Nanophase Segregation of Nanostructures: Induction of Smectic a and

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B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Nanophase Segregation of Nanostructures: Induction of Smectic a and Reentrance in a Carbon Nanotube/Nematic Liquid Crystal Composite Gowthampura Vidyashankar Varshini, Doddamane Sreenivasamurthy Shankar Rao, Prabir Kumar Mukherjee, and Subbarao Krishna Prasad J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08887 • Publication Date (Web): 01 Nov 2018 Downloaded from http://pubs.acs.org on November 2, 2018

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The Journal of Physical Chemistry

Nanophase Segregation of Nanostructures: Induction of Smectic A and Reentrance in a Carbon Nanotube/Nematic Liquid Crystal Composite G.V. Varshini,1 D.S. Shankar Rao,1* Prabir K. Mukherjee2 and S. Krishna Prasad1 1Centre for Nano and Soft Matter Sciences, Jalahalli, Bengaluru 560013, India 2Government College of Engineering and Textile Technology, Serampore, India *email: [email protected] Abstract: Although representing drastically different chemical nature and type of interactions, the similarity of shape anisotropy of the constituents has created much interest in composites of calamitic liquid crystals (LC) and carbon nanotubes (CNT). Despite a significant volume of studies on the physical properties of such composites, influence of CNT on the celebrated reentrant phenomenon in LC has not been studied. We report here that a small concentration of CNT doped to a “nematic mesophase only” material not only induces the layered smectic A mesophase, but leads to the nematic-smectic-nematic re-entrant sequence as well, demonstrating the delicate interplay between the two entities. To explain this unusual observation we propose nanophase segregation of CNT as a possible mechanism. A combination of Flory-Huggins theory and Landau-de Gennes theory has also been provided supporting the observed feature. Introduction The mutual influence of liquid crystals (LCs), an exemplary anisotropic soft matter, and carbon nanotubes (CNTs) as the archetypal nanoparticle, has been the focus of research, having major implications in fundamental science as well as technologically important; the topic has been reviewed quite exhaustively.1-3 While the CNTs stand to gain large well oriented region caused by the elastically soft LCs, effect on the physical properties of the LC phases, the orientationally ordered fluid nematic (N), the one dimensionally periodic layered smectic A (SmA) and the ferroelectric phases have been well studied. Surprisingly, composites of CNT and LC exhibiting the re-entrant nematic (RN) phase sequence have not been studied. A phase is said to be reentrant if upon a monotonic variation of thermodynamic field such as temperature or pressure, the system returns to the same structure after one or more transitions involving other phases.4-6 In 1 ACS Paragon Plus Environment

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fact the observation of RN phase in LCs completes the de Gennes’ analogy7 between normalsuperconductor and nematic-smectic transitions. The finding of N-SmA-RN sequence led to a surge of activity,8-9 with other sequences involving the isotropic,10-11 ferroelectric and ferrielectric,12 the twist grain boundary phases,13 including multiple re-entrances,14 being reported. In these systems, the occurrence of re-entrance has been entirely due to forces responsible for liquid crystallanity. An exception has been the dynamic self assembly of the layered phase due to photoisomerization. In this letter we demonstrate the induction of the SmA mesophase with a consequent N-SmA-RN phase sequence on doping CNT in very small concentrations to an otherwise “nematic mesophase-only” material. Proof for the appearance of the smectic phase is provided through optical microscopy, laser transmission, Frank elastic constant and Xray diffraction studies. We argue that a nanophase segregation mechanism to be the underlying cause for the observations, and also provide a theoretical model to support the observations. Experiment Materials The host LC material is a chosen mixture of the hexyloxy- and octyloxy cyanobiphenyl (6OCB & 8OCB from BDH) binary system (see Figure 1), well known to exhibit, over certain range of concentrations, the reentrant sequence N-SmA-RN, and a bounding of the SmA phase for 6OCB > 28.5 wt%. We selected the mixture with a 6OCB concentration of 29.4%, which lies just beyond the apex of the parabola describing the N-SmA-RN phase line. This mixture is referred to as host liquid crystal (HLC). The employed single walled CNT (Heji) –diameter ~2 nm, aspect ratio ~250 – was doped at a small concentration (0.34 weight%) into the HLC mixture details of which are explained below. Preparation of HLC+CNT composites 2 ACS Paragon Plus Environment

