Unify fractional Maxwell and fractional Kelvin–Voigt descriptions across the CMC sol–gel transition

Determine whether a single constitutive model can unify the fractional Maxwell description used for the sol-phase linear viscoelastic spectrum and the fractional Kelvin–Voigt description used for the gel-phase linear viscoelastic spectrum of acid-induced carboxymethylcellulose suspensions, so as to capture the viscoelastic spectrum across the sol–gel transition under time–temperature superposition conditions.

Background

The paper establishes that in the sol phase, acid-induced carboxymethylcellulose (CMC) suspensions exhibit a power-law linear viscoelastic response well described by a fractional Maxwell model with exponents (κ≈0.39, β≈0.72), and that in the gel phase their response is captured by a fractional Kelvin–Voigt model with exponent α≈0.40. Both phases obey time–temperature superposition, though with different scaling parameters and activation energies.

Because the high-frequency exponents κ and α are numerically similar and the spectra in both phases collapse onto master curves, the authors highlight the possibility of a single framework spanning the sol–gel transition. However, they explicitly state that it remains unclear whether such a unified model can capture the full viscoelastic spectrum across the transition, motivating this open question and referencing related progress on cellulose nanocrystal dispersions.