Nonlinear Stress Relaxation of End-Associative Star Chain 1. Behavior Under Single-Step Strain

For an unentangled four-arm star chain having long-lived associative groups (stickers) at the arm ends, a bead-spring analysis was conducted to examine nonlinear stress relaxation behavior under single-step strain. In the analysis, some stickers were disrupted by the strain to activate very fast intrinsic motion of the star chain, and the disrupted and undisrupted stickers, respectively, were treated as mobile and immobile beads during this fast process. This intrinsic motion leads the chain to average/equilibrate its conformation to an extent allowed by the constraint from the immobile beads, and the disrupted stickers are reformed after the intrinsic motion. Thus, the star chain is affinely deformed by the strain but this deformed conformation is further tuned on the strain-induced sticker disruption followed by the conformational averaging and the sticker reformation. For this tuned initial conformation, the bead-spring analysis of the slow relaxation process (governed by intact/reformed stickers) combined with a free energy analysis suggested that the star chain exhibits time-strain separable damping of its relaxation modulus under moderate strain whereas some instability of uniform deformation (possibly resulting in the yielding of the system) emerges under large strain. These results of the analyses were favorably compared with a preliminary experiment made for a transient gel of end-associative tetra-poly(ethylene glycol) star chains. Furthermore, the analyses were extended to a transient gel of associative linear chains to discuss differences/similarities of the transient gels of star and linear chains having topologically different backbones.