Communication: Intraparticle segregation of structurally homogeneous polyelectrolyte microgels caused by long-range Coulomb repulsion

Structure of swollen hollow polyelectrolyte nanogels with inhomogeneous cross-link distribution

HYPOTHESIS

Recently, it has become possible to synthesize hollow polyelectrolyte nano- and microgels. The shell permeability can be controlled by external stimuli, while the cavity can serve as a storage place for guest molecules. However, there is a lack of a detailed understanding at the molecular level regarding the role of the network topology, inhomogeneities of the distribution of cross-links, and the impact of the electrostatics on the structural response of hollow microgel to external stimuli. To bridge these gaps, molecular dynamics (MD) of computer simulations are used.

EXPERIMENTS

Here, we propose a fresh methodology to create realistic hollow microgel particles in silico. The technique involves a gradual change in the average local length of subchains depending on the distance to the center of mass of the microgel particles resulting in the microgels with a non-uniform distribution of cross-linking species. In particular, a series of microgels with (i) a highly cross-linked inner part of the shell and gradually decreased cross-linker concentration towards the periphery, (ii) microgels with loosely cross-linked inner and outer parts, as well as (iii) microgels with a more-or-less homogeneous structure, have been created and validated. Counterions and salt ions are taken into account explicitly, and electrostatic interactions are described by the Coulomb potential.

FINDINGS

Our studies reveal a strong dependence of the microgel swelling response on the network topology. Simple redistribution of cross-links plays a significant role in the structure of the microgels, including cavity size, microgel size, fuzziness, and extension of the inner and outer parts of the microgels. Our results indicate the possibilities of qualitative justification of the structure of the hollow microgels in the experiments by measuring the relative change in the size of the sacrificial core to the size of the cavity and by estimation of a power law function, [Formula: see text] , of the hydrodynamic radius of the hollow microgels as a function of added salt concentration.

Swelling, collapse and ordering of rod-like microgels in solution: Computer simulation studies

Polymer microgels have proven to be highly promising macromolecular objects for a wide variety of applications. In particular, the soft particles of an anisotropic (rod-like) shape are of special interest because of their potential use in tissue engineering or materials design. However, a little is known about the physical behavior of such microgels in solution, which inspired us to study them using mesoscopic computer simulations. For single networks, depending on the solvent quality, the dimensional characteristics were obtained for microgels of different molecular weight, crosslinking density and aspect ratio. In particular, the conditions for the rod-to-rod (preserving the nonspherical shape) and rod-to-sphere collapse were found. In addition, the effect of the liquid-crystalline (LC) ordering was demonstrated for the ensemble of rod-like microgels at different swelling ratios, and the influence of microgel aspect ratio on the volume fraction of the LC transition was shown.

Swelling and Collapse of Cylindrical Polyelectrolyte Microgels

In this study, we propose computer simulations of charged cylindrical microgels. The effects of cross-linking density, aspect ratio, and fraction of charged groups on the microgel swelling and collapse with a variation in the solvent quality were studied. The results were compared with those obtained for equivalent neutral cylindrical microgels. The study demonstrated that microgels' degree of swelling strongly depends on the fraction of charged groups. Polyelectrolyte microgels under adequate solvent conditions are characterized by a larger length and thickness than their neutral analogues: the higher the fraction of charged groups, the longer their length and greater their thickness. Microgels' collapse upon solvent quality decline is characterized by a decrease in length and non-monotonous behavior of its thickness. First, the thickness decreases due to the attraction of monomer units (beads) upon collapse. The further thickness increase is related to the surface tension, which tends to reduce the anisotropy of collapsed objects (the minimum surface energy is known to be achieved for the spherical objects). This reduction is opposed by the network elasticity. The microgels with a low cross-linking density and/or a low enough aspect ratio reveal a cylinder-to-sphere collapse. Otherwise, the cylindrical shape is preserved in the course of the collapse. Aspect ratio as a function of the solvent quality (interaction parameter) demonstrates the maximum, which is solely due to the electrostatics. Finally, we plotted radial concentration profiles for network segments, their charged groups, and counterions.

