title: Reaction rate of a composite core-shell nanoreactor with multiple nanocatalysts.
abstract: We present a detailed theory for the total reaction rate constant of a composite core-shell nanoreactor, consisting of a central solid core surrounded by a hydrogel layer of variable thickness, where a given number of small catalytic nanoparticles are embedded at prescribed positions and are endowed with a prescribed surface reaction rate constant. Besides the precise geometry of the assembly, our theory accounts explicitly for the diffusion coefficients of the reactants in the hydrogel and in the bulk as well as for their transfer free energy jump upon entering the hydrogel shell. Moreover, we work out an approximate analytical formula for the overall rate constant, which is valid in the physically relevant range of geometrical and chemical parameters. We discuss in depth how the diffusion-controlled part of the rate depends on the essential variables, including the size of the central core. In particular, we derive some simple rules for estimating the number of nanocatalysts per nanoreactor for an efficient catalytic performance in the case of small to intermediate core sizes. Our theoretical treatment promises to provide a very useful and flexible tool for the design of superior performing nanoreactor geometries with optimized nanoparticle load.
authors.affiliation: Université d'Orléans, Château de la Source, 45100, Orléans, France. Francesco.Piazza@gmail.com and Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071, Orléans, France and Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia and CSDC, via G. Sansone 1, IT-50019 Sesto Fiorentino, Firenze, Italy.
authors.forename: Marta
authors.initials: M
authors.lastname: Galanti
authors.affiliation: Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia and CSDC, via G. Sansone 1, IT-50019 Sesto Fiorentino, Firenze, Italy.
authors.forename: Duccio
authors.initials: D
authors.lastname: Fanelli
authors.affiliation: International Research Centre for Soft Matter, Beijing University of Chemical Technology, Beijing 100029, China.
authors.forename: Stefano
authors.initials: S
authors.lastname: Angioletti-Uberti
authors.affiliation: Institut für Physik, Humboldt Universität zu Berlin, 12489 Berlin, Germany and Institut für Weiche Materie und Funkionale Materialien, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany. joachim.dzubiella@helmholtz-berlin.de.
authors.forename: Matthias
authors.initials: M
authors.lastname: Ballauff
authors.affiliation: Institut für Physik, Humboldt Universität zu Berlin, 12489 Berlin, Germany and Institut für Weiche Materie und Funkionale Materialien, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany. joachim.dzubiella@helmholtz-berlin.de.
authors.forename: Joachim
authors.initials: J
authors.lastname: Dzubiella
authors.affiliation: Université d'Orléans, Château de la Source, 45100, Orléans, France. Francesco.Piazza@gmail.com and Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071, Orléans, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Piazza