Microscale Structures Arising from Nanoscale Inhomogeneities in

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Microscale Structures Arising from Nanoscale Inhomogeneities in Nematics Made of Bent Shaped Molecules Kanakapura Seshappa Krishnamurthy, Madhu Babu Kanakala, Channabasaveshwar V. Yelamaggad, and Nelamangala Vedavyasachar Madhusudana J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11481 • Publication Date (Web): 22 Jan 2019 Downloaded from http://pubs.acs.org on January 24, 2019

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The Journal of Physical Chemistry

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Microscale Structures Arising from Nanoscale Inhomogeneities in Nematics Made of Bent Shaped Molecules Kanakapura S. Krishnamurthy,*,† Madhu B. Kanakala,† Channabasaveshwar V. Yelamaggad, † and Nelamangala V. Madhusudana‡ † ‡

Centre for Nano and Soft Matter Sciences, P. O. Box 1329, Jalahalli, Bangalore 560013, India Raman Research Institute, Bangalore 560080, India

Supporting Information

ABSTRACT: Nano-scale structures in fluid media normally require techniques like freeze

fracture electron microscopy and atomic force microscopy for their visualization. As demonstrated in the present study, the surface modification of nanoscale clusters occurring intrinsically in nematics made of bent shaped molecules with either rigid or flexible cores leads to micro-scale structures, which are visible in an optical microscope. The underlying physical mechanism proposed here involves a quasiperiodic change in anchoring conditions on untreated glass plates for the medium made of islands of clusters surrounded by unclustered molecules. The resulting pattern of stripes outlines the director-normal field around line defects in the wellknown schlieren texture. The instability, which is seen over most of the nematic range, with increasing visibility under continued cooling of the sample, sets the nematics made of bent shaped molecules apart from the classical nematics of rod-shaped molecules.

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2 1. INTRODUCTION

Liquid crystals are partially ordered complex fluids formed of anisometric molecules.1 They occur in a myriad of thermodynamically distinct phases, of which, the least ordered or most symmetric is the nematic (N); with its continuous translational symmetry and long-range orientational order, it belongs to the uniaxial symmetry group D∞h. The preferred direction of alignment, or the director n, in a nematic is invariant under inversion (n↔-n), whether or not the composing molecules are polar. Most commonly, nematogens such as those used for display are rodlike molecules (Figure 1a), about 2-3 nm long and 0.5 nm across. Less common are achiral, bent-shaped nematogens of fundamental research interest, as in the present work. They are usually made of two rigid moieties linked by either a flexible (Figure 1b) or rigid (Figure 1c) core; they are typically 3-4 nm long and ~1 nm in diameter, with the bend angle around 150o. The macroscopic symmetry of the nematic phase of bent core molecules is no different from that

Figure 1. Nematogens of different shapes used in this study: (a) 4'-heptyloxy-4-cyanobiphenyl, 7OCB (rod-shaped), (b) 1”,7”-bis(4-cyanobiphenyl-4’-yl)heptane, CB7CB (flexible bent-core) and (c) 4-chlororesorcinol bis[4-(4-nundecanoyloxybenzoyloxy) benzoate] (11Cl) (rigid bent-core)

of rodlike molecules. However, as x-ray scattering2-7 and freeze fracture electron microscopic8 and other studies have established, nematics of rigid bent core molecules consist of nano clusters dispersed in the N fluid. The clusters occupy only ~5% of the volume, each with about 100 molecules organized in a few layers, with their long or bow axes inclined to the layer normal (Figure 2a). In the case of dimeric molecules with linking odd numbered alkyl chains, ACS Paragon Plus Environment

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3 neighboring molecules with their flexible linkages wrap around each other to form small double helical chains (Figure 2b). As the temperature is lowered, in many such compounds, the chains a

b

c

Figure 2. Schematic illustration of clusters (encircled in a, b) of short range order in the nematic phase with preferred axis along the horizontal. (a) Rigid core bent molecules; clusters formed of less bent conformers with smectic C type order. (b) Flexible core bent molecules; clusters with heliconical arrangement of molecules; the double helical structure in the cluster is elaborated in (c).

