Influence of gold nanorods on the structure and photonic bandgap in a twist grain boundary phase with smectic C* blocks

Journal Pre-proof Influence of gold nanorods on the structure and photonic bandgap in a twist grain boundary phase with smectic C* blocks

Rajalaxmi Sahoo, D.S. Shankar Rao, Uma S. Hiremath, C.V. Yelamaggad, Pravin Shinde, B.L.V. Prasad, S. Krishna Prasad PII:

S0167-7322(19)35428-5

DOI:

https://doi.org/10.1016/j.molliq.2019.112117

Reference:

MOLLIQ 112117

To appear in:

Journal of Molecular Liquids

Received date:

30 September 2019

Revised date:

5 November 2019

Accepted date:

10 November 2019

Please cite this article as: R. Sahoo, D.S.S. Rao, U.S. Hiremath, et al., Influence of gold nanorods on the structure and photonic bandgap in a twist grain boundary phase with smectic C* blocks, Journal of Molecular Liquids(2019), https://doi.org/10.1016/ j.molliq.2019.112117

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© 2019 Published by Elsevier.

Journal Pre-proof

Influence of Gold Nanorods on the Structure and Photonic Bandgap in a Twist Grain Boundary Phase with Smectic C* Blocks Rajalaxmi Sahoo,1,2 D.S. Shankar Rao,1* Uma S. Hiremath,1 C.V. Yelamaggad1, Pravin Shinde,3 B.L.V Prasad,3 and S. Krishna Prasad1 1 Centre for Nano and Soft Matter Sciences, Bengaluru 560013 India 2 Manipal Academy of Higher Education (MAHE), Manipal 576104, India 3 National Chemical Laboratory, Pune, India *email: [email protected]

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Abstract

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We describe the first report of the influence of gold nanorods (GNR) on the induced twist grain boundary smectic C* (TGBC*) phase in a binary mixture of achiral bent-core and chiral linear liquid crystals. The GNR concentration-dependent phase diagram of these nanocomposites shows that the thermal range of this twist grain boundary phase having smectic C* blocks phase increases by 50% for an intermediate composition compared to that for the host binary mixture without nanorods. The inclusion of the nanorods is seen to have substantial effect on the structural and photonic bandgap features of the TGBC* phase. For example, the helical periodicity gets altered in all the three dimensions: while those within the block undergo a huge increase, the one which is orthogonal to the blocks, shrinks. The spacing of the square grid pattern arising normal to the TGB helix direction increases for the nanocomposites getting even doubled for a certain composition, a feature evidenced by optical microscopy as well as optical diffraction. Xray diffraction clearly brings out the feature that the presence of GNR alters the thermal character of the transition between the TGBC* and the cholesteric phase. Quantitative analysis of the data indicates that the system would remain in the vicinity of a possible tricritical point, a behaviour having wider ramifications to understand the underlying critical phenomenon. Based on the experimental observations, and capturing the essence of the reported adaptive defect core targeting mechanism we propose a model wherein GNRs get confined in the grain boundary region. This feature offers a potential to have periodic and anisotropic plasmonic structure arising out of the synergetic interactions between the metal nanorod and the twisted grain boundary structure. Key words: TGBC* phase; 3D photonic bandgap; Gold Nano rods; Induced phase; Tricritical phenomena

1. Introduction: Nematic (N), has the molecules spontaneously oriented along a unique direction referred to as the director (n) but the system is still a fluid. When the constituent molecules are chiral, a spatial periodicity in the ordering could be superimposed, resulting in a helix normal to the director, with the phase referred to as chiral nematic or cholesteric (Ch). Lowering the system temperature could result in a layered phase with a one-dimensional periodicity along (smectic A) or at an angle 1

Journal Pre-proof (smectic C*) to the director.1 At the cholesteric to smectic A transition helical ordering collapses, breaks continuous translational symmetry to give layered structure analogues of the Normal and Meissner phases of Type I superconductors.1b,2 Continuing the analogy to the Type II superconductors exhibiting the Abrikosov flux lattice phase, an additional phase between the Ch and SmA was predicted3 and experimentally found.4 In this phase, termed the twist grain boundary (TGB) phase, the twist periodically penetrates the layer structure. The blocks of layers rotate in a systematic manner giving rise to a helix and by implication simultaneous existence of layering and a photonic bandgap structure, each of which, to an extent, independent of the other. The structure

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within the layer – SmA, SmC or SmC* – results in the TGBA, TGBC and TGBC* phases.

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Following the prediction of the TGBC phase3b in which the molecules are tilted within the layer, whose normal is perpendicular to the TGB helix, several variants of the TGBC phase have

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been observed. The one studied in Bordeaux group5 (designated as B-TGBC) and observed to have a commensurate structure, showed that the layer normals form an angle to the direction of the

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molecules which are orthogonal to the helical axis. A TGBC phase in which the normal to the plane

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is perpendicular to the TGB axis is also reported by Brunet et. al.6 The TGBC phase reported by Ribeiro et al7 denoted the S-TGBC phase –exhibited a square grid pattern and suggested that the layer normal varies within a block. In the light of this, the square grid pattern seen and assigned as

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arising from 2-d modulation with the phase labeled as undulated TGB phase, may also be noted.8 Owing to their fluid nature, in many respects, liquid crystals appear to be an ideal

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complement to unsupported nanoparticle/nanorods.9 If the nanotubes are well dispersed, they tend

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to, in general, align their long axes to be along n to minimize distortions of the LC director field and thus the free energy. Dispersion of nanorods in LCs can thus provide an inexpensive, simple, versatile and effective means of controlling nanotube orientation on a macroscopic scale and at high concentration, with no fundamental restrictions on nanotube type. Doping of nanoparticles into LCs is of interest, owing to induced chirality,10 increase in the dielectric anisotropy11 and the improved electro-optical response of liquid crystals (LCs),12 explore pathways towards tunable metamaterials,13 enable self-healing mechanisms,14 etc. Recently there has been interest in the stable suspension of surface treated CdSe quantum dots to stabilize the blue phases15 and TGB phases of chiral liquid crystals.16 Presence of spherical nanoparticles(CdSe, CdSSe and gold) in a chiral liquid crystal stabilizes/induces the TGBA phase, and argued to be due to increased stability of the one-dimensional lattice of screw dislocations at grain boundaries separating the smectic 2

Journal Pre-proof slabs. It may be noted that in all these studies involving nanoparticles, optical microscopy, heat capacity and XRay diffraction are used as probes. More importantly, there has been no investigation on the influence of incorporated nanostructures on the TGBC* phase, which exhibits wide variety of length scales including periodicity of the TGB helix, spacing of the square grid pattern and the smectic layer thickness. In this article, we report a detailed investigation carried on the effect of gold nanorods, with an aspect ratio not very much different from that of LC, in a liquid crystalline system exhibiting cholesteric to TGBC* transition. The nanorods not only stabilize the TGB phase, but with increasing concentration enhance significantly all the characteristic length scales of the

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system, viz., periodicity of the TGB helix, smectic layer thickness and spacing of the square grid

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pattern arising from the 2-d modulation. The thermal range of the TGBC* phase also increases substantially, at least for a low concentration of the nanorods.

