Electric Field Poling in Polymeric Nonlinear Optical Materials. Relaxation Dynamics, Model, and Experiment

Simulations of the electric field poling process for second-order NLO-active polymeric materials containing dipolar chromophores were performed by modeling the time-dependent dynamics of a dipole interacting with an externally applied field and subsequent force-free relaxation, employing several modifications of the Smoluchowski equation. The model examines chromophore dipole alignment/relaxation processes in both two- and three-dimensional space. The 3-D model predicts that at field-on equilibrium, the ratio, R, of the second-harmonic coefficients, d₃₃/d₃₁, approaches 3.0, in accord with static statistical-mechanical models. In contrast, the 2-D model predicts R ~ 6.0. The dimensionality in which the rotational diffusion process is confined also determines the rate of dipolar alignment/relaxation, with a slower rate predicted in the 2-D case. Suitability of the rotational diffusion model for the alignment and relaxation dynamics of appended NLO chromophores in poled polymer films is also examined. At temperatures at or above the glass transition temperature, T_g, experimentally measured d₃₃ relaxation kinetics of a prototypical chromophore-functionalized polymer, N-(4-nitrophenyl)-(S)-prolinoxy poly(p-hydroxystyrene), (S)-NPP-PHS, are well described by the bi-exponential expression predicted by the 3-D model. Below T_g, however, the dynamics are not well modeled as simple 3-D rotational diffusion, the apparent result of complex dynamical matrix interactions. Under all conditions examined, the experimental d₃₁ relaxation dynamics can be described approximately using the 2-D model. The temperature dependence of the relaxation rate above T_g is well described by the Williams-Landel-Ferry (WLF) equation, while below T_g, the reorientation process is Arrhenius-like. The d₃₃ growth kinetics are found to be accurately approximated using expressions derived from the 3-D rotational diffusion model. Below T_g the experimental activation energy determined from field-on polarization is identical within experimental error to that determined for field-off depolarization.