  Metallic nanoparticles embedded in stimuli-responsive polymers can be
regarded as nanoreactors since their catalytic activity can be changed within
wide limits: the physicochemical properties of the polymer network can be tuned
and switched by external parameters, e.g. temperature or pH, and thus allows a
selective control of reactant mobility and concentration close to the reaction
site. Based on a combination of Debye's model of diffusion through an energy
landscape and a two-state model for the polymer, here we develop an analytical
expression for the observed reaction rate constant $k_{\rm obs}$. Our formula
shows an exponential dependence of this rate on the solvation free enthalpy
change $\Delta \bar{G}_{\rm sol}$, a quantity which describes the partitioning
of the reactant in the network versus bulk. Thus, changes in $\Delta
\bar{G}_{\rm sol}$, and not in the diffusion coefficient, will be the decisive
factor affecting the reaction rate in most cases. A comparison with recent
experimental data on switchable, thermosensitive nanoreactors demonstrates the
general validity of the concept.
