Cellular Automata Modelling of Photo-Induced Oxidation Processes in Molecularly Doped Polymers

Abstract

Abstract:The possibility of employing cellular automata (CA) to model photo-induced oxidation processes in molecularly doped polymers is explored. It is demonstrated that the oxidation dynamics generated using CA models exhibit stretched-exponential behavior. This dynamical characteristic is in general agreement with an alternative analysis conducted using standard rate equations provided the molecular doping levels are sufficiently low to prohibit the presence of safe-sites which are impenetrable to dissolved oxygen. The CA models therefore offer the advantage of exploring the effect of dopant agglomeration which is difficult to assess from standard rate equation solutions. The influence of UV-induced bleaching or darkening upon the resulting oxidation dynamics may also be easily incorporated into the CA models and these optical effects are investigated for various photo-oxidation product scenarios. Output from the CA models is evaluated for experimental photo-oxidation data obtained from a series of hydrazone-doped polymers.

An Evaluation of Optical Absorbance Kinetics for the Detection of Micro-Porosity in Molecularly Doped Polymer Thin-Films

“…The relaxation process (ii) will consequently emit a photon but this is expected to be at a lower energy as the excited electrons thermalise to the lowest energy states within the DEH LUMO band. For MDP materials the LUMO and HOMO Gaussian bandwidths are expected to increase with the dopant concentration due to random dipole disorder [8,14]. For the DEH molecule which possesses a dipole moment~2.1 debye this results in a bandwidth of around 0.11 eV for c M = 50% [14].…”

“…Mitigation of photo-degradation processes in MDP thin-films consequently demands that a comprehensive understanding of the underlying processes and parameters that are dominant in driving these internal processes are fully identified and numerated. Previous work in this area has focused upon a specific photo-cyclic degradation process that is known to occur for a small hydrazone molecule p-diethylaminobenzaldehyde -1,1diphenylhydrazone (DEH) in MDP thin films [5][6][7][8]. The photo-cyclic conversion of DEH to the electronically inactive indazole (IND) product requires that the DEH molecule be first excited into a (reactive) state by appropriate absorption of UV radiation, and that excited DEH molecules have a supply of absorbed oxygen to then complete the reactive transition to IND.…”

“…The photo-cyclic conversion of DEH to the electronically inactive indazole (IND) product requires that the DEH molecule be first excited into a (reactive) state by appropriate absorption of UV radiation, and that excited DEH molecules have a supply of absorbed oxygen to then complete the reactive transition to IND. Modelling of the conversion dynamics of DEH to IND has previously been undertaken using rate-equation [7] and cellular-automata (CA) approaches [8]. From these studies it was found that the conversion dynamics of the hydrazone molecular dopant to indazole photo-product (P) could be analytically described as a function of photo-exposure time (t) by a stretched-exponential function such that:…”

“…In Equation ( 1) the fitting parameters Γ and γ are expected to be close to unity [8] provided the concentration of dopant (c M ) is kept sufficiently low (<20% by weight relative to the polymer). The other parameter τ in Equation ( 1) represents a characteristic time constant given by τ = c M /c O β where c O represents the concentration of soluble oxygen, and β gives the molecular relaxation rate of reactive DEH back to the (un-reactive) ground state.…”

“…A simple experimental methodology to investigate the conversion dynamics is therefore presented by selecting an appropriate UV exposure wavelength which may serve the dual function of initiating the photo-excitation process and providing a reference transmission signal through the film to determine the optical absorbance. As noted from previous cellular-automata simulations of the absorbance dynamics [8] the overall change in absorbance will then be determined by the changing proportion of DEH to IND as photo-exposure progress, and will be sensitive to the relative magnitude of the DEH and IND molecular absorption coefficients for the film thickness used. The proposed absorption approach may consequently offer a simple, affordable approach to investigate the porosity of thin polymer films which may be inaccessible using traditional bulk material methods [9][10][11] or which require the use of freestanding films [10][11][12].…”