Dynamics of glass forming liquids with emphasis on vibrational modes
The potential energy landscape (PEL) description is regarded as one of the fundamental landmarks in the theory of glass transition, which has found wide applications not only in the understanding of disordered materials but also in other frontiers of research, such as bio-molecules, catalysis, machine learning, and neural networks. In this context, the mechanically stable local minimum energy configurations of the PEL, which are known as inherent structures (ISs), have a major role to play in elucidating various dynamical and thermodynamic properties of the system in terms of its sojourn over the complex multi-dimensional potential energy surface (PES). However contrary to the crystals, disordered materials pose a greater challenge in understanding their properties. Due to their ordered structures, the normal modes of collective vibrational excitations in crystals can be described by plane waves, which are known as phonons, and they play a fundamental role in determining the kinetic and thermodynamic properties of crystalline solids. Notwithstanding the difficulties presented by the inherent disorder in glass-forming materials, collective excitations associated with small-amplitude vibrations of the system about their ISs can be defined. This thesis presents a study of the dynamics of glass-forming liquids with emphasis on the collective vibrational excitations of the underlying disordered solid. The vibrational spectrum of disordered harmonic solids consists of a coexisting region of extended phonon modes that obey the Debye scaling law in their density of states, g(ω) ∼ ω^(d−1) in d dimensions, and quasi-localized modes that obey a universal g(ω) ∼ ω^4 law. These excess quasi-localized modes, appearing in the boson peak region of the vibrational spectrum, are found to be substantially different in nature as compared to the modes in other parts of the spectrum. The first part of the thesis describes an investigation of the dynamics of model glass-forming systems based on the measurement of thermal transport properties, with emphasis on the role of the vibrational modes in determining the thermal conductivity. Depending on the protocol of preparation of the glass, the system explores different parts of the PEL. The distinct ISs visited by the system in its exploration of the PEL impact the thermal transport characteristics of the low-temperature glassy states significantly. The observation of lower values of thermal conductivity with slower cooling or growing age of the glass former can be rationalized in terms of the system’s exploration of ISs with progressively lower energy. This in turn has been linked to the presence of more localized normal mode excitations associated with the ISs. Further, the energy diffusivity d(ω) that measures the ability of an excitation to transport thermal energy, has been found to obey a generic d(ω) ∼ 1/(ω^3) law for the quasi-localized normal modes. The diffusivity of low-frequency delocalized phonon modes in two dimensions, on the other hand, follows a d(ω) ∼ 1/(ω^2) law, and it is possible to transform these extended modes to acquire quasi-localized character by the introduction of quenched disorder, which can be achieved via pinning a fraction of the particles. Notably, the boson peak coincides with the well-known Ioffee-Regel limit for phonons, which signals the crossover in terms of d(ω), from a regime populated by delocalized modes to a regime of quasi-localized modes. In the second part of the thesis, the low-temperature short-time dynamics of a model glass forming system in metabasins of the PEL has been examined. A metabasin is an assembly of strongly correlated basins of ISs in the PEL. Our analysis in terms of the complete vibrational spectrum reveals that the harmonic approximation is not adequate for describing the short-time dynamics at temperatures near the glass transition point. The mean-square displacements computed within the harmonic approximation deviates from that obtained from molecular dynamics simulation at a time shorter than the β-relaxation timescale (τ_β ). With the added contribution of the anharmonic terms in the Hamiltonian via an approximate scheme, the mean- square displacement obtained from the modified calculation shows an agreement with that from both molecular dynamics and metabasin dynamics to a time extending beyond τ_β . The short-time dynamics appears as a combination of the dynamics within the basins of individual ISs and the system’s exploration of different basins inside a metabasin. Moreover, our study shows that the manifestation of the low-frequency quasi-localized excitations in the dynamical quantities depends on the nature of the microscopic dynamics (Newtonian or Langevin) of the system. Our studies in the thesis thus highlight a few important features of the low-temperature dynamics of glass formers and their close connection with the system’s potential energy landscape via the collective vibrational excitations.
- Physics (PHY)