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The diffusion-control limit revisited.

E Yariv¹, I Frankel

¹Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters

|December 18, 2002

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This study addresses nonequilibrium adsorption onto new surfaces, finding that standard diffusion assumptions fail initially. A new approximation shows diffusion control is only valid at later times, impacting dynamic surface tension calculations.

Area of Science:

Physical Chemistry
Surface Science
Chemical Kinetics

Background:

Nonequilibrium adsorption phenomena are crucial in various chemical and physical processes.
Standard models often assume equilibrium or diffusion control, which may not hold for freshly formed surfaces or short timescales.
Understanding initial adsorption dynamics is key to accurate surface characterization and process modeling.

Purpose of the Study:

To develop a theoretical framework for nonequilibrium adsorption at small times.
To investigate the limitations of the diffusion-control assumption in initial adsorption stages.
To apply the derived adsorption model to calculate dynamic surface tension.

Main Methods:

Construction of a uniform small-time asymptotic approximation.

Related Experiment Videos

Analysis of a Langmuir-type adsorption system.

Introduction of a small parameter (epsilon) representing the ratio of kinetic to diffusive timescales.

Derivation of conditions for the validity of the diffusion-control approximation (t >> epsilon).

Main Results:

The common diffusion-control assumption is inconsistent at small times for nonequilibrium adsorption.
A novel asymptotic approximation is derived for early-stage adsorption.
The diffusion-control approximation is shown to be valid only for times significantly larger than epsilon.
The developed adsorption model provides a basis for calculating dynamic surface tension.

Conclusions:

Initial adsorption dynamics on fresh surfaces require specialized models beyond simple diffusion control.
The derived asymptotic approximation offers a more accurate description of early-stage adsorption.
The findings have implications for understanding surface phenomena and calculating dynamic surface tension in nonequilibrium systems.