Osmotic pressure of suspensions comprised of charged microgels

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.

Fluid-solid transitions in photonic crystals of soft, thermoresponsive microgels

Microgels are often discussed as well-suited model system for soft colloids. In contrast to rigid spheres, the microgel volume and, coupled to this, the volume fraction in dispersion can be manipulated by external stimuli. This behavior is particularly interesting at high packings where phase transitions can be induced by external triggers such as temperature in the case of thermoresponsive microgels. A challenge, however, is the determination of the real volume occupied by these deformable, soft objects and consequently, to determine the boundaries of the phase transitions. Here we propose core-shell microgels with a rigid silica core and a crosslinked, thermoresponsive poly-N-isopropylacrylamide (PNIPAM) shell with a carefully chosen shell-to-core size ratio as ideal model colloids to study fluid-solid transitions that are inducible by millikelvin changes in temperature. Specifically, we identify the temperature ranges where crystallization and melting occur using absorbance spectroscopy in a range of concentrations. Slow annealing from the fluid to the crystalline state leads to photonic crystals with Bragg peaks in the visible wavelength range and very narrow linewidths. Small-angle X-ray scattering is then used to confirm the structure of the fluid phase as well as the long-range order, crystal structure and microgel volume fraction in the solid phase. Thanks to the scattering contrasts and volume ratio of the cores with respect to the shells, the scattering data do allow for form factor analysis revealing osmotic deswelling at volume fractions approaching and also exceeding the hard sphere packing limit.

Measuring the counterion cloud of soft microgels using SANS with contrast variation

The behavior of microgels and other soft, compressible colloids depends on particle concentration in ways that are absent in their hard-particulate counterparts. For instance, poly-N-isopropylacrylamide (pNIPAM) microgels can spontaneously deswell and reduce suspension polydispersity when concentrated enough. Despite the pNIPAM network in these microgels is neutral, the key to understanding this distinct behavior relies on the existence of peripheric charged groups, responsible for providing colloidal stability when deswollen, and the associated counterion cloud. When in close proximity, clouds of different particles overlap, effectively freeing the associated counterions, which are then able to exert an osmotic pressure that can potentially cause the microgels to decrease their size. Up to now, however, no direct measurement of such an ionic cloud exists, perhaps even also for hard colloids, where it is referred to as an electric double layer. Here, we use small-angle neutron scattering with contrast variation with different ions to isolate the change in the form factor directly related to the counterion cloud, and obtain its radius and width. Our results highlight that the modeling of microgel suspensions must unavoidably and explicitly consider the presence of this cloud, which exists for nearly all microgels synthesized today.

Self-Healing of Charged Microgels in Neutral and Charged Environments

The softness of microgels depends on many aspects, such as particle characteristic lengths, sample concentration, chemical composition of the sample, and elastic moduli of the particle. Here, the response to crowding of ionic microgels is studied. Charged and uncharged ionic microgels are studied in concentrated suspensions of both neutral and ionic microgels with the same swollen size. The combination of small-angle X-ray and neutron scattering with contrast variation allows us to probe both the particle-to-particle arrangement and the response of individual ionic microgels to crowding. When the ionic microgels are uncharged, initial isotropic deswelling followed by faceting is observed. Therefore, the ionizable groups in the polymeric network do not affect the response of the ionic microgel to crowding, which is similar to what has been reported for neutral microgels. In contrast, the kind of microgels composing the matrix plays a key role once the ionic microgels are charged. If the matrix is composed of neutral microgels, a pronounced faceting and negligible deswelling is observed. When only charged ionic microgels are present in the suspension, isotropic deswelling without faceting is dominant.