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CNTs tend to aggregate due to the strong van der Waal interactions between adjacent tubes, which should be overcome to realize a homogeneous LC+CNT composite. For this purpose CNT was added into the vial containing HLC & acetone and the solution was stirred continuously for 24 hours. Subsequently the solvent was evaporated and to ensure any traces left over are removed, the sample was kept for 1 hour at 100oC, a temperature well above the isotropic point. Non-observation of sedimentation of CNT in the vial even after extended periods of time indicated a well-prepared mixture. The homogeneity of the composite and the uniform dispersion of CNT were confirmed by observing a thin film of the sample under a polarizing microscope (POM). Technique The dielectric measurements were carried out using Impedance analyser HP4194A. The samples are sandwitched between two indium tin oxide (ITO) coated glass plates, pretreated with silane (ODSE from Aldrich) solution for homeotropic alignment, a polyimide solution (PI2555 from HD Microsystem) and rubbed unidirectionally for planar alignment, were used. The Xray diffraction measurements were performed using PANalytical X'Pert PRO MP X-ray diffractometer consisting of a focusing elliptical mirror and a fast high resolution detector (PIXCEL),15 the wavelength of the radiation is 0.15418 nm. The profiles collected using this apparatus were analyzed using Fityk profile fitting software.16 Raman spectra were acquired using a Horiba Jobin Yvon XploRA confocal Raman microscope with 532 nm laser excitation. Results and Discussion Below the isotropic point (76 oC), the HLC mixture shows only the N phase right down to room temperature (~25oC), and presents the mosaic texture, characteristic of the nematic 3 ACS Paragon Plus Environment


phase. In contrast, the HLC+CNT composite presents a richer behaviour: while cooling the sample from the isotropic phase exhibits first the mosaic texture, which at a lower temperature transforms, to a fan-shaped texture that signifies the smectic A phase. Further lowering of temperature results in the return of the mosaic texture completing the phase sequence of N-SmARN with the induction of the SmA phase (see Figure 2 for POM textures). Figure 3 presents the temperature dependent He-Ne laser transmission experiment carried out on HLC and CNT+HLC composites. To maximize the change in intensity across, especially the N-SmA transition, cells providing a hybrid alignment of the molecules was employed: while the surface coating on one glass plate had a polyimide layer promoting planar alignment, the other plate had silane coating which facilitates homeotropic alignment; the intensity transmitted through the cell is a measure of the birefringence of the sample. The isotropic-nematic (I-N) transition is marked by an abrupt increase in intensity, a feature seen in both samples. However, the composite shows a notable reduction (1.8 oC,) in TIN, the I-N transition temperature. This is higher than that reported by Basu et al,17 who obtained a maximum shift of 1.1 oC. It should however be noted that these authors employed MWCNT although of comparable concentration. But both these values are far smaller compared to the unusually large shift reported by Duran et al.18 On further cooling the sample, HLC shows a very weak thermal dependence, although with a gentle maximum around 41.5oC. In contrast, the CNT composite presents a drastically different profile with a precipitous drop at 41.7oC followed by a plateau minimum and then a sharp rise around 29oC. These temperatures agree well with the N-SmA and SmA-RN transformations as seen with POM textures; the qualitative changes in intensity are also along the expected lines for a hybrid aligned sample. In the following we present two other confirmations in terms of the elastic constant and structural aspects. 4 ACS Paragon Plus Environment

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The elastic deformation of the director in the nematic phase can be described by three principal Frank coefficients: splay, twist and bend (Ks, Kt and Kb). However, owing to the condition the layer spacing is a conserved quantity, the twist and bend distortions are absent in the SmA phase. If the transition between the N and SmA phases is second order then Kt and Kb diverge on approaching the SmA phase. Thus measurements of Kb, possible through magnetic field-driven Freedericksz transformation, serve to prove the existence of the SmA phase. For these studies the samples were contained in a cell made of two indium-tin-oxide (ITO) coated glass plates pretreated with a silane solution to promote homeotropic alignment of the molecules. The cell placed inside a temperature-controlled stage was placed between the pole pieces of an electromagnet capable of a maximum field of B = 2 T with magnetic field direction perpendicular to the initial director orientation. For determining the director orientation the sample capacitance (Cp) was measured by applying a small probing field normal to the substrate surfaces. Both HLC and the composite exhibit positive dielectric anisotropy, || > , || and  indicating directions parallel and perpendicular to the director. Thus the measured capacitance corresponds to the equilibrium || for fields less than a critical value Bc, and for B > Bc the director deforms and at large fields reaches a limiting capacitance corresponding to . The critical field Bc is a direct measure of Kb through Bc   o K b /  a  , with a as the diamagnetic 1/ 2

susceptibility anisotropy.  vs. B measurements for HLC and HLC+CNT samples obtained at several temperatures are shown in Figures 4 (a) and (b) respectively. While weak changes are seen for HLC, large changes, more importantly non-monotonic variation, of Bc (the knee point in the data sets) is observed for the composite. While the HLC sample has a weak thermal dependence of Bc (Figure 4(c)), the CNT composite has a gentle dependence till ~ 45 oC, then a growth reminiscent of critical behaviour characteristic of the N-SmA transition, and a mirror-like 5 ACS Paragon Plus Environment


behaviour below 28 oC, as expected for the SmA-RN transition. The observed features are hallmarks of a system exhibiting the N-SmA-RN phase sequence, confirming our proposal that even a minute amount of CNT results in the appearance of SmA phase (and consequent reentrance) unlike the host LC mixture that has only the N phase. It may be pointed out that the non-CNT mixture also exhibits a maximum, albeit very weak, just as the transmitted intensity (Figure 3). Under normal circumstances a single mesophase, viz., nematic would lead to a monotonic variation with temperature without a maximum in Bth or Ilaser. A possible reason is that at the studied composition the system is quite close to the inflection point in the binary phase diagram, i.e., in the vicinity of the tip of the parabolic phase boundary. According to the Landau-de Gennes theory19 for the N-SmA transition the thermal variation of Bc (strictly speaking Kb) can be described by a power-law expression in reduced temperature with the same exponent as that for the temperature dependent smectic correlation length. The data were thus analyzed using x

