Bridging the gap between hard and soft colloids

Dimitris Vlassopoulos

Hard sphere suspensions and polymers can be viewed as two essential representatives of soft matter, which exhibit different properties.^1,2 Typically, the size scale of colloids is of the order of microns whereas it is nanometres for polymers. While long-range order is achieved in colloids at relatively small volume fractions, short-range order cannot be attained in polymers even at very high fractions. The origin of the stress is entropic in both systems but their respective dynamics is controlled by different mechanisms. In polymers, it is dominated by the elasticity of the chains and the existence of entanglements that hinder transverse diffusion, while in colloids, hydrodynamics and particle interactions are the key parameters. A direct consequence is that microstructural deformation under flow reflects the alteration of particle arrangements in the latter case and polymer conformation in the former. Combining these distinct features represents a formidable challenge as novel materials with new types of behaviour can be designed and fabricated, and their properties explored. For instance, hard colloidal spheres with grafted polymer chains constitute a good realization of soft colloids where in the limit of many short chains, the colloidal nature prevails whereas for a few extremely long chains the polymeric response is dominant. This renders the detailed exploration of the intermediate world of soft colloids fascinating.

Hard sphere suspensions are archetypes of many particulate materials. The excluded volume interaction that characterizes them is the simplest we can imagine: particles do not interact except at contact where they undergo a strong repulsion that prevents interpenetration or deformation. Nevertheless, hard sphere suspensions exhibit a very rich phase diagram, including liquid, crystalline and glass phases.³ Obtention of a given phase depends not only on volume fraction but also on the conditions of preparation and parameters like polydispersity, flow and gravity. For instance, crystallization can be avoided at the benefit of supercooled or glassy states by forcing the volume fraction to increase rapidly. Slightly polydisperse hard sphere suspensions form glasses when the volume fraction exceeds a value of about ϕ_g ≈ 0.58. Glasses are out-of-equilibrium materials where particles are kinetically trapped into metastable cages formed by a small number of neighbours, which restrict and eventually arrest macroscopic motion.⁴ Cages possess an intrinsic elasticity of entropic origin. They are broken upon application of external stresses exceeding the so-called yield stress, causing particles to move past one another over large distances and leading to macroscopic flow, which is in general heterogeneous.^5,6,7 The cage elasticity and yield stress are of the order of 1 Pa or less, indicating that hard-sphere glasses are very soft and fragile materials. Another important feature of glasses is that they exhibit slow dynamics and aging just like many other out-of-equilibrium materials.⁸ The way hard sphere glasses yield, flow and age at the mesoscopic and macroscopic scales are challenging topics that stimulate intense experimental and theoretical works.^4,9–11

Notwithstanding the conceptual importance of hard sphere suspensions, most systems used in real applications are soft colloids. Softness can be of various origins.^12,13 It can arise from the interaction potential itself, which allows some degree of compression beyond the effective radius of the particles. This occurs naturally as a consequence of the stabilization mechanism—electrostatic or steric—used to keep the particles apart. Another source of softness arises from the particles themselves which can be elastic and deformable. A non-exhaustive list of examples includes microgels, emulsion droplets, vesicles, and hairy particles such as block copolymer micelles, star polymers, or end-grafted or physisorbed particles.^12,13 In these materials, the upper bound of the fully disordered glassy region for hard sphere suspensions, i.e. the volume fraction at close-packing, can be easily overcome due to deformability and interpenetration, making very large volume fractions accessible. Jammed suspensions are generally highly elastic with a shear modulus of the order of 10³ Pa and have a significant yield stress, which can exceed 10² Pa.^14–16 Yielding is a gradual process that eventually leads to macroscopic flow;^17,18 the latter is often associated with wall slip, shear banding, and non local rheology depending on the type of material, surface interactions, and confinement.^7,19–22 Upon flow cessation, slow relaxations and various forms of aging phenomena take place.^8,23,24 It is important to emphasize that softness is also important in the liquid state. Suspensions of particles are known to organize in various ways under flow.^25,26 Both flow and material (particle, dispersion medium particle interactions) properties play a key role^27,28 and understanding the consequences of brush deformation on the flow in soft colloids remains a challenge.

