Synergistic Effects of Bound Micelles and Temperature on the Flexibility of Thermoresponsive Polymer Brushes.

The persistence length is a key parameter for the quantitative interpretation of the flexibility of polymers. We have studied complexes composed of a spherical poly(N-isopropylacrylamide) (PNIPAM) brush and a sodium dodecyl sulfate micelle in an effort to characterize the flexibility of tethered PNIPAM below the lower critical solution temperature TLCST . An analytical mean-field model is used to describe the persistence length Lp in a broad range of ψ, the number of bound micelles per chain. The persistence length of micelle-constrained PNIPAM is quantitatively correlated with the thermal energy kB T, electrostatic repulsion fC , and effective excluded-volume parameter νeff . The persistence length per ψ, which depends on T and fC , is found to scale with a synergistic effect fC /(ψkB T). The results reveal that the bound-micelle charges affecting the persistence length are analogous to the fixed charges of polyelectrolytes, though the bound micelles are separated by a large number of neutral monomers. The extension ⟨L⟩ of micelle-constrained PNIPAM decreases as ⟨L⟩ ∼ fC -βF with fC , where βF ≈ 0.58-0.8 depending on ψ, but as the universal power law ⟨L⟩ ∼ (fC /kB T)-0.6 with the synergistic effect fC /(kB T), irrespective of ψ. In spite of the intricate interplay among the multiple components in the system, the extension scales as a function of νeff as ⟨L⟩ ∼ (νeff /ψLp )-βV , where βV ≈ 0.35 for the significant monomer interaction and βV ≈ 0.2 for the weak or negligible monomer interaction.