 T  TAN    B2 B  B1  (1)  TAN  where B1 and B2 are constants, and TAN, the N-SmA transition temperature. The fitting which is 2 c

quite good (as also seen from the log-log plot shown in Figure 5) yielding TAN = 313.09  0.04 K and exponent x = 0.65 ± 0.02. This value of x is quite close to that expected for the XY universality class (x ~ 0.66), and in remarkable agreement with that reported20 for 8OCB (one of the constituents used here). To confirm whether similar behaviour is obtained for the RN-SmA part also, a larger temperature range data, extending to sub-ambient values, are required. Now we present structural evidence for the induction of the SmA phase in the CNT composite. Xray diffraction profiles using an apparatus described earlier15 are shown in Figure 6(a) for the HLC and HLC+CNT materials at T=36oC. The broad and diffuse profile, as expected 6 ACS Paragon Plus Environment

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for the nematic phase, remained the same throughout the temperature range of HLC, except for a slight reduction in the width at the lowest temperatures. In contrast, for the CNT composite the profiles are broad and diffuse in the high and low temperature regions, while in the intermediate regions a sharp and intense peak is seen, obviously due to the induced SmA phase. The thermal variation of the half-width-at-half-maximum (HWHM) obtained by fitting the profile is shown in Figure 6(b) and the behaviour is consistent with the observations described above. The CNT composite exhibits abrupt drop in HWHM at temperatures corresponding to the transitions to the SmA phase. In contrast, the HLC material presents a broad minimum, whose lowest value is much above seen for the SmA phase of HLC+CNT. While a flatter variation should be expected for materials with only the nematic phase, the trend in Figure 6(b) and comparable features seen for HLC in Figures 3 and 4 suggest the significant growth of smectic-like short-range (cybotactic) order owing to the proximity of HLC to the composition corresponding to the tip of the parabolic smectic phase line. Finally, we look at a possible explanation based on the molecular arrangement resulting in the induction of the smectic phase in an otherwise nematic-only material. Two other cases of such an induction in a nematic base system, reported earlier, are relevant here. Both appeal to local level segregation as the cause, and smecticity requires, at least to a certain extent, bifurcation of the aromatic and aliphatic regions of the LC molecule. In one case the minority polymer content bereft of any aromatic regions differs significantly from the LC comprising aromatic regions, resulting in segregation.21 The second case is that in which photoisomerisation drives a shape change in the guest azobenzene derivative.22 The consequent shape dissimilarity between the guest and host molecules creates a nanophase segregation23 resulting in photodriven smectic phase.22 In both cases the experimental evidence for the nanophase segregation is the

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increase in the smectic layer spacing. The Xray measurements described above indeed show (Figure 6c) an enhancement in the spacing obtained for the composite (dCNT = 3.13 nm). It should, of course, be borne in mind that for the HLC mixture (dHLC = 3.09 nm) it is the spacing of the smectic-like cybotactic region. Nevertheless, a clear increase of d (dCNT – dHLC) = 0.04 nm is seen upon addition of CNT. Taking cue from the models proposed in the earlier cases, we propose the following keeping in mind that HLC is near the tip of the parabola for concentrations below which the host system itself exhibits the smectic phase. In other words, the system has a strong bias towards formation of the smectic phase in the “catchment area” near the apex of the parabola. Thus a small perturbation due to the existence of CNT tilts the balance to induce the smectic phase. Two possibilities can be considered depending on the mutual orientation direction of LC and CNT. If in all the mesophases, the CNT remain parallel to the nematic director then near the catchment area an initial increase in the orientational order (S) will favour a better bifurcation of the aromatic and aliphatic parts of the LC molecules resulting in the SmA phase. At a much lower temperature, the increased S and its coupling to the smectic order parameter may actually introduce frustration effects, as has been envisaged for the existence of re-entrance itself. The simple mean field theory presented here in fact is in line with it. However, as we shall see below the Xray and Raman results cannot explain this possibility. Besides, the nematic-isotropic transition temperature is lowered on adding CNT, contrary to the expectation if S is increased. Concomitant reduction in the dielectric anisotropy (see Figure 7) also gives the credence to the argument that S is not increased. The second scenario is that at the molecular level, the structural dissimilarity between CNT and HLC segregates CNT into a separate layer that gets interleaved between layers comprising entirely HLC molecules, resulting in a finite d (CNT being