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2. Experimental

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The host LC material is a binary mixture comprising an achiral bent core compound (labeled 12OCN) and a chiral rod-like compound (TFMHPOBC). The molecular structures and transition

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temperatures of these materials are shown in Figure 1. The mixture employed, hereafter referred to as host liquid crystal (HLC), consists of 10 weight% of TFMHPOBC in 12OCN. It should be

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emphasized here that HLC shows the phase sequence blue phase (BP)-cholesteric (Ch)-TGBC*. It may be noted that none of these phases are present for either of the constituent compounds. Owing

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to the fact that the majority component of HLC has a bent shape (10% of calamatic (TFMHPOBC) in bent core (12OCN) material), we decided to incorporate nanoparticles which are stiff rods,

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creating an environment of antagonistic shape characters between the two systems. For this purpose we have employed gold nanorods (GNR) of width 18.9 nm and an aspect ratio of 2.33  0.02. The synthesis details of these nanorods have been given in supplementary information (see SI-6). Of specific interest for the present studies are the TEM image (FEI TALOS 200S) and the histogram of the distribution of particles, shown in Figure 2. The present investigations were conducted by varying the concentration of GNR in HLC; these nanocomposites are labeled as mGNR, where m represents the content of GNR (by weight%) in HLC. The nanocomposites were prepared by transferring weighed amounts of HLC and GNR into a vial and stirred using magnetic stirrer for 90 minutes while maintaining the temperature above the isotropic temperature of HLC. The uniform dispersion of GNR in HLC was ensured by observing a thin film of the sample under a polarizing microscope (POM- Leitz DMRXP). 3

Journal Pre-proof Laser diffraction experiments were performed to determine the spacing of the square grid pattern, a characteristic feature of the TGBC* in planar aligned samples, realized by sandwiching the material between glass plates pretreated with a polyimide layer and rubbed unidirectionally. The diffraction pattern obtained using a He-Ne laser beam incident on the sample was projected on a screen and captured using a digital camera. The captured images were analyzed using an open source image analysis software (Image J) with a user-written macro. Knowing the distance between the sample and the screen, it was straight forward application of Bragg’s law to calculate the grid spacing. For determining the smectic layer thickness, X-ray diffraction measurements were carried

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out using a PANalytical X'Pert PRO MP X-ray diffractometer consisting of a focusing elliptical mirror defining the wavelength of the radiation to be 0.15418 nm and a fast high-resolution detector

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(PIXCEL).17 The profiles collected using this apparatus were analyzed using Fityk profile-fitting

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software.18 The sample was contained in a glass capillary tube (Capillary Tube Supplies Ltd) placed inside a programmable hotstage (FP82HT/FP90) which facilitates variable temperature

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measurements; the temperature control was to a precision of 100 mK.

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The Ch and TGBC* phases are characterized by a helical structure whose axis is normal to the local director. Owing to the length scale involved the pitch value p quantifying the structure, can

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be conveniently measured using the selective reflection method employing a UV-VIS-NIR wideband spectrophotometer (Perkin Elmer lambda 750). The obtained spectra are characterized by

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a Bragg reflection band centered at min, which in turn is related to p through min = p.navg; here navg is the average refractive index of the system. Making a fair assumption that in the spectral range of

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interest the index of refraction navg is independent of temperature, min determined from the spectra can be taken to be the behavior of p. For these measurements planar aligned samples of ~10m thickness were employed.

3. Results 3.1 Optical microscopy and phase diagram The phases and phase sequence observed for the host mixture HLC are essentially retained even after the addition of GNR. Preliminary checking for phase confirmation was done using polarization optical microscopy (POM) observations. Of specific interest were the Ch and TGBC* phases, which were identified by the oily streak and grid pattern textures seen in the planar oriented molecular geometry. Proper confirmation of the TGBC* phase was obtained by the observation of the simultaneous presence of the grid texture and the Grandjean Cano lines in wedge cells whose 4

Journal Pre-proof inner surfaces were treated for planar alignment. POM photographs with planar alignment of the molecules in the Ch and TGBC* phases, are shown in Figures 3(a,b) and (d,e), respectively for HLC and a representative composite, 6GNR. The images obtained in the homeotropic alignment in the TGBC* phase, exhibiting the undulatory filament texture are presented in Figures 3(c,f) for the two materials. The partial temperature–GNR concentration (XGNR) phase diagram is shown in Figure 4. Interestingly, over the concentration range investigated, the chosen GNRs maintain good compatibility with HLC system, as evident from the fact that TBP-I, the clearing point (transition to

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the isotropic phase) is not altered significantly. If the incorporating nanostructures were to be

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entirely incompatible with the LC system, the clearing point would have shown a large reduction with consequent destabilization of the mesophase. This would be all the more so owing to the point

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that the majority of the molecules have a bent shape unlike the nanorods. Thus, the small variation in TBP-I observations in the present system are quite encouraging. In fact, in a previous work19 we

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reported that the incorporated nanorods did even increase the clearing point of a host soft-bent

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dimer, as indeed seen for the 2GNR mixture. Although, these features are in line with the fact that a stiffer rod (more rigid than bent component of HLC) facilitates a higher clearing point, the non-

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monotonic variation with XGNR rules out a simple explanation. Also interesting is the behavior of the phase line immediately below the clearing point, viz., the Blue Phase-N* boundary. Although the contour seems to be mimicking that of the TBP-I boundary, certainly each of the nanocomposites

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studied has a larger thermal range for the Blue Phase than the pure HLC. In recent times, there have

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been quite a few reports about different pathways to enhance the thermal range of BP.15, 20 Thus, the feature seen in Figure 4 provides a clear indication that imbibing nanorods is definitely one of them. Perhaps varying the aspect ratio as well as the actual size of the nanoparticles may lead to a better understanding of this behavior. The Ch-TGBC* boundary is almost a like a mirror reflection of the BP-Ch transition line, with the result that the temperature range of the Ch phase is maximized for the 2GNR mixture. Above 6% of GNR, a phase gets induced between Ch and TGBC* phases. For example, the 8GNR composite shows, in the thermal range of this induced phase, a straight filament texture (see Figure SI-1), characteristic of the TGBA, i.e., TGB phase with smectic A block structure. From the viewpoint of present studies we note that the TGBC* phase survives throughout the range studied, i.e., up to a loading factor of 8% GNR.

