Colloidal and polymeric contributions to the yielding of dense microgel suspensions.

HYPOTHESIS: Soft microgel colloids can be densely packed since particle networks can compress and interpenetrate. This evolution of the particle's internal structure associated with packing is expected to determine the linear viscoelastic properties and the yielding behavior of dense suspensions of microgel colloids. EXPERIMENTS: We investigated the volume fraction-dependent linear and non-linear rheological response of suspensions of soft core-shell particles formed by a poly(N-isopropylacrylamide) (PNIPAM) microgel core and a thin poly(ethylene glycol) (PEG) shell. FINDINGS: The linear viscoelasticity of suspensions reveals a transition from a fluid to a jammed glass state. Increasing volume fraction within the jammed state, the linear storage modulus and the yield stress show distinct regimes associated with the evolution of particle contacts, which involve progressive compression and interpenetration of the shell and core. The yielding of jammed suspensions occurs in two-steps: At small strains jammed cages are rearranged, while full disentanglement of interpenetrating networks only occurs at large deformations and results in fluidization. Yield strains and stresses increase with increasing shear rate or frequency, suggesting a progressive dominance of the timescale associated with shear over that associated with the internal dynamics of the system.

Effect of size disparity on the structure and dynamics of the small component in concentrated binary colloidal mixtures.

We determined, using confocal microscopy, the structure and dynamics of the small component in concentrated binary colloidal mixtures with moderate and large size ratios and different compositions of Polymethyl methacrylate particles. We show that when increasing the content of small spheres at fixed total volume fraction, a transition in the local environment of the small particles is observed, from a mixed environment of other small and large particles to a local environment of only small particles. The transition is rather abrupt for moderate size ratios, while it becomes particularly broad for large size ratios. This can be associated with the improved ability of the small particles to pack in between the large particles for larger size ratios. The dynamics reflect the transition with an increase of the mobility observed at intermediate mixing. This increase becomes particularly pronounced for large size ratios, leading to diffusive dynamics of the small particles, in agreement with predictions of theories of the glass transition in binary hard-sphere mixtures. The composition at which the fastest dynamics are observed is apparently independent of the size ratio.

Investigation of moderately turbid suspensions by heterodyne near field scattering.

Light scattering has proven to be a very powerful technique to characterize soft matter systems. However, many samples are turbid and hence suffer from multiple scattering which can affect the signal considerably. Multiple scattering can be reduced by diluting the sample or changing the solvent, but often this alters the sample and hence is precluded. Here we study the dynamics of a model system. In particular, we investigate the effects of moderate multiple scattering on small-angle heterodyne near field scattering (HNFS). Varying the particle concentration and size we change the degree of multiple scattering, which is quantified by the transmission of light. In dependence of the degree of multiple scattering, we analyze the statistical properties of the HNFS signal, which is the difference between two intensity patterns separated by a delay time. The distribution of intensity differences follows a Gaussian distribution if single scattering dominates and a Laplace distribution in the presence of extreme multiple scattering. We also investigate the effects of multiple scattering on the measured intermediate scattering function and the hydrodynamic radius of the particles. Reliable data are obtained for sample transmissions down to about 0.7. This is confirmed by a comparison with results from a far field cross-correlation instrument that suppresses multiple scattering contributions. Therefore, HNFS represents a technically simple but powerful method to investigate samples that are moderately multiple scattering.

Long-Lived Neighbors Determine the Rheological Response of Glasses.

Glasses exhibit a liquidlike structure but a solidlike rheological response with plastic deformations only occurring beyond yielding. Thus, predicting the rheological behavior from the microscopic structure is difficult, but important for materials science. Here, we consider colloidal suspensions and propose to supplement the static structural information with the local dynamics, namely, the rearrangement and breaking of the cage of neighbors. This is quantified by the mean squared nonaffine displacement and the number of particles that remain nearest neighbors for a long time, i.e., long-lived neighbors, respectively. Both quantities are followed under shear using confocal microscopy and are the basis to calculate the affine and nonaffine contributions to the elastic stress, which is complemented by the viscoelastic stress to give the total stress. During start-up of shear, the model predicts three transient regimes that result from the interplay of affine, nonaffine, and viscoelastic contributions. Our prediction quantitatively agrees with rheological data and their dependencies on volume fraction and shear rate.

Size-Dependent Localization in Polydisperse Colloidal Glasses.

We have investigated concentrated suspensions of polydisperse hard spheres and have determined the dynamics and sizes of individual particles using confocal microscopy. With increasing concentration, the dynamics of the small and large particles start to differ. The large particles exhibit slower dynamics and stronger localization. Moreover, as the particle size increases, the local volume fraction ϕ_{loc} also increases. In the glass state, the localization length significantly decreases beyond ϕ_{loc}≈0.67. This suggests a link between local crowding and dynamical heterogeneities. However dynamical arrest of subpopulations seems not directly linked to a large value of ϕ_{loc}, indicating the importance of collective effects.

