Director defects in a mixture of a block copolymer and a nematic

When colloidal particles are suspended in a nematic solvent, local director disturbances can occur. As an example, spherical particles, like water droplets or gas bubbles injected into a nematic liquid crystal host, have already been investigated intensively (Stark, 2001). In general, the director field in the surrounding of the bounding surface depends on the relative strength of elastic forces, the strength of the interfacial

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x y PA

Figure 1.6: Typical snapshot of the director defects in a liquid crystalline block copolymer mixture of concentrationc= 1.5 %, at a temperature of T = 25^◦C. The sample is mounted between crossed polarizers and illuminated with monochromatic light. Polarizer (P) and analyzer (A) are oriented at an angle of φ= 45^◦ with respect to the main director that is preferably aligned along thex-axis.

interaction and an optionally applied external electric or magnetic field (Kralj &

Žumer, 1992).

There are two basic possibilities of the director anchoring at the surface of the colloid. On the one side, the colloid might induce a normal anchoring, where the director is aligned perpendicular to its surface. When such a colloid is embedded into a uniformly aligned nematic host, depending on the size of the colloid, a dipolar director configuration with a hyperbolic hedgehog or a quadrupolar Saturn-ring configuration can be observed (Völtz et al., 2006). On the other side, also planar anchoring can be induced by modifying the surface of the particle, for example by adding polyvinyl alcohol to the water phase of droplets (Poulin & Weitz, 1998). If such a colloid is embedded in a homogeneously aligned nematic host, the director of the liquid crystal will continuously adapt tangential to the surface except for two surface defects.

The aggregation of mesogenic side-chain block copolymers into big clusters is an alternative method to induce such a colloid-like behavior in a nematic host. New mixtures of the block copolymer samples described above were generated by performing the polymer analogous reaction from the polystyrene-block-poly(4-hydroxystyrene)-block-polystyrene backbone to a cyanobiphenyl-functionalized block copolymer once again (details on the synthesis can be found in section 2.2). Due to the new synthesis,

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T=34.2°C T=33.6°C T=34.4°C T=34.3°C

T=34.2°C T=33.6°C

Figure 1.7: Typical snapshots (sample between crossed polarizers) of the formation of director defects when cooling with a relatively low speed ofdT /dt=−0.05K/min.

The nematic-isotropic transition takes place atTNI≈35^◦C. Above TNI, the isotropic phase between crossed polarizers yields black images. Further cooling to room temperature leads to structures as illustrated in Fig. 1.6.

differences in the degree of conversion and the solubility of the polymer are possible compared to the mixtures described so far. After the standard filling procedure of the test cells (see section 2.1 for further details), optical polarizing microscopy uncovered regular patterns instead of a completely uniform state for the sample withc= 1.5 % of the new synthesized block copolymer.

Figure 1.6 shows a typical snapshot of such a cell (d≈25µm), mounted between crossed polarizers (φ= 45^◦) and illuminated with monochromatic light. While the homogeneous gray background illustrates a planar alignment of the director parallel to thex-axis, as induced by the preparation of the cell, well distributed structures of an oval to kidney-like shape indicate locally strong disturbances of the director field, which might be caused by big aggregates of nonsoluble block copolymer. Most of the structures have a symmetry axis along they-direction that is perpendicular to the main orientation of the undisturbed director.

Dependency on thermal treatment

A variation of the thermal treatment revealed a strong influence on the formation of the structures. Figure 1.7 demonstrates the occurrence of microphase separation during a cooling process from the isotropic to the nematic range at a moderate cooling

U=0.0V U=0.8V U=0.9V U=2.5V

U=5.0V U=10V

U=0.0V

¢t=5h

Figure 1.8: Snapshots (sample between crossed polarizers) of the director defects during increasing voltageU. Note that the critical Fréedericksz voltage for pure 5CB isU_F= 0.73V. Even several hours after switching off the voltage, the initial structure of the defect does not reappear.

rate ofdT /dt=−0.05K/min. If the cooling speed was chosen too fast, the formation of regular shaped patterns could not be observed. Instead, irregular shaped defects were visible when reaching ambient temperature.

Such a dependency on the cooling rate can be compared to experiments performed by Rothet al.(2010), where the gelation of a suspension of poly(methyl mathacrylate) colloids in 5CB was investigated during the isotropic-nematic phase transition. With decreasing cooling rate, Roth et al.(2010) observed an increase of size of nematic droplets between a network that was formed by the colloidal particles. This is similar to the findings in our block copolymer mixtures, where a low cooling rate also leads to the formation of bigger domains of homogeneously aligned 5CB. When cooling slowly, small domains of 5CB have more time to coalesce into bigger ones forcing the compression and aggregation of the polymer. Strong interaction between the neat liquid crystal and the mesogenic side-chains of the polymer aggregate leads to the final director configuration with minimized free energy.

Electro-optical response

As discussed above, the application of an overcritical electric field along the z-axis causes a director deformation in an initially planar nematic liquid crystal (Fréedericksz effect). Figure 1.8 shows the intensity distribution around the colloids at different voltages. Below the Fréedericksz transition,U < U_F, the initial configuration is stable.

