Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods
UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).
Fraden et al. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible fd virus) and thick (fd-PEG, fd virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures qualitatively describes the observed phase behavior.
Isotropic, Nematic, Phase Diagram
Fraden et al. and Teramoto et al. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase trasition has also been studied theoretically and computationally. [3-5] For Fraden et al. the motivation to study binary mixtures of hard particles of multiple aspect ratios comes from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules.
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter ratio of the particles is large enough [6 –12].
Fraden et al. have presented here measurements of phase behavior of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Previously they were unable to look at the phase diagrams inthe nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory.  Onsager's theory predicts isotropic to nematic phase transitions in suspensionsof hard rods. Here Onsager's theory has been extended to binary mixtures. Phase behavior of varying diameter and length have previously been studied. [7-9,14] But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, mesurements could only be made near the I-N region. It is thought that this may be because of a number of reasons: polydispersity in particle size, high solution viscosity, and/or eak attractions. [2,15,17]
Mixtures of charged fd virus (representing thin rods) and fd virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the fd-PEG-rich nematic phase floats above the fd-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the fd-rich isotropic phase is greater than that of the fd-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.
When the evolution of experimental phase behavior is compared to d for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible rod is equivalent to the excluded volume of a shorter but thicker rigid rod . Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion  does qualitatively describes the experimental findings. Our experimental and theoretical results show that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.
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