grow and organize themselves to form a new type of nematic that lacks local reflection symmetry, called the heliconical or twist-bend nematic (NTB) phase.9,10 In the absence of external constraints, in the ground state, nematic molecules organize into a monodomain with a common director, except for thermal fluctuations of n. When a nematic layer is constrained between two untreated glass plates, often the molecules lie parallel to the substrates, but with their preferred axes disposed variously (degenerate anchoring) depending on local conditions. This continuous deformation of n may break down at some imperfections leading to topological line defects (disclinations). The pattern of such defects (the schlieren texture), observed very early by Lehmann11 and Friedel,12 is a well analysed13-15 and widely studied16,17 morphology. In a nematic composed of small molecules, the orientational field around topological defects is not directly visible, although it could be mapped through an analysis of polarization features. In fact, techniques such as bubble decoration18 and micro-precipitation19 were developed in early years to enable a direct observation of orientational distribution under a light microscope. Optical recognition of defect structures, as very recent studies show, is possible through generation of micometer scale perturbations of the field of preferred alignment; the following are some examples. Large-scale undulations of the director caused by motile bacteria in lyotropic chromonics are found to reveal optical density changes.20 Similarly, long biopolymer filaments21 ACS Paragon Plus Environment


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4 and functionalized nanoparticles22 dissolved in lyotropic nematics lead to micrometric decoration of director fields. Crystallites separating at graphene surfaces from lyotropic chromonic nanocomposites are also found to follow the director pattern around disclinations. 23 There are also some reports of the director field revealing itself directly in the absence of any external additives. For example, pretransitional bend-avoidance stripes developed in the limit of large bend to splay elastic constant ratio (k33/k11) that occurs in the immediate vicinity of the Nsmectic A transition, reveal the structure of boojums in hybrid-aligned nematic droplets.24 In a different study, it is found that, in a polymer nematic film quenched into the smectic state, the smectic layers are so modulated as to result in a pattern of stripes that map the n-field of the frozen schlieren texture.25 Compared to these observations, the direct optical appearance of defect configurations without any external decorating agents in bent core nematics (BCNs) over a wide range of temperatures reported in this study constitutes quite a different phenomenon. Notably, it does not require an underlying smectic phase. The native nanoscale structures referred to earlier organise themselves to modify the anchoring conditions on the substrates. This leads to a hitherto unreported self-decoration of the orientation field which is quasiperiodic in the micron scale. This study also includes a simple model to account for the observed phenomenon. The paper is supplemented by videos V1 and V2 referred in the text, and by related notes. The notes and the videos are available under Supporting Information, SI. 2. EXPERIMENTAL SECTION

The experiments in this study were performed on the following nematogens (see Figure 1): (i) 1”,7”-bis(4-cyanobiphenyl-4’-yl)heptane, CB7CB, (ii) mixture M of CB7CB and 4'-heptyloxy-4cyanobiphenyl, 7OCB (in the weight ratio 1:1), (iii) 4-chlororesorcinol bis[4-(4-nundecanoyloxybenzoyloxy) benzoate] (11Cl), (iv) 6CN with the structure in Figure 1c, where Cl is replaced by CN and R=OC6H13, and (v) 9CN, similar to 6CN, but with R= OC9H19; their respective phase sequences are (i) isotropic, I (116 oC) N (103 oC) twist-bend nematic, NTB, (ii) I


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5 (82 oC) N (35 oC) NTB, (iii) I (92 oC) N (73 oC) M (monotropic optically isotropic banana phase), (iv) Crystal (105 oC) N (138.3 oC) I and (v) Crystal (92 oC) N (125.6 oC) I. For optical studies, a Carl-Zeiss Axio Imager.M1m polarizing microscope with an AxioCam MRc5 digital camera was used.

