Diffusive growth of polydisperse hard-sphere crystals

Area of Science:

• Colloid and interface science
• Materials science
• Statistical mechanics

Background:

• Colloidal particles are inherently polydisperse, meaning they exist as mixtures of various sizes.
• Unlike atoms, colloidal crystals are often formed out of equilibrium due to synthesis limitations.
• The size distribution of particles in a colloidal crystal is determined by its formation process, not solely equilibrium thermodynamics.

Purpose of the Study:

• To model the crystallization process of hard-sphere colloids from an amorphous phase.
• To investigate the impact of polydispersity and non-equilibrium conditions on colloidal crystal formation.
• To predict the mean particle size in colloidal crystals and compare it with equilibrium predictions.

Main Methods:

• Computer simulations modeling the crystallization of hard-sphere colloids (with and without attractions).
• Analysis of particle size distributions within the forming crystal lattice.
• Comparison of simulation results with established equilibrium phase diagrams.

Main Results:

• The mean size of colloidal particles incorporated into the crystal is smaller than predicted by equilibrium phase diagrams.
• The crystallization process leads to a non-equilibrium state where particle composition is kinetically trapped.
• Smaller colloidal particles are preferentially incorporated due to their faster diffusion rates.

Conclusions:

• Equilibrium phase diagrams are insufficient for accurately describing real colloidal crystals due to non-equilibrium formation.
• The dynamic process of crystallization significantly influences the final particle size distribution in colloidal crystals.
• Understanding kinetic effects is crucial for predicting the properties of synthesized colloidal materials.