Critical length of a one-dimensional nucleus

Area of Science:

• Physical Chemistry
• Materials Science
• Biophysics

Background:

• One-dimensional (1D) nucleation is a fundamental process in various scientific fields, including crystal growth, amyloid fibril formation, and supramolecular polymerization.
• While nucleation rates are calculable, a clear understanding and consensus on the critical nucleus length remain elusive.
• This critical length is essential for predicting nucleation phenomena and controlling material self-assembly.

Purpose of the Study:

• To derive an analytical expression for the critical length in 1D nucleation.
• To establish a quantitative link between critical length and driving force (supersaturation).
• To clarify the influence of surface energy on the critical length of 1D nuclei.

Main Methods:

• Utilized a splitting probability approach to analyze 1D nucleation dynamics.
• Derived a novel analytical expression for the critical nucleus length.
• Investigated the dependence of critical length on supersaturation and surface energy parameters.

Main Results:

• Developed an analytical expression for critical length, defined by a 50% survival probability.
• Demonstrated that the critical length for a 1D nucleus on a crystal step is primarily dependent on supersaturation.
• Showed that the critical length is nearly independent of the kink (surface) energy.

Conclusions:

• The derived analytical expression provides a robust method for determining the critical length in 1D nucleation.
• Supersaturation is identified as the dominant factor governing critical length, offering insights into nucleation control.
• The findings contribute to a deeper understanding of nucleation processes in diverse 1D systems, impacting fields from materials science to disease research.