It was also equipped with a laser scanning confocal module (LSM 5), with PMT

detectors; this was used in the transmission mode for studies in monochromatic light, with the incident light being a circularly polarized He-Ne (543 nm) laser beam. An Instec HCS402 hotstage coupled to a STC200 temperature controller was used to maintain the sample temperature T to an accuracy of ±0.1 oC. The samples were taken in sandwich cells made of untreated glass plates unless mentioned otherwise. The cell gap d varied in the range 3-40 m. 3. RESULTS

3.1. The Schlieren Texture at the Onset of the Nematic Phase. It is useful, for later comparison, to first consider the usual schlieren morphology adopted by a bent-core nematic layer with degenerate planar anchoring, just below the temperature of transition from the isotropic phase. Figure 3(right inset) displays this texture in a CB7CB film, which is bound between untreated glass plates and viewed between crossed polarizers, as a network of interlinked dark brushes emerging from singular points (nuclei) and outlining regions wherein n +1

y

+1

n β

-1

-½ +½

Q

+1

o

α

x -1 P A

-½

 s

+½

Figure 3. Schlieren texture in nematic CB7CB at 115.8 oC showing line defects of topological charge 1 and  ½; crossed polarizers (P, A) with a λ-plate (slow axis s). Inset (top right): the same texture without the λ-plate, after size reduction. Inset (top left): a spiral +1 defect, between crossed polarizers with a λ-plate. Idealized director profiles around the defects are in white. Scale: 2 m each subdivision.



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or its trace np on the layer plane xy is parallel to the transmission axis of either polarizer. The nuclei are the terminal points of line defects (disclinations) orthogonal to the layer, viewed endon along z. Around a disclination, which here is of the wedge type as distinguished in the Volterra process of its creation,17 the director rotates smoothly through an angle 2πs, s being the topological charge or defect strength; s is simply given by N/4, N being the number of dark brushes that emanate from the nucleus. Basically, the possible equilibrium structures of disclinations are obtained by minimizing the volume integral of elastic free energy density F=½ k(n)2, where k represents the elastic constants k11 (splay), k22 (twist) and k33 (bend), assumed equal.13,14 Energy minimization requires 

2

β=0, where β is the azimuth of the director n (Figure 3). This equation has the solution β = sα

+ c, with α as the polar angle of the position vector r=OQ and c, a constant; a positive (negative) s implies β(α) to be an increasing (decreasing) function. The n-field of a +1 disclination is described by logarithmic spirals for π/2>c>0, as in Figure 3(left inset); the field lines become radial for c=0, and concentric circles, as around O in Figure 3, for c= π/2. For defects with s≠+1, the structure is invariant with respect to c, with the field pattern rotating as a whole as c is varied. For example, in Figure 3, for the –1 disclination with equilateral hyperbolic lines, cπ/6; and for the +½ disclination with confocal, parabolic field lines, c= π/2. The idealized defect configurations close to the nuclei in Figure 3, applicable to isolated disclinations, are inferred from the number of brushes, sense of their movement under varying azimuth of crossed polarizers and changes in birefringence colour occurring on introducing a tilting compensator or phase retardation plate. However, disclinations are generally not isolated as that would involve a relatively high energy (W), since W=Wo+πdks2 ln (R/r), where Wo is the core energy, R the radius of the layer of thickness d, and ro the core radius; in the presence of interacting defects, far field n configurations are modified according to the principle of superposition.15


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7 3.2. Self-Decoration of the n-Field at Lower Temperatures. The smooth variation of intensity and interference colour of the schlieren pattern, such as seen in Figure 3, are characteristics preserved over almost the entire nematic range of calamitic (rodlike) mesogens. While clusters of short range smectic order are known to be present in some nematics made of rodlike molecules,26 there is no report of their influence on the schlieren texture (Note that the stripes in ref. 24 appear just above the N-smectic A transition temperature at which k33>>k11). In BCNs, the lamellar/pseudolamellar clusters prevail over most of the nematic range. When a BCN is cooled a few oC below its clearing temperature, the schlieren pattern develops a new structure, displaying differently coloured patches of fluctuating intensity. With continued cooling, a quasiperiodic pattern of stripes of ever increasing contrast emerges (video V1.avi available in the SI illustrates the random time variation of pattern intensity distribution). The geometry of the stripes is conditioned by the director field around disclinations. In Figure 4

x

+1

+1

–1

P

P 106 o C

A

108 o C

e

+½

c

a

y

A

b

10 m



+½ s

108 o C

d

f

n A /4

2 μm 107 o C

Figure 4.

