Diffusion and Interaction Effects On Molecular Release Kinetics From Collapsed Microgels.

The efficient transport of small molecules through dense hydrogel networks is crucial for various applications, including drug delivery, biosensing, catalysis, nanofiltration, water purification, and desalination. In dense polymer matrices, such as collapsed microgels, molecular transport follows the solution-diffusion principle: Molecules dissolve in the polymeric matrix and subsequently diffuse due to a concentration gradient. Employing dynamical density functional theory (DDFT), we investigate the nonequilibrium release kinetics of nonionic subnanometer-sized molecules from a microgel particle, using parameters derived from prior molecular simulations of a thermoresponsive hydrogel. The kinetics is primarily governed by the microgel radius and two intensive parameters: the diffusion coefficient and solvation free energy of the molecule. Our results reveal two limiting regimes: a diffusion-limited regime for large, slowly diffusing, and poorly soluble molecules within the hydrogel; and a reaction-limited regime for small, rapidly diffusing, and highly soluble molecules. These principles allow us to derive an analytical equation for release time, demonstrating excellent quantitative agreement with the DDFT results-a valuable and straightforward tool for predicting release kinetics from microgels.

Randomly branching θ-polymers in two and three dimensions: Average properties and distribution functions.

Motivated by renewed interest in the physics of branched polymers, we present here a detailed characterization of the connectivity and spatial properties of 2- and 3-dimensional single-chain conformations of randomly branching polymers under θ-solvent conditions obtained by Monte Carlo computer simulations. The first part of the work focuses on polymer average properties, such as the average polymer spatial size as a function of the total tree mass and the typical length of the average path length on the polymer backbone. In the second part, we move beyond average chain behavior and we discuss the complete distribution functions for tree paths and tree spatial distances, which are shown to obey the classical Redner-des Cloizeaux functional form. Our results were rationalized first by the systematic comparison to a Flory theory for branching polymers and next by generalized Fisher-Pincus relationships between scaling exponents of distribution functions. For completeness, the properties of θ-polymers were compared to their ideal (i.e., no volume interactions) as well as good-solvent (i.e., above the θ-point) counterparts. The results presented here complement the recent work performed in our group [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016); J. Chem. Phys. 145, 164906 (2016); and Phys. Rev. E 95, 012117 (2017)] in the context of the scaling properties of branching polymers.

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.

Conformation change of an isotactic poly (N-isopropylacrylamide) membrane: Molecular dynamics.

In this work, isotactic Poly (N-Isopropylacrylamide)-PNIPAM-in neat water and in electrolyte solutions is studied by means of molecular dynamics simulations. This is done for an infinitely diluted oligomer and for an assembly of several PNIPAM chains arranged into a planar membrane configuration with a core-shell morphology. We employed two different force fields, AMBER (assisted model building with energy refinement) and OPLS-AA (all atom - optimized potentials for liquid simulations) in combination with extended simple point charge water. Despite the more water insoluble character of isotactic oligomers, our results support the existence of a coil to globule transition for the isolated 30-mer. This may imply the existence of an oligomer rich phase of coil-like structures in equilibrium with a water rich phase for temperatures close but below the coil to globule transition temperature, TΘ. However, the obtained coil structure is much more compact than that corresponding to the syndiotactic chain. Our estimations of TΘ are (308±5) K and (303±5) K for AMBER and OPLS-AA, respectively. The membrane configuration allows one to include chain-chain interactions, to follow density profiles of water, polymer, and solutes, and accessing the membrane-water interface tension. Results show gradual shrinking and swelling of the membrane by switching temperature above and below TΘ, as well as the increase and decrease of the membrane-water interface tension. Finally, concentration profiles for 1M NaCl and 1M NaI electrolytes are shown, depicting a strong salting-out effect for NaCl and a much lighter effect for NaI, in good qualitative agreement with experiments.

Sorption and Spatial Distribution of Protein Globules in Charged Hydrogel Particles.

We have theoretically studied the uptake of a nonuniformly charged biomolecule suitable for representing a globular protein or a drug by a charged hydrogel carrier in the presence of a 1:1 electrolyte. On the basis of the analysis of a physical interaction Hamiltonian including monopolar, dipolar, and Born (self-energy) contributions derived from linear electrostatic theory of the unperturbed homogeneous hydrogel, we have identified five different sorption states of the system, from complete repulsion of the molecule to its full sorption deep inside the hydrogel, passing through metastable and stable surface adsorption states. The results are summarized in state diagrams that also explore the effects of varying the electrolyte concentration, the sign of the net electric charge of the biomolecule, and the role of including excluded-volume (steric) or hydrophobic biomolecule-hydrogel interactions. We show that the dipole moment of the biomolecule is a key parameter controlling the spatial distribution of the globules. In particular, biomolecules with a large dipole moment tend to be adsorbed at the external surface of the hydrogel, even if like-charged, whereas uniformly charged biomolecules tend to partition toward the internal core of an oppositely charged hydrogel. Hydrophobic attraction shifts the states toward the internal sorption of the biomolecule, whereas steric repulsion promotes surface adsorption for oppositely charged biomolecules or for the total exclusion of likely charged ones. Our results establish a guideline for the spatial partitioning of proteins and drugs in hydrogel carriers, tunable by the hydrogel charge, pH, and salt concentration.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge.

In this work the equilibrium distribution of ions around a thermo-responsive charged nanogel particle in an electrolyte aqueous suspension is explored using coarse-grained Monte Carlo computer simulations and the Ornstein-Zernike integral equation theory. We explicitly consider the ionic size in both methods and study the interplay between electrostatic and excluded-volume effects for swollen and shrunken nanogels, monovalent and trivalent counterions, and for two different nanogel charges. We find good quantitative agreement between the ionic density profiles obtained using both methods when the excluded repulsive force exerted by the cross-linked polymer network is taken into account. For the shrunken conformation, the electrostatic repulsion between the charged groups provokes a heterogeneous polymer density profile, leading to a nanogel structure with an internal low density hole surrounded by a dense corona. The results show that the excluded-volume repulsion strongly hinders the ion permeation for shrunken nanogels, where volume exclusion is able to significantly reduce the concentration of counterions in the more dense regions of the nanogel. In general, we demonstrate that the thermosensitive behaviour of nanogels, as well as their internal structure, is strongly influenced by the valence of the counterions and also by the charge of the particles. On the one hand, an increase of the counterion valence moves the swelling transition to lower temperatures, and induces a major structuring of the charged monomers into internal and external layers around the crown for shrunken nanogels. On the other hand, increasing the particle charge shifts the swelling curve to larger values of the effective radius of the nanogel.

Size-exclusion partitioning of neutral solutes in crosslinked polymer networks: a Monte Carlo simulation study.

In this work, the size-exclusion partitioning of neutral solutes in crosslinked polymer networks has been studied through Monte Carlo simulations. Two models that provide user-friendly expressions to predict the partition coefficient have been tested over a wide range of volume fractions: Ogston's model (especially devised for fibrous media) and the pore model. The effects of crosslinking and bond stiffness have also been analyzed. Our results suggest that the fiber model can acceptably account for size-exclusion effects in crosslinked gels. Its predictions are good for large solutes if the fiber diameter is assumed to be the effective monomer diameter. For solutes sizes comparable to the monomer dimensions, a smaller fiber diameter must be used. Regarding the pore model, the partition coefficient is poorly predicted when the pore diameter is estimated as the distance between adjacent crosslinker molecules. On the other hand, our results prove that the pore sizes obtained from the pore model by fitting partitioning data of swollen gels are overestimated.