Soft Colloidal Suspensions Research Articles

Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.

3D visualization reveals the cooling rate dependent crystallization near a wall in dense microgel systems.

Controlled crystallization, melting and vitrification are important fundamental processes in nature and technology. However, the microscopic details of these fundamental phenomena still lack understanding, in particular how the cooling rate and presence of a wall influence the crystal nucleation and glass formation. Thermoresponsive microgels provide the possibility to study phase transitions at the single-particle level, owing to the ability to tune the particle size with temperature. In this study, we employ composite microgels consisting of a hard core and a crosslinked poly(N-isopropyl acrylamide-co-methacrylic acid) shell to study the crystallization of dense suspensions of soft colloids near a wall using confocal microscopy. We investigate the effect of the cooling rate on the fluid-to-solid transition close to the sample wall. The structures formed during cooling range from glassy in the case of a rapid temperature quench to crystalline when a slow cooling rate is used. Detailed analysis of the final structure reveals that the cooling rate also sets the degree of alignment of the crystal domains with the wall as a result of a balance between homogeneous and heterogeneous crystal nucleation. The results presented here yield valuable insight into the microscopic details of temperature-controlled crystallization near a wall. This understanding will help pave the way towards optimal crystallization conditions for microgel applications.

Tracer dynamics in dense soft colloidal suspensions: from free diffusion to hopping

Tracer dynamics in dense soft colloidal suspensions: from free diffusion to hopping

Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size.

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-to-gel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle X-ray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.

Behavior and mechanics of dense microgel suspensions

Suspensions of soft and highly deformable microgels can be concentrated far more than suspensions of hard colloids, leading to their unusual mechanical properties. Microgels can accommodate compression in suspensions in a variety of ways such as interpenetration, deformation, and shrinking. Previous experiments have offered insightful, but somewhat conflicting, accounts of the behavior of individual microgels in compressed suspensions. We develop a mesoscale computational model to probe the behavior of compressed suspensions consisting of microgels with different architectures at a variety of packing fractions and solvent conditions. We find that microgels predominantly change shape and mildly shrink above random close packing. Interpenetration is only appreciable above space filling, remaining small relative to the mean distance between cross-links. At even higher packing fractions, microgels solely shrink. Remarkably, irrespective of the single-microgel properties, and whether the suspension concentration is changed via changing the particle number density or the swelling state of the particles, which can even result in colloidal gelation, the mechanics of the suspension can be quantified in terms of the single-microgel bulk modulus, which thus emerges as the correct mechanical measure for these type of soft-colloidal suspensions. Our results rationalize the many and varied experimental results, providing insights into the relative importance of effects defining the mechanics of suspensions comprising soft particles.

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy.

The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant–matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap’s length scale is also accessed. On the other hand, by tuning the pH value, the diffusant–matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.

Structure and dynamics in suspensions of soft core-shell colloids in the fluid regime

We report on a detailed experimental study of the structure and short-time dynamics in fluid-regime suspensions of soft core-shell spherical particles with different molecular weights of the chains forming the soft outer shell, and therefore different degrees of particle softness, using 3D dynamic light scattering (3D-DLS). Owing to the particle softness, the liquid-crystal coexistence regime is found to be broader than that of hard-sphere (HS) suspensions. Static light scattering in the dilute regime yields form factors that can be described using a spherical core-shell model and second virial coefficients A2 > 0 indicative of purely repulsive interactions. The particle-particle interactions are longer ranged for all considered systems except those of the smaller molecular weight chain grafted particles which show a HS-like behavior. 3D-DLS experiments in the concentrated regime up to the liquid-crystal transition provide the short-time diffusion function, D(q), in a broad range of scattering wavenumbers, q, from which the structural (cage) and short-time self-diffusion coefficients D(qm) and DS = D(q ≫ qm), respectively, are deduced as functions of the effective particle volume fraction, ϕ = c/c*, where c* is the overlap concentration, calculated using the hydrodynamic particle radius, RH. The size of the nearest-neighbor cage of particles is characterized by 2π/qm, with D(q) and the static structure factor S(q) attaining at qm the smallest and largest values, respectively. Experimental data of D(qm) and DS are contrasted with analytic theoretical predictions based on a simplifying hydrodynamic radius model where the internal hydrodynamic structure of the core-shell particles is mapped on a single hydrodynamic radius parameter γ = RH/Reff, for constant direct interactions characterized by an (effective) hard-core radius Reff. The particle softness is reflected, in particular, in the corresponding shape of the static structure factor, while the mean solvent (Darcy) permeability of the particles related to γ is reflected in the dynamic properties only. For grafted particles with longer polymer chains, D(qm) and DS are indicative of larger permeability values while particles with shorter chains are practically nonpermeable. The particle softness is also evident in the effective random close packing fraction estimated from the extrapolated zero-value limit of the cage diffusion coefficient D(qm).

