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 psi, the number of bound micelles per chain. The persistence length of micelle-constrained PNIPAM is quantitatively correlated with the thermal energy k(B)T, electrostatic repulsion f(C), and effective-excluded-volume parameter nu(eff). The persistence length per psi, which depends on T and f(C), is found to scale with a synergistic effect f(C)/(psi k(B)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 > similar to f(C)(-beta F) with f(C), where beta(F) approximate to 0.58-0.8 depending on psi, but as the universal power law < L > similar to (f(C)/k(B)T)(-0.6) with the synergistic effect f(C)/(k(B)T), irrespective of psi. In spite of the intricate interplay among the multiple components in the system, the extension scales as a function of nu(eff) as < L > similar to (nu(eff)/psi L-P)(-beta v), where beta(v) approximate to 0.35 for the significant monomer interaction and beta(v) approximate to 02 for the weak or negligible monomer interaction.