We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent for two different model realizations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the previous studies. This is done by determining their differing depletion attractions via Monte Carlo simulations of PHGO and HPR particles in a pool of hard spheres and comparing them with excluded volume calculations of numerically obtained ideal configurations on the microscopic level. While the HPR model behaves as predicted by the analysis of excluded volumes, the PHGO model showcases a preference for splay between neighboring particles, which can be attributed to the special non-additive characteristics of the PHGO contact function. Lastly, we propose a potentially experimentally realizable pear-shaped particle model, the non-additive hard pear of revolution model, which is based on the HPR model but also features non-additive traits similar to those of PHGO particles to mimic their depletion behavior.
Note that these “overlaps” do not enable the pear-shaped particles to invade the space occupied by other pears according to the PHGO potential. The interactions are governed by a hard-core potential.
In these theories, every single configuration has to be treated individually to calculate depletion interactions.
Note that the MC dynamics described here do, of course, not represent true particle dynamics or trajectories.
Here, the term “overlap” might be misleading as the particles do not technically overlap in terms of their PHGO contact function but according to the best possible illustration using the Bézier representation. However, it also has to be mentioned that the spheres interact with the pear according to this Bézier shape. Thus, the solvent particles interact with the PHGO particles in terms of a different effective shape than two PHGO particles with each other.