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orthogonal to the nematic director has in fact been contemplated by other authors.24-25) Obviously for packing reasons, the tube axis of CNT must now be perpendicular to the layer normal. However, there is a little fallacy here. Considering that the interleaving layer consists of only one CNT along the layer normal direction, the increase in spacing must be comparable to 2 nm, 50 times larger than experimentally observed. A similar discrepancy is seen in the photodriven case,22 and it may be proposed that the observed d is a spatial average, and also that the concentration of CNT is very small (0.34%). A larger concentration doping of CNT, if realizable may achieve the expected d values. It must be noted that unlike in the previous cases mentioned above, both the host (LC) and the guest (CNT) have a similar shape (rod-like) and thus one should not expect a nanophase segregation of CNT to a separate region. However, the aspect ratios are substantially different, with the LC having values of ~ 6 and the CNT ~ 250. For a nematic, a large nanoparticle, like CNT, can orient itself along the nematic director (n) direction to reduce any frustration in orientation of LC molecules around the CNT. This is compatible with the libration of the LC molecules permitted along n. Thus, for concentrations immediately beyond the parabola, the frustration caused by the contradictory requirements of HLC favouring a smectic and the CNT wanting to retain a nematic order may be overcome by creating nanophase segregation. Support for this scenario is also seen in the Raman sprectroscopy measurements obtained by having the nematic director parallel or perpendicular to the polarizing axis of the laser (Figure 8). The peak at 1608 cm-1 due to the aromatic rings in the host LC does create an experimental difficulty to separate the contribution from the G band of CNT. However, we have been quite successful in doing so and note that prominently in the SmA phase, and to a lesser extent in the N phase (close to the induced SmA), the G band peak is stronger for the n perpendicular laser polarization, than for the parallel case. This is to be indeed expected for the



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nanophase segregation mentioned above. Experiments wherein composition of the HLC and the CNT content in the composite are varied can be expected to throw more light on these unique features. Even as a strategy to control the nature of self-assembly by combination of drastically different aspect ratios of the entities could be a generically important and provide a new dimension to explore in soft condensed matter.

Theory In the experimental explanation, we use the results of the different probes, XRD, Raman, etc. to suggest segregation as a possibility. However, in the light of the fact that there has been no Landau model that brings out the nanophase segregation we have explored the standard approach and obtain the possibility of the induction of the phase. In an effort to understand the induction of the SmA and RN phases in the HLC+CNT mixture we use a combination of FloryHuggins and Landau-de Gennes theories.26-27 The total free energy per unit volume of the HLC+CNT mixture can be written as ―1 ―1 𝐹 = 𝑘𝐵𝑇[𝑣𝐶𝑁𝑇 𝜑ln 𝜑 + 𝑣𝐿𝐶 (1 ― 𝜑)ln (1 ― 𝜑 + 𝑣0―1𝜒𝜑(1 ― 𝜑)] 𝜑

+ 𝑘𝐵𝑇𝑣𝐶𝑁𝑇

[ (1 ― )𝑆 1

𝑢

2

3

2 𝐶𝑁𝑇

𝑢

𝑢

― 9𝑆3𝐶𝑁𝑇 + 6𝑆4𝐶𝑁𝑇

]

1 1 1 1 1 + (1 ― 𝜑)[ 𝑎𝑆2 ― 𝑏𝑆3 + 𝑐𝑆4 + 𝛼𝜓20 + 𝛽𝜓40 2 3 4 2 4 1 1 1 1 + 2𝜆𝜓20𝑆 + 2𝛿𝜓20𝑆2]+𝜑(1 ― 𝜑) ― 2𝛾𝑆2𝑆𝐶𝑁𝑇 + 2𝜂𝜓20𝑆𝐶𝑁𝑇

[

]

(2)

The first bracket in the free energy (2) describes the free energy of isotropic mixing.26 The second bracket is the contribution of the CNT dispersed in HLC.28 The third bracket corresponds to the free energy of HLC (6OCB+8OCB) which describe the N-SmA phase transition27 and the 10 ACS Paragon Plus Environment

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last bracket is the free energy associated with the coupling between the order parameters of HLC and CNT. 𝑘𝐵 is the Boltzman constant and T is absolute temperature. Here 𝑆 and 𝜓0 are the nematic and smectic order parameters, 𝑆𝐶𝑁𝑇 the degree of orientaional ordering of CNT,28 𝜑 and (1- 𝜑) the volume fractions of CNT and HLC, 𝜒 the Flory-Huggins interaction parameter. Here 𝜋

𝜋

𝑣𝐶𝑁𝑇 ≈ 4𝐿𝐷2 and 𝑣𝐿𝐶 ≈ 4𝑙𝑑2 are the volumes occupied by CNT and LC, having 𝐿, 𝑙 and 𝐷,𝑑 as their length and diameter. 𝑢 =

