Diffusion-influenced reactions in a hollow nano-reactor with a circular hole

Abstract

Hollow nanostructures are paid increasing attention in many nanotechnology-related communities in view of their numerous applications in chemistry and biotechnology, e.g. as smart nanoreactors or drug-delivery systems. In this paper we consider irreversible, diffusion-influenced reactions occurring within a hollow spherical cavity endowed with a circular hole on its surface. Importantly, our model is not limited to small sizes of the aperture. In our scheme, reactants can freely diffuse inside and outside the cavity through the hole, and react at a spherical boundary of given size encapsulated in the chamber and endowed with a given intrinsic rate constant. We work out the solution of the above problem, enabling one to compute the reaction rate constant to any desired accuracy. Remarkably, we show that, in the case of narrow holes, the rate constant is extremely well-approximated by a simple formula that can be derived on the basis of simple physical arguments and that can be readily employed to analyze experimental data.

Loading and Release of Charged and Neutral Fluorescent Dyes into and from Mesoporous Materials: A Key Role for Sensing Applications

“…In fact, the concentration of the cationic dye close to the Apart from electrostatic interactions, van der Waals forces can also play an important role in the loading and delivery processes. In fact, it has been demonstrated recently that such local interactions of van der Waals type between the porous host and guest molecules can modulate the macroscopic transport from the pores to the solution [71,72]. These authors concluded that stronger guest-matrix attractions (through van der Waals interactions) produced slower release kinetics and retained a higher amount of guest in the pores.…”

Biocatalytic virus capsid as nanovehicle for enzymatic activation of Tamoxifen in tumor cells

“…Another model has been developed that consider the diffusion coefficients of the reacting molecules and critical distance for the reaction with the Stokes–Einstein equation (relating the diffusion coefficient of a species to its radius and the solvent viscosity). A Smoluchowski reaction expression is obtained that includes a steric factor, which characterizes the diffusion rate into the porous cavity by absorption . However, the Smoluchowski reaction rate constant does not consider the nanoreactor geometry and the crowding effects.…”

Note: Diffusion-limited annihilation in cavities

“…Specifically, the radius R of the spherical cavity should exceed 45b in cases (1) and (3) and 187b in case (2), respectively, and the cubic cavity edge L should exceed 72b in cases (1) and (3) and 300b in case (2). In smaller cavities, the survival probabilities still decay as single exponentials but with the rate constants that are higher than the simple estimate k Sm /V cav in cases (1) and ( 2) and one half of this ratio in case (3). As the cavity size further decreases, the decay kinetics becomes multi-exponential.…”

“…Similar arguments suggest that the asymptotic estimates in Eqs. ( 4) and (5) work not only when one particle is fixed at the center of a large spherical cavity (R → ∞) but also in case (1), where both particles diffuse with diffusivity D. The situation changes when one of the particles is fixed on the wall of a large cavity [case (3)]. The reason is that here only one half of the surface of the immobile particle is available for the contact.…”