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Journal Pre-proof 3.2 Grid spacing Figure 5 shows the POM pictures of the square grid pattern for HLC (0GNR) and one representative GNR composite (4GNR); such patterns seen for the other two concentrations – 2GNR and 6GNR – are given in Figure SI-2. Even at a qualitative level, it can be seen that the grid spacing (dG) is influenced by the presence of GNR. The large dG value observed for the composite is reminiscent of structures termed as “giant block” TGB phase.21 For quantitative comparison of this modulation in the plane normal to the TGB helix we performed laser diffraction measurements. A He-Ne laser beam was made to pass through the planar aligned sample, which resulted in a

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diffracted pattern whose symmetry reflects the 2D modulation of the structure normal to the beam

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direction. A representative diffraction pattern captured on a screen is shown in Figure 6a. Figure 6b depicts the raw curve of such pattern extracted using ImageJ software along the diagonal passing

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through the origin. Peak position obtained by fitting such profiles into standard peak form, then using Bragg’s equation the spacing of the square grid pattern can be calculated. Figure 7 shows the

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thermal variation of dG in the TGBC* phase for all the composites. The variation is linear in the

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TGBC* phase, but shows divergence behavior near TGBC*-Ch transition. The grid or the lattice spacing (dG) taken at fixed reduced temperature of Tred1 = -15oC (with Tred1 = (T-Tc1), where Tc1 is

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the Ch-TGBC* transition temperature) also is seen to have a non-monotonic dependence with an initial increase up to 4% beyond which there is a decrease with the concentration of GNR in the mixture (see the inset of Figure 7). Another convenient method for quantitative determination of

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the grid spacing using just the polarizing microscopy images is illustrated in Figure SI-3. For this

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purpose we have used an image obtained for the 2GNR composite (Figure SI-2). Employing an open source software (ImageJ) a one-d scan of intensity vs. position is obtained from the captured images containing the grid pattern. A Fourier transform of this profile is shown in Figure SI-3(b). The data are fit to a Gaussian expression, and the peak position after applying the calibration correction obtained using a stage micrometer scale, directly yields the spacing of the grid. The value obtained in this manner agreed quite well with the data from the diffraction pattern, proving the efficacy of this simple method. 3.3 Selective reflection The selective reflection property of the Ch phase, also retained in the TGB phases, enables the deployment of the UV-Vis-NIR spectroscopy to measure the pitch of the helix. Figure 8a shows representative spectrometer scans taken at different temperatures for HLC and 6GNR. The 6

Journal Pre-proof minimum in the transmitted light in each spectrum corresponding to the selective reflection wavelength min is related to the pitch of the helix through the average refractive index of the medium. In both cases min is already in the IR region even close to the transition to BP and exhibits substantial variation over the entire temperature range investigated. It is also seen that the profiles are broader for the nanocomposite than for HLC. We shall return to this point later. The detailed dependence of min on the reduced temperature Tred2 = T-Tc2, where Tc2 is the BP-Ch transition temperature, is shown in Figure 8b. Interestingly, away from Tc2 (Tred2 = 0), the datasets for all the materials studied here collapse to a single profile, suggesting that the influence of NRs on the

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photonic band gap is minimal. However, min increases appreciably on lowering the temperature,

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especially in the vicinity of Tc1. In fact, HLC exhibits an abrupt jump in the value, a feature characteristic of a first-order transition. In contrast, the nanocomposites exhibit GNR concentration-

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dependent behaviour. The lowest concentration (XGNR = 2) composite has a gradual and smooth

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variation across the concentration. With increasing concentration of GNR the steepness of this change increases to the extent that for XGNR = 6, the behaviour is reminiscent of the divergence seen

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for second order transitions. Measurements could not be made deep in the TGBC* phase owing to min reaching limiting value of the apparatus. Inset of Figure 8b presents min at a representative

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fixed reduced temperature (Tred2 = -20 K). The value varies nonmonotonically with XGNR content, diminishing for XGNR=2, and then showing a much larger increase. Although this behavior is

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similar to the reduction of Tc1 with XGNR, it is not clear of why they should be related.

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A second parameter of interesting in the raw profiles shown in Figure 8a is the width of the peaks: The profiles are seen to broaden on going from the Ch to the TGBC* phase. Also, in both the phases, the profiles are broader for the nanocomposite than for HLC. To do a quantitative comparison, we fitted the profiles to a Gaussian expression, by floating min, (taken as the fullwidth-at-half-maximum), and the strength. Figure 9 shows the temperature dependence of  for 0GNR and 6GNR materials. In both cases increases with decrease in temperature with the magnitude of as well as the slopebeing higher for 6GNR. Inset of Figure 9 shows concentration dependence of at a fixed reduced temperature Tred2 = -19 K in the cholesteric phase. It can be seen that  has a steep increase for 6GNR. Recalling that  represents the width of the photonic band gap, the results demonstrate that a convenient way to enhance the width of PBG is to introduce nanorods into the system. In fact, the large value for 6GNR is thus appealing to 7

Journal Pre-proof applications such as wide-band selective IR reflectors for environment control. Since the central wavelength of PBG (o) itself is easily tunable, a similar tunability of  if achieved in the visible region, thereby covering the entire visible spectrum, could result in a white light selective mirror.