𝜑𝐿 𝐷

is related to the volume fraction of CNT. 𝑣0 is the volume of

cell of the Flory lattice. We assume 𝑣𝐿𝐶 = 𝑣0. As usual we assume, 𝑎 = 𝑎0(𝑇 ― 𝑇1∗ (𝑦)) and 𝛼 = 𝛼0(𝑇 ― 𝑇2∗ (𝑦)) with 𝑎0 > 0, 𝛼0 > 0. For HLC 𝑇1∗ (𝑦) = 𝑇1 + 𝑡1𝑧 and 𝑇2∗ (𝑦) = 𝑇2 +𝑡2𝑧 ,20 with 6𝑂𝐶𝐵

𝑦

𝑧 = 8𝑂𝐶𝐵 = 1 ― 𝑦, 𝑦 being the concentration of 6OCB. We choose 𝑏 > 0, 𝑐 > 0 and 𝛽 > 0 for the stability of the free energy (2). The parameters λ, δ, 𝛾 and η are coupling constants. λ is chosen negative and δ is chosen positive to favour the SmA phase over the nematic phase. The coupling cosntants 𝛾 and η are chosen positive. Here δ allows reentrant effects.29-31 Minimization of Eq. (2) with respect to CNT order parameter 𝑆𝐶𝑁𝑇 (neglecting the higher order terms like 𝑆3𝐶𝑁𝑇 and 𝑆4𝐶𝑁𝑇), we get 𝑆𝐶𝑁𝑇 =

(𝛾

)

𝜂

(1 ― 𝜑) 2𝑆2 ― 2𝜓20

(

―1 𝑘𝐵𝑇𝑣𝐶𝑁𝑇 1―

(3)

)

𝑢 3

After the substitution of 𝑆𝐶𝑁𝑇 (Eq. (3)) into Eq. (2), we get ―1 ―1 𝐹 = 𝑘𝐵𝑇[𝑣𝐶𝑁𝑇 𝜑ln 𝜑 + 𝑣𝐿𝐶 (1 ― 𝜑)ln (1 ― 𝜑 + 𝑣0―1𝜒𝜑(1 ― 𝜑)] 1

1

1

1

1

+𝜑(1 ― 𝜑)[2𝑎𝑆2 ― 3𝑏𝑆3 + 4𝑐 ∗ 𝑆4 + 2𝛼𝜓20 + 4𝛽 ∗ 𝜓40 1

1

+2𝜆𝜓20𝑆 + 2𝛿 ∗ 𝜓20𝑆2]

𝑐∗ = 𝑐 ―

(4)

𝛾2

(

)

𝑢

―1 2𝑘𝐵𝑇𝑣𝐶𝑁𝑇 1―3

𝜑(1 ― 𝜑)


(5)


𝜂2

𝛽∗ = 𝛽 ― 𝛿∗ = 𝛿 +

(

𝑢

(

𝑢

―1 2𝑘𝐵𝑇𝑣𝐶𝑁𝑇 1―3

)

𝛾𝜂 ―1 2𝑘𝐵𝑇𝑣𝐶𝑁𝑇 1―3

)

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𝜑(1 ― 𝜑)

(6)

𝜑(1 ― 𝜑)

(7)

Now the minimization of Eq. (4) with respect to 𝜓0, we obtain 𝜓20 = ―

(𝛼 + 𝜆𝑆 + 𝛿 ∗ 𝑆2)

(8)

𝛽∗

From Eq. (8) it is clear that in the SmA phase, when 𝜓0 increases 𝑆 also increases if 𝜆 < 0, 𝛿 ∗ > 0. Naturally Eq. (3) is called the smectic line. Now the substitution of 𝜓0 from Eq. (8) into Eq. (4), the free energy (4) can be rewritten as ―1 ―1 𝐹 = 𝑘𝐵𝑇[𝑣𝐶𝑁𝑇 𝜑ln 𝜑 + 𝑣𝐿𝐶 (1 ― 𝜑)ln (1 ― 𝜑 + 𝑣0―1𝜒𝜑(1 ― 𝜑)] 𝛼2

𝛼𝜆

1

1

1

+𝜑(1 ― 𝜑)[ ― 4𝛽 ∗ ― 2𝛽 ∗ 𝑆 + 2𝑎 ∗∗ 𝑆2 ― 3𝑏 ∗∗ 𝑆3 + 4𝑐 ∗∗ 𝑆4]

(9)

where the renormalized coefficients are 𝑎 ∗∗ = 𝑎 ― 𝑏 ∗∗ = 𝑏 ―

𝛿∗𝛼 𝛽

∗

𝜆2

(10)

― 2𝛽 ∗

3𝜆𝛿 ∗

(11)

2𝛽 ∗

𝑐 ∗∗ = 𝑐 ∗ ―

𝛿∗2

(12)

𝛽∗

The equilibrium condition can be written as 𝛼𝜆

― 2𝛽 ∗ + 𝑎 ∗∗ 𝑆 ― 𝑏 ∗∗ 𝑆2 + 𝑐 ∗∗ 𝑆3 = 0

(13)

