Oxygen Diffusion in a Polystyrene Optical Fibre Surrounded by an Oxygen Gas Barrier

In the context of the LHCb SciFi project natural aging of the scintillating plastic fibres was observed. The observed loss of transparency of the fibre is attributed to an oxygenation reaction of polystyrene, the fibre core material. This note treats the oxygen diffusion into the polystyrene fibre core by solving a differential equation of diffusion using a model of the polystyrene core cylinder surrounded by a fibre cladding which may act as an oxygen barrier. The calculations show that the diffusion is generally faster than the oxygenation reaction. The fibre core will be always kept in the equilibrium saturation state with 20-30 ppm oxygen. Therefore, the rate-limiting reaction is not the oxygen diffusion, but the oxidation reaction, which determines the slow aging of a plastic scintillating fibre.