Theory of Solvation-Controlled Reactions in Stimuli-Responsive Nanoreactors

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.