Nanoparticle filtering in charged hydrogels: Effects of particle size, charge asymmetry and salt concentration

The understanding of particle transport mechanisms in biological and synthetic hydrogels is crucial for the development of advanced drug delivery methods. We propose a simple model for the diffusion of charged nanoparticles in cross-linked, charged hydrogels based on a cubic periodic environment and an electrostatic interaction potential of varying range and strength, encompassing attractive and repulsive scenarios. The long-time diffusive properties are investigated by use of Brownian dynamics simulations and analytical methods. A number of experimentally observed phenomena attributed to nonsteric interactions between hydrogel polymers and diffusing particle are naturally reproduced by our model. Charged particles diffuse slower than uncharged particles, regardless of the sign of the surface charge, but with a stronger hindrance effect for attractive electrostatic interactions. This is explained in terms of charged particles sticking to the polymer network in regions of strong opposite charge and their exclusion from similarly charged regions. In the case of attractive interactions between hydrogel polymers and the diffusing particle, smaller charged particles diffuse slower than larger ones. This stands in contrast to a size filtering scenario but is in agreement with experimental findings. In the case of repulsive interactions, a range of differently sized particles diffuse equally fast. We compare our model predictions with published experiments on charged particle diffusion in hydrogels and confirm that electrostatic interactions are a key factor influencing the diffusivity of charged nanoparticles and that oppositely charged gels are much more effective in slowing down a charged particle than similarly charged gels.

Dynamics of ion migration in nanopores and the effect of DNA-ion interaction

We have carried out Brownian dynamics calculations to investigate the effect of DNA-ion interaction on ion transport in a nanopore. We calculated the self-diffusion coefficient of monovalent ions in the presence of DNA in a nanopore and compared the result with that through an open pore, that is, without the presence of DNA. We find that the self-diffusion coefficient of the co-ions is essentially unaffected by the DNA. The self-diffusion coefficient of the counterions, on the other hand, is significantly reduced depending on the ion concentration. At high ion concentration, around 1 M, the effect of DNA on counterion diffusion is relatively small, causing a slight reduction in counterion diffusion coefficient. At low concentrations of a few millimolar, the effect is much larger, resulting in a reduction in counterion diffusion coefficient by a factor of about 2.5. The variation in the self-diffusion of the counterion is well described by accounting for the contributions from two components: the adsorbed counterions and the free counterions. Detailed dynamics of the DNA-counterion interaction is characterized by the varying length of the transient adsorption time of the counterions to the DNA charge sites and the exchange rate with the environment. This variation in counterion adsorption time is attributed to the ionic electric screening effect, which is in turn determined by the ion concentration.

Self-diffusion of non-interacting hard spheres in particle gels

Different kinds of particle gels were simulated using a process of random aggregation of hard spheres. The mean square displacement of Brownian spherical tracer particles through these rigid gels was monitored and the average diffusion coefficient, normalized with the free diffusion coefficient (D), was obtained. For each gel structure the effect of the gel volume fraction (φ) and size ratio of the tracer (d) on the relative diffusion coefficient was investigated systematically. The volume fraction that is accessible to the tracers (φ(a)) was determined in each case. D was found to be approximately the same if φ(a) was the same, independent of φ, d and the gel structure. However a different behaviour is found if the tracers can penetrate the strands of the gel. A state diagram of d versus φ is given that shows the critical values (d(c), φ(c)) at which all tracers become trapped. Different values are found for different gel structures. The dependence of D on φ/φ(c) is independent of d, while the dependence of D on d/d(c) is independent of φ.