identical to the “face” mask through which the reactor is illuminated. The “face” image remains for about 1 h, but the continuous lines transform into dotted lines (Figure 1A and B). Similar behavior is observed in the Turing patterns in the unilluminated area: most of the stripes that emerge initially mutate into spotlike Turing patterns after 30–60 min. If we increase I briefly (2–7 min) to suppress the image and then decrease it back to within the bistable region, the original image slowly reappears. Longer exposure to strong light erases the memory of the medium. If we decrease I below the bistable region, new spots begin to emerge around and within the “face” and eventually cover the entire area. Figure 1C shows a space–time plot made from a cross section of Figure 1B taken immediately after the light intensity was decreased. The emergence of new stationary spots is seen as the advent of vertical white bands. [*] Dr. A. Kaminaga, Dr. V. K. Vanag, Professor I. R. Epstein Department of Chemistry and Volen Center for Complex Systems, MS 015 Brandeis University Waltham, MA 02454 (USA) Fax: (+1)781-736-2516 E-mail: [email protected]