3.4 Xray diffraction Figure SI-4 shows representative raw profile (obtained from Xray diffraction experiment) in the cholesteric and TGBC* phase for HLC and 6GNR. It can be seen that the peak is broad in the

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cholesteric, but sharp and also intense in the TGBC* phase for both the materials. Introduction of GNR reduces the FWHM in both cholesteric and smectic phases. Also remarkable feature is that in

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the transition region HLC exhibits coexistence of peaks contributed by the two phases, a feature characteristic of a first order transition. Figure 10(a) shows temperature dependence of the layer

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thickness d for different materials studied. It may be noted that in the TGBC* phase the layering is

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an equilibrium one. The fact that layer thickness data can be provided in the Ch phase indicates that the cybotactic (or short-range) layer ordering is substantial although the global ordering is merely

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that of a fluid. This is even more surprising since the transition is first order as seen from d, the jump in layer thickness and the presence of the coexistence of peaks coming from wave vectors

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corresponding cholesteric and TGBC* phases for HLC. Going by the conventional wisdom that first order transition hardly tolerates short range ordering in the disordered phase means that one

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has to invoke the fact that systems with bent-core molecules tend to stabilize layering order. As

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XGNR increasesd decreases with almost a continuous variation for XGNR 2%, suggesting the transition could have become second order. Another interesting feature is the increase in spacing with increase in XGNR in both Ch and TGBC* phases. Such an enhancement in layer spacing is not uncommon in the smectic phase, and argued to be due to nanophase segregation of a minority, but incompatible, constituent in the system.22 In the cholesteric phase enhancement is due to nanophase segregation in the smectic domains seen in the cholesteric environment. Figure 10(b) shows such enhancement in dCh, spacing in the cholesteric phase as a function XGNR at Tred1=2 K. dCh increases up to 4% GNR concentration and then stabilizes. We shall return to this point later. Figure 10(c) shows thermal variation of the full width at half maximum normalized with the layer spacing (FWHM/d) for the representative materials, namely 0GNR and 6GNR. As expected the peak gets sharpened on going from cholesteric to the TGBC* phase. Interesting feature is that in both Ch and

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Journal Pre-proof TGBC* phases the FWHM value decreases with increase XGNR indicating increase in the smectic correlation in the TGBC* phase and enhanced cybotactic ordering in the cholesteric phase, on introduction of GNR. Such a feature has been observed wherein addition of CNT into nematic liquid crystal induced/stabilizes smectic ordering.23 Just as the layer thickness, FWHM/d also shows a jump in the value (accompanied by coexistence) for HLC, whereas the nanocomposites present a continuous variation. Similar behavior is observed for the peak intensity also. These features are exemplified in figures SI-5(a) and SI-5(b). A behaviour that may be noticed in the FWHM data above Tred1 especially for the nanocomposite is that the value exhibits a gradual variation from an

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essentially constant magnitude deep in the Ch phase, to finally level off well in the TGB phase.

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Drawing parallels between reports wherein such an observation was associated with the existence of the chiral line liquid (NL*), it may be suggested that in the present case also the N L* phase

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intervenes between the Ch and TGBC* phases. Taking that stand, it is seen that HLC also presents such a character albeit over a very short temperature range. Thus, it appears that incorporation of

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GNR also stabilizes/enhances the NL* range. As seen from Figure 10(c), this range is ~ 5 oC, and

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thus the largest observed till-date.16,24,25 Additional support in the form of high resolution ac calorimetry, the tool which has been used earlier16,24,25 to establish the presence of the NL* phase

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would strengthen this proposal. For the sake of clarity we continue to address the combined region of the proposed NL* and the Ch phase above it, simply as the region of the Ch phase. Figure 11(a) shows the thermal variation of tilt angle in the TGBC* phase extracted using the relation

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= cos-1(dC/dCh), where dC and dCh are the spacing numbers in the TGBC* and cholesteric phase

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respectively. This is done with the presumption that to be compatible with the cholesteric structure, the short-range correlation should be of the SmA type or at least with very small tilt angle. Consequently, the tilt angle has a precipitous increase at the Ch-TGBC* transition followed by a more gradual change at lower temperatures. Interestingly, while this happens through a jump for HLC the variation is continuous for XGNR. Fitting the thermal variation of  for composites to a power law expression,  ~ (T-Tc1) -------(1), where Tc1 is the Ch-TGBC* transition temperature, yields the  values, as shown in Figure 11(c). The values, ranging from 0.23 to 0.27, assume significance owing to the fact that 0.25 is the exponent for the temperature dependence of the order parameter26 when the system is at the 9

Journal Pre-proof tricritical point (TCP). Thus, the composites could be in the immediate vicinity of such a TCP. It must however be pointed out that the Ch-SmC* transition, although permitted by symmetry to be a second order transition (and thus has the possibility to have a TCP), is expected to be first order always owing to the Brazovskii fluctuations.27 It is not clear whether such fluctuations are important for the Ch-TGBC* transition as well. Even in the case where the NL* phase would be intervening between the Ch and the TGBC*, instances wherein NL* phase has short range order of the TGBC* are not known, thus an isosymmetric transformation involving TGBC* and the NL* phase may not be anticipated. In the light of these details we do not expect a supercritical behavior

aspect.

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in the place of a second transition. Experiments in other systems may shed more light on this Furthermore the magnitude of reduces as the concentration of GNR increases. For

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example, at a reduced temperature of T–Tc1 = -8oC, the magnitude of  reduces by 16% from HLC

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to 6GNR (see Figure 11(b)). In contrast, the dch, the layerspacing value in the upright phase (Ch phase) increases by only about 2%. The feature that  decreases with XGNR is especially important

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from the viewpoint of the model, which will be discussed later.

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4. Discussion

Let us begin by summarizing the characteristics exhibited by all the mixtures studied here: (i)

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Planar-treated wedge cells present Grandjean-Cano (GC) lines, (ii) homeotropic cells show the filamentary growth and (iii) XRD exhibits smectic-like low angle peaks. These parameters establish

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that the phase is prima facie, a TGB phase. With respect to the value (of the peak due to short-range order) in the Ch phase, the layer spacing is much smaller in the TGB phase indicating that the

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molecules are tilted with respect to the smectic layer normal. The fact that in the planar situation, a square pattern gets superimposed on the GC lines, establishes that there are modulations in all the three directions, although the periodicity of the modulation along the TGB twist direction is different than those in the orthogonal plane. Taken as a combination, these features are the wellknown signatures of the TGBC* phase. Now, let us look at the differences that the addition of GNR makes to these features. Comparing images in Figures 3(b) and (e) it is seen, even at a qualitative level, that GC lines are more widely separated for the case with GNR. The filamentary growth texture seen for pure HLC is also observed for the nanocomposites (see Figure 3(c) and (f)). XRD data (Figure 10) shows that there is a dilation of the layer by about 2% in the presence of the nanorods.

