Monte Carlo simulation of two‐dimensional hard body systems with extreme values of the Poisson's ratio

Monte Carlo computer simulations with variable shape of the periodic box were performed for a few two‐dimensional, hard‐body models showing elastically isotropic solid phases. Two examples of homo‐molecular (i.e. consisting of identical molecules) systems of anisotropic molecules are discussed which form unusual solid phases, showing negative Poisson's ratio and know as auxetic ones, at densities and pressures higher than the elastically isotropic solid phases. Sharp extremes of the Poisson's ratio were observed for both systems at freezing of the orientational degrees of freedom of the molecules: a minimum was observed for the system for which the auxetic phase with frozen rotation is isotropic and a maximum was found for the other system. This indicates that isotropic auxetic phases can have auxetic precursors with much more negative Poisson's ratios than those characterizing the auxetic phases themselves. An example of a hetero‐molecular (i.e. mixture consisting of different molecules), elastically isotropic system is also discussed – the polydisperse hard disc system. The simulations revealed a maximum of the Poisson's ratio in the close packing limit at any nonzero polydispersity. Although no manifestation of any auxetic behaviour has been found in this system, the obtained results indicate other unusual effect – a jump (discontinuity) of the Poisson's ratio at close packing when the polydispersity tends to zero. The results obtained in this work demonstrate that the Poisson's ratio can play the role of a sensitive indicator of (at least) some structural changes in solids. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)