Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

No abstract

We demonstrate the fabrication of good quality surface alignment layers on glass by Direct Laser Writing method using a 2-photon polymerisation technique. We use commercially available photosensitive resins to print alignment layers by scanning the focal point of a femtosecond laser near the resin-glass interface. This results in down to ~ 100 nm thin alignment layers that provide good planar anchoring of 5CB and MLC13300, with the easy axis of alignment along the scanning direction. The azimuthal anchoring strength is ~ 5 × 10 −6 J/m 2 and is an order of magnitude weaker compared to commercial rubbed polyimide alignment layer. The threshold voltage for Fréedericksz transition in a 90° twisted nematic cell is slightly increased compared to conventional rubbed polyimide for printed alignment layers. The turn-on switching time is longer for printed layers compared to polyimide alignment layers, whereas the turn-off time is shorter for printed alignment layers. The advantage of this new method is in its flexibility, as we demonstrate printing of complex surface alignment patterns with alignment layer thickness below 100 nm.

No abstract

The key reason behind the richness of different structures and patterns displayed in nature is the universal mechanism of symmetry breaking. It shapes configurations at all length scales encountered in universe. Structures reached via symmetry breaking transitions are commonly described in terms of order parameter fields. One of the simplest systems where symmetry breaking concepts have already been explored in detail, are various liquid crystal (LC) phases. The reason behind this is rich variety of structures exhibited by LCs and their convenient experimental accessibility. Consequently, a wide spectrum of different theoretical tools have been developed in LCs. In this contribution the orientational ordering of housing block in San Francisco, which we choose as a typical large-city representative, was studied. Following nematic LC analogy we determine the local degree of ordering. The structural pattern of the city displays a domain-type pattern. The average degree of ordering within a domain strongly correlates with crime rate within it. Therefore, the results confirm an intuitive expectation that structures define properties. This model can be used as a helpful tool in education as it provides a way of understanding complex topics with the help of well-known every day phenomena. Key words: education, liquid crystal analogy, order parameter, city structure, crime rate, soft mater education.