Optimization algorithm for rate equations with an application to epitaxial graphene

Area of Science:

• Materials Science
• Chemical Engineering
• Computational Chemistry

Background:

• Accurate rate theories are crucial for understanding chemical processes.
• Existing nucleation theories may not fully capture complex phenomena like graphene growth.
• Experimental data fitting is essential for validating and refining theoretical models.

Purpose of the Study:

• To develop and present an algorithm for optimizing rate coefficients in rate theories.
• To apply the algorithm to refine a rate theory for graphene nucleation and growth.
• To investigate the temperature dependence of graphene island density and its implications for nucleation mechanisms.

Main Methods:

• An iterative algorithm that searches parameter space to minimize error against experimental data.
• Optimization of rate coefficients for nucleation and growth processes.
• Application to graphene formation on Ruthenium (Ru(0001)) and Iridium (Ir(111)) surfaces.

Main Results:

• The algorithm successfully optimizes rate coefficients by fitting to experimental data.
• A corrected rate theory for graphene nucleation and growth was developed.
• Observed exponential decrease in graphene island density with increasing temperature, contrasting with conventional theory's power law prediction.

Conclusions:

• The developed algorithm provides a robust method for refining rate theories.
• A distinct nucleation mechanism is operative for graphene island formation at elevated temperatures.
• The findings necessitate revisions to conventional nucleation theories for specific systems like graphene growth.