Tactoids are droplets of a nematic phase that under suitable conditions form in dispersions of elongated colloidal particles. We theoretically study the shape and the director-field configuration of such droplets for the case where a planar anchoring of the director field to the interface is favored. A minimum of four regimes can be identified in which the droplets have a different structure. Large droplets tend to be nearly spherical with a director field that is bipolar if the surface tension is strongly anisotropic and homogeneous if this is not so. Small droplets can become very elongated and spindlelike if the surface tension is sufficiently anisotropic. Depending on the anchoring strength, the director field is then either homogeneous or bipolar. We find that the more elongated the tactoid, the more strongly it resists the crossing over from a homogeneous to a bipolar structure. This should have implications for the nucleation rate of the nematic phase. Our calculations qualitatively describe the size dependence of the aspect ratio of tactoids found in recent experiments.

We present a theory of the dependence on sequence of the three-dimensional size of large single-stranded (ss) RNA molecules. The work is motivated by the fact that the genomes of many viruses are large ssRNA molecules-often several thousand nucleotides long-and that these RNAs are spontaneously packaged into small rigid protein shells. We argue that there has been evolutionary pressure for the genome to have overall spatial properties-including an appropriate radius of gyration, R g-that facilitate this assembly process. For an arbitrary RNA sequence, we introduce the (thermal) average maximum ladder distance (͗MLD͘) and use it as a measure of the ''extendedness'' of the RNA secondary structure. The ͗MLD͘ values of viral ssRNAs that package into capsids of fixed size are shown to be consistently smaller than those for randomly permuted sequences of the same length and base composition, and also smaller than those of natural ssRNAs that are not under evolutionary pressure to have a compact native form. By mapping these secondary structures onto a linear polymer model and by using ͗MLD͘ as a measure of effective contour length, we predict the R g values of viral ssRNAs are smaller than those of nonviral sequences. More generally, we predict the average ͗MLD͘ values of large nonviral ssRNAs scale as N 0.67؎0.01 , where N is the number of nucleotides, and that their R g values vary as ͗MLD͘ 0.5 in an ideal solvent, and hence as N 0.34 . An alternative analysis, which explicitly includes all branches, is introduced and shown to yield consistent results.branched polymer ͉ ladder distance ͉ radius of gyration ͉ secondary structure ͉ viral RNA

We theoretically investigate the director field inside spindle-shaped nematic droplets, known as tactoids. Tactoids typically form in dispersions of rod-like colloidal particles. By optimising the bulk elastic and surface energies, we find that the director field crosses over smoothly from a homogeneous to a bipolar configuration with increasing droplet size, in a process that we postulate to involve two virtual point defects that move in from infinity towards the poles on the surface of the droplet. Our calculations show that these hypothesised virtual defects become true surface point defects or boojums only in the limit of infinite droplet volume, and that the more elongated the droplets are, the larger their volume has to be before a uniform director field distorts so as to become discernibly bipolar. The theory agrees well with available experimental data on the size dependence of the aspect ratio of tactoids.