Now for 𝜓20 = 0, Eq. (8) is a parabola which can be written as 𝜆

𝑆𝜓 = 0 = ― 2𝛿 ∗ ±

2

( ) 𝜆

2𝛿

∗

𝛼

― 𝛿∗


(14)

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𝜆2

Real value of 𝑆𝜓 = 0 exists for 𝑇 ≤ 𝑇2∗ + 4𝛼 𝛿 ∗ . Equation (14) defining the (𝑆,𝑇(𝜑)) the region 0

of parabola where the induced SmA phase can exist. Consequently 𝑇 𝑣𝑒𝑟𝑠𝑢𝑠 𝜑 curve should also be a parabola where induced SmA can exist. Figure 9 shows the temperature dependence of the combined nematic and induced SmA free energy curves for HLC+CNT mixtures for different CNT concentration. The concave free energy curve corresponding to the higher temperature 60𝑜 C is the stable nematic phase. The free energy corresponding to the lower temperature is the stable induced SmA phase. The SmA free energy decreases with increasing temperature. At some intermediate concentration nematic and SmA free energies overlap. Equation (7) shows that 𝛿 ∗ increases with increase of 𝜑 i.e. increasing the concentration of CNTs. For low values of 𝜑, 𝛿 ∗ is weak and the conditions (8) and (14) are satisfied causing induced SmA phase to appear. The insertion of CNTs along the N director increases the nematic order parameter S, which in turns favours the stability of the SmA phase through the basic coupling term λ. For large λ and weak 𝛿 ∗ (low value of φ ). This parabola is just a straight line. So there is no RN phase and N-SmA transition occurs. Thus the SmA phase is induced even for low values of 𝜑. For higher value of 𝜑, 𝛿 ∗ is stronger, SmA phase disappears and RN phase appears, with consequent of N-SmA-RN sequence. The appearance of RN phase is caused when a high value of 𝑆 disfavors the smectic positional ordering 𝜓0. This is possible for the large and positive value of 𝛿 ∗ i.e. large 𝜑. Without CNT, SmA-RN transition takes place at the intersection of the N and SmA equilibrium curves with the smectic line. In the presence of the CNT, SmA-RN transition is induced at a temperature higher than that without CNT. Close to the SmA-RN transition, predicted to be continuous, the smectic order decreases the orientational order.

Conclusion 13 ACS Paragon Plus Environment


In conclusion we have demonstrated that doping a small of amount of CNT leads to selfassembly of the layered smectic phase, and a consequent reentrant phase sequence in a host LC exhibiting a nematic mesophases only. Evidence for the appearance of the smectic phase is provided in terms of optical microscopy textures, laser transmission, elastic constant and Xray diffraction measurements. We propose an argument based on nanophase segregation to be the cause for the unusual induction of the smectic phase. Experiments are underway to find out the influence of the chemical nature and aspect ratio of the nanoparticles. Acknowledgement Funding support from the Thematic project (SR/NM/TP-2 5/2016), Nano Mission, DST, New Delhi, India, is gratefully acknowledged.


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References 1) Lagerwall, J. P. F.; Scalia, G. Carbon nanotubes in liquid crystals. J. Mater. Chem. 2008, 18, 2890-2898. 2) Yadav, S.P.; Singh, S. Carbon nanotube dispersion in nematic liquid crystals: An overview. Progress in Materials Science 2016, 80, 38-76. 3) Dierking, I.; Scalia, G.; Morales, P. Liquid crystal–carbon nanotube dispersions. J. Appl. Phys., 2005, 97, 044309-1-5. 4) Chen, L.; Bokov, A.A.; Zhu, W.; Wu, H.; Zhuang, J.; Zhang, N.; Tailor, H. N.; Ren, W.; Ye, Z.G. Magnetoelectric relaxor and reentrant behaviours in multiferroic Pb(Fe2/3W1/3)O3 crystal. Scientific Reports 2016, 6, 22327. 5) Simons, Y.B.; Wohlman, O. E.; Oreg, Y.; Imry, Y. Phase diagram of reentrant and magnetic-field-induced superconducting states with Kondo impurities in bulk and proximity-coupled compounds, Phys. Rev. B 2012, 86, 064509-1-5. 6) Narayanan, T.; Kumar, A. Reentrant phase transitions in multicomponent liquid mixtures. Phys. Rep. 1994, 249, 135-218. 7) de Gennes, P.G. An analogy between superconductors and smectics A. Solid State Communications, 1972, 10, 753-756. 8) For a review, see e.g., Cladis P. E., in Physical Properties of Liquid Crystals, edited by Demus, D.; Goodby, J. Gray, G. W.; Spiess, H.-W.; Vill, V (Wiley VCH, Weinheim, 1999). 9) Prasad, A.; Malay Kumar Das. Static dielectric properties of two nematogenic compounds and their binary mixtures showing induced smectic Ad and re-entrant nematic phases, Phys. Scr. 2011, 84, 015603-1-9. 10) Lee, W. K.; Wintner, B. A.; Fontes, E.; Heiney, P.A.; Ohba, M.; Haseltine, J. N.; Smith, A.B. Reentrant isotropic phase in a discotic liquid crystal mixture. Liq. Cryst., 4, 1989, 87-102. 11) Fernsler, J. G. et al. Aggregation-driven, re-entrant isotropic phase in a smectic liquid crystal material. Liq. Cryst., 2017, 44, 769–783. 12) Shankar Rao, D.S.; Krishna Prasad, S.; Chandrasekhar, S.; Mery, S.; Shashidhar, R. Xray, Dielectric and High Pressure Studies on a Compound Exhibiting Ferro-, Ferri- and Antiferroelectric Smectic phases. Mol. Cryst. Liq. Cryst., 1997, 292, 301-310. 13) Shankar Rao, D. S.; Krishna Prasad, S.; Raja, V. N.; Yelamaggad, C. V.; Nagamani, S. A. Observation of a Reentrant Twist Grain Boundary Phase. Phys. Rev.Lett. 2001 87, 085504-1-4. 14) Raja, V.N.; Ratna, B.R.; Shashidhar, R.; Heppke, G.; Bahr, Ch.; Marko, J.F.; Indekeu, J.O.; Berker, A.N. Pressure studies on phase transitions in 4-alkoxyphenyl-4’nitrobenzoyloxybenzoates. Phys. Rev. A 1989, 39, 4341-4344. 15) Shankar Rao, D. S.; Vijay Kumar, M.; Krishna Prasad, S.; Hiremath, U. S.; Sarvamangala, M.; Basavaraja, S. Novel columnar–calamitic phase sequences in a binary system of bent-core and rod-like mesogens. J. Mater. Chem. C, 2013 1, 7488-7497. 15 ACS Paragon Plus Environment