s

Configurations of n in nematic CB7CB well above the transition point to NTB (103 oC). The

corresponding n-field (dashed-lines, in white) are circular in (a, b) and right-handed logarithmic spirals in (c,d), for the +1 defect; they are rectangular hyperbolae for the –1 defect in (e). Panel (f) shows a defect free, quasiplanar uniform region wherein the n stripes are along y while n is along x. White light illumination. Scale in (b) is common to (a-d, f).



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exemplifying these features, the stripes do not directly outline the director field. They correspond to the profiles of the inplane normal n to the director n. In other words, the n-lines for the +1 defect are concentric circles in Figure 4a,b, and right-handed spirals in Figure 4c,d; they are, in Figure 4e, rectangular hyperbolae for the -1 defect. The +1 defect configuration is readily understandable considering that the free energy of a +1 defect is minimized for c=0 when the elastic anisotropy =(k11–k33)/(k11+k33) is negative, and for c=π/2 when  is positive.16 For BCNs, it is established that the bend modulus k33 is generally low (see ref. 27 and citations therein); and, in particular, it is near zero for the flexible core dimers so that  >0.28 That the stripes in Figure 4 extend along n is also clear from an experimental determination of the optic axial direction. For example, the region of Figure 4f, when examined between crossed polarizers along (x, y), appears almost dark due to the distortion causing the stripes being very weak; with the microscope stage turned through 45o, and under a tilting compensator, the near uniform brightness of the sample shows extinction only provided the compensator slow axis is parallel to the stripes. It is thus easy to see that, in Figure 2b,c, the spiral trajectories of stripes (which, incidentally, are quite common in +1 defects) and the corresponding n-field lines are of opposite handedness. It may be noted that the alternating green and orange colours of the stripes in Figure 4b,d,f are due to interference of polarized light. Even when unpolarized light is incident on the specimen, with a quarter wave plate followed by an analyzer in the transmitted light path, birefringence bands are observed due to the separation of extraordinary light, which in turn is caused by the focusing property of the periodically distorted medium (described below); expectedly, the alternating colours of the stripes interchange on rotation of the analyzer through 90o or between the real and virtual focal planes. The stripes that outline the n field are indeed the focal lines produced by the lensing property of the quasiperiodic distortion. They are observed either as real or virtual images


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9 depending on whether the plane of focus is, for the light incident from below, above or below that of distortion, respectively (exemplified in video V2.avi available in the SI, showing z-stacked images). Importantly, the stripes appear with maximum contrast for linearly polarized light vibrating perpendicular to them; they disappear when the light

a -½

b

e

-½ +1

-½

A

-½

P P

c

P

d

/4

Figure 5. A network of -1/2 disclinations surrounding a +1 defect in CB7CB at 105.1 oC. Dashed lines in frame c indicate the n field and full lines, the n field. Double arrows are polarizers. Frames a-c depict the transmission images from laser scanning microscopy (using He-Ne 543 nm beam). Frame d shows the n field (overlaid on the image in frame c) obtained using the OrientationJ plugin of ImageJ. (e) Enlarged version of frame (c) showing the defects vividly (false color). Scale: 5 m each subdivision.

vibration is, instead, parallel (Figure 5b). The distortion of the optical axis is hence confined to the plane orthogonal to the stripes. By using circularly polarized incident light as in Figure 5c, the n field can be seen over the entire visual field, albeit with reduced contrast. As mentioned above, the elastic anisotropy  is close to 1 in BCNs. Thus, when s=+1/2, the energy of the configuration is minimized through splay avoidance; the n-lines then generally assume the U-shape ( =1 inset, Figure 6a); correspondingly, n- lines would be uniform in one half-space and radiate in the other, mimicking the n-field under bend avoidance ( = –1 inset, Figure 6a). These conclusions arrived at for isolated defects are applicable in practice to two or more line defects, ACS Paragon Plus Environment


