Understanding particle transport in hydrogels is an important step for the development of advanced drug delivery techniques. A large body of experimental research has shown that besides excluded volume effects and hydrodynamics, other nonsteric particle-gel interactions can also determine particle mobility in hydrogels. In this thesis, we aim to systematically investigate the effect of long-ranged repulsive or attractive particle-gel interactions on the particle mobility and to determine general particle diffusion mechanisms in hydrogels. For this, we present general models to simulate diffusion of particles in gels with different particle-gel interactions.
First, we introduce a model for the diffusion of particles smaller than the mesh size in hydrogels with electrostatic particle-gel interactions. The gel is comprised of a spatially ordered, cubic symmetric fiber lattice. The diffusive behavior is highly charge asymmetric: Particles are slowed down more strongly by attractive than by repulsive electrostatic interactions. Furthermore, the particle mobility is highly sensitive to the ionic strength, particularly for electrostatic attraction, in agreement with experimental data.
Second, we examine the effect of spatial disorder of the polymer lattice on the particle diffusive behavior. The effect of spatial disorder is linked to the presence of long-ranged particle-gel interactions. For repulsive interactions, an intermediate degree of disorder minimizes the particle mobility inside the gel but for high degrees of disorder, the diffusivity increases again. For attractive interactions, disorder slows down diffusion since particles are immobilized in regions with locally increased fiber density. A comparison between simulations with spatially disordered gels and published experimental data reveals qualitative agreement.
Third, we extend our model to simulate the diffusion of particles in heterogeneous gels with mixed electrostatically attractive and repulsive interaction sites, as relevant for biological hydrogels. Mixed interaction sites are modeled with a random distribution of attractive and repulsive fiber sections. Interaction disorder, in the form of randomly mixed interaction sites, and spatial disorder have a qualitatively similar effect on the particle diffusivity. Charged particles of either sign are immobilized, since attractive particle-gel interactions determine the diffusive behavior. Qualitative agreement between simulation and experiments carried out by our collaborators from the group of Prof. Dr. DeRouchey is found.
Finally, we examine the effect of hydrodynamic interactions in conjunction with long-ranged particle-gel interactions. %Agreement between simulation and experiment is improved when hydrodynamic interactions are included. Repulsive interactions decrease the effect of hydrodynamic interactions on the particle diffusivity, whereas attractive interactions increase the effect of hydrodynamic interactions, due to spatial particle-fiber correlations.
With our simulations we elucidate the effects of various model features such as spatial disorder, interaction disorder and hydrodynamic interactions on the particle mobility and the detailed microscopic mechanisms governing particle diffusion in hydrogels.