Modeling coloration of a radiochromic film with molecular dynamics-coupled finite element method

Abstract

© 2017 by the authors. Radiochromic films change color upon exposures to radiation doses as a result of solid-state polymerization (SSP). Commercially available radiochromic films are primarily designed for, and have become widely used in, clinical X-ray dosimetry. However, many intriguing properties of radiochromic films are not yet fully understood. The present work aimed at developing a theoretical model at both atomic and macroscopic scales to provide a platform for future works to understand these intriguing properties. Despite the fact that radiochromic films were primarily designed for clinical X-ray dosimetry, dose-response curves for the Gafchromic EBT3 film obtained for ultraviolet (UV) radiation were employed to develop our model in order to avoid complications of ionization, non-uniform energy deposition, as well as dispersed doses caused by secondary electrons set in motion by the indirectly ionizing X-ray photons, which might introduce added uncertainties to the model and overshadow the basic SSP processes. The active layer in the EBT3 film consisted of diacetylene (DA) pentacosa-10,12-diynoate monomers, which were modelled using molecular dynamics (MD). The degrees of SSP in the atomic scale upon different UV exposures were obtained to determine the absorption coefficients of the active layer, which were then input into the finite element method (FEM). The classical steady-state Helmholtz equation was engaged to model the reflection from the active layer using the FEM technique. The multifrontal massively parallel sparse direct solver (MUMPS) was employed to solve the present numerical problem. Very good agreement between experimentally and theoretically obtained coloration in terms of net reflective optical density was achieved for different UV exposures. In particular, for UV exposures larger than ~40 J/cm2, the reflected light intensity decreased at a lower rate when compared to other UV exposure values, which was explained by the densely cross-linked structure under near-complete polymerization, and thus the lower efficiency for further bond formation between DA monomer strands.