Theoretical and Computational Study on Dynamically Heterogeneous Systems

Abstract

Dynamic heterogeneity has gained much attention for describing distinctive properties of the supercooled liquids. In this thesis, dynamically heterogeneous systems are investigated using computational methods. First, the dimensional dependence of dynamic heterogeneity in the supercooled liquid systems using kinetically constrained models (KCMs) is investigated. Higher dimensional generalization of 1-dimensional East model and its variation with an embedded probe particle are used as a representative fragile liquid system. We investigate the upper critical dimension of our model system using the fractional scaling behavior of the Stokes-Einsten relation. In contrast to previous simulation studies on the hard sphere model and theoretical studies based on the mean field approach, our study suggests that the East model has an infinite upper critical dimension. Second, the dynamic heterogeneity in the fragile-to-strong crossover model of the supercooled liquids is studied using the model that linearly interpolates between the strong-liquid and the fragile-liquid by an asymmetry parameter b. We investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows a constant power law exponent under the temperature change, and the exponent has the value between the strong liquid and the fragile liquid values. We find a smooth transition of the exponent from 0.66 to 0.73 as b is decreased. Lastly, the dynamic heterogeneity and its length scale found in the coarse-grained ionic liquid model system is numerically investigated. Cations and anions composing the ionic liquids are modeled as two spheres with positive charges and a single sphere with a negative charge, respectively. To study the effect of the charge distributions on the cations, two schematic models with different charge distributions are used and the model without charge is also considered as a counterpart. All three models show significant increase of the dynamic heterogeneity as the temperature is lowered. The dynamic heterogeneity is quantified via the well-known four-point susceptibility which measures the fluctuation of time correlation functions. The dynamic correlation length is calculated by fitting the dynamic structure factor with the Ornstein-Zernike form. Obtained time and length scales exhibit power law relations at low temperatures, similar to various supercooled liquid models. Especially, the model systems with charge show unusual crossover behaviors which is not observed in the uncharged model system. We ascribe the crossover behavior to the enhanced cage effect caused by charges on the particles.