Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2010 Jun 28;132(24):244703. doi: 10.1063/1.3442446.
The orientational correlation functions measured in the time-resolved second-harmonic generation (TRSHG) and time-resolved sum-frequency generation (TRSFG) experiments are derived. In the laboratory coordinate system, the Y(l) (m)(Omega(lab)(t))Y(2) (m)(Omega(lab)(0)) (l=1,3 and m=0,2) correlation functions, where the Y(l) (m) are spherical harmonics, describe the orientational relaxation observables of molecules at interfaces. A wobbling-in-a-cone model is used to evaluate the correlation functions. The theory demonstrates that the orientational relaxation diffusion constant is not directly obtained from an experimental decay time in contrast to the situation for a bulk liquid. Model calculations of the correlation functions are presented to demonstrate how the diffusion constant and cone half-angle affect the time-dependence of the signals in TRSHG and TRSFG experiments. Calculations for the TRSHG experiments on Coumarin C314 molecules at air-water and air-water-surfactant interfaces are presented and used to examine the implications of published experimental results for these systems.
在时间分辨二次谐波产生（TRSHG）和时间分辨和频产生（TRSFG）实验中测量了取向相关函数。在实验室坐标系中，Y(l)（m）（Ω(lab)(t)）Y(2)（m）（Ω(lab)(0)）（l=1,3 和 m=0,2）相关函数，其中 Y(l)（m）是球谐函数，描述了界面处分子的取向弛豫可观测量。采用摇摆在圆锥模型来评估相关函数。理论表明，与体相液体的情况相反，取向弛豫扩散常数不能直接从实验衰减时间获得。呈现了相关函数的模型计算，以演示扩散常数和圆锥半角如何影响 TRSHG 和 TRSFG 实验中信号的时间依赖性。呈现了在空气-水和空气-水-表面活性剂界面上香豆素 C314 分子的 TRSHG 实验的计算，并用于检查这些系统的已发表实验结果的含义。