Kinetics of the glass transition of fragile soft colloidal suspensions.

Microscopic relaxation time scales are estimated from the autocorrelation functions obtained by dynamic light scattering experiments for Laponite suspensions with different concentrations (CL), added salt concentrations (CS), and temperatures (T). It has been shown in an earlier work [D. Saha, Y. M. Joshi, and R. Bandyopadhyay, Soft Matter 10, 3292 (2014)] that the evolutions of relaxation time scales of colloidal glasses can be compared with molecular glass formers by mapping the waiting time (tw) of the former with the inverse of thermodynamic temperature (1/T) of the latter. In this work, the fragility parameter D, which signifies the deviation from Arrhenius behavior, is obtained from fits to the time evolutions of the structural relaxation time scales. For the Laponite suspensions studied in this work, D is seen to be independent of CL and CS but is weakly dependent on T. Interestingly, the behavior of D corroborates the behavior of fragility in molecular glass formers with respect to equivalent variables. Furthermore, the stretching exponent β, which quantifies the width w of the spectrum of structural relaxation time scales, is seen to depend on tw. A hypothetical Kauzmann time tk, analogous to the Kauzmann temperature for molecular glasses, is defined as the time scale at which w diverges. Corresponding to the Vogel temperature defined for molecular glasses, a hypothetical Vogel time tα (∞) is also defined as the time at which the structural relaxation time diverges. Interestingly, a correlation is observed between tk and tα (∞), which is remarkably similar to that known for fragile molecular glass formers. A coupling model that accounts for the tw-dependence of the stretching exponent is used to analyse and explain the observed correlation between tk and tα (∞).

Characteristics of the secondary relaxation process in soft colloidal suspensions

A universal secondary relaxation process, known as the Johari-Goldstein (J-G) β-relaxation process, appears in glass formers. It involves all parts of the molecule and is particularly important in glassy systems because of its very close relationship with the α-relaxation process. However, the absence of a J-G β-relaxation mode in colloidal glasses raises questions regarding its universality. In the present work, we study the microscopic relaxation processes in Laponite suspensions, a model soft glassy material, by dynamic light scattering (DLS) experiments. α- and β-relaxation timescales are estimated from the autocorrelation functions obtained by DLS measurements for Laponite suspensions with different concentrations, salt concentrations and temperatures. Our experimental results suggest that the β-relaxation process in Laponite suspensions involves all parts of the constituent Laponite particle. The ergodicity breaking time is also seen to be correlated with the characteristic time of the β-relaxation process for all Laponite concentrations, salt concentrations and temperatures. The width of the primary relaxation process is observed to be correlated with the secondary relaxation time. The secondary relaxation time is also very sensitive to the concentration of Laponite. We measure primitive relaxation timescales from the α-relaxation time and the stretching exponent (β) by applying the coupling model for highly correlated systems. The order of magnitude of the primitive relaxation time is very close to the secondary relaxation time. These observations indicate the presence of a J-G β-relaxation mode for soft colloidal suspensions of Laponite.

Effect of Connectivity on the Structure and the Liquid–Solid Transition of Dense Suspensions of Soft Colloids

Aqueous solutions of multiarm flower-like poly(ethylene oxide) (PEO) were formed and connected to various degrees by self-assembly. The structure was rendered permanent by in situ UV-irradiation. Dense suspensions of these single and connected soft colloids were studied by static and dynamic light scattering and viscosity measurements. The concentration dependence of the osmotic compressibility, the dynamic correlation length, and the viscosity of single flowers was shown to be close to that of equivalent PEO star-like polymers demonstrating that the effect of forming loops on the interaction is small. It was found that the osmotic compressibility and the dynamic correlation length of dense suspensions are not influenced by the bridging. However, when flower polymers are connected into clusters, motion in dense suspensions needs to be collective over larger length scales. This causes a much stronger increase of the viscosity for dense suspensions of interpenetrated clusters compared to single-flower polymers.

