Model of laser-driven mass transport in thin films of dye-functionalized polymers

Abstract

Based on Newtonian fluid dynamic relations, a model is constructed to describe laser-induced mass transport in thin films of polymers containing isomerizable azobenzene chromophores, in which surface profile diffraction gratings can be inscribed with an interference pattern of coherent light. The Navier–Stokes equations for laminar flow of a viscous fluid are developed to relate velocity components in the film to pressure gradients in the polymer film, by definition of boundary layer conditions. This general laminar flow model is applicable to the formation of surface gratings through a variety of mechanisms. Considering the mechanism of an isomerization-driven free volume expansion to produce internal pressure gradients, a specific model is developed to describe polymer flow resulting from laser-induced isomerization of the bulky chromophores. This yields an expression relating the time evolution of the surface gratings to properties which could be varied experimentally, such as those of the irradiating light, inscription geometry, and bulk polymer, which incorporates no arbitrary fitting parameters or integration constants. In the general model, the rate of grating inscription is predicted to vary directly with the intensity of the inscription laser, to vary inversely with the molecular weight of the polymer below the limit of entanglement, and to scale with the third power of the initial thickness of the film. Considering an isomerization pressure mechanism, the model predicts the rate of grating inscription to further vary with the free volume requirements of the induced geometric transformation of the dye molecules, and the polarization state of the inscription laser. Predictions from the model were tested against the results of experiments to vary these parameters, and are shown to be in good agreement.