Above UF, the director changes its orientation resulting in an intensity variation around the defects (see Fig. 1.8 at0.8V). However, at relatively low voltages above U_F, there is no intensity variation in the near proximity of the defects. This indicates

a strong anchoring of the director on the surface of the colloid. With further increase of the voltage, the boundary between the undistorted and the distorted region tightens towards the defect until the kidney-like shape is getting destroyed (see Fig. 1.8 at5V and10V).

After switching off the voltage, outside of the defects the initial gray level degenerates very quickly, indicating that the main part of the director reorients back to the planar state. In contrast, the initial director configuration around the colloid does not reappear completely, even after waiting times of several hours (see lower left image in Fig. 1.8). Possibly, a reformation of the polymer chains and the director field might occur on much larger timescales. However, the kidney-shaped structures can be regenerated by heating the sample aboveT_NI and slowly cooling down again.

Empirical description of the director distribution

It has been shown that liquid crystalline side-chain polymers with a sufficiently large degree of polymerization form an oblate configuration in a planar nematic host. The symmetry axis of this oblate object is expected to be parallel to the director (Kempe et al., 2004). Thus, as a raw approximation, the director defect generating aggregate of polymer can be modeled by an ellipsoid-like shape.

Due to their nonsolubility in the nematic phase, the end blocks of the block copolymer are assumed to build the core of the agglomeration, whereas the middle blocks with the attached mesogens are expected to be preferably on the surface. In addition, due to a relatively short spacer length between backbone and mesogen, a normal director orientation on the surface of the agglomerate is assumed. Furthermore, the agglomerate is expected to be penetrated by the liquid crystal, thus the director field will be considered for the inner and the outer region. Crossed polarizers with orientation along the x- and the y-direction (φ = 0^◦ instead of φ= 45^◦) did not demonstrate any spatial intensity variation. Therefore, a strong azimuthal rotation of the director (twist) within thex-y-plane can be excluded.

The three-dimensional director field is constructed iteratively along they-direction (see Fig. 1.9 a). Aty = 0, the boundary of the colloid is assumed to have the shape of an ellipse with half axis of lengthain the x-direction andc in thez-direction (see Fig. 1.9 b). In experimental observations, the positions of the defects were found to be very stable, leading to the assumption that the polymer agglomerations have a strong connection to the upper and the lower boundary of the cell. Thus, we use truncated ellipses, implying that the distancedbetween upper and lower boundary of the liquid crystal layer is smaller than2c. In thex-z-plane, the two-dimensional analytical form of the ellipse is described byf(x) =±c

q

1−^x_a²², with positive and negative sign forz >0 and z <0, respectively.

With increasing distance from the center (y 6= 0) the short half axis of the ellipse is assumed to decrease iteratively until it reaches zero aty =±b. In contrast, the long half axis is assumed to be independent of y. This yields a three-dimensional

description of the whole surface as

Assuming that the director is normal to the surface of the single ellipses and that there is no rotation in the x-y-plane, the director field in the outer region of the agglomerate is then described by its rotation angle of

θ_out(x, y) = arctan

The inner part is constructed such that the director is continuously reorienting back towards a planar alignment. The deflection from this planar orientation is supposed to be maximum at the surface of the colloid, without any discontinuity toθ_out, and to be zero at x= 0and z= 0. This can be guaranteed by the factor ^|x| which leads to the director distribution of

θ_in(x, y, z) = |x|

Figure 1.10 illustrates the distribution of the director field, applying Eqs. (1.10), (1.11) and (1.13) with parameters a = 20µm, b = 15µm, c = 18µm and a cell height ofd= 26µm<2c. The intensity is calculated by numerical integration of the phase difference δ according to Eqs. (1.5) - (1.6) and applying this to Eq. (1.7). The refractive indices n_||= 1.71andn⊥= 1.53were chosen according to the literature values for pure 5CB (Blinov & Chigrinov, 1996). The wavelength of lightλ= 637nm was used with respect to the experimental illumination. Although this model is only a raw approximation and does not take any anchoring strength into account, the comparison of Fig. 1.6 and Fig. 1.11 illustrates a qualitative agreement. This reinforces the idea of a penetrated block copolymer agglomerate and the uniform distortion of the director field.

Figure 1.9: Sketch of the idealized shape of the director defect generating agglomeration of polymer. a) Illustration of the iterative construction along the y-direction via two-dimensional ellipses. b) Definition of the relevant parameters: The short axis a is decreasing along the positive and negative y-direction, while the long axis c is constant. The whole agglomerate is assumed to have a length of 2b along the y-direction.

Figure 1.10: Theoretical distribution of the director according to Eqs. (1.10), (1.11) and (1.13) for parameters a= 20µm, b = 15µm, c = 18µm and a cell height of d= 26µm. The green line indicates the surface of the agglomerate f(x) while the blue dashes represent the director field. The left panel shows the distribution at y= 0, the right one corresponds toy =±¹⁴₁₅b.

Figure 1.11: Theoretical intensity distribution according to the model described in the text. The intensity distribution is calculated by applying Eqs. (1.5) - (1.7) to the director distribution that is shown in Fig. 1.10 and described in the text.