Nonlocal polymer driven diffusion model: nonlocal temporal behaviour and non ideal kinetics

摘要

Two extensions of the Nonlocal Polymer Driven Diffusion model (NPDD) describing grating formation in photopolymers are proposed. The inclusion of a nonlocal spatial response function has been shown to predict high spatial frequency cutoff in photopolymers. Here the nature of the temporal response of photopolymer is discussed and a nonlocal temporal response function proposed. A number of different possible spatial response functions are also examined. The extended model is then solved using a finite element technique and the results compared to the purely spatial response case. The kinetics of photosensitive polymer holographic recording are then examined. Assuming primary termination dominates the chain formation process a model is proposed based on a quadratic relationship which is shown to exist between the monomer concentration and polymerisation rate. The model is solved using a four-harmonic expansion. Results are then fitted numerically to growth curves of experimentally monitored diffraction efficiencies of gratings recorded in an acrylamide-based photopolymer system. Physical parameters such as diffusion constant and polymerisation rate are extracted and compared to the literature.