Scavenging One of the Liquids versus Emulsion Stabilization by Microgels in a Mixture of Two Immiscible Liquids

It is known that microgels can serve as soft, permeable and stimuli-responsive alternative of solid colloidal particles to stabilize oil-water emulsions. The driving force for the adsorption of the microgels on interface of two immiscible liquids is a shielding of unfavorable oil-water contacts by adsorbed subchains, that is, the decrease of the surface tension between the liquids. Such phenomenon usually proceeds if volume fractions of the two liquids are comparable with each other and the microgel concentration is not high enough. The natural question arises: what is going on with the system in the opposite case of strongly asymmetric mixture (one of the liquids (oil) has a very small fraction) or high microgel concentration (the overall volume of the microgels exceeds the volume of the minor oil component)? Here we demonstrate that the microgels uptake the oil whose concentration within the microgels can be orders of magnitude higher than outside, leading to the additional microgel swelling (in comparison with the swelling in water). Thus, the microgels can serve as scavengers and concentrators of liquids dissolved in water. At first glance, this effect seems counterintuitive. However, it has a clear physical reason related to the incompatibility of oil and water. Absorption of the oil by microgels reduces unfavorable oil-water contacts by microgel segments: the microgels have a higher concentration of the segments at the periphery, forming a shell. The microgels with uptaken oil are stable toward aggregation at very small oil concentration in the mixture. However, an increase in the oil concentration can lead to aggregation of the microgels into dimers, trimers, and so on. The increasing concentration of oil mediates the attraction between the microgels: the oil in the aggregates appears to be localized in-between the microgels instead of their interior, which is accompanied by the release of the elastic stress of the microgels. A further increase in the oil concentration results in a growth of the size of the oil droplets between the microgels and the number of the microgels at the droplet's periphery, that is, the emulsion is formed.

Interpolyelectrolyte Complex Dissociation vs Polyelectrolyte Desorption from Oppositely Charged Surface upon Salt Addition

The structure of complexes formed by oppositely charged polyelectrolytes and adsorbed layers on charged surfaces is sensitive to low-molecular-weight salt. Furthermore, if the concentration exceeds some threshold value, the complexes and adsorbed chains can be "dissolved". This is due to the screening of the electrostatic interactions between charged units. In the current paper, we perform a comparative analysis of "dissolution" (dissociation) of complexes and layers upon addition of salt. For this, the conventional Brownian dynamics of computer simulations is used. We demonstrate that the complex based on linear chains dissociates at lower salt concentration than that required for desorption of equivalent chains from an oppositely charged surface. The physical reason is the difference in the symmetry of the electric field, which binds the chains into the complex (layer). In the salt-free regime, the intensity of the electric field (and attractive force) between two linear chains decays with the distance R between them, like for two spherical objects, ∼R^-2, if R is bigger than the characteristic size of the chain. On the contrary, the attractive force of the chain to the infinite surface does not depend on the distance to the surface (the electric field is constant). Therefore, if attractive forces in the condensed states of the two systems are equal, one needs to add more salt to screen the constant force than the decaying one. The computer simulation results on the adsorption of the chains were compared with the experimental data obtained for adsorption of cationic poly(4-vinylpyridine) on the surface of anionic liposomes. Good quantitative agreement was achieved.

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.

A study of the complex interaction between poly allylamine hydrochloride and negatively charged poly(N-isopropylacrylamide-co-methacrylic acid) microgels

