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Recent experimental discoveries of novel nematic types with polar order,including ferroelectric nematic and splay nematic have brought the resurgenceof the interest in polar and modulated phases. One of the most importantfactors that is widely believed to be crucial for the formation of the newphases is the pear-like shape of the mesogenic molecules. Such molecules weretreated using second-virial density functional theory in [De Gregorio, P\textit{et al.}, \textit{Soft Matter}, 2016, \textbf{12(23)}, 5188-5198], wherethe authors showed that the $K_{11}$ splay elastic constant can become negativedue to solely entropic reasons leading to long-range splay and polarcorrelations. To verify whether the predictions are correct, we performed MonteCarlo simulations of the same hard-core molecules used in the DFT study. As ourresults suggest, no polar or modulated liquid crystalline phases emerge; polarand splay correlations are at most short-range or completely absent. On theother hand, a polar ferroelectric splay crystal was observed.

Splay and polar order in a system of hard pear-like molecules:  confrontation of Monte Carlo numerical simulations with density functional  theory calculations