On tuning microgel character and softness of cross-linked polystyrene particles

Stress overshoot, hysteresis, and the Bauschinger effect in sheared dense colloidal suspensions

The mechanical nonlinear response of dense Brownian suspensions of polymer gel particles is studied experimentally and by means of numerical simulations. It is shown that the response to the application of a constant shear rate depends on the previous history of the suspension. When the flow starts from a suspension at rest, it exhibits an elastic response followed by a stress overshoot and then a plastic flow regime. Conversely, after flow reversal, the stress overshoot does not occur, and the apparent elastic modulus is reduced while numerical simulations reveal that the anisotropy of the local microstructure is delayed relative to the macroscopic stress.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a 'soft colloids make strong glass-forming liquid'-type of behavior observed close to the nominal glass transition volume fraction, φ_g. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φ_g. Above φ_g, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

Wide-angle static and dynamic light scattering under shear

We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with a sub-micron characteristic length scale. The shear device consists in two parallel plates, and the optical setup allows us to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus: a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.

Pathways and challenges towards a complete characterization of microgels

Due to their controlled size, sensitivity to external stimuli, and ease-of-use, microgel colloids are unique building blocks for soft materials made by crosslinking polymers on the micrometer scale. Despite the plethora of work published, many questions about their internal structure, interactions, and phase behavior are still open. The reasons for this lack of understanding are the challenges arising from the small size of the microgel particles, complex pairwise interactions, and their solvent permeability. Here we describe pathways toward a complete understanding of microgel colloids based on recent experimental advances in nanoscale characterization, such as super-resolution microscopy, scattering methods, and modeling.

Influence of Softness on the Stability of Binary Colloidal Crystals

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB₄ phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.

Soft Interactions Modify the Diffusive Dynamics of Polymer-Grafted Nanoparticles in Solutions of Free Polymer

We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using X-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard-sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve solely as a function of normalized length scales. Instead, the diffusivities can be collapsed across two orders of magnitude in free polymer molecular weight and concentration and one order of magnitude in grafted molecular weight by incorporating the ratio of free to grafted polymer molecular weights. These results suggest that the soft interaction potential between polymer-grafted nanoparticles and free polymer allows polymer-grafted nanoparticles to diffuse faster than predicted based on bulk rheology and modifies the coupling between grafted particle dynamics and the relaxations of the surrounding free polymer.

Formation of Laves phases in buoyancy matched hard sphere suspensions

Colloidal Laves phases (LPs) are promising precursors for photonic materials. Laves phases have not yet been observed to form in experiments on colloidal suspensions of hard spheres (HS), even though they have been reported in computer simulations. LP formation so far has been achieved only for binary mixtures of colloidal charged spheres or ligand-stabilized nano-particles after drying. Using static light scattering, we monitored LP formation and annealing in a binary mixture of buoyant hard sphere approximants (size ratio Γ = 0.77, number or molar fraction of small spheres xS = 0.76) for volume fractions in the fluid-crystal coexistence regions. All samples spontaneously formed MgZn2 type LPs on the time scale of weeks to months via bulk nucleation and growth. Irrespective of the initial suspension volume fractions, the LP volume fraction at coexistence is ΦCOEX = 0.59 which is significantly below the close packing limit ΦMAX = 0.615 and remarkably close to the expectation from simulation. At low volume fractions, crystals anneal to high quality during coarsening which is in line with recent theoretical expectations for the thermodynamic stability of different LP types. At large volume fractions, however, the diffractograms evolve towards a more MgCu2-like appearance which we attribute to the formation of randomly stacked LPs. Such structures are not known from atomic systems.

New insights into re-entrant melting of microgel particles by polymer-induced aggregation experiments

While microgels are in general described as soft particles, polystyrene (PS) microgels can be synthesized in a way that cross-link density has only a minor influence on their physical properties. Even though the particles swell in a good solvent, the imparted slight softness still allows a mapping on hard sphere behaviour for a large range of cross-link densities [Schneider et al., Soft Matter, 2017, 13, 445]. Nevertheless, the hard sphere analogy breaks down as soon as polymer chains are added to these systems. Quantitative differences between PS microgels and true hard sphere systems appear and the differences between stronger and weaker cross-linked PS microgels can be observed. To gain deeper insights into the origin of these deviations from true hard sphere behaviour, this work is addressed to a systematic study of the colloid-polymer interactions in PS microgel-polymer mixtures. We investigated the aggregation behaviour (namely aggregation concentration and cluster structure) as a function of colloid size, cross-link density and colloid-polymer size ratio in very dilute colloidal suspensions. Our results show that the interplay of cross-link density and polymer size is a key parameter for the strength of the colloid-polymer interactions. Furthermore, the centre-to-centre distance of the colloidal particles in the formed clusters decreases if the cross-link density is decreased, allowing for a higher packing density. This may also explain the unusually high fluid packing fractions observed in the re-entry region of the phase diagram of PS microgel-free PS polymer mixtures.

Internal structure and swelling behaviour of in silico microgel particles

Microgels are soft colloids that, by virtue of their polymeric nature, can react to external stimuli such as temperature or pH by changing their size. The resulting swelling/deswelling transition can be exploited in fundamental research as well as for many diverse practical applications, ranging from art restoration to medicine. Such an extraordinary versatility stems from the complex internal structure of the individual microgels, each of which is a crosslinked polymer network. Here we employ a recently-introduced computational method to generate realistic microgel configurations and look at their structural properties, both in real and Fourier space, for several temperatures across the volume phase transition as a function of the crosslinker concentration and of the confining radius employed during the 'in-silico' synthesis. We find that the chain-length distribution of the resulting networks can be analytically predicted by a simple theoretical argument. In addition, we find that our results are well-fitted to the fuzzy-sphere model, which correctly reproduces the density profile of the microgels under study.

Correction: Polymer-enforced crystallization of a eutectic binary hard sphere mixture

Correction for 'Polymer-enforced crystallization of a eutectic binary hard sphere mixture' by Anna Kozina et al., Soft Matter, 2012, 8, 627-630.