  The application of a polymer brush in sensing, actuation, self-folding, among
others acutely depends on the tuneable bending of a brush-grafted substrate
caused by the stress in the brush. However, the stress in a stimuli-responsive
brush has not been investigated. In this work, we study the stress in the
stimuli-responsive planar polymer brushes of neutral water-soluble polymers
with low to very high graft densities using strong stretching theory (SST).
First, SST with the Langevin force-extension relation for a polymer chain is
extended to the study of stimuli-responsive brushes. Stress profile and other
properties of a Poly(N-isopropylacrylamide) (PNIPAm) brush are then obtained
using the extended SST and an empirical Flory-Huggins parameter. The model
predicts that the stress in a PNIPAm brush is inhomogeneous and compressive at
all temperatures and graft densities. The resultant stress is predicted to
increase in magnitude with increasing graft density. Moreover, it decreases in
magnitude with an increase in temperature before plateauing in low graft
density brushes. In contrast, its magnitude increases weakly with increasing
temperature in high density brushes. This contrasting behavior is traced to the
minimum in interaction free energy density \emph{vs} polymer volume fraction
curve for PNIPAm solution at a large volume fraction, and stiffening of chains
due to finite extensibility. Furthermore, our results indicate that the ability
to tune the resultant stress by changing temperature diminishes with increasing
graft density.