Directed percolation identified as equilibrium pre-transition towards non-equilibrium arrested gel states.

The macroscopic properties of gels arise from their slow dynamics and load-bearing network structure, which are exploited by nature and in numerous industrial products. However, a link between these structural and dynamical properties has remained elusive. Here we present confocal microscopy experiments and simulations of gel-forming colloid-polymer mixtures. They reveal that gel formation is preceded by continuous and directed percolation. Both transitions lead to system-spanning networks, but only directed percolation results in extremely slow dynamics, ageing and a shrinking of the gel that resembles synaeresis. Therefore, dynamical arrest in gels is found to be linked to a structural transition, namely directed percolation, which is quantitatively associated with the mean number of bonded neighbours. Directed percolation denotes a universality class of transitions. Our study hence connects gel formation to a well-developed theoretical framework, which now can be exploited to achieve a detailed understanding of arrested gels.

Creep and flow of glasses: strain response linked to the spatial distribution of dynamical heterogeneities.

Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely colloidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dynamics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different behaviors are also reflected in the average particle dynamics, quantified by the mean squared displacement of the individual particles, and the fraction of active regions. Both microscopic quantities are found to be proportional to the macroscopic strain, despite the non-equilibrium and non-linear conditions during creep and the transient regime prior to steady flow.

Different mechanisms for dynamical arrest in largely asymmetric binary mixtures.

Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.

Transient dynamics during stress overshoots in binary colloidal glasses.

We investigate, using simultaneous rheology and confocal microscopy, the time-dependent stress response and transient single-particle dynamics following a step change in shear rate in binary colloidal glasses with large dynamical asymmetry and different mixing ratios. The transition from solid-like response to flow is characterised by a stress overshoot, whose magnitude is linked to transient superdiffusive dynamics as well as cage compression effects. These and the yield strain at which the overshoot occurs vary with the mixing ratio, and hence the prevailing caging mechanism. The yielding and stress storage are dominated by dynamics on different time and length scales, the short-time in-cage dynamics and the long-time structural relaxation respectively. These time scales and their relation to the characteristic time associated with the applied shear, namely the inverse shear rate, result in two different and distinct regimes of the shear rate dependencies of the yield strain and the magnitude of the stress overshoot.

Residual stresses in glasses.

The history dependence of glasses formed from flow-melted steady states by a sudden cessation of the shear rate γ[over ˙] is studied in colloidal suspensions, by molecular dynamics simulations and by mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of γ[over ˙]t, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables but differing static properties.

Transient dynamics in dense colloidal suspensions under shear: shear rate dependence.

A combination of confocal microscopy and rheology experiments, Brownian dynamics (BD) and molecular dynamics (MD) simulations and mode coupling theory (MCT) have been applied in order to investigate the effect of shear rate on the transient dynamics and stress-strain relations in supercooled and glassy systems under shear. Immediately after shear is switched on, the microscopic dynamics display super-diffusion and the macroscopic rheology a stress overshoot, which become more pronounced with increasing shear rate. MCT relates both to negative sections of the generalized shear modulus, which grow with increasing shear rate. When the inverse shear rate becomes much smaller than the structural relaxation time of the quiescent system, relaxation through Brownian motion becomes less important. In this regime, larger stresses are accumulated before the system yields and the transition from localization to flow occurs earlier and more abruptly.

Yielding of hard-sphere glasses during start-up shear.

Concentrated hard-sphere suspensions and glasses are investigated with rheometry, confocal microscopy, and Brownian dynamics simulations during start-up shear, providing a link between microstructure, dynamics, and rheology. The microstructural anisotropy is manifested in the extension axis where the maximum of the pair-distribution function exhibits a minimum at the stress overshoot. The interplay between Brownian relaxation and shear advection as well as the available free volume determine the structural anisotropy and the magnitude of the stress overshoot. Shear-induced cage deformation induces local constriction, reducing in-cage diffusion. Finally, a superdiffusive response at the steady state, with a minimum of the time-dependent effective diffusivity, reflects a continuous cage breakup and reformation.

Small-angle neutron scattering of percolative perfluoropolyether water in oil microemulsions.