Further, across the transition to the TGBC* phase the layer thickness varies in a

continuous fashion for the nanocomposites as against the precipitous drop seen for the pure HLC 10

Journal Pre-proof sample. As already discussed we attribute this to the change in the nature of the Ch-TGBC* transition between pure HLC and the composites. Concomitant differences also get exhibited in the FWHM values. In this context, it may be useful to quote a remark made by Trcek25: “It is intriguing that the all available heat capacity results obtained in TGBA and even in TGBC systems show existence of both NL* and TGBA(C) phases with strongly first order TGBA(C)-NL* and SmA(C)*TGBA(C) phase transitions. These findings are in clear discrepancy with current theoretical calculations28 predicting the all TGB-related transitions to be of the second order.” This observation is in line with the finding that HLC exhibits a first order transition. Thus, the incorporation of

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nanoparticles (at least nanorods as in the present case) provides a convenient path to make the

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system closer to the theoretical expectation. Also to be noted is the fact that the saturated tilt angle is smaller for the nanocomposites. The case of the grid spacing arising from the 2-d modulation

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orthogonal to the TGB axis is even more dramatic with the spacing getting doubled for the high

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concentration nanocomposite. 4.1 Model

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Before describing the possible arrangement of molecules in the TGBC* phase when GNR is present, it is educative to look at the description provided in the case wherein nanostructures have

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been incorporated into systems involving the TGBA/TGBC phase. Let us again emphasize that there have been no observations of cases with nanostructures in the TGBC* phase nor any

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theoretical concepts put forward for this situation. Thus we continue with arguments made for the TGBA phase. The international consortium of authors16,25 has put forwarded four different

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mechanisms to explain stabilization of a defect-ridden phase by the inclusion of nanoparticles. Two of these, the adaptive defect core targeting or ADCT mechanism and another, associated with the saddle-splay elasticity, are applicable for cases with smaller and lighter particles such as the II-VI semiconductor NPs; the ADCT16(b) involves slight perturbation of the phase field connected with the smectic order parameter. The authors argue that for larger and denser, but spherical, NPs such as Au NPs, two other mechanisms assume significance. One of them appeals to the energy penalty caused by the dilatation of smectic layers to be driving the NPs to be in the cores of defects. The last of the proposed mechanisms expects “reduction of screw dislocation fluctuations caused by the formation of heavy (metallic) anisotropic NPs clusters in their cores”.25 None of these mechanisms have been considered for nanostructures where the individual entity itself is anisotropic, such as in the present case of GNR. Thus, for want of such a consideration, we could presume that the last 11

Journal Pre-proof quoted mechanism, which reduces the screw dislocation fluctuations owing to anisotropic nanostructures, albeit clusters of isotropic entities, is applicable for our system. Interestingly, employing platelet-like nanostructures Trcek etal.,16(a),25 obtained results suggesting strongly anisotropic NPs are less effective in stabilising the TGBA phase, presumably due to inconsistent LC ordering outside of the topological defects. In the light of this, our results which show increase in the TGBC* thermal range for an intermediate concentration of GNR (X=2) indicate that rods may still be effective in stabilizing the TGB phase, at least when their concentration is not too high. Favourable concentration may provide situations conducive to stabilize the TGB phase by getting

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incorporated in to the defect cores. But at higher concentrations, it is possible that the crowding of

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NPs allows them to be outside the defect regions resulting in disruption of the LC ordering. Consequently, the energy penalty may increase to such an extent that the system would rather

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reduce the thermal range of the defect-ridden phase.

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Keeping these features in mind we depict schematically the disposition of GNRs in the TGBC* structure (see Figure 12). For pure packing reasons, we expect the long axis of GNR to be

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lined up along the undulation of the grain boundary, rather than being along the TGB helix. If the out-of-grain boundary orientation of GNR were to be possible, owing to its substantial length, it

na

will disrupt the communication between the smectic blocks thus destabilizing the TGBC* structure itself. The ligands which cap the GNR, being organic in nature, help them to associate well with the

ur

grain boundaries. Again for packing reasons, instead of staying normal to the GNR surface to adapt “porcupine architecture”, the ligands would want to bend such that a large portion of their length

Jo

remains parallel to the long axis of GNR. The layer thickness has been observed to increase on incorporating the nanorods, a feature which could be taken to suggest nanophase segregation on lines similar to those invoked in situations involving incompatible constituents.22 However, let us also note that the increase in spacing is only by ~0.08 nm, which is only small fraction of even the diameter of GNR (19 nm). If the nanophase segregation mechanism leading to GNR residing in the space between the smectic layers were to be operable, the increase in spacing should have been much larger even allowing for the small concentration of the nanorods. Thus the model we propose does not have GNR between the layers. For the same reason we can also rule out them being present inside the TGB blocks, but rather get restricted to the grain boundary regions. None of the experimental data that we have presented here permit us to comment on the orientation of the GNR within the grain boundaries. If the ligand-LC interaction dominates then the long axes of the GNRs 12

Journal Pre-proof would be preferentially oriented along the screw dislocations. The helical nature of the smectic C* structure (Figure 12) is expected to be uniform throughout the block. Owing to the large value of the TGB pitch (> 1 m), the block size could also be considered to be quite large. This can create a situation wherein the influence of the grain boundaries is reduced in the mid-region of the blocks. Thus the 2-d modulation may not be anymore symmetric with respect to the TGB helical axis. Detailed studies in this regard are needed to look at regions close to and away from the grain boundaries. A final comment that we would like to make is regarding the stability of the TGBC* phase owing to inclusion of nanorods. Contrary to the argument proposed by Trcek et al 16(a),25 that

of

strongly anisotropic nanostructures are not conducive for stabilizing the TGB phase, our studies

ro

clearly show that at least the nanorods do stabilize (compare the TGBC* thermal range for 0GNR and 2GNR systems) the TGBC* in addition to inducing the upright TGB phase (for 8GNR).

