Ribbon polymers in poor solvents: layering transitions in annular and tubular condensates

We study the structures of a ribbon or ladder polymer immersed in poor solvents. The anisotropic bending rigidity coupled with the surface tension leads ribbon polymers to spontaneous formation of highly anisotropic condensates in poor solvents. Unlike ordinary flexible polymers these condensates undergo a number of distinct layering transitions as a function of chain length or solvent quality, and the size of condensates becomes non-monotonic function of chain length. We show that the fluctuations of the condensates are in general small and these condensates are stable. Recently considerable attention has been devoted to the physics of semiflexible polymers, i.e., chains which have significant bending stiffness. These kinds of polymers exhibit interesting physics in the form of liquid crystalline phases and are of great importance in biology and biophysics. For example, DNA is the most well-known semiflexible polymer. Much of the interest has focused on semiflexible chains with isotropic bending elasticity [1–7]. Macroscopically this corresponds to modeling the chain as a cylinder with a circular cross section. In many cases, however, the cross section is highly anisotropic [8–12]. The anisotropic polymer can be modeled as a ribbon, of length L, width w, and thickness t assuming L ≫ w > t (fig.1) with anisotropic bending elasticity. Indeed, if the ribbon is composed of an isotropic material, the ratio of the elastic constants for bend in the easy and hard directions is ǫe/ǫh = (t/w) 2 [13] . This strong dependence on the ratio of t/w implies that the ribbon polymer shows a very anisotropic elastic response. On the chemical scale, the chains do not normally consist of an isotropic material, and details of chemical bonding are important for bend, thus, even higher ratios of ǫe/ǫh are possible. Some of the solution properties, in particular the liquidcrystalline behavior, have been studied theoretically [10]. Here we study the structure of a single ribbon polymer immersed in a poor solvent. Assuming the system is well beW t