Negatively charged poly(N-isopropylacrylamide-co-methacrylic acid) (P(NIPAm-co-MAA)) microgels undergo size changes in response to changes in temperature and pH. Complexation of these microgels with positively charged polyelectrolytes can greatly affect their physical properties and their capacity for encapsulating active molecules. Here we study the interaction between (P(NIPAm-co-MAA)) microgels and a model positively charged polyelectrolyte, poly allylamine hydrochloride (PAH), with different molecular weights. Experiments were conducted at temperatures below and above the lower critical solution temperature (LCST) of the microgel (30-32 °C), at 20 and 40 °C, respectively, and for PAH at molecular weights of 15, 50, and 140 kDa. Below the LCST, dynamic light scattering and zeta potential measurements with molecular simulation show that for the 15 kDa PAH there is preferential accumulation of PAH inside the microgel, whereas for the higher molecular weight PAH, the polyelectrolyte deposits mainly on the microgel surface. Above the LCST, PAH is preferentially located on the surface of the microgels for all molecular weights studied as a result of charge segregation in the hydrogels. Confocal scanning laser microscopy and flow cytometry were used to quantify rhodamine labelled PAH associated with the microgel. Isothermal titration calorimetry studies give insight into the thermodynamics of the interaction of PAH with the hydrogels, and how this interaction is affected by the molecular weight of PAH. Finally, microgels with encapsulated doxorubicin were exposed to PAH, revealing that the drug is displaced from the microgel by the PAH chains.

Nanogels and Microgels: From Model Colloids to Applications, Recent Developments, and Future Trends

Nanogels and microgels are soft, deformable, and penetrable objects with an internal gel-like structure that is swollen by the dispersing solvent. Their softness and the potential to respond to external stimuli like temperature, pressure, pH, ionic strength, and different analytes make them interesting as soft model systems in fundamental research as well as for a broad range of applications, in particular in the field of biological applications. Recent tremendous developments in their synthesis open access to systems with complex architectures and compositions allowing for tailoring microgels with specific properties. At the same time state-of-the-art theoretical and simulation approaches offer deeper understanding of the behavior and structure of nano- and microgels under external influences and confinement at interfaces or at high volume fractions. Developments in the experimental analysis of nano- and microgels have become particularly important for structural investigations covering a broad range of length scales relevant to the internal structure, the overall size and shape, and interparticle interactions in concentrated samples. Here we provide an overview of the state-of-the-art, recent developments as well as emerging trends in the field of nano- and microgels. The following aspects build the focus of our discussion: tailoring (multi)functionality through synthesis; the role in biological and biomedical applications; the structure and properties as a model system, e.g., for densely packed arrangements in bulk and at interfaces; as well as the theory and computer simulation.

Star polymers as unit cells for coarse-graining cross-linked networks

Reducing the complexity of cross-linked polymer networks by preserving their main macroscale properties is key to understanding them, and a crucial issue is to relate individual properties of the polymer constituents to those of the reduced network. Here we study polymer networks in a good solvent, by considering star polymers as their unit elements, and first quantify the interaction between their centers of masses. We then reduce the complexity of a network by replacing sets of its bridged star polymers by equivalent effective soft particles with dense cores. Our coarse graining allows us to approximate complex polymer networks by much simpler ones, keeping their relevant mechanical properties, as illustrated in computer experiments.

Concentration-dependent swelling and structure of ionic microgels: simulation and theory of a coarse-grained model

We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by effective interparticle interactions. The model synthesizes the Flory-Rehner theory of cross-linked polymer gels, the Hertz continuum theory of effective elastic interactions, and a theory of density-dependent effective electrostatic interactions. Implementing the model using Monte Carlo simulation and thermodynamic perturbation theory, we compute equilibrium particle size distributions, swelling ratios, volume fractions, net valences, radial distribution functions, and static structure factors as functions of concentration. Trial Monte Carlo moves comprising particle displacements and size variations are accepted or rejected based on the total change in elastic and electrostatic energies. The theory combines first-order thermodynamic perturbation and variational free energy approximations. For illustrative system parameters, theory and simulation agree closely at concentrations ranging from dilute to beyond particle overlap. With increasing concentration, as microgels deswell, we predict a decrease in the net valence and an unusual saturation of pair correlations. Comparison with experimental data for deionized, aqueous suspensions of PNIPAM particles demonstrates the capacity of the coarse-grained model to predict and interpret measured swelling behavior.

