Numerical Simulation of Vibrational Sum Frequency Generation Intensity for Non-Centrosymmetric Domains Interspersed in an Amorphous Matrix: A Case Study for Cellulose in Plant Cell Wall

Vibrational sum frequency generation (SFG) spectroscopy can specifically probe molecular species non-centrosymmetrically arranged in a centrosymmetric or isotropic medium. This capability has been extensively utilized to detect and study molecular species present at the two-dimensional (2D) interface at which the centrosymmetry or isotropy of bulk phases is naturally broken. The same principle has been demonstrated to be very effective for the selective detection of non-centrosymmetric crystalline nanodomains interspersed in three-dimensional (3D) amorphous phases. However, the full spectral interpretation of SFG features has been difficult due to the complexity associated with the theoretical calculation of SFG responses of such 3D systems. This paper describes a numerical method to predict the relative SFG intensities of non-centrosymmetric nanodomains in 3D systems as functions of their size and concentration as well as their assembly patterns, i.e., the distributions of tilt, azimuth, and rotation angles with respect to the lab coordinate. We applied the developed method to predict changes in the CH and OH stretch modes characteristic to crystalline cellulose microfibrils distributed with various orders, which are relevant to plant cell wall structures. The same algorithm can also be applied to any SFG-active nanodomains interspersed in 3D amorphous matrices.