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10 provided the interdefect separation is large. In Figure 6b, for example, the n-lines of the s=+1/2 defect are predominantly splayed out (indicated by the dotted white line); and the n-lines, indicated by the continuous white line, are strongly bent. When  =1, the energy cost for the -1/2 singularity is expected to be more than that for the +1/2 singularity (see Fig. 28, ref. 16) since the n-field in the first case will, of necessity, involve some splay. The total energy of the dipole configuration is minimized when the dipole is oriented n

a A P

b = -1

/4

-½

n

c

A s

-½

+½

y

x

+½

 =+1 +½

P A

d

-½ A /4

s

Figure 6. (a) Topological dipoles in the N phase of CB7CB at 113 oC; most of the dipoles are predominantly oriented along the far field director n, as the one encircled by a continuous line, and very few across n, as the one encircled by a dotted line. (b-d) Detailed director-normal map for dipoles oriented (b) along and (c,d) normal to the far field uniform director; dotted and continuous white lines represent, respectively, the n and n fields; CB7CB, 107 oC.

along the far field director. This is the reason for many of the dipoles in Figure 6a oriented largely along the vertical. Dipoles disposed transversely to the far field director (e.g., the dipole encircled by the dotted line in Figure 6a), are rather rare, their formation enforced by the complex n-field of many interacting dipoles around. Figures 6b,c show in detail the typical configuration of a dipole so oriented. The +1/2 defect here has the n lines strongly bent and n lines significantly splayed out. Half-strength disclinations are often seen to form clusters. In Figure 7a,b is shown an angular quadrupole for which the angle ψ between the lines joining disclinations of like charges is slightly different from π/2. This is the distorted version of the so-called ACS Paragon Plus Environment

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11

a

b

/4

A

P

c

A s

d

y

x Figure 7. Multipole clusters in the N phase with an underlying NTB phase. (a,b) CB7CB, 105 oC and (c,d) Mixture M, 40 oC. Scale bar: 10 m. Semicircles and triangles (in white) indicate the location of +1/2 and -1/2 defects, respectively.

Lehman cluster, or a square quadrupole, with ψ = π/2 that destabilizes under angular fluctuations.29 Higher multipoles are also observed as in Figure 7c,d; under the complex many body interaction, the dipoles and multipoles are seen to be quasistatic, instead of decaying and disappearing through annihilation of oppositely charged defects. The formation of striped n patterns around defect lines is not exclusive to nematics which exhibit the NTB phase at lower temperatures. It is also observed with rigid bent core compounds (11Cl, 6CN and 9CN; see sec. 5), showing that the distortion is not necessarily related to the heliconical short range order. This is exemplified in Figure 8 with the texture of some half-strength disclinations in 11Cl which also exhibits an 88.4 oC

A x

b

+½

+½ y

a

P

A /4 s (b, c)


c


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12 Figure 8. Disclinations in the nematic phase of rigid bent core compound 11Cl. Frames (a,b) of the same region depict a pair of opposite +1/2 disclinations. Frame (c) depicts a +1 and a few ±1/2 defects. White circle, semicircle and triangle indicate +1, +1/2 and -1/2 defects, respectively. Scale: 2 m each subdivision.

unidentified optically isotropic mesophase at low temperatures. In Figure 8a,b, two +1/2 defects are seen facing each other with their n-fields, expectedly, as in Figure 6b. Figure 8c shows a +1 defect and several 1/2 strength defects of either sign. In 6CN and 9CN, only a few vertical disclinations could be observed with the pattern of quasiperiodic stripes around them. But the stripes were very spotty with strong intensity fluctuations. Typical textures observed with 9CN and 6CN are presented in Figure 9. While Figure 9a

a

+1

–1/2

–1/2 /4

A

s

9CN b –1

+1 6CN Figure 9. Disclinations in nematic 6CN at 137.8 oC and 9 CN at 123.3 oC with the director distribution around them decorated by quasiperiodic distortion. Inset in Figure 9b is the central area of -1 defect between crossed polarizers. Scale: 2 μm each subdivision.

shows a spiral type +1 defect and two -1/2 defects in close proximity, Figure 9b shows a tangential +1 defect (with radial stripes and circular n-lines) and a -1 defect that may actually be a -1/2 doublet (as indicated by the appearance between crossed polarizers shown in the inset).


