Using the AKARI, Wide-field Infrared Survey Explorer (WISE), Infrared Astronomical Satellite (IRAS), Sloan Digital Sky Survey (SDSS) and Hubble Space Telescope (HST) data, we investigated the relation of polycyclic aromatic hydrocarbon (PAH) mass ($M_{rm PAH}$), very small grain mass ($M_{rm VSG}$), big grain mass ($M_{rm BG}$) and stellar mass ($M_{rm star}$) with galaxy merger for 55 star-forming galaxies at redshift $z<0.2$. Using the SDSS image at $z<0.1$ and the HST image at $z>0.1$, we divided the galaxies into merger galaxies and non-merger galaxies with the morphological parameter asymmetry $A$, and quantified merging stages of galaxies based on the morphological indicators, the second-order momentum of the brightest 20$%$ region $M_{20}$ and the Gini coefficient. We find that $M_{rm PAH}/M_{rm BG}$ of merger galaxies tend to be lower than that of non-merger galaxies and there are no systematic differences of $M_{rm VSG}/M_{rm BG}$ and $M_{rm BG}/M_{rm star}$ between merger galaxies and non-merger galaxies. We find that galaxies with very low $M_{rm PAH}/M_{rm BG}$ seem to be merger galaxies at late stages. These results suggest that PAHs are partly destroyed at late stages of merging processes. Furthermore, we investigated $M_{rm PAH}/M_{rm BG}$ variations in radiation field intensity strength $G_0$ and the emission line ratio of $[{rm O,{scriptsize I}}]lambda 6300/{rm H}alpha$ which is a shock tracer for merger galaxies and find that $M_{rm PAH}/M_{rm BG}$ decreases with increasing both $G_0$ and $[{rm O,{scriptsize I}}]/{rm H}alpha$. PAH destruction is likely to be caused by two processes; strong radiation fields and large-scale shocks during merging processes of galaxies.
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