Kinetics of deposition in the diffusion-controlled limit

Area of Science:

• Physics
• Materials Science
• Physical Chemistry

Background:

• Particle diffusion and adsorption are fundamental processes in various scientific fields.
• Understanding irreversible adsorption kinetics is crucial for surface science and nanotechnology.
• The behavior of diffusing particles near a boundary presents complex theoretical challenges.

Purpose of the Study:

• To investigate the adsorption kinetics of diffusing particles onto a substrate.
• To determine the asymptotic behavior of surface coverage over time.
• To analyze the influence of particle shape and substrate dimensionality on adsorption.

Main Methods:

• Theoretical analysis of particle diffusion in a half-space.
• Mathematical modeling of irreversible adsorption upon contact.
• Derivation of asymptotic coverage formulas for different particle shapes and dimensions.

Main Results:

• For planar disks in 3D, coverage approaches a jamming limit as t^{-1}.
• General asymptotic behavior is t^{-1/(d-1)} for d-dimensional substrates (d>1).
• For 1D substrates, coverage decays as e^{-t/ln(t)}; spherical and square particles also analyzed.

Conclusions:

• The rate of coverage saturation depends significantly on particle geometry and substrate dimensionality.
• The jamming limit represents a key characteristic of irreversible adsorption processes.
• This work provides a theoretical framework for understanding particle-surface interactions in diffusion-limited systems.