Local viscoelasticity at resin-metal interface analyzed with spatial-decomposition formula for relaxation modulus

A spatial-decomposition formula is presented for viscoelasticity. In this formula, the relaxation modulus is decomposed with respect to a spatial coordinate and the local viscoelasticity is analyzed with the spatially decomposed stress-stress time correlation function. The spatial-decomposition formula is then applied to a planar interface between resin and metal by using the Kremer-Grest model at a variety of adhesion strengths. It was observed that when the resin-metal interaction is strong, the resin forms a layer structure extending over a spatial range which is larger by an order of magnitude than the segment size of the resin. The motion of the resin is suppressed there, and the effect of the interface is localized near the wall only when the adhesion is weak. Actually, the layer region is more viscous than the bulk when the resin interacts strongly with the wall, in the sense that the stress-stress correlation in the former region persists over longer times. The resin-metal interaction in the spatial scale corresponding to the segment size does not affect the equal-time correlation of the local stress significantly and modifies mainly the decay with time of the local stress of the resin within the layers. The present work demonstrates that the spatially decomposed relaxation modulus can be a general framework for analyzing the viscoelasticity at the interface and revealing the relationship of the adhesion to the stress-stress correlation in the segment-scale space and time.