6.7 Geometric Activity
137
Fig. 6.28 (a) Deformation of a flat sheet near the boundary (shown by the white dashed line) between
the isotropic (top) and nematic (bottom) phases. Depressions and bulges are shown by dark and
light colors, respectively (Zakharov and Pismen, 2017a). (b) Scheme showing the establishment of
a nematic texture in the presence of a non-mesogenic dopant. (c) Deformation of a circular patch.
The color scale shows the nematic order parameter (Zakharov and Pismen, 2017b)
Patterns and shapes of chemically modified nematic elastomers can also be built
up starting from a monomer mixture. No prepatterning is needed then; instead, a
dopant is added at a chosen location, as sketched in Fig. 6.28b, and the nematic
pattern is established spontaneously in accordance with boundary conditions. If
equilibrium separation of isotropic and nematic phases is allowed to be attained,
the dopant concentrates in a compact isotropic domain with a boundary of minimal
length. Irrespective of the sign of the gradient interaction parameter, the nematic
director should rotate by 2π around a closed boundary of the isotropic domain. By
symmetry, we expect the isotropic domain to be placed centrally; then, in spite of the
circulation of the director, no defects arise. In the absence of other constraints, the
director will align either radially or circumferentially, depending on this parameter’s
sign. In the latter case, transition into the isotropic state causes the radius of the flat
disk to extend and its circumference to shrink, whence its nematic domain will bend
into a cone upon actuation. More interesting shapes arise in the opposite case of
radial alignment. A shrinking radius and extending circumference generate one of
these alternative forms in Fig. 6.28c, where the number of “petals” grows with the
extension ratio.
Similar actuation of curved surfaces affects the number of defects. The nematic
alignment field on a cylinder would commonly be smooth, but a point dopant source
at the boundary induces circulation of the nematic director by π around the isotropic
domain. The total circulation caused by two such sources at both ends is compensated
by two defects with the charge −1/2. The defects are placed axially on the side
opposite to the sources in a long cylinder (Fig. 6.29a), but are shifted to a middle
location with circumferential separation when the cylinder is squat, as in Fig. 6.29b.
The sign reversal of the gradient interaction coefficient between the pictures on the
left and on the right just causes the entire distribution to rotate by π/2, but the
shapes are, of course, very different, with radial bulging and shrinking interchanged.
Local deformation at defects is not resolved at the scale of the picture and would be
suppressed if the layer thickness exceeded the size of the defect core. Textures with
137
Fig. 6.28 (a) Deformation of a flat sheet near the boundary (shown by the white dashed line) between
the isotropic (top) and nematic (bottom) phases. Depressions and bulges are shown by dark and
light colors, respectively (Zakharov and Pismen, 2017a). (b) Scheme showing the establishment of
a nematic texture in the presence of a non-mesogenic dopant. (c) Deformation of a circular patch.
The color scale shows the nematic order parameter (Zakharov and Pismen, 2017b)
Patterns and shapes of chemically modified nematic elastomers can also be built
up starting from a monomer mixture. No prepatterning is needed then; instead, a
dopant is added at a chosen location, as sketched in Fig. 6.28b, and the nematic
pattern is established spontaneously in accordance with boundary conditions. If
equilibrium separation of isotropic and nematic phases is allowed to be attained,
the dopant concentrates in a compact isotropic domain with a boundary of minimal
length. Irrespective of the sign of the gradient interaction parameter, the nematic
director should rotate by 2π around a closed boundary of the isotropic domain. By
symmetry, we expect the isotropic domain to be placed centrally; then, in spite of the
circulation of the director, no defects arise. In the absence of other constraints, the
director will align either radially or circumferentially, depending on this parameter’s
sign. In the latter case, transition into the isotropic state causes the radius of the flat
disk to extend and its circumference to shrink, whence its nematic domain will bend
into a cone upon actuation. More interesting shapes arise in the opposite case of
radial alignment. A shrinking radius and extending circumference generate one of
these alternative forms in Fig. 6.28c, where the number of “petals” grows with the
extension ratio.
Similar actuation of curved surfaces affects the number of defects. The nematic
alignment field on a cylinder would commonly be smooth, but a point dopant source
at the boundary induces circulation of the nematic director by π around the isotropic
domain. The total circulation caused by two such sources at both ends is compensated
by two defects with the charge −1/2. The defects are placed axially on the side
opposite to the sources in a long cylinder (Fig. 6.29a), but are shifted to a middle
location with circumferential separation when the cylinder is squat, as in Fig. 6.29b.
The sign reversal of the gradient interaction coefficient between the pictures on the
left and on the right just causes the entire distribution to rotate by π/2, but the
shapes are, of course, very different, with radial bulging and shrinking interchanged.
Local deformation at defects is not resolved at the scale of the picture and would be
suppressed if the layer thickness exceeded the size of the defect core. Textures with