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13 In twist-bend nematogens, the quasiperiodic director distortion linked to the schlieren structure may or may not persist after transiting from the nematic to the NTB state. In the mixture M, the stripe state is preserved after the transition, with greatly enhanced contrast and temporal stability (Figure 10a). By contrast, in pure CB7CB, there occurs a structural transformation with the stripe state giving way to the focal conic domain (FCD) state. As evident from a comparison of Figure 10b with 10c, the FCDs extend normal to the original stripe direction. These results may be compared with the natural textures of the NTB phase, which are derived by cooling a nematic sample planarly aligned along, say, x. In the NTB phase of the mixture M, apart from focal conics, two types of stripe morphology are found. One of them shows the stripes along the rubbing direction x, with

a

b

c

104 oC

103 oC

+1

y 31 oC

x

Figure 10. Changes in the nematic schlieren texture at the onset of the NTB phase. (a) The n-stripes around the halfstrength defects prevailing below the transition point in the mixture M of CB7CB and 7OCB are greatly increased in distortion amplitude and also temporally steady. In panel (b), double arrows indicate the n directions around the +1 defect in the nematic phase of CB7CB; in (c) showing the same region as (b), focal conic domains of the N TB phase extend across the n-stripes. Scale bar: 10 μm.

a well-defined periodicity that is revealed regardless of the state of polarization of incident light. The corresponding distortion is very similar to that of Bobylev-Pikin flexoelectric domains, involving both polar and azimuthal periodicities.30,31 In the second type, the stripes, which are real or virtual focal lines, form along the normal y to the rubbing direction, but without any regularity of spacing. They disappear when the incident light vibration is parallel to y, indicating the director deviation causing their appearance to be confined to the xz-plane, with z along the layer normal. Significantly, in ACS Paragon Plus Environment


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14 90o-twist cells, these stripes appear in orthogonal directions, showing them as due to distortions near the substrates. The two striped states can occur together in different sample regions. In planarly aligned CB7CB, mostly, PFCDs (parabolic FCDs) and usual FCDs (with confocal hyperbolic and elliptical singular lines) are found; however, stripes of the second type, identified as oily streaks, are also formed in electrically aligned homeotropic CB7CB.32 From these observations, it appears that the texture in Figure 10a is structurally similar to that of the stripes around disclinations in the nematic phase. 4. Discussion Summarizing the observations, the following are the notable features: (1) The director field (n) is outlined by quasi-periodic stripes with the wave vector q along n. (2) This self-decoration of the n field is seen only when the nematogenic molecules have a bent shape, either with a rigid core or a flexible core comprising, for example, a chain of odd number of methylenes connecting two rigid dimeric moieties. (3) The nematic layer is bound between two untreated glass plates so that it develops the schlieren texture composed of many disclinations. (4) The stripes are spotty, with a nonuniform intensity along their lengths. (5) The spacing between adjacent stripes  (~3 μm) is essentially independent of the sample thickness d, when the latter varies in the range of about 3-40 μm. (6)  is also essentially independent of temperature, though the stripes are better visualized at lower temperatures in the nematic range. From the point (5) above, it is clear that the stripes are formed only near the surfaces of the cell. The bent shape of molecules of either type gives rise to a much smaller value of the bend elastic constant k33 compared to the splay elastic constant k11, the anisotropy (k33–k11), which has the opposite sign to that in nematics made of rod-like molecules, increasing in magnitude at lower temperatures. The rotational and shear viscosities are also much larger in bent core nematics than in calamitic nematics. Nematic fluids of rigid BC mesogens are found to be inhomogeneous, involving a distribution of small smectic C type clusters,4-8 wherein the