16) Wojdyr, M. Fityk: a general-purpose peak fitting program. J. Appl. Crystallogr. 2010 43, 1126-1128 (2010). 17) Basu, R.; Sigdel, K. P.; Iannacchione, G. S. Effect of carbon nanotubes on the isotropic to nematic and the nematic to smectic-A phase transitions in liquid crystal and carbon nanotubes composites. Eur. Phys. J. E, 2011 34, 34. 18) Duran, H.; Gazdecki, B.; Yamashita, A.; Kyu, T. Effect of carbon nanotubes on phase transitions of nematic liquid crystals. Liq. Cryst. 2005, 32, 815-821. 19) Barois, P. Phase Transition Theories, Handbook of Liquid Crystals, Demus, D.; Goodby, J.; Gray, G.W.; Speiss, H.-W.; Vill, V. Wiley-VCH, Verlag, 1998 20) Gooden, C.; Mahmood, R.; Brisbin, D.; Baldwin, A.; Johnson, D. L.; Neubert, M. E. Simultaneous Magnetic-Deformation and Light-Scattering Study of Bend and Twist Elastic-Constant Divergence at the Nematic-Smectic-A Phase Transition. Phys. Rev. Lett., 1985 54, 1035-1038. 21) Guymon, C. A.; Hoggan, E. N.; Clark, N. A.; Rieker, T. P.; Walba, D. M.; Bowman, C.N. Effect of Monomer Structure on Their Organization and Polymerization in a Smectic Liquid Crystal. Science, 1997, 275, 57-59. 22) Krishna Prasad, S.; Nair, G. G.; Hegde, G. Dynamic Self‐Assembly of the Liquid‐Crystalline Smectic A Phase. Adv. Mater, 2005, 17, 2086-2091. 23) Lansac, Y.; Glaser, M. A.; Clark, N. A.; Lavrentovich, O. D. Photocontrolled nanophase segregation in a liquid-crystal solvent. Nature, 1999, 398, 54-57 (1999). 24) Galerne, Y. Interactions of carbon nanotubes in a nematic liquid crystal. I. Theory. Phys. Rev. E 2016, 49, 042702-1-11. 25) Petrov, D. A.; Skokov, P. K.; Zakhlevnykh, A. N. Magnetic field induced orientational transitions in liquid crystals doped with carbon nanotubes. Beilstein J. Nanotechnol, 2017, 8, 2807-2817. 26) Flory, P.J., Principles of Polymer Chemistry, (1953) Cornell University, Ithaca. 27) de Gennes, P.G.; Prost, J., The Physics of Liquid Crystals (Oxford University, Oxford, 1993). 28) Popa-Nita, V.; Kralj, S. Liquid crystal-carbon nanotubes mixture. J. Chem. Phys., 2010, 132, 024902-1-8. 29) Gullion, D.; Cladis, P.E.; Stamatoff, J. X-Ray Study and Microscopic Study of the Reentrant Nematic Phase. Phys. Rev. Lett., 1978, 41, 1598-1601. 30) Cladis, P. E. New Liquid-Crystal Phase Diagram, Phys. Rev. Lett., 1975, 35, 48-51. 31) Pershan P.S.; Prost, J. Landau theory of the reentrant nematic-smectic A phase transition. J. Phys. Lett. (Paris) 1979, 40, L-27-30.


