Backflow-mediated domain switching in nematic liquid crystals

We study the dynamics of the nematic liquid crystal kickback effect upon removal of a primary electric field and its amplification by a perpendicular secondary electric field resulting in the formation of domains with a reverse director orientation. Using computational fluid dynamics, we show that the domain formation is a robust phenomenon that takes place also in the complex case of multiple irregular random Freedericksz domains in three dimension as they appear in a realistic experimental situation. We propose domain switching by kickback amplification as a tool for self-insertion of shell-like inhomogeneities into an otherwise perfectly uniform director field configuration.

Figure 1

Kickback in a 2D square cell (in-plane switching) upon removal of the in-plane vertical electric field [30]: subsequent snapshots [(a)–(c)] of the velocity fields (left column), director fields, and director angular velocity fields (schematically represented by levels of gray: darker levels represent faster clockwise rotation). Rigid anchoring in the horizontal direction is assumed at all four edges. The strength of the initial electric field is $E=10$. The units are defined in Sec. 2c. In the kickback phase (a) the director in the central region rotates reversely (counterclockwise in this example) due to the strong reverse backflow, which is generated predominantly by the horizontal boundaries. The region of the reverse rotation is depicted brightest and is encircled by the dashed contour line of the stationary director field. Note the weak reverse director deformation in the center (b), when the kickback transient has almost ceased and the backflow and the director rotation in the center are about to change direction (c).

Figure 2

Kickback in a 2D square cell, amplified by a horizontal field, leading to the formation of a reverse domain followed by its slow shrinking. Subsequent snapshots [(a)–(c)] of the velocity (left column) and director fields are shown. The velocity scales are larger than in Fig. 1 due to the presence of the electric field. $E_1=E_2=35$.

Figure 3

Primary and secondary field strengths, $E_1$ and $E_2$, required for switching.

Figure 4

Color and grayscale legend for the selected director component applies to all subsequent figures. In grayscale, black domains are darker than red domains (cf. Fig. 6).

Figure 5

Coalescence of Freedericksz domains over the course of time. $E_1=200$, mesh size is $300\times 300$. The color and grayscale coding, Fig. 4, represents the vertical component $n_y$ of the director.

Figure 6

Multiple domain switching in two dimensions. $E_1=E_2=200$, mesh size is $300\times 300$, $n_y$ is coded according to Fig. 4. Initially, shortly after the application of the secondary electric field, the backflow is concentrated at the domain walls (a). As a contrast, when the switched domains are slowly shrinking (b), the flow is global.

Figure 7

A cubic monodomain in an electric field along $z$ exhibits three types of domain walls at its boundaries (a). Reverse domains of the switched configuration (the secondary electric field is along $x$) are presented by the enclosing contour surfaces; the flow field is represented by the stream lines (b). $E_1=E_2=70$, mesh size is $80\times 80\times 80$. A 2D cross section shown in Fig. 8 is indicated by the frame (b).

Figure 8

The $xz$ cross section through the center of the cube indicated in Fig. 7: subsequent snapshots [(a)–(c)] of director fields (left) (with $n_z$ coded according to Fig. 4) and velocity fields. Note the screened flow (a).

Figure 9

Coalescence of Freedericksz domains created by a primary electric field $E_1=35$ normal to the cell plane.

Figure 10

(a) Freedericksz domains just before the switching. The director points, e.g., up outside the contour surface and down inside it. The rectangle indicates the 2D cross section shown in Fig. 11. (b) Snapshot of the switched state. The reverse domains lie inside the contour surfaces; $n_z$ is coded according to Fig. 4. Note their anvil-like vertical shape. Velocity streamlines (c) of the switched state in the same moment, showing the localization of the flow to individual domains. $E_1=E_2=35$, mesh size: $300\times 300\times 30$.

Figure 11

The $xz$ cross section indicated by the rectangle in Fig. 10: subsequent snapshots [(a)–(d)] of superimposed director fields (with $n_z$ coded according to Fig. 4) and velocity fields.