A water in oil microemulsion system composed of water, surfactant, and oil, the latter two components of perfluoropolyether (PFPE) type, has been studied by small-angle neutron scattering (SANS) with the aim of knowing the microstructure of the system and to have an insight on the connection between microstructure characterization and percolation behavior. In fact, along the dilution line W/S = 11 of the phase diagram, dielectric spectroscopy and conductivity studies revealed a dynamic percolation process taking place approaching and above the dynamic percolation threshold, leading to a system composed of droplet clusters with percolation thresholds varying with temperature from a 0.501 volume fraction of the dispersed phase at 9.3 degrees C to 0.205 at 32.5 degrees C. The SANS experimental spectra of this work have been studied by modeling the microemulsion droplets as adhesive hard spheres. For all of the samples, the surfactant area per polar head has been also measured in the Porod region of the SANS spectra. Geometric and potential parameters as well as the osmotic pressure, the second virial coefficient, and the distance between droplets have been extracted from data as a function of droplets concentration. At low concentration, that is, below percolation thresholds, the droplets behave as hard spheres, whereas at threshold and above, adhesion changes significantly the samples. In fact, for each temperature, the measured size increases versus concentration from 30 to 50 A, and the area per polar head decreases correspondingly, suggesting that a process of dynamic fusion of droplets occurs in the system above threshold, that is, couples of droplets stick and unstick continuously with interdigitation of the surfactant tails.

Structure, dynamics, and rheology of colloid-polymer mixtures: from liquids to gels.

We investigate the structural, dynamical, and viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples varied from fluids to gels. In the liquid phase, an increasing correlation length of the density fluctuations when approaching the gelation boundary was observed by static light scattering and microscopy, indicating clustering and formation of space-spanning networks. Simultaneously, the correlation function determined by dynamic light scattering decays completely, indicating the absence of dynamical arrest. Clustering and formation of transient networks when approaching the gelation boundary is supported by significant changes in the viscoelastic properties of the samples. Upon increasing the polymer concentration beyond the gelation boundary, the rheological properties changed qualitatively again, now they are consistent with the formation of colloidal gels. Our experimental results, namely, the location of the gelation boundary as well as the elastic (storage) and viscous (loss) moduli, are compared to different theoretical models. These include consideration of the escape time as well as predictions for the viscoelastic moduli based on scaling relations and mode coupling theories.

Asymmetric poly(ethylene-alt-propylene)-poly(ethylene oxide) micelles: a system with starlike morphology and interactions.

We report on an experimental study of single particle properties and interactions of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP-PEO) starlike micelles. The starlike regime is achieved by an extremely asymmetric block ratio (1:20) and the number of arms (functionality) is changed by varying the composition of the solvent (the interfacial tension). Small angle neutron scattering (SANS) data in the dilute regime can be modeled by assuming a constant density profile in the micellar core (compact core) and a starlike density profile in the corona (starlike shell). The starlike morphology of the corona is confirmed by a direct comparison with SANS measurements of dilute poly butadiene star solutions. Comparison of structure factors obtained by SANS measurements in the concentrated regime shows in addition that the interactions in the two systems are equivalent. Micellar structure factors at several packing fractions can be modeled by using the ultrasoft potential recently proposed for star polymers [Likos, Phys. Rev. Lett. 80, 4450 (1998)]. The experimental phase diagram of PEP-PEO micelles is quantitatively compared to theoretical expectations, finding good agreement for the location of the liquid-solid boundary and excellent agreement for the critical packing fraction where the liquid-to-bcc crystal transition takes place for f<70. The functionality, i.e., the coronal density, strongly influences the nature of the solid phase: for f<70 the system crystallizes into a bcc phase, high f>70 formation of amorphous arrested states prevents crystallization.

Small-angle neutron scattering of mixed ionic perfluoropolyether micellar solutions.

Aqueous mixed micellar solutions of perfluoropolyether carboxylic salts with ammonium counterions have been studied by small-angle neutron scattering. Two surfactants differing in the tail length were mixed in proportions n2/n3 = 60/40 w/w, where n2 and n3 are the surfactants with two and three perfluoroisopropoxy units in the tail, respectively. The tails are chlorine-terminated. The mixed micellar solutions, in the concentration range 0.1-0.2 M and thermal interval 20-40 degrees C, show structural characteristics of the interfacial shell that are very similar to ammonium n2 micellar solutions previously investigated; thus, the physics of the interfacial region is dominated by the polar head and counterion. The shape and dimensions of the micelles are influenced by the presence of the n3 surfactant, whose chain length in the micelle is 2 A longer than that of the n2 surfactant. The n3 surfactant favors the ellipsoidal shape in the concentration range 0.1-0.2 M with a 1/2 ionization degree of n2 micelles. The very low surface charge of the mixed micelles is attributed to the increase in hydrophobic interactions between the surfactant tails, due to the longer n3 surfactant molecules in micelles. The closer packing of the tails decreases the micellar curvature and the repulsions between the polar heads, by surface charge neutralization of counterions migrating from the Gouy-Chapman diffuse layer, leading to micellar growth in ellipsoids with greater axial ratios.

Starlike micelles with starlike interactions: a quantitative evaluation of structure factors and phase diagram.

Starlike PEP-PEO block copolymer micelles offer the possibility to investigate the phase behavior and interactions of regular star polymers (ultrasoft colloids). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by small-angle neutron-scattering can be quantitatively described in terms of an effective potential for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid-solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.