Scaling Laws in the Diffusive Release of Neutral Cargo from Hollow Hydrogel Nanoparticles: Paclitaxel-Loaded Poly(4-vinylpyridine).

We study the nonequilibrium diffusive release of electroneutral molecular cargo encapsulated inside hollow hydrogel nanoparticles. We propose a theoretical model that includes osmotic, steric, and short-range polymer-cargo attractions to determine the effective cargo-hydrogel interaction, ueff*, and the effective diffusion coefficient of the cargo inside the polymer network, Deff*. Using dynamical density functional theory (DDFT), we investigate the scaling of the characteristic release time, τ1/2, with the key parameters involved in the process, namely, ueff*, Deff*, and the swelling ratio. This effort represents a full study of the problem, covering a broad range of cargo sizes and providing predictions for repulsive and attractive polymer shells. Our calculations show that the release time through repulsive polymer networks scales with q2eßueff*/Deff* for ßueff* ≫ 1. In this case, the cargo molecules are excluded from the shell of the hydrogel. For attractive shells, the polymer retains the cargo molecules on its internal surface and its interior, and the release time grows exponentially with the attraction strength. The DDFT calculations are compared to an analytical model for the mean first passage time, which provides an excellent quantitative description of the kinetics for both repulsive and attractive shells without fitting parameters. Finally, we apply the method to reproduce experimental results on the release of paclitaxel from hollow poly(4-vinylpyridine) nanoparticles and find that the slow release of the drug can be explained in terms of the strong binding attraction between the drug and the polymer.

Nonequilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions.

Hollow hydrogels represent excellent nano- and microcarriers due to their ability to encapsulate and release large amounts of cargo molecules (cosolutes) such as reactants, drugs, and proteins. In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and dynamic density functional theory to investigate the full nonequilibrium encapsulation kinetics of charged and dipolar cosolutes by an isolated charged hollow hydrogel immersed in a 1:1 electrolyte aqueous solution. Our analysis covers a broad spectrum of cosolute valences ( zc) and electric dipole moments (µc), as well as hydrogel swelling states and hydrogel charge densities. Our calculations show that, close to the collapsed state, the polar cosolutes are predominantly precluded and the encapsulation process is strongly hindered by the excluded-volume interaction exerted by the polymer network. Different equilibrium and kinetic sorption regimes (interface versus interior) are found depending on the value and sign of zc and the value of µc. For cosolutes of the same sign of charge as the gel, the superposition of steric and electrostatic repulsion leads to an "interaction-controlled" encapsulation process, in which the characteristic time to fill the empty core of the hydrogel grows exponentially with zc. On the other hand, for cosolutes oppositely charged to the gel, we find a "diffusion-controlled" kinetic regime, where cosolutes tend to rapidly absorb into the hydrogel membrane and the encapsulation rate depends only on the cosolute diffusion time across the membrane. Finally, we find that increasing µc promotes the appearance of metastable and stable surface adsorption states. For large enough µc, the kinetics enters an "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake. Our study represents the first attempt to systematically describe how the swelling state of the hydrogel and other leading physical interaction parameters determine the encapsulation kinetics and the final equilibrium distribution of polar molecular cargo.