Bulk and interfacial stresses in suspensions of soft and hard colloids

We explore the influence of particle softness and internal structure on both the bulk and interfacial rheological properties of colloidal suspensions. We probe bulk stresses by conventional rheology, by measuring the flow curves, shear stress versus strain rate, for suspensions of soft, deformable microgel particles and suspensions of near hard-sphere-like silica particles. A similar behaviour is seen for both kinds of particles in suspensions at concentrations up to the random close packing volume fraction, in agreement with recent theoretical predictions for sub-micron colloids. Transient interfacial stresses are measured by analyzing the patterns formed by the interface between the suspensions and their solvent, due to a generalized Saffman–Taylor hydrodynamic instability. At odds with the bulk behaviour, we find that microgels and hard particle suspensions exhibit vastly different interfacial stress properties. We propose that this surprising behaviour results mainly from the difference in particle internal structure (polymeric network for microgels versus compact solid for the silica particles), rather than softness alone.

Shear Thickening in Concentrated Soft Sphere Colloidal Suspensions: A Shear Induced Phase Transition

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

Investigation of the dynamical slowing down process in soft glassy colloidal suspensions: comparisons with supercooled liquids

The primary and secondary relaxation timescales of aging colloidal suspensions of Laponite are estimated from intensity autocorrelation functions obtained in dynamic light scattering (DLS) experiments. The dynamical slowing down of these relaxation processes are compared with observations in fragile supercooled liquids by establishing a one-to-one mapping between the waiting time since filtration of a Laponite suspension and the inverse of the temperature of a supercooled liquid that is rapidly quenched towards its glass transition temperature. New timescales associated with primary and secondary relaxation processes, such as the characteristic timescale associated with the slowdown of the secondary relaxation process and the glass transition time, are extracted to describe the phenomenon of dynamical arrest in Laponite suspensions. In results that are strongly reminiscent of those extracted from supercooled liquids approaching their glass transitions, it is demonstrated that a strong coupling exists between the primary and secondary relaxation processes of aging Laponite suspensions in the cage-forming regime. Furthermore, the experimental data presented here clearly demonstrate the self-similar nature of the aging dynamics of Laponite suspensions within a range of sample concentrations.

Structure and Dynamics of Soft Repulsive Colloidal Suspensions in the Vicinity of the Glass Transition

We use a combination of different scattering techniques and rheology to highlight the link between structure and dynamics of dense aqueous suspensions of soft repulsive colloids in the vicinity of a glass transition. Three different latex formulations with an increasing amount of the hydrophilic component resulting in either purely electrostatically or electrosterically stabilized suspensions are investigated. From the analysis of the static structure factor measured by small-angle X-ray scattering, we derive an effective volume fraction that includes contributions from interparticle interactions. We further investigate the dynamics of the suspensions using 3D cross-correlation dynamic light scattering (3DDLS) and rheology. We analyze the data using an effective hard sphere model and in particular compare the linear viscoelasticity and flow behavior to the predictions of mode coupling theory, which accounts for a purely kinetic glass transition determined by the equilibrium structure factor. We demonstrate that seemingly very different colloidal systems exhibit the same generic behavior when the effects from interparticle interactions are incorporated using an effective volume fraction description.

The jamming perspective on wet foams

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can {\em jam} into a rigid, disordered state where they withstand finite shear stresses before yielding. The jamming transition has been studied extensively, in particular in computer simulations of frictionless, soft, purely repulsive spheres. Foams and emulsions are the closest realizations of this model, and in foams, the (un)jamming point corresponds to the wet limit, where the bubbles become spherical and just form contacts. Here we sketch the relevance of the jamming perspective for the geometry and flow of foams --- and also discuss the impact that foams studies may have on theoretical studies on jamming. We first briefly review insights into the crucial role of disorder in these systems, culminating in the breakdown of the affine assumption that underlies the rich mechanics near jamming. Second, we discuss how crucial theoretical predictions, such as the square root scaling of contact number with packing fraction, and the nontrivial role of disorder and fluctuations for flow have been observed in experiments on 2D foams. Third, we discuss a scaling model for the rheology of disordered media that appears to capture the key features of the flow of foams, emulsions and soft colloidal suspensions. Finally, we discuss how best to confront predictions of this model with experimental data.