An anionic shell shields a cationic core allowing for uptake and release of polyelectrolytes within core-shell responsive microgels

To realize carriers for drug delivery, cationic containers are required for anionic guests. Nevertheless, the toxicity of cationic carriers limits their practical use. In this study, we investigate a model system of polyampholyte N-isopropylacrylamide (NIPAM)-based microgels with a cationic core and an anionic shell to study whether the presence of a negative shell allows the cationic core to be shielded while still enabling the uptake and release of the anionic guest polyelectrolytes. These microgels are loaded with polystyrene sulfonate of different molecular weights to investigate the influence of their chain length on the uptake and release process. By means of small-angle neutron scattering, we evaluate the spatial distribution of polystyrene sulfonate within the microgels. The guest molecules are located in different parts of the core-shell microgels depending on their size. By combining these scattering results with UV-vis spectroscopy, electrophoretic mobility and potentiometric titrations we gain complementary results to investigate the uptake and release process of polyelectrolytes in polyampholyte core-shell microgels. Moreover, Brownian molecular dynamic simulations are performed to compare the experimental and theoretical results of this model. Our findings demonstrate that the presence of a shell still enables efficient uptake of guest molecules into the cationic core. These anionic guest molecules can be released through an anionic shell. Furthermore, the presence of a shell enhances the stability of the microgel-polyelectrolyte complexes with respect to the cationic precursor microgel alone.

Amphiphilic Arborescent Copolymers and Microgels: From Unimolecular Micelles in a Selective Solvent to the Stable Monolayers of Variable Density and Nanostructure at a Liquid Interface

Amphiphilic arborescent block copolymers of two generations (G2 and G3) and polymer microgels, obtained via cross-linking of diblock copolymers, were studied in a selective solvent and at liquid interface via dissipative particle dynamics (DPD) simulations. Depending on the primary structure, single arborescent macromolecules in selective solvent can have both core-corona and multicore structures. Self-assembly of the G2, G3, and microgels in the selective solvent is compared with equivalent linear diblock copolymers. The latter self-assemble into spherical micelles of large enough aggregation number. On the contrary, stability of unimolecular micelles is a feature of the arborescent copolymers and microgels, whereas their ability to aggregate is very low. Adsorption of the single molecules at liquid (oil-water) interface leads to their flattening and segregation of the amphiphilic blocks: hydrophilic and hydrophobic blocks are exposed toward water and oil, respectively. Depending on the character of interactions between monomer units, which can be controlled by temperature or solvent(s) quality, Janus, patchy, and nanosegregated structures can be formed within the macromolecules. Their self-assembly at the interface can lead to the formation of both loose and dense monolayers, which can be homogeneous and nanostructured. The pretty fast adsorption kinetics of G2 macromolecules make them efficient stabilizers of emulsions.

Tunable Permeability of Cross-Linked Microcapsules from pH-Responsive Amphiphilic Diblock Copolymers: A Dissipative Particle Dynamics Study

Using dissipative particle dynamics simulation, we probe the tunable permeability of cross-linked microcapsules made from pH-sensitive diblock copolymers poly(ethylene oxide)-b-poly(N,N-diethylamino-2-ethyl methacrylate) (PEO-b-PDEAEMA). We first examine the self-assembly of non-cross-linked microcapsules and their pH-responsive collapse and then explore the effects of cross-linking and block interaction on the swelling or deswelling of cross-linked microcapsules. Our results reveal a preferential loading of hydrophobic dicyclopentadiene (DCPD) molecules in PEO-b-PDEAEMA copolymers. Upon reduction of pH, non-cross-linked microcapsules fully decompose into small wormlike clusters as a result of large self-repulsions of protonated copolymers. With increasing degree of cross-linking, the morphology of the microcapsule becomes more stable to pH change. The highly cross-linked microcapsule shell undergoes significant local polymer rearrangement in acidic solution, which eliminates the amphiphilicility and therefore enlarges the permeability of the shell. The responsive cross-linked shell experiences a disperse-to-buckle configurational transition upon reduction of pH, which is effective for the steady or pulsatile regulation of shell permeability. The swelling rate of the cross-linked shell is dependent on both electrostatic and nonelectrostatic interactions between the pH-sensitive groups as well as the other groups. Our study highlights the combination of cross-linking structure and block interactions in stabilizing microcapsules and tuning their selective permeability.

