# Linear viscoelasticity of unentangled corona blocks and star arms

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## Abstract

ABA-type triblock copolymers form micellar structures consisting of B-rich cores and A-rich coronas in A-selective solvents. The relaxation of A corona is known to be qualitatively similar to but quantitatively different from that of a star-shaped A chain due to the geometric (spatial) constraint by the core and the thermodynamic (osmotic) constraint. The effect of the geometric constraint on the block dynamics can be modeled by a chain with one end grafted onto an impenetrable wall. We show that the impenetrable wall slightly accelerates the end-to-end vector relaxation in a direction normal to the wall while it slightly decelerates the viscoelastic terminal relaxation. To test this prediction, we performed linear viscoelastic measurements for model systems: For polystyrene–polyisoprene–polystyrene (SIS) triblock copolymers in S-selective solvent (diethyl phthalate) forming micelles, the viscoelastic relaxation of unentangled S blocks (corona blocks) was indeed slower compared with that of star-branched S chains having the same molecular weight. Nevertheless, the deceleration was stronger than that expected from our theory, and possible reasons were discussed.

## Keywords

Block copolymer Tethered chain Linear viscoelasticity Relaxation time## Notes

### Acknowledgments

Q.C. thanks the financial support from the G-COE program at the Institute for Chemical Research, Kyoto University. T.U. thanks the support by Grant-in-Aid (KAKENHI) for Young Scientists B 25800235. The authors thank Prof. Hiroshi Watanabe for continuous support and encouragement on this work. The authors thank Prof. Yo Nakamura for kindly providing star-shaped PS used in this work. The authors thank Prof. Toshiji Kanaya for kindly allowing the authors to do the SAXS measurements in his laboratory.

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