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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.
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 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 system undergoing sol-gel transition passes through a unique point, known as the critical gel state, where it forms the weakest space spanning percolated network. We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear (LAOS) rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition, and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable K-BKZ constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. The proposed model with slight adjustment of the damping function, inferred using a spectral method, compares well with experimental data at all frequencies.
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