The Packing Landscapes of Quasi-One Dimensional Hard Sphere Systems
Zaeifi Yamchi, Mahdi
When a liquid is cooled below its equilibrium freezing temperature, it becomes supercooled and the molecular motions slow down until the system becomes kinetically arrested, forming a glass, at the glass transition temperature. These amorphous materials have the mechanical properties of a solid while retaining the structural properties of a liquid, but do not exhibit the usual features of a thermodynamic phase transition. As such, they present a number of important challenges to our understanding of the dynamics and thermodynamics of condensed phases. For example, supercooled liquids are classified on the basis of the temperature dependence of their transport properties and structural relaxations times. Strong liquids display an Arrhenius behavior, with the logarithm of their viscosity growing linearly with inverse temperature. Fragile liquids behave in a super-Arrhenius manner, where the viscosity appears to diverge at temperatures above absolute zero, suggesting the possibility of an underlying thermodynamic origin to the glass transition. Some complex, network forming liquids, such as water and silica have also been shown to have a dynamical crossover from fragile to strong liquid behavior as the temperature is decreased. The potential energy landscape paradigm, combined with inherent structure formalism, provide a framework for connecting the way particles pack together with the thermodynamics and dynamics of the liquid and glassy phases. However, the complexity of this multi-dimensional surface makes it difficult to fully characterize and rigorous relationships between the nature of particle packing and glass forming properties have not been established. The goal of this thesis is to study some of the general features of glass transition and find the connection between the dynamics and the thermodynamics of glass forming liquids. To this end, the packing landscapes of quasi-one-dimensional hard discs and hard spheres are studied. A two dimensional system of hard discs with diameter σ, confined between two hard walls (lines) of length L, separated by a distance 1<Hd/σ< 1+√(3/4), is studied by using the Transfer Matrix (TM) method and Molecular Dynamics (MD) simulations. The complete packing landscape is characterized in terms of the density distribution of inherent structures and the number of local defect states. It is shown that this model exhibits a dynamic fragile-strong liquid crossover at the maximum in the constant pressure heat capacity (Cp) for the system, similar to that observed in anomalous network forming liquids such as water and silica. Furthermore, we find that rescaling the relaxation times of systems with different channel widths by the relaxation time at the Cp maximum causes all the data to collapse on a single master curve. The Cp maximum occurs at a critical value of the defect concentration. At high defect concentrations, where the defects interact, the fluid is fragile. When the defect concentration is low, relaxation appears to occur through the hopping of isolated defects, leading to Arrhenius dynamics. This suggests the thermodynamics associated with the Cp maximum is intimately related to the dynamic crossover. A system of three-dimensional hard spheres confined in a narrow channel was used to study the effect of a more complicated landscape on the dynamics of the system. For this system, the thermodynamic and dynamic properties of the system were studied for two different channel diameters, the 1<Hd/σ<1+√(3/4) case, which only allows first neighbors contact for the spheres and, 1+√(3/4)< Hd/σ < 1.98, which allows second neighbors contact to exist. For the first case, the TM method was implemented to obtain the thermodynamic properties and MD simulation was used to measure the dynamics. For the case that the second neighbor contact is allowed 1+√(3/4)< Hd/σ < 1.98. The thermodynamic and dynamic properties were obtained using MD simulations. In this channel diameter range, the system creates chiral helical jammed packings and defect states appear where sections of helices with different local chiralities come into contact. The equation of state (EOS) shows the presence of two heat capacity maxima. The high density Cp maximum is linked to fragile strong crossover. Finite size scaling analysis shows that the low density Cp maximum is related to an orientational order transition stabilized by the presence of the defects. This type of transition has been shown to exist in bulk two-dimensional systems but this work is the first study that provides strong evidence of the existence of this transition in a quasi-one-dimensional system in a system with short-range interactions.
DegreeDoctor of Philosophy (Ph.D.)
SupervisorBowles, Richard K.
CommitteeSteer, Ron P.; Urquhart, Stephen G.; Soteros, Chris E.; Patey, Gren N.
Copyright DateSeptember 2014
Glass transition, Inherent structure landscape, Fragile-Strong crossover, Quasi-one dimensional system