Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale

Area of Science:

• Biophysics
• Surface Science
• Crystallography

Background:

• Adsorption of rod-like molecules, like antifreeze proteins (AFPs), to crystal surfaces requires precise orientational alignment.
• Existing kinetic models do not fully account for molecular geometry or enforce orientation constraints during adsorption.
• AFPs binding to ice surfaces exemplify this phenomenon, facing an entropic barrier due to alignment requirements.

Purpose of the Study:

• To develop a diffusion-controlled adsorption theory for antifreeze proteins (AFPs) binding to flat ice surfaces with specific orientations.
• To provide analytical solutions for the attachment rate constant, incorporating molecular geometry and orientational constraints.
• To offer a framework for predicting adsorption kinetics in systems with orientation-dependent binding.

Main Methods:

• Formulation of the diffusion equation with appropriate boundary conditions for oriented adsorption.
• Development of analytical solutions to determine the attachment rate constant.
• Inclusion of molecular parameters like length and aspect ratio, and solvent conditions.

Main Results:

• The derived attachment rate constant depends on AFP length, aspect ratio, binding distance threshold, temperature, and viscosity.
• The theory explicitly accounts for the entropic barrier arising from orientational constraints.
• Provides a more accurate kinetic model for AFP adsorption than previous approaches.

Conclusions:

• The new diffusion-controlled adsorption theory accurately models AFP binding to ice surfaces by considering molecular geometry and orientation.
• The model's predictions are sensitive to AFP dimensions and solvent properties.
• The developed methods can be extended to understand crystal growth via oriented attachment.