2. Liquid Crystal Elastomers for Biomedical Applications

The Poisson’s ratio (ν) of a material is defined as the negative ratio of the transverse strain to the axial strain in the direction of loading. For many materials, this value is positive and reflects a need to conserve volume. Materials with a negative Poisson’s ratio display the unexpected property of lateral expansion when stretched, rather like a Hoberman^® sphere, with an equal and opposing densification when compressed ^[4][5]. FigureFigure 6 1 presents a schematic of the behaviour of auxetic and non-auxetic materials.

Figure 16. Schematic diagram of positive and negative Poisson’s ratio deformation. (a) Non-auxetic behaviour in which an initially undeformed material (dashed outline) undergoes longitudinal extension and lateral contraction (solid line) for a tensile load applied in the longitudinal (x) direction. (b) Auxetic behaviour in which an initially undeformed material (dashed outline) undergoes longitudinal and lateral extension (solid line) for a tensile load applied in the longitudinal (x) direction.

Materials with a negative Poisson’s ratio are referred to as auxetic materials. The vast majority of auxetic materials are cellular auxetics. Cellular auxetics are porous materials, where a volume increase results from the reorganisation of the internal cellular structure and a reduction in density. The auxeticity in molecular auxetics, however, arises from changes in their microstructure, perhaps resulting from molecular segments rotating upon deformation ^[6]. In molecular auxetics, only one axis shows a negative Poisson’s ratio, and this is coupled to a large contraction in another axis to maintain constant volume and the original sample density.

Until recently, molecular auxetics were only found in nature, for example, in 69% of cubic metals, α-cristobalite, and numerous examples of the zeolite class of materials ^[7][8][9]. Cellular auxetics are abundant in nature; for example, this behaviour has been reported in cow teat skin ^[10], cat skin ^[11], cancellous bone ^[12], tendons ^[13] and membranes found in the cytoskeleton of red blood cells ^[13][14]. Unlike molecular auxetics, many examples of synthetic cellular auxetics exist, such as the Hoberman^® sphere ^[4], ultra-high molecular weight polyethylene (UHMWPE) ^[15] and paper ^[16].

Recently, studies have identified the benefits of using auxetic materials in skin healing ^[17]. Skin healing is facilitated by the migration of cells to the wound site. Small simple wounds, such as small finger-pricks, rarely need assistance in healing. However, when complex wounds occur, such as burns, or when more widespread tissue regeneration is required, assistance can promote faster healing and minimise scarring. Tissue regeneration can be facilitated if a suitable scaffold is provided, the desired cells replicate more easily and grow along the predefined structure. Polylactic acid-based fibres which can be produced by electrospinning are cellular auxetics ^[17][18]. The auxeticity of these scaffolds are particularly attractive because of their ability to apply an enhanced negative pressure on the wound site.

Auxetic skin sensors have also recently been developed ^[19]. The auxetic nature of these skin sensors is particularly appealing because they display excellent mechanical compliance to dynamic body motions. Human skin displays a negative Poisson’s ratio in some regions—expanding biaxially during bending, exhalation and muscle tension. Often, polymer films are unable to maintain contact with the skin under large body motions due to their positive Poisson’s ratio. The usage of auxetic sensors can therefore maintain conformational contact ^[19].

Recently, a side-chain LCE was the first ever synthetic material to display molecular auxetic behaviour ^[2]. This polyacrylate-based LCE showed that volume was conserved when strained, confirming that the material was a molecular auxetic. The Poisson’s ratio displayed by the material was up to −0.8. The auxetic behaviour was not observed at low strains, but at higher strains (>80%). Once the strains necessary to display auxetic behaviour of the LCE were reached, a coincident negative order parameter was also observed. It is believed that the auxetic response is related to the inherent Mechanical Fréedericksz transition displayed by some LCEs ^[2]. FigureFigure 7 2 shows the change in the thickness (strain in the z-direction, ε_z) of the polyacrylate based auxetic LCE in response to strain in the x-direction, ε_x. Shown also is the change in birefringence as a function of strain, displaying a decrease in retardance as the strain is increased, reaching a minimum at ε_x = 1.14, where what is believed to be a negative order parameter is observed. A further increase in ε_x results in the retardance increasing again. The relationship between the liquid crystal order and the emergence of auxetic behaviour of the LCE is still being explored. The reason as to why some LCEs display the Mechanical Fréedericksz transition whereas others do not is also currently unclear.

Figure 27. (a) z-axis strain, ε_z in response to imposed x-axis strain, ε_x, measured via direct observation of the polyacrylate-based auxetic LCE in the xz plane (green crosses) and through the application of the constant volume condition to strain measurements of the xy plane (orange boxes). Errors are measurement errors (n = 1). (b) Negative order from polarising microscopy. Polarising microscopy textures at different strains. The birefringence colours indicate the retardance initially decreases, becoming zero at ε_x = 1.14, before increasing again. Scale bar, 5 mm. (c) shows the constituents used to synthesise the auxetic LCEs reproduced with permission from Nature from Mistry et al. ^[2].

These auxetic LCEs show exciting potential for biomimetic applications. As previously discussed, the auxeticity of materials used in skin sensors and skin healing scaffolds significantly enhances their performance compared to the non-auxetic counterparts. Molecular auxetics could be used in composites which mimic the stress-strain and auxetic behaviour of human skin ^[19]. Conventional auxetics have an “open” microstructure, which confers reduced mechanical properties ^[9]. In many cases, these “open” microstructures display a tensile strength that is too weak for practical applications due to their microscale porosity; however, these limitations could be circumvented by molecular auxetics due to their “closed” microstructure.

Another potential application is the use of LCEs as artificial blood vessels; the auxeticity would allow the vessels to withstand the high pressure of blood through the vessels, which are less prone to rupture as a result of thinning ^[20].

Furthermore, a range of tissues display auxetic behaviour ^[13][14]. The discovery of the inherent auxeticity of these tissues has a range of implications for tissue engineers in mimicking the properties of these auxetic tissues. The mechanical characteristics of engineered tissue ideally should match or enhance the mechanical properties of healthy, normal host tissues, permitting full functionality, enabling it to fulfil its role in vivo. Cells exist in their natural in vivo environment embedded within an extracellular matrix, which is the natural scaffold of the body produced by the cells within tissues. Therefore, if the target tissue is auxetic, an auxetic scaffold would most closely match the properties of this tissue. The matching of this characteristic would be beneficial in recreating the loading environment that cells would naturally experience. As will be discussed in further detail later in this review, LCEs have already been considered and have shown to be suitable for use as tissue replacements, as their actuation properties make them ideal candidates for use as artificial muscles. Exploiting the auxeticity of some LCEs is, therefore, promising for potential applications in tissue engineering.

This discovery of a molecular auxetic has overcome a long-standing limitation in the auxetics industry and there is, therefore, a lot of potential for these materials not just in biomedicine, but in the wider materials world ^[21][22]. The main challenge lies within understanding and, if necessary, making adaptations to ensure the biocompatibility of the materials.