1D fluids with repulsive nearest-neighbour interactions: Low-temperature anomalies

Abstract

A limited number of 2D and 3D materials under a constant pressure contract in volume upon heating isobarically; this anomalous phenomenon is known as the negative thermal expansion (NTE). In this paper, the NTE anomaly is observed in 1D fluids of classical particles interacting pairwisely with two competing length scales: the hard-core diameter $a$ and the finite range $a'>a$ of a soft repulsive potential component. If $a'\le 2a$, the pair interactions reduce themselves to nearest neighbours which permits a closed-form solution of thermodynamics in the isothermal-isobaric ensemble characterized by temperature $T$ and pressure $p$. We focus on the equation of state (EoS) which relates the average distance between particles (reciprocal density) $l$ to $T$ and $p\ge 0$. The EoS is expressible explicitly in terms of elementary or special functions for specific, already known and new, cases like the square shoulder, the linear and quadratic ramps as well as certain types of logarithmic interaction potentials. The emphasis is put on low-$T$ anomalies of the EoS. Firstly, the equidistant ground state as the function of the pressure can exhibit, at some ``compressibility'' pressures, a jump in chain spacing from $a'$ to $a$. Secondly, the analytical structure of the low-$T$ expansion of $l(T,p)$ depends on ranges of $p$-values. Thirdly, the presence of the NTE anomaly depends very much on the shape of the core-softened potential.