Internal dynamics of microgels: A mesoscale hydrodynamic simulation study

We analyze the dynamics of polymers in a microgel system under different swelling conditions. A microgel particle consists of coarse-grained linear polymers which are tetra-functionally crosslinked and undergoes conformational changes in response to the external stimuli. Here, a broad range of microgel sizes, extending from tightly collapsed to strongly swollen particles, is considered. In order to account for hydrodynamic interactions, the microgel is embedded in a multiparticle collision dynamics fluid while hydrophobic attraction is modelled by an attractive Lennard-Jones potential and swelling of ionic microgels is described through the Debye-Hückel potential. The polymer dynamics is analyzed in terms of the monomer mean square displacement and the intermediate scattering function S(q, t). The scattering function decays in a stretched-exponential manner, with a decay rate exhibiting a crossover from a collective diffusive dynamics at low magnitudes of the wavevector q to a hydrodynamic-dominated dynamics at larger q. There is little difference between the intermediate scattering functions of microgels under good solvent conditions and strongly swollen gels, but strongly collapsed gels exhibit a faster decay at short times and hydrodynamic interactions become screened. In addition, we present results for the dynamics of the crosslinks, which exhibit an unexpected, semiflexible polymer-like dynamics.

Explicit description of complexation between oppositely charged polyelectrolytes as an advantage of the random phase approximation over the scaling approach

Formation of single globules via 1 : 1 complexation of oppositely charged linear chains occurs prior to coacervation. F_corr is proved to be negative which is the difference between the random phase approximation (RPA) correction term and the self-energy of the chains.

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

The equilibrium distribution of monovalent and trivalent ions within a thermo-responsive charged nanogel is investigated using Monte Carlo simulations and Ornstein–Zernike equations.

Swelling, structure, and phase stability of compressible microgels

Microgels are soft colloidal particles that, when dispersed in a solvent, swell and deswell in response to changes in environmental conditions, such as temperature, concentration, and pH. Using Monte Carlo simulation, we model bulk suspensions of microgels that interact via Hertzian elastic interparticle forces and can expand or contract via trial moves that allow particles to change size in accordance with the Flory-Rehner free energy of cross-linked polymer gels. We monitor the influence of particle compressibility, size fluctuations, and concentration on bulk structural and thermal properties by computing particle swelling ratios, radial distribution functions, static structure factors, osmotic pressures, and freezing densities. For microgels in the nanoscale size range, particle compressibility and associated size fluctuations suppress crystallization, shifting the freezing transition to a higher density than for the hard-sphere fluid. As densities increase beyond close packing, microgels progressively deswell, while their intrinsic size distribution grows increasingly polydisperse.

A polymer microgel at a liquid-liquid interface: theory vs. computer simulations

We propose a mean-field theory and dissipative particle dynamics (DPD) simulations of swelling and collapse of a polymer microgel adsorbed at the interface of two immiscible liquids (A and B). The microgel reveals surface activity and lowers A-B interfacial tension. Attempting to occupy as large an interfacial area as possible, the microgel undergoes anisotropic deformation and adopts a flattened shape. Spreading over the interface is restricted by polymer subchain elasticity. The equilibrium shape of the microgel at the interface depends on its size. Small microgels are shown to be more oblate than the larger microgels. Increasing microgel cross-link density results in stronger reduction of the surface tension and weaker flattening. As the degree of immiscibility of A and B liquids increases, the microgel volume changes in a non-monotonous fashion: the microgel contraction at moderate immiscibility of A and B liquids is followed by its swelling at high incompatibility of the liquids. The segregation regime of the liquids within and outside the microgel is different. Being segregated outside the microgel, the liquids can be fully (homogeneously) mixed or weakly segregated within it. The density profiles of the liquids and the polymer were plotted under different conditions. The theoretical and the DPD simulation results are in good agreement. We hope that our findings will be useful for the design of stimuli responsive emulsions, which are stabilized by the microgel particles, as well as for their practical applications, for instance, in biocatalysis.