-p

Presumably rod-shaped inclusions are better for the purpose than the platelet structures attempted earlier.16(a),25 Investigations employing nanorods of different dimensions and aspect ratios should

re

also throw more light on several of these observations and arguments.

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5. Summary

The influence of gold nanorods on the structure and photonic bandgap characters of the TGBC*

na

phase have been described. For this purpose, a host binary system comprising primarily an achiral bent-core mesogen doped with a chiral linear liquid crystal was employed. Interestingly, over the

ur

concentration range studied, the presence of the latter liquid crystal induces the TGBC* phase, not

Jo

existent in either of the pure materials. Inclusion of the nanorods into this host mixture initially enhances the thermal range of the TGBC* phase, but for higher concentration of GNR, brings it down to the original range. We have investigated the modulations that exist in all the three directions for this unique TGB phase: significant variations are seen for the pitch of the TGB helix determined by the selective reflection method as well as the Gradjean-Cano lines, as well as the spacing of the square grid pattern arising normal to the TGB helix direction; presence of GNR doubles the latter parameter. Temperature dependent Xray diffraction studies measuring the layer thickness and in turn the tilt of the molecules with respect to the layer normal, clearly shows change in the order of the cholesteric-TGBC* transition from first to second order. Based on the features observed and literature reports on composites containing metal nanoparticles and exhibiting other variants of the TGB phase we propose a model wherein GNRs get confined in the grain boundary

13

Journal Pre-proof region. Exploiting the anisotropic plasmonic feature of GNR, the observations reported offer the possibility to realize periodic and anisotropic plasmonic structures, the periodicity as well as the anisotropy being tunable parameters through temperature, particle shape and material characteristics.

6. Acknowledgement Funding support from the Thematic project (SR/NM/TP-2 5/2016), Nano Mission, DST, New

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Delhi, India, is gratefully acknowledged.

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References

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1) (a) S. Chandrasekhar, Liquid crystals, Cambridge University Press, 2nd edition (1994); (b) P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Oxford Science, Publication, Oxford (1993); (c) G. Vertogen and W. H. Jeu, Thermotropic Liquid Crystals– Fundamentals, Springer, (1998) 2) P. G. de Gennes, Solid State Commun. 10 (1972) 753 3) (a) S. R. Renn and T. C. Lubensky, Phys. Rev. A, 38 (1988) 2132; (b) S. R. Renn, Phys. Rev. A, 45 (1992) 953. 4) J. W. Goodby, M. A. Waugh, S. M. Stein, E. Chin, R. Pindak & J. S. Patel, Nature (London) 337 (1989) 449; G. Srajer, R. Pindak, M. A. Waugh, J. W. Goodby, and J. S. Patel, Phys. Rev. Lett., 64 (1990) 1545; L. Navailles, P. Barois, and H. T. Nguyen, Phys. Rev. Lett., 71 (1993) 545; W. Kuczynski and H. Stegemeyer, Mol. Cryst. Liq. Cryst., 260, (1995), 377; Proc. SPIE Int. Soc. Opt. Eng., 3318 (1997) 90; for reviews, see J. W. Goodby, in Structure and Bonding, Liquid Crystals II, edited by D. M. P. Mingos (SpringerVerlag, Berlin, 1999); H. S. Kitzerow, in Chirality in Liquid Crystals, edited by H. S. Kitzerow and C. Bahr (Springer-Verlag), New York, 2001; Geetha G. Nair, S. Krishna Prasad and C. V. Yelamaggad, Ferroelectrics, 277 (2002) 117; Ravindra Dhar, Phase Transitions, 79, (2006) 175; I. Dierking, Symmetry, 6 (2014) 444. 5) L. Navailles, R. Pindak, P. Barois, and H. T. Nguyen, Phys. Rev. Lett.,74 (1995) 5224. 6) M. Brunet, L.Navailles, and N.A. Clark, Eur. Phys. J. E, 7 (2002) 5. 7) A.C. Ribeiro, Ph.Barois, Y. Galerne, L. Oswold, and D. Guillon, Eur. Phys. J. B, 11 (1999) 121. 8) P. A. Pramod, R. Pratibha, and N. V. Madhusudana, Curr. Sci., 73 (1997) 761; G. G. Nair, Curr. Sci., 74 (1998) 98. 9) I. Dierking, G. Scalia, P. Morales, D. LeClere, Adv. Mater., 16, (2004) 865; I. Dierking, G. Scalia, P. Morales, J. Appl. Phys., 97 (2005) 44309-1. 10) R. Basu, C. Rosenblatt and R. P. Lemieux, Liq. Cryst., 39, (2012) 199. 11) (a) W. Lee, C. Wang and Y. Shih, Appl. Phys. Lett., 85 (2004) 513; (b) C. Huang, C. Hu, H. Pan and K. Lo, Jpn. J. Appl. Phys., 44 (2005) 8077; (c) C. Huang, H. Pan and C. Hsieh, Jpn. J. Appl. Phys., 45 (2006) 6392. 12) H. Chen, W. Lee and N. Clark, Appl. Phys. Lett., 90 (2007) 033510. 14

