# Difference between revisions of "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$^{\circ}.$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 and sterically stabilizes the rods while at high temperatures the polymer forms tight hydrophobic coils. The rods then become attractive. The electrostatic forces are controlled independently. At low salt concentrations, the Debye screening length is large as is the electrostatic repulsion between particles. At high salt concentrations, the screening length becomes very small, and the electrostatic repulsion weakens.

Thus, increasing the temperature will make the particles attractive, and the sample will go through the sol-gel transition. Increasing the salt concentration makes the particles less repulsive and should make a gel form more easily (at lower temperatures), which the researchers observed.

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 mixed istropic-nematic phase widens (see figure 1). Huang et. al. do not observe the widening of the isotropic-nematic temperature range. Rather, the solutions form gels at temperatures below the expected widening temperature.

Figure 1. A phase diagram of both theory and experiments. The gel transition is observed in practice, but was not predicted by theory. The gel point is at a lower temperature than the widening of the mixed isotropic-nematic phase. Figure 2 from [1]

The simplest way that the researchers observe the formation of a gel is simply by looking at their sample. Before gelation, the samples are viscous fluids. After gelation, the scientists tilt their vials and do not see the substance flow. The gelation is reversible by lowering the temperature. Huang et. al. quantify their observations of the sol-gel transition using dynamic light scattering and rheometry.

## 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 researchers 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. The phase of the material depends on temperature, particle concentration, and ionic strength. Phase diagrams are an efficient method of viewing multiple relationships between the phases and the parameters they depend on. Figure 1 shows a phase diagram for one salt concentration.

Open Questions:

In the conclusion of their paper, the authors restate their finding that the gel phase occurred 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)." I wonder if the gel formed from a nematic solution has different characteristics than a gel formed from an isotropic solution. What does the structure of a gelled network of rod-like particles look like?