Disorder and excess modes in hard-sphere colloidal systems

The anomalous thermodynamic properties of glasses remain incompletely understood, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low-frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe a strong enhancement of low-frequency modes. Using a novel method (Zargar R. et al., Phys. Rev. Lett. 110 (2013) 258301) to determine the free energy, we also determine the entropy and the specific heat experimentally. It follows that the emergence of the excess modes and high values of the specific heat are directly related and are specific to the glass: even for solids containing a very large amount of defects, both the low-frequency density of states and the specific heat are significantly smaller than for the glass. Copyright c © EPLA, 2014 The vibrational density of states (DOS) and the normal modes of solids provide a direct route to study its thermodynamics and mechanical properties [1]. In perfect crystalline solids, because of their long-range order, vibrational states are well understood as plane-wave phonon modes [2–5]. However, for more disordered systems the nature of vibrations remains elusive [6]. Structurally disordered systems such as liquids, glasses and amorphous materials exhibit a number of peculiar properties that are anomalous compared to those of the crystals [6–16]. These properties include anomalous acoustic behavior, a peak in the temperature dependence of the specific heat Cp/T , and a Boson peak observed in inelastic scattering of light or neutrons [13–16]. These suggest the existence of an excess vibrational density of states over and above the predictions of the Debye model: at the maximum in Cp/T , the vibrational density of states, D(ω), scaled with the DOS of a perfect crystal, goes through a maximum which is called the “Boson peak” [17–22]. The relation between the Boson peak and the disorder remains a topic that is hotly debated [12,13]; it seems clear that there is some relation between the two, but a direct link between the Boson peak and structural disorder in glassy systems has been difficult to demonstrate [17–25]. In this letter, we study the effects of structural disorder on the vibrational modes and the thermodynamics of colloidal hard spheres. This system, as we will show below, allows us to determine both the DOS and the thermodynamic properties of the glassy and crystalline states, and to provide a direct comparison between the two states of matter. We apply the covariance matrix analysis [7,26,27] to determine the density of states and the normal modes of vibrations from the particle displacements for a nearly perfect crystal, crystals with different amounts of defects, and for completely disordered systems (glasses). We find that there is a strong enhancement of low-frequency modes in the DOS for glasses however, no significant excess of modes is observed for very defected crystals, regardless of the amount of disorder (crystalline defects) present. We also experimentally determine the entropy, which is a measure of the specific heat at constant temperature, for several hard-sphere systems with different amounts of disorder. We show that while the specific heat increases gradually with increasing amount of disorder for crystals, it shows a discontinuous jump between a very defected crystal and a glass, as does the amplitude of the excess modes. These observations confirm independently that the excess of modes is an intrinsic property of glassy systems that is uniquely due to their vibrational