The Kern–Frenkel Model¶
Overview¶
Questions¶
What are patchy particles?
What is the Kern-Frenkel potential?
How can I evaluate the Kern-Frenkel potential between two particles?
Objectives¶
Describe the Kern–Frenkel model mathematically and graphically.
Patchy Particles¶
In the Introducing Molecular Dynamics tutorial, you simulated a system of particles interacting through the Lennard-Jones pair potential. The Lennard-Jones pair potential is spherically symmetric. In other words, the pair potential does not depend on the relative orientation of the interacting particles.
Some systems are better represented by anisotropic pair potentials that depend on relative particle orientations. For example, patchy particles interact via anisotropic pair potentials where some relative orientations are more attractive than others.
The Kern–Frenkel Model¶
The Kern–Frenkel model, introduced in a 2003 Journal of Chemical Physics paper, models particles with a single patch. It consists of a directional pairwise energetic interaction in addition to hard sphere volume exclusion. The pair potential between particles and at a center-to-center separation and orientations and is of the form
where is the strength of the patchy interaction, is sum of the radii of particles and , is the range of the square well attraction, and is an orientational masking function given by
where is the director of the patch on particle and is the half-opening angle of the patch.
Graphically, this pair potential corresponds to the following: two particles interact with energy if the gray shaded regions on the two particles overlap at all, if the blue shaded regions on the two particles overlap, and zero otherwise.