Linking self-assembly, rheology, and gel transition in attractive colloids

We propose a microscopic framework based on nonequilibrium statistical mechanics to connect the microscopic level of particle self assembly with the macroscopic rheology of colloidal gelation. The method is based on the master kinetic equations for the time evolution of the colloidal cluster size distribution, from which the relaxation time spectrum during the gelation process can be extracted. The relaxation spectrum is a simple stretched exponential for irreversible diffusion limited colloidal aggregation gelation, with a stretching exponent df 3, where df is the mass fractal dimension. As opposed to glassy systems, the stretched exponential relaxation does not result from quenched disorder in the relaxation times, but from the selfassembly kinetics in combination with the fractal character of the process. As the master kinetic equations for colloidal aggregation do not admit bond percolation solutions, the arrest mechanism is driven by the interconnection among fractal clusters when excluded volume becomes active, i.e., at sufficiently high packing of clusters. The interconnections between rigid clusters decrease the soft modes of the system and drive a rigidity percolation transition at the cluster level. Using the Boltzmann superposition principle, the creep and the full rheological response can be extracted for both irreversible and thermoreversible colloidal aggregation. In the case of thermoreversible gelation, the attraction energy is finite and plays the role of the control parameter driving a nonequilibrium phase transition into a nonequilibrium steady state the gel . A power law spectrum coexisting with a stretched exponential cut off is predicted leading to power law rheology at sufficiently high frequency. Our theory is in good agreement with experimental data of different systems published by other authors, for which no theory was availabl

Steric Effects on the Rheology of Nanocomposite Genls of Organoclay in Dicarboxyl-Terminated Polybutadiene

Nanocomposite gels were formed by mixing organically modified clay into a linear, end-functionalized polymer (dicarboxyl-terminated polybutadiene). Two differently sized but otherwise similar counterions were chosen for preparing the organoclay. Hydrogen bonding between polymer and clay causes the polymer/clay interface to grow by splitting the clay aggregates into smaller clay particles, then swelling these particles, exfoliating the clay sheets, and eventually assuming a stable dispersion in the polymer matrix. The clay with the larger counterion exfoliates faster, but does not form the stronger network (lower modulus, lower yield stress), and it needs more clay to reach its gel point (percolation threshold [curly or open phi]c). These seemingly contradictory observations (fast exfoliation but weak gel and later gel point) are attributed to steric effects of the larger macro-counterion. Parameters of the study are clay concentration [curly or open phi] and distance from the gel point. The low frequency linear viscoelastic behavior was analyzed using a percolation model (near [curly or open phi]c) and a power law in concentration (far above [curly or open phi]c). The use of two different organoclays allows comparison of the observed phenomena. The extent of agreement between experimental data and known models was used to theorize that the particle–polymer interactions are the controlling factor in the increasing solid-like behavior with increasing clay content

An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transition

Concentrated, non-crystallizing colloidal suspensions in their approach of the glass state exhibit distinct dynamics patterns. These patterns suggest a powerlaw rheological constitutive model for nearglass viscoelasticity, as presented here. The rheological parameters used for this model originate in the mode-coupling theory. The proposed constitutive model provides explicit expressions for the steady shear viscosity, the steady normal stress coefficient, the modulus-compliance relation, and the α peak of G''. The relaxation pattern distinctly differs from gelatio

Viscoelasticity and Shear Flow of Concentrated, Non-Crystallizing Colloidal Suspensions: Comparison with Mode-Coupling Theory

We present a comprehensive rheological study of a suspension of thermosensitive particles dispersed in water. The volume fraction of these particles can be adjusted by the temperature of the system in a continuous fashion. Due to the finite polydispersity of the particles (standard deviation: 17%), crystallization is suppressed and no fluid-crystal transition intervenes. Hence, the moduli G′ and G″ in the linear viscoelastic regime as well as the flow curves (shear stress σ(math) as function of the shear rate math) could be measured in the fluid region up to the vicinity of the glass transition. Moreover, flow curves could be obtained over a range of shear rates of 8 orders of magnitude, while G′ and G″ could be measured spanning over 9 orders of magnitude. Special emphasis has been laid on precise measurements down to the smallest shear rates/frequencies. It is demonstrated that mode-coupling theory generalized in the integration through transients framework provides a full description of the flow curves as well as the viscoelastic behavior of concentrated suspensions with a single set of well-defined parameters