Beyond simple self-healing: How anisotropic nanogels adapt their shape to their environment

The response of soft colloids to crowding depends sensitively on the particles’ compressibility. Nanogel suspensions provide model systems that are often studied to better understand the properties of soft materials and complex fluids from the formation of colloidal crystals to the flow of viruses, blood, or platelet cells in the body. Large spherical nanogels, when embedded in a matrix of smaller nanogels, have the unique ability to spontaneously deswell to match their size to that of the nanogel composing the matrix. In contrast to hard colloids, this self-healing mechanism allows for crystal formation without giving rise to point defects or dislocations. Here, we show that anisotropic ellipsoidal nanogels adapt both their size and their shape depending on the nature of the particles composing the matrix in which they are embedded. Using small-angle neutron scattering with contrast variation, we show that ellipsoidal nanogels become spherical when embedded in a matrix of spherical nanogels. In contrast, the anisotropy of the ellipsoid is enhanced when they are embedded in a matrix of anisotropic nanogels. Our experimental data are supported by Monte Carlo simulations that reproduce the trend of decreasing aspect ratio of ellipsoidal nanogels with increasing crowding by a matrix of spherical nanogels.

Experimental determination of the bulk moduli of hollow nanogels

The softness of an object can be quantified by one of the fundamental elastic moduli. The bulk modulus of the particle is most appropriate in the presence of isotropic compressions. Here, we use small-angle neutron scattering with contrast variation to directly access the bulk modulus of polymeric nanocapsules - pNIPAM-based hollow nanogels. We show that the size of the cavity is the most important quantity that determines the softness of hollow nanogels. During initial compression, the polymer collapses into the cavity and leads to a large change in the particle volume, resulting in a very small initial bulk modulus. Once the cavity is partially occupied by the polymer, the hollow nanogels become significantly stiffer since now the highly crosslinked network has to be compressed. Furthermore, we show that the larger the cavity, the softer the nanogel.

Resolving the different bulk moduli within individual soft nanogels using small-angle neutron scattering

The bulk modulus, K, quantifies the elastic response of an object to an isotropic compression. For soft compressible colloids, knowing K is essential to accurately predict the suspension response to crowding. Most colloids have complex architectures characterized by different softness, which additionally depends on compression. Here, we determine the different values of K for the various morphological parts of individual nanogels and probe the changes of K with compression. Our method uses a partially deuterated polymer, which exerts the required isotropic stress, and small-angle neutron scattering with contrast matching to determine the form factor of the particles without any scattering contribution from the polymer. We show a clear difference in softness, compressibility, and evolution of K between the shell of the nanogel and the rest of the particle, depending on the amount of cross-linker used in their synthesis.

How Softness Matters in Soft Nanogels and Nanogel Assemblies

Softness plays a key role in determining the macroscopic properties of colloidal systems, from synthetic nanogels to biological macromolecules, from viruses to star polymers. However, we are missing a way to quantify what the term "softness" means in nanoscience. Having quantitative parameters is fundamental to compare different systems and understand what the consequences of softness on the macroscopic properties are. Here, we propose different quantities that can be measured using scattering methods and microscopy experiments. On the basis of these quantities, we review the recent literature on micro- and nanogels, i.e. cross-linked polymer networks swollen in water, a widely used model system for soft colloids. Applying our criteria, we address the question what makes a nanomaterial soft? We discuss and introduce general criteria to quantify the different definitions of softness for an individual compressible colloid. This is done in terms of the energetic cost associated with the deformation and the capability of the colloid to isotropically deswell. Then, concentrated solutions of soft colloids are considered. New definitions of softness and new parameters, which depend on the particle-to-particle interactions, are introduced in terms of faceting and interpenetration. The influence of the different synthetic routes on the softness of nanogels is discussed. Concentrated solutions of nanogels are considered and we review the recent results in the literature concerning the phase behavior and flow properties of nanogels both in three and two dimensions, in the light of the different parameters we defined. The aim of this review is to look at the results on micro- and nanogels in a more quantitative way that allow us to explain the reported properties in terms of differences in colloidal softness. Furthermore, this review can give researchers dealing with soft colloids quantitative methods to define unambiguously which softness matters in their compound.

