Derivation of the phase-field-crystal model for colloidal solidification

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• The phase-field-crystal (PFC) model is a powerful tool for simulating crystal nucleation and growth.
• Understanding colloidal solidification dynamics is crucial for materials engineering.

Purpose of the Study:

• To derive phase-field-crystal (PFC) model dynamics from the microscopic Smoluchowski equation using dynamical density-functional theory (DDFT).
• To propose and validate a less approximate variant of the PFC model for colloidal systems.
• To compare PFC model predictions with DDFT for colloidal crystal growth undercooling.

Main Methods:

• Derivation of PFC dynamics from the Smoluchowski equation via DDFT.
• Development of a novel, less approximate PFC model variant.
• Numerical simulations comparing PFC models and DDFT for a 2D colloidal suspension of dipoles.

Main Results:

• PFC dynamics can be rigorously derived from the Smoluchowski equation for overdamped colloidal systems.
• A new PFC model variant with fewer approximations is proposed.
• Good agreement between PFC models and DDFT requires significant free energy scaling to match the bulk freezing point.

Conclusions:

• The study provides a theoretical foundation for using PFC models in colloidal solidification.
• The findings highlight the importance of accurate free energy descriptions in PFC models for quantitative predictions.
• The validated PFC models offer a computationally efficient approach for studying crystal growth in colloidal suspensions.