# Phase Behavior and Rheology of Attractive Rod Like Particles

## Overview

• [1] Huang, F., Rotstein, R., Fraden, S., Kasza, K., & Flynn, N. Soft Matter. 5, 2766-2771 (2009).
• Keywords: Isotropic, Nematic, Viscoelastic, Sol-Gel Transition, Colloidal Rods, Phase Transition

## Summary

Huang, Rotstein, Fraden, Kasza, and Flynn study an aqueous solution of rod-shaped particles to look for transitions between isotropic, nematic, liquid, and gel states. The transitions are a function of particle concentration, temperature, and salt concentration in the water. For this experiment, Huang et. al. create particles by coating bacteriofage fd with poly(N-isopropylacrylamide) (PNIPAM). The researchers use both rheological measurements and light scattering measurements as well as qualitative observations to characterize an unexpected sol-gel transition.

The bacteriofage fd (a polymer with negative surface charge) is itself approximately rod-shaped. The researchers coat the bacteriofage fd with the polymer PNIPAM to give the particle-particle interactions a temperature dependence. The water solubility of PNIPAM is strongly temperature dependent. Below 32$\,^{\rm C}$ $^{\circ} C$, the polymer is soluable, while above 32 $^{\circ} C$, the polymer becomes hydrophobic. Thus, at low temperatures, the polymer extends from the bacteriofage fd into the water, while at high temperatures, the polymer forms tight coils. The particle interactions include steric stabilization and electrostatic forces. The researchers also varied the ion content of the water to change the particle-particle interactions.

Theory predicts that low particle concentrations yield isotropic solutions, high concentrations yield nematic solutions, and intermediate concentrations yield a mixed isotropic-nematic phase. Theory also predicts that as temperature increases, the temperature range of this istropic-nematic widens (see figure 1). Huang et. al. do not observe the widening of the isotropic-nematic temperature range. Rather, the solutions formed gels at temperatures below the expected widening temperature.

Figure 1. A phase diagram of both theory and experiments. Figure 2 from [1]

The researchers compared two samples: a) a low concentration of rod-like particles (9.6 mg/ml) which is isotropic, and b) a higher concentration of rod-like particles (21 mg/ml) which has nematic structure. Both solutions have an ionic strength of 144mM.

## Soft Matter Details

Experimental Methods:

In the sol-gel experiments described above, the scientists use dynamic light scattering to observe the liquid solutions turning into gels. In the liquid state, the diffusion coefficient is low. As the solution gels, the diffusion coefficient increases. The researchers use dynamic light scattering as an effective means of measuring the temperature at which gelation begins.

The researches also use a rheometer to measure the viscoelastic moduli of the materials. The moduli, G' and G", increase when the sample undergoes a sol-gel transition.

In compiling their data, the scientists find it useful and insightful to scale their data onto a master curve. The advantage of this is that one can "probe viscoelasticity for a much larger frequency range than that experimentally accessible (p. 2770)."

Phase Behavior:

The phases studied in Phase Behavior and Rheology of Attractive Rod-like Particles are isotropic, nematic, liquid, and gel. These phase of the material dependends on temperature, particle concentration, and ion concentration. Phase diagrams are an efficient method of viewing multiple relationships between the phases and the parameters they depend on.

Open Questions/Ongoing Research:

In the conclusion of their paper, the authors restate their finding that the gel state occured at temperatures lower than the broadening of the isotropic-nematic coexistance region, and wonder if this is true for "all attractive rod-like systems (p. 2770)."