Stochastic self-assembly of incommensurate clusters.

Area of Science:

• Physical Chemistry
• Biophysics
• Statistical Mechanics

Background:

• Nucleation and molecular aggregation are fundamental to physical and biological systems.
• These processes often occur in confined spaces with finite particle numbers.
• Understanding these phenomena is crucial for various scientific and technological applications.

Purpose of the Study:

• To analyze homogeneous nucleation and self-assembly using a discrete stochastic master equation.
• To derive exact analytical formulae for cluster size distributions.
• To compare discrete models with traditional mass-action Becker-Döring equations.

Main Methods:

• Derivation and analysis of a fully discrete stochastic master equation.
• Enumeration of highest probability steady states.
• Derivation of analytical formulae for quenched and equilibrium mean cluster size distributions.
• Comparison with results from mass-action Becker-Döring equations.

Main Results:

• Striking differences observed in equilibrium mean cluster concentrations between discrete and mass-action models.
• Discreteness-induced broadening of cluster size distributions occurs due to mass 'incommensurability'.
• This broadening effect is periodic with system mass and significant even for large systems with finite mass-to-cluster size ratios.

Conclusions:

• Classic mass-action theories are qualitatively inaccurate in a newly defined scaling regime characterized by mass incommensurability.
• Discrete stochastic effects significantly alter equilibrium cluster size distributions, challenging traditional models.
• The findings highlight the importance of discreteness in understanding nucleation and self-assembly in confined systems.