Soft Elasticity

Because of their anisotropy, the mechanical response of aligned nematic LCEs varies depending upon the direction of applied stress. When stress is applied along the direction of alignment (parallel to the director, ${\displaystyle {\widehat {n}}}$), the strain responds in a linear fashion, with a slope dictated by the material’s Young’s modulus. This linear stress-strain behavior continues until the material reaches its yield stress, at which point it may neck or strain harden before eventually failing. The shape of the stress-strain curve for LCEs stretched parallel to their aligned direction matches that of most classical rubbers and can be described using treatments such as rubber elasticity.

In contrast, when stress is applied perpendicular to the direction of alignment, the strain behavior exhibits a drastically different response. For an unconstrained LCE, after an initial region where the stress-strain response matches that of classical rubbers, the material exhibits a large plateau where near-constant stress leads to ever-increasing strain. The term “soft elasticity” describes this large plateau region.^[7] After a critical strain is reached in this region, the stress-strain response returns to that of LCEs stretched in a direction parallel to their director.

The theory used to describe soft elasticity first arose to explain experimental observations of the phenomena in unconstrained LCEs that reoriented in the presence of an external electric field.^[8] The theory of soft elasticity states that when an LCE is stretched in a direction perpendicular to its alignment direction, its chains rotate and reorient to align in the direction of applied stress. Assuming that the LCE chains are allowed to freely move in all three dimensions, this reorientation occurs without a change in the elastic free energy of the system. This implies that there is no energy barrier to the rotation of the LCE chains, meaning that zero-stress would be required to fully reorient them.

Experimentally, a small but non-zero stress is required to induce soft elasticity and achieve this chain rotation. This deviation from the theoretical prediction arises due to the fact that real LCEs are not truly free in all three dimensions, and are instead geometrically restricted by neighboring chains. As a result, some small, finite stress is necessary in experimental systems to induce chain reorientation. Once the chain has fully rotated and is aligned parallel to the direction of applied stress, the subsequent stress-strain response is again described by that of rubber elasticity.

Soft elasticity has also been exploited to develop materials with unique and useful properties. By controlling the local liquid crystal alignment in an LCE, films with spatially varying mechanical anisotropy can be fabricated.^[9] When strained, different regions of these chemically homogeneous films stretch to different extents as a result of the relative orientation of the director to the applied stress. This has the effect of localizing deformation to predetermined regions. This predictable deformation is useful because it allows for the design of soft electronic devices that are globally compliant but locally stiff, ensuring important components do not break when the film is deformed.

Actuation

Upon transitioning from a liquid crystalline phase to an isotropic (orientationally disordered) phase, or vice versa, an LCE sample will spontaneously deform into a different shape. For example, if a nematic LCE transitions to its isotropic state, it will undergo contraction parallel to its director and expansion in the perpendicular plane. Any stimulus that drives the ordered ⇔ disordered phase transition can induce such actuation (or 'activation'). A patterned director field thus allows an LCE sample to morph into a radically different shape upon stimulation, returning to its original shape when the stimulus is removed. Due to its reversibility, large strain, and the potential to prescribe extremely complex shape changes, this shape morphing effect has attracted much interest as a potential tool for creating soft machines such as actuators or robots. As a simple example, consider a thin disk-shaped LCE sheet with a 'concentric-circles' (everywhere azimuthal) in-plane director pattern. Upon heating to the isotropic state, the disk will rise into a cone, which can be used to lift a weight thousands of times the weight of the LCE itself.^[10]