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15 molecules are disposed with their long axes tilted relative to the layer normal. The clusters are nanometric in size, consisting of ~100 molecules, and occupy only ~5% of the total volume. The ‘rigid’ bent cores of these molecules usually have the somewhat flexible ester linking groups; and, as one of the authors (NVM) has argued,33 the layered clusters are actually formed by the less bent excited state conformers. The dimeric molecules with flexible chains have a wide distribution of conformations, and, in the case of CB7CB in particular, calculations based on realistic torsional potentials about various bonds have shown that the angle θ between the two rod-like end moieties has a broad peak at ~120o, and a much smaller peak at θ ~30o. The latter corresponds to hair-pin conformations, and the steady reduction of both the principal dielectric constants || and ε⊥ as the temperature is lowered implies a corresponding increase in the more straightened conformations. X-ray scattering also shows that in both the higher temperature nematic and the lower temperature NTB phases, the bent molecules have an intercalated structure.10 This implies that the conformers with the larger  interact to form space filling double helical chains, which in turn align to form the NTB phase at a low enough temperature. Note that the observation of the orientation fields in the present paper pertains mainly to the higher temperature nematic phase in which the helical chains are expected to be short lived dynamic structures that become more prevalent as the transition to the NTB phase is approached. .

It is clear that when the constituents are bent shaped molecules of either type, the

nematic liquid crystal is not homogeneous on the scale of 10s of nanometers, but is made of the main molecular species interspersed with differently ordered aggregates of 100s of molecules. On a larger scale, the medium has the usual averaged orientational order described by the uniaxial apolar symmetry D h. Usually, techniques like freeze fracture electron microscopy are needed to visualize the nanoscale heterogeneity in the structure. As argued in the following, the stripe patterns seen in the cells described earlier are indeed caused by the structural heterogeneity, an unusual example in which a nanoscale inhomogeneity gives rise to micrometric features accessible under a light microscope. ACS Paragon Plus Environment


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16 The untreated glass plates can be expected to preferentially attract the aromatic moieties of the bent molecules, thus giving rise to a relatively weak planar anchoring of the director. The absence of any preferred azimuthal orientation of the director on the surfaces in turn results in the presence of many disclination lines running between the two plates of the cell. The heterogeneity of the medium may be expected to be reflected on the surface as well. In the case of the nematic with rigid BC molecules, clusters made of a few layers with tilted molecules dot the surface, surrounded by single molecules with planar anchoring. The layers of the clusters, however, prefer to lie flat on a surface (Figure 11a). This of course locally gives rise to a tilted anchoring of the molecules. In nematics made of bent flexible-core dimers, the conformers with the appropriate shape wind round each other to form a small double helical chain. When such a ‘short-range ordered twist bend helix’ lies flat on the glass plate, the molecules on the sides of the cylindrical structure are oriented at an angle to the surface, and this favours a tilted orientation of the neighbouring unassociated single molecules as well, as in the case of the

(a)

(b) Figure 11. Wavy bend distortion near the substrate in the nematic phase of (a) rigid- and (b) flexible-core bent mesogens. Rectangular blocks indicate the smectic C clusters in (a) and heliconical clusters in (b) located at the sites maximum director deviation.

clusters of rigid BC molecules (Figure 11b). A sharp variation of the director field around the nanometer sized cluster or helical cylinder costs too much elastic energy. Instead, the cluster or helical cylinder can change the local anchoring energy to favour a slightly tilted director field. Assuming that the tilt angle θ≪1, the anchoring energy per unit area is given by –wθ2/2, w being the anchoring energy coefficient. As the surrounding area still favours θ =0, in the continuum ACS Paragon Plus Environment

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17 one may assume a quasi periodic variation of the θ profile on the surface. In the nematics made of bent molecules, the bend elastic constant k33 is quite small so that, on the surface, θ may be written as

where the amplitude θo

Microscale Structures Arising from Nanoscale Inhomogeneities in

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