Mixing of Two Immiscible Liquids within the Polymer Microgel Adsorbed at Their Interface

We report on the behavior of two immiscible liquids within polymer microgel adsorbed at their interface. By means of dissipative particle dynamics (DPD) simulations and theoretical analysis in the framework of the Flory-Huggins (FH) lattice theory, we demonstrate that the microgel acts as a "compatibilizer" of these liquids: their miscibility within the microgel increases considerably. If the incompatibility of the liquids is moderate, although strong enough to induce phase separation in their 1:1 composition, they form homogeneous mixture in the microgel interior. The mixture of highly incompatible liquids undergoes separation into two (micro)phases within the microgel likewise out of it; however, the segregation regime is weaker and the concentration profiles are characterized by a weaker decay (gradient) in comparison with those of two pure liquids. The enhanced miscibility is a result of the screening of unfavorable interactions between unlike liquid molecules by polymer subchains. We have shown that better miscibility of the liquids is achieved with densely cross-linked microgels. Our findings are very perspective for many applications where immiscible species have to be mixed at interfaces (like in heterogeneous catalysis).

Multi-Shell Hollow Nanogels with Responsive Shell Permeability

We report on hollow shell-shell nanogels with two polymer shells that have different volume phase transition temperatures. By means of small angle neutron scattering (SANS) employing contrast variation and molecular dynamics (MD) simulations we show that hollow shell-shell nanocontainers are ideal systems for controlled drug delivery: The temperature responsive swelling of the inner shell controls the uptake and release, while the thermoresponsive swelling of the outer shell controls the size of the void and the colloidal stability. At temperatures between 32 °C < T < 42 °C, the hollow nanocontainers provide a significant void, which is even larger than the initial core size of the template, and they possess a high colloidal stability due to the steric stabilization of the swollen outer shell. Computer simulations showed, that temperature induced switching of the permeability of the inner shell allows for the encapsulation in and release of molecules from the cavity.

Swelling of ionic microgel particles in the presence of excluded-volume interactions: a density functional approach

In this work a new density functional theory framework is developed to predict the salt-concentration dependent swelling state of charged microgels and the local concentration of monovalent ions inside and outside the microgel.

Hollow and Core-Shell Microgels at Oil-Water Interfaces: Spreading of Soft Particles Reduces the Compressibility of the Monolayer

We investigate the influence of a solid core and of the cross-link density on the compression of microgel particles at oil-water interfaces by means of compression isotherms and computer simulations. We investigate particles with different morphology, namely core-shell particles containing a solid silica core surrounded by a cross-linked polymer shell of poly(N-isopropylacrylamide), and the corresponding hollow microgels where the core was dissolved. The polymer shell contains different amounts of cross-linker. The compression isotherms show that the removal of the core leads to an increase of the surface pressure at low compression, and the same effect can be observed when the polymer cross-link density is decreased. Low cross-link density and a missing core thus facilitate spreading of the polymer chains at the interface and, at high compression, hinder the transition to close hexagonal packing. Furthermore, the compression modulus only depends on the cross-link density at low compression, and no difference can be observed between the core-shell particles and the corresponding hollow microgels. It is especially remarkable that a low cross-link density leads to a high compression modulus at low compression, while this behavior is reversed at high compression. Thus, the core does not influence the particle behavior until the polymer shell is highly compressed and the core is directly exposed to the pressure. This is related to an enhanced spreading of polymer chains at the interface and thus high adsorption energy. These conclusions are fully supported by computer simulations which show that the cross-link density of the polymer shell defines the degree of deformation at the interface. Additionally, the core restricts the spreading of polymer chains at the interface. These results illustrate the special behavior of soft microgels at liquid interfaces.