簡單液體及水在短時間內的動力學行為:瞬間正則模分析

Abstract

在本篇論文中，我們將運用分子動力模擬(Molecular dynamics simulation)，Voronoi analysis，及瞬間正則模(Instantaneous normal mode) 的方法研究液體在短時間內的動力學行為。在第二章中，我們提出在介於彈道運動(ballistic motion)與結構擴散(structural relaxation)的時間尺度下，由開始在徑向分佈函數的第一個極大值內的溶劑粒子所給予的撞擊力量，造成在徑向分佈函數的第一個極大值附近的溶劑粒子擴張。藉由這個擴張模型，我們可以解釋在salvation time correlation function中所發現的小凸出隆起。在三章中，Lennard-Jones (LJ) 2n-n的瞬間正則模頻譜將被用來研究吸引力在potential energy landscape中所扮演的角色。我們進行兩個系列的分子動力模擬，其分別為在固定溫度與密度下改變LJ 2n-n的交互作用的範圍與在不同的n值下改變密度，從類似氣體的低密度到類似液體的高密度。在第一個系列的分子動力模擬中，吸引力的存在將會降低瞬間正則模中虛模(imaginary modes)所佔的比例，這代表著擴散係數將會因為吸引力的存在而降低。在第二個系列的分子動力模擬中，如果密度夠低，我們發現在瞬間正則模的頻譜上將會有一些奇異點，而這些奇異點將可以用雙原子的運動來解釋。在第四章中，我們提出了在鎵液體中瞬間共振模(instantaneous resonant modes)存在的證據，而瞬間共振模的發生是由局部密度變動所造成的體積膨脹和在鎵液體的假交互作用(pseudo-potential)中排斥核(repulsive core)中的特別曲率下降所造成的。並且藉由追蹤瞬間正則模，我們估計瞬間共振模的生命期大概是在fs的尺度。在第五章中，我們同時運用瞬間正則模和Voronoi的方法研究液態水。隨者非球性(asphericity)的增加，在不同Voronoi Group (VG)中瞬間正則模的實部平均頻率會移往高頻方向而且虛部所佔的比例將會下降。這兩個現象大約可以用在不同VG中氫鍵結構解釋。透過計算在不同VG中水分子瞬間正則模的平均本徵向量的強度，我們可以了解為何隨者非球性的增加，擴散係數會下降。

In this dissertation, we study the short-time dynamics of liquids, from simple liquids to water, through molecular dynamics (MD) simulations, the Voronoi analysis, and the instantaneous-normal-mode (INM) analysis. In chapter II, we propose that the solvents around the first maximum of the radial distribution function expand at a time scale between inertia motion and structural relaxation. This expansion is triggered by the impulses given by the solvents that were initially inside the first maximum of the radial distribution function. In terms of this expansion, the bump in the salvation time correlation function can be explained. In chapter III, the INM spectra of the Lennard-Jones (LJ) 2n-n are studied for the role of attractive forces on the potential energy landscapes of simple systems. Two series of MD simulations are performed by either changing the interaction range of the pair potential in the LJ 2n-n fluid at a fixed temperature and density or varying the densities of supercritical LJ 2n-n fluids, from gas-like to liquid-like, at different range of attractive forces. In the first series of MD simulation, the attractive force in a simple system plays a role to reduce the fraction of imaginary modes and implicitly reduce the self-diffusion coefficient. In the second series of MD simulation, some singularities are found in the INM spectra, if the density is low enough. The origin of these singularities can be understood by the binary motions at separations corresponding to the extreme curvatures of the interaction potential. In chapter IV, the existence of the low-frequency, quasilocalized vibrational excitations, which is termed as instantaneous resonant modes (IRMs), in gallium liquids has been proposed. The occurrence of the IRMs is attributed to the cooperation of the local volume expansion due to density fluctuation and the exotic repulsive core of the gallium pseudo-potential. Also, through tracing the INMs, we estimate the lifetimes of IRMs to be in the fs order. In chapter V, the INM method and the Voronoi analysis have been applied concurrently in studying liquid water. With increasing the asphericity of Voronoi groups (VGs), the mean frequency of the real part of the INM density of states (DOSs) shift toward high-frequency end and the fraction of the imaginary DOSs decreases. Qualitatively, these two phenomena can be understood by the hydrogen bonding status in different VGs. Also, the fact that the self-diffusion coefficient decreases with increasing asphericity can be explained by the mean magnitude of the INM eigenvectors of water molecules at different VGs.