The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a “true” pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a “true” hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.
The standard deviation of the diameter distribution has to be with the mean diameter .
Additional overlap rules (like adding non-additive features to the blunt ends) are required to imitate the interactions between PHGO particles with physical hard shapes.
The parameter σw indicates the width of the pear-shaped particles.
Note that the “normalization” factor in this case indicates that g(r) converges toward 1 for large distances: limr→∞g(r) = 1.
This only applies to the smectic-A phase. For other smectic phases, it is still more convenient to use the director as a reference.
Note here, that r∥ can become negative. For pear-shaped particles, positive longitudinal distances correspond to a distance in the direction of the thin narrow end, while negative distances have to be assigned to particles, which are placed in the direction of the thick blunt end.
Note that the functions do not contain information about the likeliness of such configurations occurring.