It is therefore evident that colloids of varying softness are valuable for a lot of applications and industrial processes. Key questions of fundamental and applied interest concern the nature of the glass and jamming transitions in soft colloids, the linear and nonlinear rheological behaviour of soft suspensions throughout the entire concentration range from dilute to jammed and the possible flow-induced order, the roles of solvent type and quality, slow dynamics and aging, the importance of particle shape and the design of new tailored architectures. The scope of these topics extends far beyond the field of soft colloids since many of them are potentially relevant to other classes of materials like molecular-glass formers, metallic glasses and granular materials. Addressing these questions represents a fascinating challenge which requires the skills of statistical and condensed-matter physicists, chemical engineers, materials scientists, physicists and biophysicists as well a combination of theoretical and experimentally approaches.

The present themed issue on “Bridging the gap between soft and hard colloids” fingerprints the wide range of scientific and technological challenges that have emerged over the last few years. It reflects the great richness of the field and the opportunities for further developments. The different contributions of this issue are grouped in eight gross areas below.

The role of softness on crystallization

Starting from a metastable supercooled state, the selection mechanisms of polymorphs upon crystal nucleation are different in hard and soft spheres, in the latter case the bond orientational order being the key (DOI: 10.1039/c2sm07007c). Ionic microgel particles represent one of the main prototypes for exploring the physics of soft colloidal particles. Varying their crosslink density (hence their stiffness) has consequences on their phase behaviour as the liquid-crystal phase coexistence region increases with decreasing particle stiffness (DOI: 10.1039/c2sm06973c). Ultrasoft overlapping particles form what are known as cluster crystals, whose nucleation rates are accelerated by shear, and which under flow organize into well-defined quantized patterns, controlled by particle interaction and flow characteristics (DOI: 10.1039/c1sm06899g).

Particle dynamics in crowded dispersions

New approaches and techniques have been developed to probe the local dynamics and associate it with the mesoscopic behaviour of jammed particle suspensions, such as caging and nanomechanical properties. Three examples are presented here: (i) the rotational motion in a jammed dispersion of particles consisting of an anti-ferromagnetic core and a thermosensitive microgel shell (DOI: 10.1039/c2sm07076f); (ii) the rich vibration spectroscopy of clusters of spherical polystyrene latex particles via Brillouin light scattering (DOI: 10.1039/c2sm07034k); (iii) and the long-time tracer diffusion in soft sphere glasses which is predicted to be more than three times faster than in hard sphere glasses (DOI: 10.1039/c1sm06932b).

Predictive microstructural theories for linear and nonlinear rheology

This broad topic continues to attract the interest of leading groups in the field worldwide. Mode coupling theory (MCT) remains the main predictive tool for glassy suspensions. Interestingly, below close packing, the linear viscoelasticity of core–shell microgels is indistinguishable from that of true hard sphere systems, since their soft shells essentially do not deform (DOI: 10.1039/c2sm07011a). MCT is shown to form the basis for the understanding of the nonlinear rheology of glasses through the development of schematic constitutive equations where for example the application of two equal and opposite step strains leads to a nonvanishing residual stress signifying plastic deformation (DOI: 10.1039/c2sm06891e). Further advances with the use of MCT showcase the use of different interaction potentials (nonoverlapping disks and magnetic dipoles) to study the structure and viscoelasticity of binary glasses (DOI: 10.1039/c2sm07010c). Microscopic models based on Smoluchowski theory are shown to be particularly important in linking microstructure to rheology. Recent developments include the prediction of the pair distribution function and elastic moduli of jammed microgel suspensions (DOI: 10.1039/c2sm06940g) and the rheology of concentrated suspensions of repulsive particles with hydrodynamic interactions (DOI: 10.1039/c2sm07187h).

Nonlinear flow phenomena in colloidal glasses

Yielding and shear banding are important phenomena associated with the flow of glasses, gels and jammed solids. Whereas they appear in all these systems, important subtleties and the role of softness remain in large unresolved. This prompts a direct phenomenological comparison of rheology and yielding as function of volume fraction for different types of hard and soft colloids (DOI: 10.1039/c2sm07113d). Mesoscopic modelling accounting for local plastic events that give rise to global stress redistribution over the system and hence macroscopic flow, can predict formation of permanent shear bands that originate from local restructuring (DOI: 10.1039/c2sm07090a). Transient shear banding upon flow start-up has been studied experimentally as function of time and measurement geometry for simple yield-stress fluids (Carbopol microgels) and shown to persist throughout the whole sample or eventually result in complete fluidization and homogeneous flow, depending on the applied shear rate (DOI: 10.1039/c2sm06918k).

