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 T_LCST. An analytical mean-field model is used to describe the persistence length L_p 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 k_BT, electrostatic repulsion f_C, and effective excluded-volume parameter ν_eff. The persistence length per ψ, which depends on T and f_C, is found to scale with a synergistic effect f_C/(ψk_BT). 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⟩ ∼ f_C^-β with f_C, where β_F ≈ 0.58-0.8 depending on ψ, but as the universal power law ⟨L⟩ ∼ (f_C/k_BT)^-0.6 with the synergistic effect f_C/(k_BT), irrespective of ψ. In spite of the intricate interplay among the multiple components in the system, the extension scales as a function of ν_eff as ⟨L⟩ ∼ (ν_eff/ψL_p)^-β, where β_V ≈ 0.35 for the significant monomer interaction and β_V ≈ 0.2 for the weak or negligible monomer interaction.