Changes in the Form Factor and Size Distribution of Nanogels in Crowded Environments

Particle size disparities suppress crystallization. However, soft deformable nanogels can change the size of the larger particles in suspension and crystallize even at a high initial size-polydispersity. Using neutron scattering with contrast variation, the response of individual nanogels in crowded environments was probed, and an increase of the parameter describing size-polydispersity was found, which is often interpreted as deformation. Here, computer simulations are used to generate deformed nanogels and the corresponding form factor. The data are fitted with the spherical model used to analyze scattering data. The fits show the same qualitative increase of the parameter related to the size-polydispersity with increasing particle deformation. Starting from the simulated deformed spheres, we also reproduce experimental scattering data. A further analysis of the particle shows that the size disparities between nanogels do not increase significantly. In contrast, their shapes strongly vary from one nanogel to the other.

Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Emergence of Non-Hexagonal Crystal Packing of Deswollen and Deformed Ultra-Soft Microgels under Osmotic Pressure Control

Highly solvent swollen poly(N-isopropylacrylamide-co-acrylic acid) microgels are synthesized without exogenous crosslinker, making them extremely soft and deformable. These ultralow crosslinked microgels (ULC) are incubated under controlled osmotic pressure to provide a slow (and presumably thermodynamically controlled) approach to higher packing densities. It is found that ULC microgels show stable colloidal packing over a very wide range of osmotic pressures and thus packing densities. Surprising observation of co-existence between hexagonal and square lattices is also made over the lower range of studied osmotic pressures, with microgels apparently changing shape from spheres to cubes in defects or grain boundaries. It is proposed that the unusual packing behavior observed for ULC microgels is due to the extreme softness of these particles, where deswelling causes deformation and shrinking of the particles that result in unique packing states governed by contributions to the entropy at the colloidal system, single particle and ionic levels. These observations further suggest that more detailed experimental and theoretical studies of ultra-soft microgels are required to obtain a complete understanding of their behavior in packed and confined geometries.

Glass-liquid and glass-gel transitions of soft-shell particles

We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective volume fraction by temperature and particle concentration, liquid, repulsive glass. and attractive gel phases are observed. The dynamics slow down with increasing volume fraction in the liquid phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liquid-glass transition above 50 vol.% that is independent of the particles' concentration and temperature. In an overpacked state at effective volume fractions above 1, the dispersion does not show a liquid phase but undergoes a gel-glass transition at an effective volume fraction of 34 vol.%. At the same concentration, extrema of subdiffusive dynamics are found in the liquid phase at lower weight fractions. We interpret this as dynamic precursors of the glass-gel transition.

Characterization of the volume fraction of soft deformable microgels by means of small-angle neutron scattering with contrast variation

The volume occupied by colloids in a suspension - namely the volume fraction - is the thermodynamic variable that determines the phase behavior of these systems. While for hard incompressible spheres this quantity is well defined, for soft compressible colloids such as microgels - polymeric crosslinked networks swollen in a good solvent - the determination of the real volume occupied by these particles in solution is particularly challenging. This fact depends on two aspects: first the surface and, therefore, the volume of the microgels is hard to define properly given their external fuzziness; second, microgels can osmotically deswell, deform or interpenetrate their neighbors, i.e. change their shape and size depending on the solution concentration. Here, the form factors of few hydrogenated microgels embedded in a matrix of deuterated but otherwise identical microgels are measured using small-angle neutron scattering with contrast variation. From the analysis of the scattering data, the variation of the volume of the microgels as a function of concentration is obtained and used to calculate the real microgel volume fraction in solution. Soft neutral microgels are shown to facet already at low concentrations while in contrast, harder microgels maintain their shape and change their volume.

Absence of crystals in the phase behavior of hollow microgels

Solutions of microgels have been widely used as model systems to gain insight into atomic condensed matter and complex fluids. We explore the thermodynamic phase behavior of hollow microgels, which are distinguished from conventional colloids by a central cavity. Small-angle neutron and x-ray scattering are used to probe hollow microgels in crowded environments. These measurements reveal an interplay among deswelling, interpenetration, and faceting and an unusual absence of crystals. Monte Carlo simulations of model systems confirm that, due to the cavity, solutions of hollow microgels more readily form a supercooled liquid than for microgels with a cross-linked core.