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13) R. Pratibha, K.Park, I. Smalyukh, W. Park, Opt. Exp., 17 (2009) 19459. 14) A.C. Balazs, T. Emrick, T. P. Russell, Science, 2006, 314 (2006) 1107. 15) G. Cordoyiannis, , P. L.Pérez, C. S. P. Tripathi, B. Rožic, U. Tkalec,V. Tzitzios, E. Karatairi G. Nounesis, Z. Kutnjak, I. Muševic, C. Glorieux, S. Kralj and J. Thoen, Liq. Cryst., 37, (2010), 1419; E. Karatairi, B. Rožič, Z. Kutnjak, V. Tzitzios, G. Nounesis, G. Cordoyiannis, J. Thoen, C. Glorieux, and S. Kralj, Phys. Rev. E, 81 (2010) 041703. 16) (a) M. Trcek, G. Cordoyiannis, V. Tzitzios, S. Kralj, G. Nounesis, I. Lelidis and Z. Kutnjak, Phys. Rev. E 90 (2014) 032501-1; (b) G. Cordoyiannis, V. S. R Jampani, S. Kralj, S. Dhara, V. Tzitzios, G. Basina, G. Nounesis, Z. Kutnjak, C. S. P. Tripathi, P. L.Perez, D. Jesenek, C. Glorieux, I. Musevic, A. Zidansek,H. Ameinitschand J. Thoen, Soft Matter 9 (2013) 3956; (c) M. Trček, G. Cordoyiannis, B. Rožič, V. Tzitzios, G. Nounesis, S. Kralj,I. Lelidis, E. Lacaze, H. Amenitsch and Z. Kutnjak, Liq. Cryst., 44 (2017) 1575. 17) D.S. Shankar Rao, M. Vijay Kumar, S.Krishna Prasad, U.S. Hiremath, M. Sarvamangala, S. Basavaraja, J. Mater. Chem. C, 1 (2013) 7488. 18) M.Wojdyr, Fityk: a general-purpose peak fitting program, J. Appl. Crystallogr., 43 (2010) 1126. 19) Pragnya Satapathy, Srividhya Parthasarathi, D.S.Shankar Rao, Madhubabu Kanakala, C.V.Yelamaggad and S.Krishna Prasad, Bull. Mater. Sci., 116 (2018) 1. 20) H. Yoshida, Y.Tanaka, K. Kawamoto, H. Kubo, T. Tsuda, A. Fujii, S. Kuwabata, H. Kikuchi and M. Ozaki, Appl. Phys. Express, 2 (2009) 121501. 21) J. Fernsler, L. Hough, R.F. Shao, J. E. Maclennan, L. Navailles, M. Brunet, N. V. Madhusudana, O. M.Monval, C. Boyer, J. Zasadzinski, J. A. Rego, D. M. Walba and N. A. Clark, PNAS,102 (2005)14191. 22) Y. Lansac, M. A. Glaser, N. A. Clark and O. D. Lavrentovich, Nature, 398 54 (1999); S. Krishna Prasad, G. G. Nair, G. Hegde, Adv. Mater., 17 (2005) 2086; C.A. Guymon, E.N. Hoggan, N.A. Clark, T.P. Rieker, D.M. Walba, C.N. Bowman, Science, 275 (1997) 57. 23) G.V. Varshini, D.S. Shankar Rao, P. K. Mukherjee and S. Krishna Prasad, J. Phys. Chem. B, 122, (2018), 10774; G.V.Varshini, D.S. ShankarRao, P.K.Mukherjee, S. Krishna Prasad, Journal of Molecular Liquids, 286 (2019) 110858-1. 24) L. Navailles, B. Pansu, L. Gorre-Talini, H. T. Nguyen, Phys. Rev. Lett., 81, (1998), 4168. 25) Maja Trcek, PhD thesis, Univ. Ljubljana, Ljubljana (2017) 26) Introduction to Phase Transitions and Critical Phenomena, H. E. Stanley, Oxford University Press 1971; C. C. Huang and J. M. Viner, in Liquid Crystals and Ordered Fluids edited by A. C. Griffin and J. F. Johnson (Plenum, New York, 1984), Vol. 4, p. 643 27) S. A. Brazovskii, Sov. Phys. JETP 41, 85 (1975); J. Swift, Phys. Rev. A 14 (1976) 2274; C. Bagnuls and C. Bervillier, Phys. Rev. B 32 (1985) 7209. 28) I. Lukyanchuk, Phys. Rev. E, 57 (1998) 574.

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12OCN

Iso

129oC

N

109oC

Sm C

94oC

B2

75oC

B2’

B2”

68oC

55oC

Cr

116 oC

𝐒𝐦 𝐂𝐀∗

Cr

ro

125.1oC

Sm A

68 oC

-p

Iso

of

TFMHPOBC

117.4 C

94.4 C

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118.4 C

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HLC: 10% of TFMHPOBC in 12OCN Iso BP Ch TGBC* o o o

80.7oC

SmC*

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Figure 1: Molecular structures and transition temperatures of the liquid crystal materials used. The HLC mixture shows a phase sequence, not present in either of the pure mesogens and importantly, exhibits the TGBC* over a large thermal range of 14 K.

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100 nm

ro

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(a)

(b)

-p re lP

8

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0 1.6

2.1

Model

Lorentz

Equation

y = y0 + (2*A/PI )*(w/(4*(x-xc)^2 + w^2)) 0.91929

Reduced Chi-Sqr

0.9686

Adj. R-Square

Value

na

No. of particles

16

2.6

Aspect Ratio

Standard Error

B

y0

-0.46104

0.93656

B

xc

2.33394

0.01564

B

w

0.59191

0.07775

B

A

15.93304

2.45218

B

H

17.13655

3.1

Figure 2: (a) TEM image of gold nanorods establishing their anisotropic shape. (b) Size histogram determined from the TEM image, from which the length and diameter of the nanorods are estimated to be 43.7 nm and 18.9 nm, respectively; the aspect ratio data fitted to a Lorentzian expression yield the peak value to be 2.33  0.02.

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(c ) 0GNR - TGBC*

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(b) 0GNR - TGBC*

(a) 0GNR - Ch

20 m

(e) 6GNR - TGBC*

20 m

(f) 6GNR - TGBC*

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50 m

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(d) 6GNR - Ch

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50 m

20 m

20 m

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Figure 3: POM photographs showing planar aligned samples in the (a) and (d) cholesteric, (b) and (e) TGBC* phase for 0GNR and 6GNR respectively. Particularly to be noticed is the square grid pattern along with Grandjean Cano lines, a texture characteristic of the TGBC* phase. Also shown are the undulated filamentary texture observed in the homeotropic geometry for (c) 0GNR and (f) 6GNR samples.

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120

BP

Iso

116

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o

o

T ( C)

R ( C)

18

12

TGBC* 85 2

TGBA

ro

Ch

4

lP

0

8

-p

4 XGNR (%)

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0

95

na

XGNR (%)

6

8

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Figure 4: Temperature–GNR concentration (XGNR) phase diagram; XGNR =0 represents the host binary system. Interestingly for XGNR =8, the upright TGB phase is induced. Notably, not only the TGBC* phase is stabilized in the presence of GNR, its thermal range gets enhanced for a certain concentration (XGNR=2) by as much as 50% in comparison to the range for the host mixture, as seen in the inset.

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4GNR

ro

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0GNR

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10 m

na

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10 m

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Figure 5: Representative POM photographs showing the square grid pattern in the TGBC* phase obtained using planar aligned samples of HLC (0GNR) and the nanocomposite (4GNR). The increase in the grid spacing for the nanocomposite, is evident.

