The Occurrence of Liquid Crystal Phases in Insects
Liquid crystals appear throughout many areas in everyday modern life- most commonly in the form of a ‘Liquid Crystal Display’ (LCD), which is used for many electronic displays (1) and have become an essential part of everyday life. They are also found throughout the natural world, with the most visually striking example being the iridescent colouring (structural colours (2)) exhibited by many insect species, which plays an important role in the survival of the beetle. This phenomenon has been the subject of scientific research for a number of years – starting with work done by Michelson in the early 20th century (3), and is due to the interaction of polarised light and the structure on their exoskeletons. Knowledge of how beetles interact with light has been used primarily in the design of biomimetic systems, such as miniature optical devices (4) and in the design of tuneable optical diodes which are used in liquid crystal lasers (5).
In order to fully understand why some beetles appear to be iridescent, one must understand the basics of liquid crystals, chirality and how polarised light interacts with liquid crystals, which shall be discussed in this essay, which aims to serve as an introduction to the subject.
At the most basic level, a liquid crystal is a material that forms intermediate phases between a disordered, isotropic liquid and an ordered crystalline solid (6). They can be split into two broad categories: thermotropic, which are formed from geometrically isotropic molecules as a function of temperature and can be further subdivided into calamitic phases (rod-like molecules) and discotic phases (disc-like molecules) (7) and lyotropic, which form in solvents, usually amphiphilic molecules in water (8). For the purposes of this essay, only the calamitic phases of thermotropic liquid crystals will be considered. The main calamitic phases are the nematic and smetic phases, as seen in Figure 1, with the nematic phase being the most common and least ordered phase, with the highest symmetry (8). The nematic phase has no positional order, but does have long range orientational order, i.e. the molecules align with their long axes parallel to the preferred direction of orientation, which is defined by a unit vector, called the director, n(9).
Figure 2: Representation of linearly polarised light travelling through a birefringent crystal. The vertical component is slower and becomes out of phase with the horizontal component. Reproduced from (11).
Liquid crystals exhibit an optical property known as birefringence, which means they have two different refractive indices that are dependent on the polarisation and direction of propagation of the light (10)- although light transmitted along the director experiences a refractive index, regardless of polarisation. The optical axis is defined as the direction along which the liquid crystal appears to be isotropic. The refractive index for light polarised normal to the plane of incidence (along the fast axis) and the director is the ordinary refractive index, no. The refractive index for light polarised parallel to the plane of incidence is the extraordinary index, ne(11). The birefringence is therefore given by:
This birefringence effects how the liquid crystal interacts with linearly polarised light, which can be considered to be composed of a horizontally polarised component and a vertically polarised one, and for any angle of incidence other than 0° or 90°, the incident light will be spilt into two rays, which propagate through the crystal at different velocities (defined by ne and no) (12). The result of this is that, except in special circumstances, the light will be re-emitted as elliptically polarised light, as seen in Figure 2.
An important concept to understand when studying liquid crystals is chirality, which is incredibly common throughout nature and has been a subject of scientific interest since the 19th century and the work of Louis Pasteur, who declared chiral crystals must consist of asymmetric molecules (13). Chirality occurs when two molecules are identical in composition (known as enantiomers) but are non-superimposable mirror images of each other (i.e. there is no mirror symmetry), leading to a significant effect on the properties of the molecules (8).
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Chirality can therefore have a significant impact on liquid crystals and their properties- for the purposes of this essay, the chiral nematic (cholesteric) phase shall be considered. The structure of the chiral nematic phase is shown in Figure 3, which shows that the molecules are twisted relative to each other, so the director must twist throughout the sample, leading to a periodic helicoidal structure (seen in Figure 4), with a pitch p, defined as the distance along the helical axis corresponding to a 360° rotation of the molecules (see Figure 3) (14).
It is this structure that is responsible for the optical properties shown by liquid crystals, in particular it selectively reflects circularly polarised light, which is the main cause of iridescence. Chiral nematic liquid crystals also exhibit birefringence, so when circularly polarised light, which is composed of left and right handed circularly polarised components, interacts with the crystal, one of the components will be fully reflected, whilst the other is transmitted (15)- this phenomenon is known as selective reflection. The reflected component will retain it’s original handedness, and there is no clear relationship between the handedness of the helicoidal structure and the component of circularly polarised light it reflects, i.e. one enantiomer will reflect the left handed polarised light, the other will reflect the right handed light (8). This selective reflection means that a chiral nematic liquid crystal will only reflect a maximum of 50% of the incident light.
The periodic nature of this helicoidal structure means that the chiral nematic phase with a pitch comparable to the wavelength of visible light will reflect light in such a way that is analogous to Bragg Reflection (4) and there are two scenarios to consider: normal and oblique incidence. For normal incidence the reflection has a maximum at:
Where n is the average refractive index, given by
. The width of this reflection peak is given by:
is the birefringence. Any incident light that has a wavelength in the range given by , will be transmitted (14). For oblique incidence, where the light enters at some angle
, equation  is modified to:
Now the above concepts have been introduced and explained, one can see how they are employed throughout the natural world, and are responsible for the iridescence seen in some beetle species. This iridescence is understood to be the result of selective reflection of circularly polarised light, usually the left-handed component (but can reflect the right-handed component, depending on the incident angle and wavelength of the light (16)), due to the formation of birefringent chitin layers, which are placed in helicoidal layers (17) in such a fashion that resembles a chiral nematic liquid crystal layer (18), as seen in Figure 5, and will often have a pitch gradient (15). The reflected colour produced is dependent on
from , some species will appear to be more of metallic silver, because
covers a wider range of wavelengths (19).
