Osmotic pressure of permeable ionic microgels: Poisson-Boltzmann theory and exact statistical mechanical relations in the cell model

Osmotic swelling behavior of surface-charged ionic microgels

In recent years, ionic microgels have garnered much attention due to their unique properties, especially their stimulus-sensitive swelling behavior. The tunable response of these soft, permeable, compressible, charged colloidal particles is increasingly attractive for applications in medicine and biotechnologies, such as controlled drug delivery, tissue engineering, and biosensing. The ability to model and predict variation of the osmotic pressure of a single microgel with respect to changes in particle properties and environmental conditions proves vital to such applications. In this work, we apply both nonlinear Poisson-Boltzmann theory and molecular dynamics simulation to ionic microgels (macroions) in the cell model to compute density profiles of microions (counterions, coions), single-microgel osmotic pressure, and equilibrium swelling ratios of spherical microgels whose fixed charge is confined to the macroion surface. The basis of our approach is an exact theorem that relates the electrostatic component of the osmotic pressure to the microion density profiles. Close agreement between theory and simulation serves as a consistency check to validate our approach. We predict that surface-charged microgels progressively deswell with increasing microgel concentration, starting well below close packing, and with increasing salt concentration, in qualitative agreement with experiments. Comparison with previous results for microgels with fixed charge uniformly distributed over their volume demonstrates that surface-charged microgels deswell more rapidly than volume-charged microgels. We conclude that swelling behavior of ionic microgels in solution is sensitive to the distribution of fixed charge within the polymer-network gel and strongly depends on bulk concentrations of both microgels and salt ions.

Ionisation and swelling behaviour of weak polyampholyte core-shell networks - a Monte Carlo study

The network charge of polyampholyte microgels can be tuned by varying the pH of the surrounding solution, and a charge reversal from a positively charged microgel at low pH to a negatively charged microgel at high pH can be achieved. In a titration experiment, it is difficult to tell apart the ionisation of the acidic and basic monomers in the network and to determine the distribution of charges in the network, whereas using Metropolis Monte Carlo simulations, both the degree of ionisation and the distribution of ionised monomers can be determined separately for both species. Building on our earlier work on alternating polyampholyte microgels, we now investigated the pH-dependent ionisation and the swelling behaviour of polyampholyte core-shell microgels under good solvent conditions. For this purpose, we performed Metropolis Monte Carlo simulations for a bead-spring model using the constant-pH method. As in our previous study on alternating microgels, the width of the U-shaped curve of the microgels volume as a function of pH depends on the relative dissociation constants of acid and base, and the microgel volume can be approximated by a linear function of the total network charge. Due to the spatial separation of acid and base in core-shell systems, the ionisation is less enhanced compared to a microgel with an alternating distribution of the two species. Nevertheless, we still see an influence of the presence of one species on the ionisation behaviour of the other species under good solvent conditions. Furthermore, the isoelectric point is shifted towards higher pH, which is caused by a higher charge density in the core compared to that in the shell. Added salt changes the Donnan equilibrium, which determines the counterion distribution within and outside of the microgel. At the same time, it contributes to the electrostatic screening of the network charges, leading to a narrowing of the U-shaped volume transition curve.

Osmotic pressure and swelling behavior of ionic microcapsules

Ionic microcapsules are hollow shells of hydrogel, typically 10-1000 nm in radius, composed of cross-linked polymer networks that become charged and swollen in a good solvent. The ability of microcapsules to swell/deswell in response to changes in external stimuli (e.g., temperature, pH, and ionic strength) suits them to applications, such as drug delivery, biosensing, and catalysis. The equilibrium swelling behavior of ionic microcapsules is determined by a balance of electrostatic and elastic forces. The electrostatic component of the osmotic pressure of a microcapsule-the difference in the pressure between the inside and outside of the particle-plays a vital role in determining the swelling behavior. Within the spherical cell model, we derive exact expressions for the radial pressure profile and for the electrostatic and gel components of the osmotic pressure of a microcapsule, which we compute via Poisson-Boltzmann theory and molecular dynamics simulation. For the gel component, we use the Flory-Rehner theory of polymer networks. By combining the electrostatic and gel components of the osmotic pressure, we compute the equilibrium size of ionic microcapsules as a function of particle concentration, shell thickness, and valence. We predict concentration-driven deswelling at relatively low concentrations at which steric interactions between particles are weak and demonstrate that this response can be attributed to crowding-induced redistribution of counterions. Our approach may help to guide the design and applications of smart stimuli-responsive colloidal particles.

Metal ions modulation of the self-assembly of short peptide conjugated nonsteroidal anti-inflammatory drugs (NSAIDs)

Metal ions are essential components that help maintain the processes of normal life, and they can be used to fabricate self-assembled building blocks for peptide derivatives, proteins and nucleic acids. Here, we have developed a novel strategy to construct supramolecular hydrogels modulated using metal cations. Upon introducing a variety of metal ions into aqueous solutions of a gelator (naproxen-FF), including a nonsteroidal anti-inflammatory drug (NSAID) and dipeptide, we obtain stable hydrogels under neutral or alkaline conditions. It is found that these hydrogels with three-dimensional nanofiber networks exhibit excellent mechanical properties and thixotropy, as well as superb responsivity to multiple metal ions. Due to the significance of potassium ions in biological processes, the K-triggered hydrogel has been chosen as a model, and its self-assembly mechanism has been explored via various spectral analysis processes. In addition, the self-assembly performances of peptides are significantly affected by the chemical structures of the gelator molecules. This work provides deep insight into the aggregation mechanism of dipeptide-conjugating drug molecules through introducing a variety of metal ions, laying the foundation for further biological applications.

Ionic equilibria and swelling of soft permeable particles in electrolyte solutions

We discuss osmotic equilibria between soft permeable particles, of radius R and volume charge density ρ, and bulk electrolyte solutions of inverse Debye length κ. Existing models are based on a simplified assumption of weakly charged particles. Here we derive analytical approximations for the distribution of potentials, ions and pressure in a system, suitable even when ρ is quite large. Our theory is valid not only for "large" particles (κR≫ 1), where the central part is fully screened, but also for weakly screened "small" particles (κR≤ 1) with overlapping inner diffuse layers. Besides, we present novel coarse-grained simulations to validate the analysis and illustrate the variation of potential/ion profiles in response to changes in κR and ρ. Our simulations also allow us to argue that swelling of both "large" and "small" particles is uniform, although their inner non-uniform local pressure profiles are essentially and qualitatively different. These results are directly relevant for a variety of permeable charged objects, from polymer micro- and nanogels to more rigid porous colloids.