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(a) 0GNR

4GNR

ro

0GNR

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0.5cm

0.5cm

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(b)

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0

distance (cm)

1

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0

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Gray scale

re

200

Figure 6: Laser diffraction pattern obtained for (a) 0GNR and 4GNR samples from the square grid pattern of the type shown in Figure 5. (b) The position-intensity profile of a line drawn across the diffraction pattern for the 0GNR sample.

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4GNR

2.5

6GNR

dG (m)

2.4

o

Tred1 = -15 C

dG (m)

1.2 0

6

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2GNR

XGNR (%)

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TGBC*

1.3 -20

o

-10

0

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Tred1 ( C)

-p

Ch

0GNR

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Figure 7: Temperature dependence (Tred1={T —Tch-TGBC*}) of the grid spacing (dG) for different GNR concentrations. Away from the TGBC*-Ch transition, the variation is weak, but on approaching it, a divergence is seen, the extent of which is dependent on XGNR. The magnitude of dG increases with increasing XGNR up to 4%, beyond which the trend reverses, a feature exemplified in the dG vs. XGNR behavior at a fixed reduced temperature (see the inset).

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Transmission (arb. units)

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(1)

(3)

(4)

(2)

(b)

2000

Tred2 = - 20 K

min (nm)

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1600

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min (nm)

1800

2500

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 (nm)

-p

1000

of

14

4

XGNR (%)

na

0

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0GNR 2GNR

BP

Ch

4GNR 6GNR

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1000 -30

-20

o

-10

0

Tred2 ( C)

Figure 8: (a) Representative raw scans well in the Ch (scans 1,3) and in the Ch phase near to the transition (scans 2,4) for 0GNR and 6GNR, respectively. It should be noticed that in all cases, the profiles get broadened on introduction of GNR. The minimum in the profiles (min) is associated with the TGB helical pitch. (b) Thermal variation of min for different XGNR provided in terms of reduced temperature Tred2 (={T-TBP-Ch}). Right from the transition and well into the Ch phase, the min variation for the different concentrations collapse onto a single profile, whereas on approaching TGBC* phase separate out as a consequence of the different extents of divergence. For each dataset the Ch-TGBC* transition point is indicated by a short vertical line. The non-monotonic dependence of the magnitude of min at a fixed Tred2= -20 K is shown in the inset. 23

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Tred2 = -19 K

 (nm)

180

240

 (nm)

130 0

4

XGNR (%)

6GN

R

BP 0GNR

100

o

-10

0

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-p

Tred2 ( C)

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-20

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Ch

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Figure 9: Thermal variation of the full-width-at-half-maximum (of the raw profiles such as those shown in Figure 8, for representative materials, 0GNR and 6GNR.  increases on the approaching Ch-TGBC* transition, demonstrating that the photonic bandgap (PBG) enlarges in the TGBC* phase. Interestingly, over the entire temperature range values are higher for 6GNR, further increasing PBG. Inset shows the concentration dependence of which shows a strong increase for 6GNR.

24

d (Å)

1.2 -10

0GNR o

Tred1 ( C)

0

2GNR 4GNR 6GNR

TGBC* (b)

d (Å)

51.5

Tred1 = 2 K

50.7

48

0

(a) 0

ro

o

Tred1 ( C)

XGNR (%)

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-p

-10

4

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51

Ch

(c)

3.0

FWHM/d x10

-3

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Figure 10: (a) Thermal variation of the smectic layer thickness ‘d’ for all the materials studied. Whereas in the TGBC* phase the values correspond to the equilibrium situation, in the Ch phase it arises from the short-range cybotactic order. It should be noticed that d increases with increase in XGNR in both Ch and TGBC* phases. Filled circles mark the data in the co-existence region. Figure (b) shows layer thickness dependence on XGNR in the Ch phase at a particular Tred1, which shows an increase with XGNR. For the pure material (0GNR), the jump in d at the Ch-TGBC* transition (Tred1=0, indicated by vertical dash line) establishes its first order character, whereas for the nanocomposites increasingly continuous variation at the transition points to the transformation being second order. (c) Thermal variation of FWHM normalized with the layer spacing for 0GNR and 6GNR. Introduction of GNR sharpens the diffraction profile (reduced FWHM/d) at all temperatures, in both the Ch and TGBC* phases.

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 (deg)

20

4GNR 6GNR

(a)

Ch TGBC* (c)

19

0.23

(b)

16 2

4

XGNR (%)

o

4

XGNR (%)

-5

0

Tred1 ( C)

re

-p

-10

0

6

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

0

o

Tred1 = -8 C

ro

0.27

 (deg)

10

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Figure 11: (a) Thermal variation of layer tilt angle  for all the materials studied. Solid line is fit to a powerlaw expression (eq.1). Magnitude of  diminishes with increasing XGNR as enunciated in panel (b) having data at a fixed reduced temperature. Figure (c) shows XGNR dependence of the power-law exponent remaining in the vicinity of that expected for the tricritical point. The error bar in determining the value of  is smaller than the symbol size used.

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Undulating GB

TGB helical axis

Smectic layers

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LC molecules in SmC* SmC* helical axis

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GNR with ligands

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Figure 12: Schematic representation of the TGBC* phase when gold nanorods are incorporated. The grain boundaries (GB) are presumed to be undulating in the plane normal to the TGB helical axis. Specifically noted is that the GNRs are contained in the plane of GB, a feature proposed to be resulting in enhanced stability of the TGBC* phase.

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Influence of Gold Nanorods on the Structure and Photonic Bandgap in a Twist Grain Boundary Phase with Smectic C* Blocks Rajalaxmi Sahoo,1,2 D.S. Shankar Rao,1* Uma S. Hiremath,1 C.V. Yelamaggad1, Pravin Shinde,3 B.L.V Prasad,3 and S. Krishna Prasad1 1 Centre for Nano and Soft Matter Sciences, Bengaluru 560013 India 2 Manipal Academy of Higher Education (MAHE), Manipal 576104, India 3 National Chemical Laboratory, Pune India *email: [email protected]

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Escalation in the TGBC* thermal range by inclusion of GNRs. Enhancement in square grid periodicity by GNR. Switch from first order to second order cholesteric-TGBC* transition by GNR. Potential for independently controlled 3D photonic bandgap system.

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Highlights of the studies

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