We investigated the volumetric anomaly of a two-dimensional system of particles embedded in the surface of an inert sphere. The interaction between particles was modeled with a purely repulsive Gaussian potential. The phase diagram of the model exhibits one single fluid phase since the absence of an attractive term in the potential rules out a liquid–vapour phase transition while the curved geometry inhibits the formation of a long-range-ordered crystalline arrangement. Nonetheless, we found that the thermodynamic behavior of the model is, in some aspects, qualitatively reminiscent of that observed in a much more complex liquid such as supercooled water confined in cylindrical silica nanopores. In fact, upon cooling the fluid isobarically, the number density exhibits – over a range of moderately low pressures – a two-fold anomaly: a maximum followed, at lower temperatures, by a shallow minimum. Interestingly, a minimum also shows up in the density of the two-dimensional triangular solid which, for similar values of pressure and temperature, is the stable phase in a flat space. The two loci, traced by the thermodynamic parameters for which the density attains its minimum value in the fluid and in the solid phase, run very close to each other, a behavior which suggests that the emergence of the density minimum is not affected by the nature of the stable host phase but is more basically rooted in the properties of the interatomic potential.
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