It has been well established by theory and simulations that the reaction rates of diffusion-limited reactions can be affected by the spatial dimension in which they occur. The types of reactions A + B → C, A + A → A, and A + C→, C have been shown, theoretically and/or by simulation, to exhibit non-classical reaction kinetics in low and fractal dimensions. We present here experimental results from several 1D and fractal systems.
An A+B → C type reaction was experimentally investigated in a long, thin capillary tube in which the reactants, A and B, are initially segregated. This initial segregation of reactants means that the net diffusion is along the length of the capillary only, making the system effectively 1D and allowing some of the properties of the resulting reaction front to be studied. The reaction rate of excitonic fusion, A + A →A, as well as trapping, A + C→ C, reactions were observed via phosphorescence(P) and delayed fluorescence(F) of naphthalene within the channels of Vycor glass, in isotopically mixed naphthalene crystals and in the isolated chains of dilute polymer blends. In these experiments, the non-classical kinetics are measured in terms of the heterogeneity exponent, h, from the equation: Rate ∼ F =; kt-hpn,, which gives the time dependence of the rate coefficient. Classically h =; 0, while h =; 1/2 in 1D, as well as in the fractal dimensions discussed here, for A + A → A as well as A + C →C type reactions.