Dual Origin of Viscoelasticity in Polymer-Carbon Black Hydrogels: A Rheometry and Electrical Spectroscopy Study

Abstract

Nanocomposite gels formed by mixing nanoparticles and polymers offer a limitless creative space for the design of functional advanced materials with a broad range of applications in materials and biological sciences. Here, we focus on aqueous dispersions of hydrophobic colloidal soot particles, namely, carbon black (CB) dispersed with a sodium salt of carboxymethylcellulose (CMC), a food additive known as cellulose gum that bears hydrophobic groups, which are liable to bind physically to CB particles. Varying the relative content of CB particles and cellulose gum allows us to explore a rich phase diagram that includes a gel phase observed for a large enough CB content. We investigate this hydrogel using rheometry and electrochemical impedance spectroscopy. CB−CMC hydrogels display two radically different types of mechanical behaviors that are separated by a critical CMC-to-CB mass ratio r c . For r < r c , i.e., for low CMC concentration, the gel is electrically conductive and shows a glassy-like viscoelastic spectrum, pointing to a microstructure composed of a percolated network of CB particles decorated by CMC. In contrast, gels with a CMC concentration larger than r c are nonconductive, indicating that the CB particles are dispersed in the cellulose gum matrix as isolated clusters, and act as physical cross-linkers of the CMC network, hence providing mechanical rigidity but limited conductivity enhancement to the composite. Moreover, in the r > r c concentration range, CB−CMC gels display a power-law viscoelastic spectrum that depends strongly on the CMC concentration. These relaxation spectra can be rescaled onto a master curve, which exhibits a power-law scaling in the high-frequency limit, with an exponent that follows Zimm theory, showing that CMC plays a key role in the gel viscoelastic properties for r > r c . Our results offer an extensive experimental characterization of CB−CMC dispersions that will be useful for designing soft nanocomposite gels based on hydrophobic interactions.

Acid-Induced Gelation of Carboxymethylcellulose Solutions

“…Moreover, in the high-frequency limit, G̃ ′ ∼ G̃ ″ ∼ ω̃ 1 / 2 , which is reminiscent of the power-law rheology of critical gels and in remarkable agreement with a Rouse scaling. This high-frequency response also contrasts with the 2/3 scaling exponent reported for CMC (and polyacrylamide) hydrogels cross-linked by colloidal particles. ,, …”

“…This high-frequency response also contrasts with the 2/3 scaling exponent reported for CMC (and polyacrylamide) hydrogels cross-linked by colloidal particles. 24,28,29 To further elucidate the self-assembly of CMC upon acidification, we use small-angle neutron scattering (SANS) and report the scattering intensity spectra I(q) in Figure 3. For viscoelastic liquids, i.e., at pH > 3, the signal-to-noise ratio is low, and I(q) decays roughly as q −2 .…”

“…Moreover, in the gel state, the loss factor always displays a power-law regime at low frequency, followed by a high-frequency plateau [Figure (a)]. This prompts us to fit the viscoelastic spectra for pH < pH c by a compact mechanical model, namely, a fractional Kelvin−Voigt (FKV) model, which is sketched as an inset in Figure (b). It consists of a spring G 0 in parallel with a spring-potor Scott Blairelement , characterized by a dimensionless exponent α and a quasi-property double-struckV (with dimension Pa·s α ).…”

Non-Maxwellian viscoelastic stress relaxations in soft matter

“…150,152 In this sense, the fractional Maxwell gel is an exact mechanical analog to the Cole–Cole model 186 which has been historically used in modeling anomalous dielectric relaxation in complex materials. 151,154,158,187…”

A review of the shear rheology of carbon black suspensions

“…The similarity of the SAOS curves across the wide range of frequencies implies that there is structural similarity between carbon black gels prepared with different shear histories and different carbon black loadings. Legrand et al [19] recently showed that such similarity is violated upon addition of adsorbing polymer to the suspending medium or when the carbon black in the suspension is concentrated such that it forms a paste which incorporates capillary interfaces homogeneously distributed throughout its volume. SAOS is conducted in the linear viscoelastic region (LVR) where the microstructure remains unaltered by deformation.…”