Structural Transition in a Fluid of Spheroids: A Low-Density Vestige of Jamming

Abstract

A thermodynamically equilibrated fluid of hard spheroids is a simple model of liquid matter. In this model, the coupling between the rotational degrees of freedom of the constituent particles and their translations may be switched off by a continuous deformation of a spheroid of aspect ratio t into a sphere (t ¼ 1). We demonstrate, by experiments, theory, and computer simulations, that dramatic nonanalytic changes in structure and thermodynamics of the fluids take place, as the coupling between rotations and translations is made to vanish. This nonanalyticity, reminiscent of a second-order liquid-liquid phase transition, is not a trivial consequence of the shape of an individual particle. Rather, free volume considerations relate the observed transition to a similar nonanalyticity at t ¼ 1 in structural properties of jammed granular ellipsoids. This observation suggests a deep connection to exist between the physics of jamming and the thermodynamics of simple fluids. DOI: 10.1103/PhysRevLett.116.098001 The thermodynamics of a fluid of simple spheres is wellknown and almost completely understood [1,2]. However, the constituents of real matter are typically nonspherical. Their translational degrees of freedom are coupled to their rotations [3]. A system of spheroids, ellipsoids of revolution, is arguably the simplest model of matter, where such a coupling exists. This model has recently been realized in colloidal and granular matter experiments, providing an important insight onto the local bulk structure of fluids [4,5] and jammed packings [6]. While a very good agreement between experiment and theory has been achieved for the fluids [5,7], these studies dealt with only one specific particle aspect ratio, t ¼ 1.6. The dependence of the fluid structure on the aspect ratio of the constituent particles has not been tested, so that the fundamental role played in these fluids by rotational degrees of freedom remains unknown. The understanding of jammed packings of ellipsoids is incomplete, as well. Many common order metrics are minimized for the, so-called, "maximally random jammed" (MRJ) packings [8]. Yet, it remains unclear, how the various protocols of compression, commonly starting from a fluidlike initial state, explore the available phase space and whether any fundamental physical reason exists for the convergence of many common compression protocols towards packings with densities close to that of the MRJ state [8][9][10][11][12][13].In this work, we study the dependence of the bulk structure in fluids of ellipsoids on the aspect ratio t ¼ a=b of the constituent particles, where a and b are the polar and the equatorial diameters, respectively. We combine experiments, theory, and Monte Carlo (MC) simulations, to explore the fundamental role of the rotational degrees of freedom in these fluids, in the vicinity of the so-called "sphere point" (t ¼ 1), where the coupling between rotations and translations vanishes. We demonstrate that the critical dependence of this coupling on ϵ ≡ jt − 1j, for ϵ → 0, gives rise...

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