Abstract
We explore length segregation in binary mixtures of spherocylinders of lengths L1 and L2 which are tangentially confined on a spherical surface of radius R. The orientation of the spherocylinders is constrained along an externally imposed direction field on the sphere which is either along the longitude or the latitude lines of the sphere. In both situations, integer orientational defects at the poles are imposed. Using computer simulations we show that these topological defects induce a complex segregation picture also depending on the length ratio factor γ = L2/L1 and the total packing fraction η of the spherocylinders. When the binary mixture is aligned along the longitude lines of the sphere, shorter rods tend to accumulate at the topological defects of the polar caps whereas longer rods occupy the central equatorial area of the spherical surface. In the reverse case of latitude ordering, a new state can emerge where longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. As a reference situation, we consider a defect-free situation in the flat plane and do not find any length segregation there at similar γ and η; hence, the segregation is purely induced by the imposed topological defects. We also develop an Onsager-like density functional theory which is capable of predicting length segregation in ordered mixtures. At low density, the results of this theory are in good agreement with the simulation data.
Highlights
We explore length segregation in binary mixtures of spherocylinders of lengths L1 and L2 with the same diameter D which are tangentially confined on a spherical surface of radius R
When the alignment is along the longitudinal lines of sphere, see Figure 1(a), shorter rods in the mixture accumulate at the polar caps of sphere around the defects whereas longer rods occupy the equatorial area of the spherical surface
In a reference situation of a flat plane without any defects, there is no length segregation at similar γ and η, proving that the segregation is purely induced by the imposed topological defects
Summary
Another example are hard rod-like particle mixtures which have been recently considered in various situations 3–9 and exhibit bulk segregation 10–12 These are more complex than spheres since they possess an additional orientational degree of freedom. For rod-like particles tangentially confined to a sphere there is a pure curvature effect but there are more complex options by constraining the orientations along an imposed director field. In this paper we explore the impact of imposed topological defects on segregation in binary mixtures of hard rods of different lengths. We confine the particles tangentially on a spherical surface and align their orientation along certain prescribed directions which possess two integer-defects at the poles.
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