Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD)

The Nonlocal Polymer Driven Diffusion (NPDD) model successfully predicts high spatial frequency cut-off and higher harmonic generation, experimentally evident in holographic gratings recorded in free radical chain photopolymer materials. In this paper the NPDD model is extended to include a nonlocal material temporal response. Previously it was assumed that following a brief transient period, the spatial effect of chain growth was instantaneous. However, where the use of short exposures is necessary, as in optical data storage, temporal effects become more significant. Assuming that the effect of past chain initiations will have less effect on monomer concentration at a later point in time than current initiations, a normalized exponential function is proposed to describe the process. The extended diffusion model is then solved using a Finite-Difference Time-Domain technique to predict the evolution of the monomer and polymer concentrations during and after grating recording. The Lorentz-Lorenz relation is used to determine the corresponding refractive index modulation and The Rigorous Coupled Wave Method applied to determine and/or process diffraction efficiencies. A fitting technique is then used which first solves the diffusion model as described and determines a set of parameters which give best fits to the experimental data. Results show that the inclusion of the nonlocal temporal response is necessary to accurately describe grating evolution for short exposures i.e. continued polymer chain growth for some period after recording resulting in an increase in the refractive index modulation. Monomer diffusion is also shown to influence refractive index modulation post-exposure. Monomer diffusion rates determined to be of the order of D ~ 10-11 cm2/s and the time constant of the nonlocal material temporal response function being of the order of τn ~ 10-2s.