Rheological properties of acid-induced carboxymethylcellulose hydrogels

Cellulose ethers represent a class of water-soluble polymers widely utilized across diverse sectors, spanning from healthcare to the construction industry. This experimental study specifically delves into aqueous suspensions of carboxymethylcellulose (CMC), a polymer that undergoes gel formation in acidic environments due to attractive interactions between hydrophobic patches along its molecular chain. We use rheometry to determine the linear viscoelastic properties of both CMC suspensions and acid-induced gels at various temperatures. Then, applying the time-temperature superposition principle, we construct master curves for the viscoelastic spectra, effectively described by fractional models. The horizontal shift factors exhibit an Arrhenius-like temperature dependence, allowing us to extract activation energies compatible with hydrophobic interactions. Furthermore, we show that acid-induced CMC gels are physical gels that display a reversible yielding transition under external shear. In particular, we discuss the influence of pH on the non-linear viscoelastic response under large-amplitude oscillatory shear. Overall, our results offer a comprehensive description of the linear and non-linear rheological properties of a compelling case of physical hydrogel involving hydrophobic interactions.

💡 Research Summary

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This paper presents a comprehensive rheological investigation of sodium carboxymethylcellulose (NaCMC) aqueous suspensions that form physical hydrogels when the pH is lowered. The authors prepared NaCMC solutions with a molecular weight of approximately 213 kg mol⁻¹ and a degree of substitution (DS) of 0.88 at concentrations ranging from 1 % to 4.5 % w/w. After thorough mixing, the suspensions were acidified using HCl (1 M for most samples, 12 M for the most concentrated ones) to achieve final pH values between 0 and 7.2. Rheological measurements were performed on an ARES‑G2 strain‑controlled rheometer equipped with a sand‑blasted 2° cone‑and‑plate geometry (20 mm radius, 46 µm truncation). Temperature was varied from 5 °C to 40 °C using a Peltier plate, and a standard protocol consisting of a high‑shear pre‑treatment (γ̇ = 50 s⁻¹, 3 min), a 20‑minute recovery under small‑amplitude oscillations (γ₀ = 1 %, ω = 2π rad s⁻¹), and a frequency sweep (0.01–100 rad s⁻¹) was applied to obtain the linear viscoelastic spectra (G′(ω), G″(ω)).

Linear viscoelasticity – liquid state
For a representative liquid sample (3 % w/w CMC, pH ≈ 3.6), both storage and loss moduli display a broad power‑law behavior over three decades of frequency. The data are accurately described by a fractional Maxwell (FM) model consisting of two Scott‑Blair elements in series:

( G^{*}(ω)=\frac{K(iω)^{κ}B(iω)^{β}}{K(iω)^{κ}+B(iω)^{β}} )

where K and B are quasi‑elastic constants and κ (≈ 0.39) and β (≈ 0.72) are dimensionless exponents (κ < β). In the low‑frequency limit (ω ≪ ω₀) the suspension exhibits a critical‑like response, G′ ≈ G″ ∝ ω^{0.7}, markedly different from the ω² and ω scaling expected for a simple polymer solution. This deviation is attributed to transient hydrophobic associations between sparsely substituted cellulose segments, which bring the system close to the gel point.

Time‑temperature superposition (TTS) was applied by normalizing the moduli with η₀ ω₀ and the frequency with ω₀, where

( η₀ = \bigl(K^{β-1}/B^{κ-1}\bigr)^{1/(β-κ)} ) and ( ω₀ = (K/B)^{1/(β-κ)} ).

All spectra from 5 °C to 40 °C collapse onto a single master curve, confirming that temperature changes affect both the characteristic relaxation time (horizontal shift) and the overall elastic scale (vertical shift). The horizontal shift factor ω₀⁻¹ follows an Arrhenius law, ω₀⁻¹ ∝ exp(−Eₐ/k_BT), with an activation energy Eₐ = 81 ± 9 kJ mol⁻¹. This value exceeds typical activation energies for polymer melts (≈ 50 kJ mol⁻¹) and is consistent with the energy required to break hydrophobic contacts. The vertical shift factor η₀ ω₀ increases with temperature, indicating that higher temperatures modestly increase the number of physical cross‑links, possibly due to reduced solvent quality.

Linear viscoelasticity – gel state
When the pH is lowered further (e.g., pH ≈ 1.6) the same concentration yields a solid‑like gel. In this regime G′ becomes nearly frequency‑independent at low ω (≈ 10³ Pa), while G″ follows a ω^{0.5} dependence. The data are fitted with a fractional Kelvin‑Voigt (FKV) model:

( G^{*}(ω)=K + (iωη)^{α} )

with α ≈ 0.5, representing a spring in parallel with a fractional dashpot. This behavior aligns with classical rubber elasticity (G′ ≈ 3k_BT/ξ³) and confirms that the gel network is built from reversible, non‑covalent hydrophobic associations. The same TTS scaling applied to the gel spectra yields a master curve, and the temperature dependence of the elastic scale mirrors that observed in the liquid state.

Non‑linear rheology – yielding transition
Large‑amplitude oscillatory shear (LAOS) experiments were performed by increasing the strain amplitude from 0.1 % to 100 %. As the amplitude grows, tan δ and G″ exhibit a pronounced peak, signalling a yielding transition where the network ruptures under shear. The position of the peak shifts to lower stresses for lower pH, indicating that stronger acidification weakens the network’s resistance to flow. After the peak, G′ partially recovers, demonstrating that the gel is a physical (reversible) network rather than a chemically cross‑linked material. Intracycle analysis (tracking G′ and G″ within a single oscillation) reveals heterogeneous solid‑to‑liquid transformations, supporting a picture of spatially localized failure zones that coexist with intact regions during yielding.

Implications and applications
The study establishes three key points: (1) CMC hydrogels are governed by hydrophobic interactions, which generate reversible physical cross‑links; (2) temperature and pH simultaneously modulate both the dynamics (relaxation time) and the density of these cross‑links, as captured by the Arrhenius activation energy and the vertical shift factor; (3) fractional rheological models (FM for the liquid, FKV for the gel) provide a unified framework to describe linear and non‑linear responses. The extracted activation energy (~81 kJ mol⁻¹) offers a quantitative benchmark for designing CMC‑based formulations where precise control of viscosity and elasticity is required, such as in food thickeners, pharmaceutical suspensions, or construction additives. By tuning pH and temperature, manufacturers can tailor the gel’s yield stress, recovery behavior, and flow properties without resorting to covalent cross‑linkers, enabling environmentally friendly and reversible material systems.