Aging and heterogeneous dynamics in soft glassy materials

When the average relaxation time of a glassy suspension changes with aging time and temperature without affecting the shape of the relaxation spectrum, the principle of time-temperature superposition works, as demonstrated for the case of clays (DOI: 10.1039/c2sm07071e). Recently developed advanced scattering techniques of high resolution, such as real-space analysis of dynamic correlations in conjunction with confocal microscopy, can be applied to study the relaxation in glassy suspensions. A comparative study shows that jammed soft spheres exhibit far longer-range correlations compared to hard sphere glasses, a difference attributed to the strong internal elasticity of the former (DOI: 10.1039/c2sm25267h).

Long hairy particles

Besides the deformability that characterizes a wide range of soft particles such as microgels, hair interpenetrability at high fractions and ultrasoft interaction potential are two additional features of long hairy particles. Star polymers are a much studied system in this area, whose potential is tuned by changing the number of arms. Hybrid mesoscale simulations including hydrodynamic interactions are very powerful in predicting the rheology as a function of concentration in good solvent, in agreement with experimental data (DOI: 10.1039/c2sm07009j). Grafted particles with different number and size of long grafts serve as model systems forming quasi-one-dimensional nanocomposites with tunable mechanical properties (DOI: 10.1039/c2sm06915f).

The role of dispersing medium in the properties of suspensions

Solvent quality plays a key role on the interactions of colloidal particles and in this regard it can serve as a means to tailor their properties. This is particularly important for grafted particles where the solvent quality for the grafts can be varied significantly while preserving colloidal stability; the consequences on the structural properties and conformation of grafts are explored theoretically (DOI: 10.1039/c2sm06836b). Another demonstration of the importance of softness, which leads to novel results with respect to hard sphere systems, is made by mixing star and linear polymers. Depletion-induced star clusters form upon adding linear polymers, which are irregular and transient, as suggested by molecular dynamics simulations and MCT (DOI: 10.1039/c2sm06849d). Nanocomposites, created by the addition of small particles to long polymer matrices, have been studied extensively due to their importance in enhancing mechanical properties. However, many important questions remain unanswered. Here we see how we can understand the so-called Payne effect, i.e. the decrease of modulus at high strain amplitudes, in composites made of inorganic particles added to elastomers, by quantitatively accounting for interparticle contacts (DOI: 10.1039/c2sm06885k). Oligo-tethered nanoparticles suspended in small polymers represent a versatile model system for investigating jamming transitions and associated rheological phenomena, which can be discussed in the framework of the soft glassy rheology model, a key alternative to MCT (DOI: 10.1039/c2sm06889c). Dispersing particles in liquid crystalline solvent has a great impact on their relaxation dynamics and aging behaviour as a consequence of the solvent anisotropy (DOI: 10.1039/c2sm06986e).

Developments in synthetic and surface chemistry

As is typical in soft matter research, this field has benefited a great deal from the synergy of chemistry, physical experiments and theoretical rationalization. Undoubtedly however, the advances in synthesis and characterization provide new directions for fabricating novel materials with unique properties that can be tailored at molecular level and open new opportunities for investigating further the physics and applications of complex colloids. Two such cases are included in this issue and demonstrated the limitless opportunities in this exciting field. A review of the formation of crystalline one- and two-component colloidal monolayers shows the possibilities for applications in nanolithography and sets the challenges ahead (DOI: 10.1039/c2sm06650a). Preparation of metallic nanoparticles grafted with microgels is another important development offering tunable colloidal systems with tunable optical response (DOI: 10.1039/c2sm06396k).

 

Although a great number of investigations on hard (in particular) and soft colloids exist, only in the last few years they have been put into context and the field has emerged as very important in soft matter. Hence we believe that this themed issue is timely. Recent developments have been triggered by significant advances in theoretical modelling and simulations as well as experimental techniques. We hope that the readers of this issue will appreciate the large potential impact of this emerging field and the ample possibilities for further progress. It is a most exciting area for research in this branch of soft matter physics and technology.

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