Gelation phase diagrams of colloidal rod systems measured over a large composition space

Abstract

Rheological modifiers tune product rheology with a small amount of material. To effectively use rheological modifiers, characterizing the rheology of the system at different compositions is crucial. Two colloidal rod system, hydrogenated castor oil and polyamide, are characterized in a formulation that includes a surfactant (linear alkylbenzene sulfonate) and a depletant (polyethylene oxide). We characterize both rod systems using multiple particle tracking microrheology (MPT) and bulk rheology and build phase diagrams over a large component composition space. In MPT, fluorescent particles are embedded in the sample and their Brownian motion is measured and related to rheological properties. From MPT, we determine that in both systems: (1) microstructure is not changed with increasing colloid concentration, (2) materials undergo a sol-gel transition as depletant concentration increases and (3) the microstructure changes but does not undergo a phase transition as surfactant concentration increases in the absence of depletant. When comparing MPT and bulk rheology results different trends are measured. Using bulk rheology we observe: (1) elasticity of both systems increase as colloid concentration increases and (2) the storage modulus does not change when PEO or LAS concentration is increased. The differences measured with MPT and bulk rheology are likely due to differences in sensitivity and measurement method. This work shows the utility of using both techniques together to fully characterize rheological properties over a large composition space. These gelation phase diagrams will provide a guide to determine the composition needed for desired rheological properties and eliminate trial-and-error experiments during product formulation.

Fig. 1. Microrheological measurements of HCO and PA with increasing colloid concentration. The logarithmic slope of the MSD, α, is constant with increasing colloid concentration from 0–0.8 wt%, indicating that the system remains in the sol phase (α ≈ 1).

Fig. 2. Microrheological measurements of (a) HCO and (b) PA with increasing PEO concentration, which increases depletion interactions. The blue dashed line indicates the critical relaxation exponent, n, for LAS : colloid ≤ 16. The black dashed line indicates the value of n for LAS : colloid > 16. The shaded area is the sol–gel transition region. In all measurements the LAS concentration is held constant at 12.8 wt%. The logarithmic slope of the MSD, α, decreases and passes through the sol–gel transition region for all colloidal gel systems as depletion interactions are increased, indicating that the system transitions from a sol to a gel.

Fig. 3. Microrheological measurements of (a) HCO and (b) PA with increasing LAS concentration. These samples do not contain depletant (PEO concentration is 0 c/c*). The logarithmic slope of the MSD, α, increases with increasing LAS concentration and remains above the sol–gel transition region for all concentrations measured. This indicates that the system microstructure does change with a change in LAS concentration but the material remains in the sol phase for all concentrations.

Fig. 4. MPT phase diagrams for (a) HCO and (b) PA. The three axes are the concentration of each component and the color of the markers are the value of α. Warm colors are low α values where probe particle movement is restricted. Cool colors are high α values where probe particle movement is less restricted and, in some cases, freely diffusing.

Fig. 5. Bi-color MPT phase diagrams for (a) HCO and (b) PA. A surface is added to separate the phase diagrams into two regimes: LAS : colloid ≤ 16 and LAS : colloid > 16. The colors are the state of the material with red indicating the gel phase and blue indicating the sol phase.

Fig. 6. Bulk rheological measurements for varying concentrations of (a) HCO and (b) PA colloidal rod systems. The three axes are the concentration of each component and the color of the data indicates the value of the storage modulus, G′. Warm colors are the maximum measured storage moduli, which indicates higher elasticity of the material. Cool colors represent minimum storage moduli, which indicates low to no elasticity of the material.

Fig. 7. Normalized bulk rheology phase diagrams for (a) HCO and (b) PA. The storage modulus is normalized using where G′* is the maximum storage modulus. Warm colors are higher values and cool colors are lower values.