Nonlinear Stress Relaxation of End-Associative Star Chain 2. Behavior Under Double-Step Strain

For an unentangled four-arm star chain having long-lived associative groups (stickers) at the arm ends, bead-spring analysis was conducted for the nonlinear stress relaxation under double-step strain. The analysis considered strain-induced sticker disruption activating the fast intrinsic motion and partial equilibration of the chain, as in the case of the relaxation under the single-step strain examined in the accompanying paper (Ref. 1 of this paper). However, under the double-step strain, the conformation of a given arm keeps its memory from the first step strain γ1 (imposed at time −tw) when the second step strain γ2 is imposed at a later time 0. Namely, the conformation just before imposition of the second strain is different for the arms that carry the stickers having or not having been disrupted by the first strain, so that the analysis needs to be conducted for a whole cascade of the conformational memory, from the conformations on imposition of the first strain to those on imposition of the second strain. For the star chain having four arms, the conformational distribution in this cascade was still manageably narrow, and the bead-spring analysis allowed us to formulate the stress σ(t; γ1, γ2) at time t > 0 (after imposition of the second strain). It turned out that σ(t; γ1, γ2) thus deduced from the analysis captures the features of preliminary data obtained for tetra-PEG chains associating at the arm ends, confirming the importance of the cascaded memory and the isochronal cross-correlation of the arm conformations for those chains. In addition, for the case of γ2 ≅ −γ1/2, differences were found between the data and σ(t; γ1, γ2) deduced from the widely adopted BKZ constitutive equation, which further demonstrated the importance of the cascaded memory and cross-correlation not incorporated in this equation.