  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) 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 "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.
