Diffusionskinetik

Diffusionskinetik is the study of how the rate of processes is governed by diffusion. It describes the time evolution of concentration fields due to random motion of particles and how this transport controls observed rates in chemical, physical, and materials contexts. The central framework uses Fick's laws: Fick's first law states that the diffusive flux J is proportional to the negative gradient of concentration, J = -D ∂c/∂x, with D the diffusion coefficient; Fick's second law, ∂c/∂t = D ∂^2c/∂x^2, describes how concentrations change in time. In three dimensions, the diffusion equation involves the Laplacian, and D encapsulates particle mobility, depending on temperature, medium, and microstructure. In solids, D often follows Arrhenius behavior D = D0 exp(-Ea/RT).

A key distinction in diffusion kinetics is between diffusion-controlled (diffusion-limited) and reaction-controlled processes. In diffusion-controlled cases, the overall rate is set by how fast species can diffuse to encounter each other or a reactive site; intrinsic reaction steps are rapid in comparison. Conversely, when chemical steps are slow, the process is kinetically limited. In dilute solutions, diffusion-limited bimolecular reactions can be approximated by Smoluchowski theory, giving k_diff ≈ 4πDR for spheres of radii R and R' with total diffusion coefficient D.

Applications span electrochemistry, catalysis, corrosion, battery electrolytes, polymer science, and drug delivery, where transport constraints determine performance. Experimental methods to probe diffusion include pulsed-field gradient NMR, FRAP (fluorescence recovery after photobleaching), and tracer diffusion measurements. Understanding diffusionkinetik helps interpret rates when transport and reaction compete, offering a framework to predict and optimize system behavior.