# Physical Interpretation of the Partition Function for Colloidal Clusters

October 1, 2018Fig.5. 24 of the 720 colorings, or label permutations, of the octahedron. All of these colorings are equivalent through rotations.*

Colloidal clusters consist of small numbers of colloidal particles bound by weak short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well described by a statistical mechanical model originally developed for molecules. To explain why this model fits experimental data so well, grad student Ellen Klein, Prof. Manoharan, and a colleague from SEAS derive the partition function classically, with no quantum-mechanical considerations, in a *Physical Review E *article. By comparing and contrasting the derivation in particle coordinates with that in center-of-mass coordinates, they physically interpret the terms in the center-of-mass formulation, which is equivalent to the high-temperature partition function for molecules. Finally, they discuss, from a purely classical perspective, how and why cluster characteristics such as the symmetry number, moments of inertia, and vibrational frequencies affect the equilibrium probabilities.

*E.D. Klein, R.W. Perry, and V.N. Manoharan, "Physical interpretation of the partition function for colloidal clusters,"* Phys. Rev. E* 98 (2018) DOI: 10.1103/PhysRevE.98.032608.