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I

80

N o

T ( C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Sm A 20

RN 24

X60CB (%)

28

Figure 1: Partial temperature-concentration (weight% of 6OCB) phase diagram of the binary system 6OCB/8OCB. The vertical dashed line represents the composition on which the measurements have been carried out.



Figure 2: POM textures at different temperatures in the HLC (left panel) and its composites with CNT (right panel).


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Ilaser

5

1

3

Ilaser (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

HLC

I

N

74 T (oC) 80

HLC+CNT RN

Sm A

25

35

N

o

T ( C)

45

55

Figure 3: Thermal variation of the transmitted laser intensity (Ilaser) for the HLC and the CNT+HLC composite. For HLC, Ilaser shows weak temperature dependence with a broad maximum, whereas the composite exhibits abrupt changes which correspond to the N-SmA and SmA-RN transitions. The inset shows the changes seen across the isotropic -nematic transition, the temperature of which is lower by about 1.8oC for the composite.



1.6

(c)

(a)

1.0



2

2

Bth (T )

A

0

RN

SmA

N

3

B (kG)

1.0

6

(b) D



G F E

0.8

HLC+CNT 0

5

H

T CN C+

0.0

HLC

C

B

0.7

HL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10 B (kG)

HLC 25

o

T ( C)

45

65

Figure 4: Raw profiles showing magnetic field dependence of the normalized permittivity || for (a) HLC at A=68.3, B=49.2 and C=25.5oC and (b) HLC+CNT composite at D=69.8, E=43.0, F=40.7, G=27.8 and H=26.3oC. (c) The threshold 𝐵2𝑡ℎ, taken to be the knee point in the data of panels (a) and (b) is presented as a function of temperature. While HLC presents a weak thermal dependence the composite shows critical divergence on approaching the smectic phase from both N and RN phases. The vertical dashed lines indicate the transition temperatures for the N-SmA and SmA-RN transitions.


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10

0

2

2

Bth (T )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

-1

10

-3

10

-2

(T-TN-SmA)/TN-SmA (K)

Figure 5: Double logarithmic plot of the square of the threshold field versus reduced temperature. The solid line represents fit to equation 1.



20

0.02

o

T=36 C

(a)

HL C+

CN

T

Int. (arb. units)

0.06

HWHM2 (deg)

HLC

0 2.6

2.8

2 (deg)

3.0

HLC

25

(b)

25

HLC

31.0

HLC+CNT

35

o

T ( C)

(c)

HLC+CNT

31.3

d (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

o

T ( C)

45

45

Figure 6: (a) One-dimensional intensity versus 2 profiles for HLC and the composite. While the former is broad and diffuse, the latter depicts a sharp and intense peak, typical of smectic phase. (b) Thermal variation of HWHM of the peaks with HLC having a smooth variation, an abrupt drop in the SmA phase for the composite. Even the lowest value for HLC is much higher than that in the SmA phase, as it should be. (c) Temperature dependence of the spacing corresponding to the XRD peak, presenting qualitative changes similar to that for HWHM are seen. To be noted is that the value for the composite is higher than for HLC.


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1.7

(a)

Iso

 N

  0.6 1.7

(b)



Iso

 SmA



N

0.6 -40

-20

o

(T-TIso) ( C)

0

Figure 7: Thermal variation of dielectric constant ( ) normalized to the value at the transition to the isotropic phase, for (a) HLC and (b) HLC+CNT composite samples; the data are given in terms of reduced temperature T-TIso where TIso is the isotropic-nematic transition temperature for the set. The dielectric anisotropy given by the difference between  and , is seen to be lower for the composite. The transition from the nematic (N) to the inducted smectic A (SmA) phase in the composite is marked by a dashed vertical line.




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n  laser beam

n  laser beam

N

N

Int. (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Sm A

Sm A

RN

RN

1520

1620 -1

Raman shift (cm )

1520

1620 -1

Raman shift (cm )

Figure 8: Raman spectra at representative temperatures in the N, SmA and RN phases, taken with two configurations having the director n parallel (left panels) and perpendicular (right panels) to the polarization of the incoming laser beam for the composite. While the very strong peak, indicated by the down arrow, corresponds to the signal from the biphenyl moiety of the LC, the G band signal from CNT, occurring at ~1580 cm-1, is shown with upward arrow. It is important to note that this peak is prominently seen for the n  laser beam configuration in the SmA phase, weakly so in the N phase, and hardly present in the RN phase.



Figure 9: Temperature dependence of the combined equilibrium nematic and induced SmA free energies (𝑓𝑁, 𝑆𝑚𝐴) versus CNT concentration (φ) for HLC+CNT mixtures. The free energy curve corresponding to the higher temperature 60oC is the stable nematic phase, the free energy corresponding to the lower temperature is the stable induced SmA phase.


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TOC Graphic


Nanophase Segregation of Nanostructures: Induction of Smectic a and

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