The evolution of viscoelastic properties near the sol-gel transition is studied by performing oscillatory rheological measurements on two different types of systems: a colloidal dispersion and a thermoresponsive polymer solution under isothermal and non-isothermal conditions. While undergoing sol-gel transition, both the systems pass through a critical point. An approach to the critical point is characterized in terms of divergence of zero-shear viscosity and the subsequent appearance of the low-frequency modulus. In the vicinity of the critical gel state, both the viscosity and the modulus show a power-law dependence on the relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both sides of the critical point and also shows a power-law dependence on relative distance from the critical gel point. The critical (power-law) exponents of the zero-shear viscosity and modulus are observed to be related to the exponents of the longest relaxation time by the hyperscaling laws. The dynamic critical exponent has also been calculated from the growth of the dynamic moduli. Remarkably, the critical relaxation exponent and dynamic critical exponent predicted from the scaling laws precisely agree with the experimental values from the isothermal as well as non-isothermal experiments. The associated critical exponents show remarkable internal consistency and advocate the universality of scaling relations for different kinds of systems undergoing the sol-gel transition.

In this work, we study temperature-induced state change of an aqueous solution of triblock copolymer composed of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), PEO-PPO-PEO (Pluronic F127), at different concentrations using rheology. While this temperature-dependent state change visually appears like a liquid–soft solid transition, and the soft solid state has been termed as a gel in the literature, there is a debate regarding the precise microstructure of the soft solid state. We observe that over a concentration domain of interest, an aqueous solution of F127 overwhelmingly demonstrates all the characteristic rheological features of not just a sol–gel–glass transition at low temperatures and glass–liquid transition at high temperatures, but also that associated with the individual states, such as sol, post-gel, and glass. The temperature at which the gel–glass transition is observed decreases while the temperature associated with glass–liquid transition increases with an increase in the concentration of F127. Based on the observed behavior, we propose a mechanism that considers the change in micelle volume fraction and alteration of the hydrophilicity of PEO corona as a function of temperature. Finally, we construct a phase diagram and discuss the similarities and differences with respect to various phase diagrams of F127 solution available in the literature.

A material undergoing sol–gel transition evolves from the pre-gel (sol) state to the post-gel state through the critical gel state. It is well-known that critical gels exhibit power-law rheology. The faster decay of the relaxation modulus in the pre-gel state can be empirically described by modifying this power-law decay with a stretched exponential factor. A phenomenological analytical expression for the relaxation modulus in the post-gel state is proposed by invoking the symmetry associated with the evolution of the relaxation time on either side of the critical gel state and by accounting for natural constraints. This expression, which depends on the extent of cross-linking, can be suitably transformed to obtain analytical expressions for the dynamic moduli and the continuous relaxation time spectrum. Thus, the proposed model facilitates a comprehensive description of viscoelastic evolution from the pre-gel to the post-gel states. It is validated by carrying out experiments on a model colloidal gel-forming system and by considering other diverse gel-forming systems studied in the literature. After calibrating the parameters of the phenomenological model, it is found to be in excellent agreement with experimental data. Such a well-calibrated phenomenological model can be used to determine any linear viscoelastic response over a wide range of frequencies and extents of cross-linking encompassing the entire sol–gel transition.

In this work, we study the onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, LAPONITE®, at the critical gel state while undergoing the sol-gel transition. The critical gel state is characterized by a power-law dependence of stress relaxation modulus on time and structurally represents the weakest space spanning percolated fractal network. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasilinear integral model is developed with the time–strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well, leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation. We show that, for a critical gel, if the onset of nonlinearity happens to be the point of failure, the Boltzmann superposition principle very naturally leads to the Basquin law of failure.