When examined under a bright field microscope, the exoskeleton of an iridescent beetle for example the Chrysina gloriosa appears to be composed of primarily of hexagonal cells, along with some pentagonal and heptagonal cells (4), as seen in Figure 6. Sharma et al (2009) examined this pattern using a pattern recognition method known as Voronoi analysis, which showed that the majority of cells were hexagonal, the concentration of pentagonal cells was highest at the highly curved head, and heptagons appear to be randomly distributed- the formation of such irregularities is due to the nature of fitting such a structure onto a curved body- hexagons are not always the most energetically efficient formation (20).
This structure is termed the ‘Bouligand Structure’ (21), as Bouligand carried out extensive work, studying and comparing these structures to a chiral nematic liquid crystal structure (22).
As discussed previously, the helicoidal structure reflects light in a Bragg-like manner, in the structure of Chrysina gloriosa, this reflection appears yellow at the centre of the cell and green elsewhere (4) (as seen in Figure 6)- it was noted that increasing the range of incident angles (i.e. decreasing
, increased the size of the yellow core. This implies that cos
will increase, so according to Equation , a longer wavelength will satisfy the Bragg condition, and the peak reflection wavelength will increase (4). For Chrysina gloriosa, at normal incidence, a range of wavelengths from 500-600nm are reflected, with reflection peaks 530nm (corresponding to green) and 580nm (corresponding to yellow) (15). This broad reflection is due to the continuous pitch gradient and irregularities on the wax layer (outermost skin layer).
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One particularly interesting example of an iridescent beetles are the Plusiotis genus, which were extensively studied by Jewell et al (23), in particularly the Plusiotis boucardi, which scatters the reflected light over a much larger range of angles than other species of the same genus (23). When examined using bright field microscopy, the exoskeleton of the Plusiotis boucardi, appears to be very similar to the Chrysina gloriosa, composed of hexagonal cells with a green background and a bright yellow centre, however, unlike Chrysina gloriosa, the edges of this yellow centre appear to be tinged red (23), as seen in Figure 8.
Figure 8: Bright field microscopy image of the exoskeleton of Plusiotis boucardi. A similar hexagonal structure to Chrysina gloriosa can be seen, with a green background and borders, and a bright yellow centre, with red edges. Reproduced from (23). (Scale of 10
Figure 9: Reflection spectra collected from Plusiotis boucardi. The 3 reflection peaks at 519nm, 588nm and 620nm are visible. Reproduced from (23).
It was observed that the green light was most strongly reflected from the borders of the cells and the centres, red/orange light was reflected from a precise spot at the centre of the cell, which coincides with the green spot, resulting in the observed yellow centre (23). Reflection spectra of the light reflected from Plusiotis boucardi, were taken, revealing 3 main reflection peaks, one at 519nm, corresponding to green light, one at 588nm, corresponding to orange, and one at 620nm, corresponding to red (23) (see Figure 9). The peaks at 519 and 620nm are expected, but the peak at 588nm is unusual, this indicates that there are two distinct helicoidal structures with different pitches present, which is confirmed by transmission electron microscopy images, which show a cuticular wax layer and a thick melanin layer, with the regions between these layers corresponding to the hexagonal structure discussed above, and the 588nm peak must be the result of interference between these two regions (23).
There are many reasons that some beetle species exhibit iridescence- the most obvious one being camouflage, as most of these beetles reflect brilliant green colours, which enable them to blend into their surroundings (24). However, it can act as a signal either as a warning to predators – some tiger beetles appear to mimic the colouring of the poisonous blister beetle (25) or as a sexual signal, for example, leaf beetles show sexually dimorphic iridescent colouring, which indicates it must play a role in sexual selection (26). However, it is still somewhat unclear how other insect and animal species perceive polarised light and whether they are able to distinguish between linearly and circularly polarised light, so consequently this is currently an topic of much research among scientists (27; 28). These structural colours are also thought to play a role in the thermal regulation of an insect’s body, for instance, species of tiger beetles that are found on white beaches, appear to be white, as they have evolved to selectively reflect a broad range of wavelengths (white light), in order to absorb less heat (29).
Overall it is clear, that in order to understand the iridescent appearance of certain beetle species, an understanding of many areas of physics is required, which have been explored in this essay. Being able to replicate these structural colours is a current area of great interest, as it would be incredibly beneficial to the development of optical devices, including such devices which mimic the optical effects of scarabeid beetles (30), allowing a great deal of control over the materials reflectivity, or even in anti-counterfeiting measures, by creating unique identifiers on bank notes (31). There is still a great deal of work to be done in this area, in particular understanding how chitin is formed in some iridescent species (32) and more detailed information of how polarised light interacts with patterns on a micro and nanoscale (33).
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