Theory of Solvation-Controlled Reactions in Stimuli-Responsive Nanoreactors

TL;DR

This paper develops an analytical model showing how solvation free enthalpy changes, rather than diffusion coefficients, primarily control reaction rates in stimuli-responsive nanoreactors, validated by experimental data.

Contribution

It introduces a new analytical expression linking reaction rates to solvation free enthalpy in stimuli-responsive nanoreactors, emphasizing solvation effects over diffusion.

Findings

Reaction rate exponentially depends on solvation free enthalpy change.

Changes in solvation free enthalpy dominate over diffusion coefficient effects.

Model aligns with experimental data on thermosensitive nanoreactors.

Abstract

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.