diffusionlimited

Diffusionlimited (diffusion-limited) describes processes in which molecular diffusion is the rate-determining step, rather than the intrinsic speed of the chemical transformation. In solution chemistry and related fields, a diffusion-limited reaction occurs when the rate at which reactants encounter one another controls the overall rate; once they meet, the reaction proceeds rapidly. Classical descriptions use diffusion theory, notably the Smoluchowski model, which yields a diffusion-controlled rate constant k_D = 4π(D_A+D_B)R for two spherical reactants with diffusion coefficients D_A, D_B and an effective capture radius R. If the probability of reaction on encounter is less than unity, the system lies between diffusion- and reaction-control and is described by extended models such as Collins-Kimball.

A closely related concept is diffusion-limited aggregation (DLA), where particles diffuse and irreversibly stick to a growing cluster upon contact. DLA produces ramified, fractal-like structures with characteristic dimensions depending on space dimensionality (roughly 1.71 in two dimensions and about 2.5 in three dimensions).

Applications and contexts include electrochemical limiting currents, catalysis in viscous or crowded environments, and enzyme or protein interactions in gels, where diffusion can dominate the observed kinetics. Diffusion-limited behavior contrasts with reaction-limited processes, in which the slow intrinsic reaction step governs the rate even when encounters are frequent.

Modeling uses partial differential equations for diffusion, boundary conditions for reactive encounters, or Monte Carlo simulations of random walks to study diffusion-limited growth and reactions.

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