Nanoparticles for Drug Delivery: Review of the Formulation and Process Difficulties Illustrated by the Emulsion-Diffusion Process

The elaboration of nanoparticles aqueous suspensions aimed at the drug delivery and related process development appear as difficult tasks, due to specificities related to the nanometric size. Such small sizes are required for specific applications in pharmacy. The switch of micrometric to nanometric field represents an actual challenge and cannot be considered as a simple scaling-down of chemical engineers. Ideas and concepts developed first in nanosciences have been adapted to the pharmaceutical application in drug delivery. In spite of drastic constraints due to pharmaceutical application, some parameters allow the control. A brief and not exhaustive review of the state-of-the-art on polymer particles used in the drug delivery field is presented. Attention was more particularly paid on preparation processes and their constraints by describing advantages and drawbacks of each process. The adaptation to the pharmaceutical field, the difficulties and pitfalls which are shared, with most research works in nanoscience, are illustrated thanks to our own results on nanocapsules obtained by "emulsion-diffusion" process presented as a case-study. Thanks to these results, we illustrate the peculiar features and difficulties encountered regarding nanocapsules preparation and characterization. Indeed, such a process allows to prepare nanocapsules of few hundreds nanometers diameter having an oil core surrounded by a polymeric membrane. The characterization of such soft particles colloidal suspensions is often difficult and involves heavy investigation techniques in order to highlight physical mechanisms leading to the nanocapsule properties. This is a key step regarding the final properties as a drug delivery system.

Thermal vitrification in suspensions of soft colloids: Molecular dynamics simulations and comparison with experiments

Dense suspensions of multiarm star polymers are known to develop liquidlike microstructure, which has been attributed to the similarities between high functionality stars and colloidal particles interacting via soft, long ranged potentials. Recent experimental studies reported a counterintuitive solidification of suspensions with f=128 , upon increase of the temperature in marginal solvents. We present our results from molecular dynamics simulations of dense suspensions of multiarm star polymers. Star polymers are modeled as "soft spheres" interacting via a theoretically developed potential of mean field. Our results show a transition towards a "glassy" state at a temperature very close to the one reported experimentally. The features of the transition are consistent with those of ideal glass transitions, as described by ideal mode coupling theory. Furthermore, our findings illustrate the road to vitrification for these soft-colloidal suspensions. Higher temperatures result in arm expansion that causes jamming and more than compensates for faster short time, temperature induced kinetics.

Aging processes and scale dependence in soft glassy colloidal suspensions.

The aging behavior of colloidal suspensions of laponite, a model synthetic clay, is investigated using light scattering techniques. In order to measure the complete dynamic structure factor as a function of time and of wave vector, we have developed an original optical setup using a multispeckle technique for simple light scattering. We have thus measured the correlation of the scattered light intensity as a function of the age of the sample t(w) for various concentrations. For sufficiently concentrated samples, we observe a two-stage relaxation process. The fast relaxation is diffusive, stationary, and reminiscent of the liquidlike behavior observed in less concentrated samples. The slow relaxation behavior, however, is more complex. It exhibits two successive regimes as the sample ages. In the first regime, the decay time tau(a) increases exponentially with t(w) as long as tau(a)<t(w). In the second one, "full aging" is observed in which tau(a) is proportional to t(w). In this second regime, the relaxation of concentration fluctuations are hyperdiffusive, scaling as exp[-(t/tau(a))(beta)] with beta=1.35+/-0.15. In addition, the spatial dependence of this relaxation time scales as tau(a)(q) approximately q(-x) with x approximately 1.3.

Acoustic excitations in suspensions of soft colloids

Vibrational modes in suspensions of soft colloids in a fluid can be detected experimentally by Brillouin light scattering. Besides the usual acoustic mode, being essentially the longitudinal phonon of the liquid matrix, an "opticlike" mode is observed in giant starlike micelles at low volume fractions. We propose that this opticlike mode is due mainly to the internal vibration of each hairy particle.

Shear thickening as a consequence of an acoustic resonance in sheared colloidal crystals

A model is presented that predicts the critical shear rate of shear thickening of soft sphere colloidal suspensions. It is based on the idea that shear in a colloidal crystal leads to a periodic variation of the elastic modulus with time. At a specific shear rate an acoustic resonance occurs which leads to an increase of the viscosity. Good agreement with experimental results could be obtained by fitting the single parameter of the model.