Deep Learning Analysis of the Propagation of Stabilizing Additive Hydrolysis in a Cross-Linked Polyethylene Pipe

Cross-linked polyethylene (PEX-a) pipe is being increasingly used for water transport and heating applications. Its long-term stability is improved through the addition of stabilizing additive molecules that protect the pipe from environmental factors such as exposure to hot water, chlorine, and UV light. We have used infrared (IR) microscopy to measure line profiles of IR spectra across the pipe wall thickness for pipes that have been exposed to recirculating hot water at different fixed temperatures T for different aging times t . To analyze this large body of data, we used a deep learning approach involving a β-variational autoencoder (β-VAE) model. The leading latent variable L1 corresponds to the hydrolysis of a stabilizing additive molecule, and we track the penetration depth δ of the hydrolysis front radially outward from the inner wall of the pipes. The radial profiles of L1 collected for different aging temperatures T and times t allow us to interpret the propagation of the hydrolysis front as a simple diffusion process for which the activation energy E a is large compared with the thermal energy k B T . In addition, we determine time scaling factors a ( T ) for the data sets collected at different temperatures T that allow us to collapse all of the data onto a master curve of δ versus scaled aging time t ′ = a ( T ) t, and to determine that an increase in the aging temperature T of 10 °C corresponds to a decrease in the aging time t by a factor of 1.8. Our results illustrate a distinct advantage of the β-VAE analysis: it provides a useful, interpretable representation of our very large data set, allowing us to achieve a detailed physical understanding of the stabilizing additive hydrolysis phenomenon.