Abstract
A combined experimental and theoretical method to simultaneously determine diffusivity and free-energy profiles of particles that penetrate into inhomogeneous hydrogel systems is presented. As the only input, arbitrarily normalized concentration profiles from fluorescence intensity data of labeled tracer particles for different penetration times are needed. The method is applied to dextran molecules of varying size that penetrate into hydrogels of polyethylene-glycol chains with different lengths that are covalently cross-linked by hyperbranched polyglycerol hubs. Extracted dextran bulk diffusivities agree well with fluorescence correlation spectroscopy data obtained separately. Empirical scaling laws for dextran diffusivities and free energies inside the hydrogel are identified as a function of the dextran mass. An elastic free-volume model that includes dextran as well as polyethylene-glycol linker flexibility quantitively describes the repulsive dextran-hydrogel interaction free energy, which is of steric origin, and furthermore suggests that the hydrogel mesh-size distribution is rather broad and particle penetration is dominated by large hydrogel pores. Particle penetration into hydrogels for steric particle-hydrogel interactions is thus suggested to be governed by an elastic size-filtering mechanism that involves the tail of the hydrogel pore-size distribution.
Highlights
The penetration of particles into hydrogels is relevant for technological applications [1,2], drug delivery [3], and biological systems such as biofilms [4], the extracellular matrix [5], and mucus [6]
We study synthetic hydrogels that consist of polyethylene-glycol (PEG) linkers of different molecular masses that are permanently cross-linked by hyperbranched polyglycerol hubs [2]
We investigate the filtering function of hydrogels by theoretical analysis of time-resolved concentration profiles of the labeled dextran molecules as they penetrate into the hydrogel
Summary
The penetration of particles into hydrogels is relevant for technological applications [1,2], drug delivery [3], and biological systems such as biofilms [4], the extracellular matrix [5], and mucus [6]. Mucus is a penetration barrier against pathogens, e.g., virions or bacteria, whereas it allows the permeation of many nonpathogens, e.g., nutrients, that are absorbed through the mucosa of the small intestine [9]. Studies have suggested that based on the type of mucus, the combination of different mechanisms gives rise to the protective barrier function [10,11], in addition to the advective transport of pathogens through mucus shedding or clearance [12,13], which is not considered here. One typically distinguishes steric size-filtering mechanisms from interaction-filtering mechanisms [6,14]; the latter
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