Dynamics of elongation of nematic tactoids in an electric field.

Nematic tactoids are spindle-shaped droplets of a nematic phase nucleated in the co-existing isotropic phase. According to equilibrium theory, their internal structure and shape are controlled by a balance between the elastic deformation of the director field, induced by the preferred anchoring of that director field to the interface, and the interfacial free energy. Recent experiments on tactoids of chitin nanocrystals dispersed in water show that electrical fields can very strongly elongate tactoids, at least if the tactoids are sufficiently large in volume. However, this observation contradicts the predictions of equilibrium theory as well as findings from Monte Carlo simulations that do not show this kind of extreme elongation to take place at all. To explain this, we put forward a relaxational model based on the Oseen-Frank free energy of elastic deformation of a director field coupled to an anisotropic surface free energy. In our model, we use two reaction coordinates to describe the director field and the extent of elongation of the droplets and evaluate the evolution of both as a function of time following the switching on of an electric field. Depending on the relative magnitude of the fundamental relaxation rates associated with the two reaction coordinates, we find that the aspect ratio of the drops may develop a large and very long-lived overshoot before eventually relaxing to the much smaller equilibrium value. In that case, the response of the curvature of the director field lags behind, explaining the experimental observations. Our theory describes the experimental data reasonably well.

Relaxational dynamics of the T-number conversion of virus capsids.

We extend a recently proposed kinetic theory of virus capsid assembly based on Model A kinetics and study the dynamics of the interconversion of virus capsids of different sizes triggered by a quench, that is, by sudden changes in the solution conditions. The work is inspired by in vitro experiments on functionalized coat proteins of the plant virus cowpea chlorotic mottle virus, which undergo a reversible transition between two different shell sizes (T = 1 and T = 3) upon changing the acidity and salinity of the solution. We find that the relaxation dynamics are governed by two time scales that, in almost all cases, can be identified as two distinct processes. Initially, the monomers and one of the two types of capsids respond to the quench. Subsequently, the monomer concentration remains essentially constant, and the conversion between the two capsid species completes. In the intermediate stages, a long-lived metastable steady state may present itself, where the thermodynamically less stable species predominate. We conclude that a Model A based relaxational model can reasonably describe the early and intermediate stages of the conversion experiments. However, it fails to provide a good representation of the time evolution of the state of assembly of the coat proteins in the very late stages of equilibration when one of the two species disappears from the solution. It appears that explicitly incorporating the nucleation barriers to assembly and disassembly is crucial for an accurate description of the experimental findings, at least under conditions where these barriers are sufficiently large.

Effect of electric fields on the director field and shape of nematic tactoids.

Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the coexisting isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide, and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the coexisting isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust to optimize the sum of the elastic, surface, and Coulomb energies of the system. By means of a combination of a scaling analysis and a numerical study, we investigate the elongation and director field's behavior of the tactoids as a function of their size, the strength of the electric field, the surface tension, anchoring strength, the elastic constants, and the electric susceptibility anisotropy. We find that tactoids cannot elongate significantly due to an external electric field, unless the director field is bipolar or quasibipolar and somehow frozen in the field-free configuration. Presuming that this is the case, we find reasonable agreement with experimental data.