Chiral Phases of a Confined Cholesteric Liquid Crystal: Anchoring

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Chiral Phases of a Confined Cholesteric Liquid Crystal: AnchoringDependent Helical and Smectic Self-Assembly in Nanochannels Sylwia Calus, Mark Busch, Andriy V. Kityk, Wiktor Piecek, and Patrick Huber J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03553 • Publication Date (Web): 16 May 2016 Downloaded from http://pubs.acs.org on May 21, 2016

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The Journal of Physical Chemistry

Chiral Phases of a Confined Cholesteric Liquid Crystal: Anchoring-Dependent Helical and Smectic Self-Assembly in Nanochannels Sylwia Całus,† Mark Busch,‡ Andriy V. Kityk,∗,¶ Wiktor Piecek,§ and Patrick Huber∗,‡ Faculty of Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, 42-200 Czestochowa, Poland, Institute of Materials Physics and Technology, Hamburg University of Technology (TUHH), D-21073 Hamburg, Germany, Faculty of Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, P-42-200 Czestochowa, Poland, and Institute of Applied Physics, Department of New Technologies and Chemistry,Military University of Technology, Ul. gen. Sylwestra Kaliskiego 2, P-00-908 Warszawa, Poland E-mail: [email protected],+48343250-815; [email protected],+4940428783135

(May 13, 2016) Abstract ∗

To whom correspondence should be addressed Faculty of Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, 42-200 Czestochowa, Poland ‡ Hamburg University of Technology ¶ Faculty of Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, P-42200 Czestochowa, Poland § Institute of Applied Physics, Department of New Technologies and Chemistry,Military University of Technology, Ul. gen. Sylwestra Kaliskiego 2, P-00-908 Warszawa, Poland †

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Chiral liquid crystals (ChLCs) allow a fundamental insight into the interplay of molecular chirality and the formation of macroscopic, self-assembled helices. They also exhibit unique optical properties, in particular huge polarization rotation, which is employed in a wide range of photonic technologies. Here, we present a study of linear and circular optical birefringence in combination with X-ray diffraction experiments on an archetypical ChLC, i.e. the cholesteric ester CE6, confined in cylinders of mesoporous alumina and silica with distinct polymer surface graftings resulting in normal or tangential wall anchoring. The unconfined ChLC exhibits a discontinuous, first-order isotropic-to-chiral nematic (cholesteric) phase transition with the formation of doubletwist helices and a discontinuous cholesteric-to-smectic A transition. The thermotropic behavior of the confined ChLC, explored in a channel radii range of 7 nm to 21 nm, deviates substantially from bulk behavior. There is no isotropic state. In contrast, a chiral paranematic phase with a preferred arrangement of the ChLC at the channel wall is found. For normal anchoring a radial-escape structure evolves upon cooling. The phase transition to the smectic phase is completely suppressed. For tangential anchoring, a large optical activity indicates a continuous paranematic-to-cholesteric transition with double-twist helices aligned parallel to the long axes of the cylinders. Upon cooling, these helical structures, known as basic building blocks of blue ChLC phases, transform in a continuous manner to a cylinder-aligned smectic A phase.

1. INTRODUCTION The term ”chirality", introduced 1894 by Lord Kelvin, 1 refers to the fact that an object cannot be superimposed to its mirror image. This asymmetry has turned out as decisive in a huge variety of natural phenomena and technological processes, where chiral entities interact, react and self-assemble, in particular in interface-dominated and nanostructured systems. 2–9 In the field of liquid crystalline (LC) systems entirely novel phases were found for chiral


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(polymer SE-130 coating)

(c)

(b')

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*

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Normal anchoring (NA)

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Tangential anchoring (TA)

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(e)

(d) (f)

T

1

*

T

N

(1)

?

1

*

*

N

PN

(2)

Figure 1: Illustrations of collective molecular ordering of chiral molecules inside cylindrical nanochannels as discussed in the text. The P Nk∗ (a) and P N⊥∗ (d) states are characterized by the same liquid isotropic core region, but the channel wall anchoring differs resulting from different surface graftings (polymer coatings). The confined cholesteric Nk∗ (b) and N⊥∗ (1) (e) states represent double-twist and simple-twist cylinders, see also the corresponding cross sections (b’) and (e’) exemplifying the corresponding twisted planes. The cholesteric N⊥∗ (2) state (f), an alternative to the N⊥∗ (1) configuration, represents an escaped radial-twist structure. The confined SmA-state (c) represents a lamellar structure with smectic layers parallel to the long channel axis.



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compared to achiral mesogens. 2,10 Both types of mesogens form nematic (N) and smectic phases with orientational and/or positional order. However, the handedness of the interaction of chiral molecules results in the additional tendency to form twisted arrangements, and thus helical structures. Chiral nematics (N*), which are also known as cholesterics, are organized in planes with no positional ordering. The molecular axes are parallel to a layerdependent direction. This direction or more strictly spoken the director rotates about an axis perpendicular to the layer with a well-defined periodicity (pitch) - see Fig. 1. Often, the periodicity of the helices is very sensitive to the temperature 2 and is of the order of the wavelengths of visible light. Another remarkable class of phases typical of chiral mesogens are the so-called blue phases, 11 termed BP I-BP III. Whereas BP I is an amorphous phase, BP II and BP III possess body-centred cubic and simple-cubic symmetry. The blue phases are liquid phases, thus the molecules do not have positional order. The delicate balance between the local preference for a double-twist structure over a single-twist in a helical phase and the global topological constraint that prevents a double-twist structure from filling the whole space without introducing discontinuities yields three-dimensional regular stacks of so-called double-twist cylinders 11 and topological defect lines. 11,12 The existence of BPs is intimately related to the extent of chirality of a molecule. It can be modelled by the addition of a chiral term to the free energy of a nematic LC. 13–16 When this term is small (low chirality), it leads to a direct I-N* transition. For high chirality, however, the intermediate blue phases become energetically more preferred than cholesteric ones in the vicinity of the I-N* transition. Resulting from this remarkable phase behavior chiral nematics exhibit unique optical properties, such as circular dichroism, giant optical activity, Bragg reflection, 17 electro-optic effects and low-threshold Laser emission. 18 Obviously these effects are not only of high fundamental interest, they also have been exploited extensively in applications employing bulk ChLCs. 19,20 Recently, the interest in the manipulation of matter at the nanoscale has also stimulated


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both fundamental and applied research with regard to nano-confined ChLCs. For example, it could be demonstrated that confinement of chiral nematics opens up the possibility to build organic-inorganic lasers with continuously-tunable lasing wavelength by embedding a ChLC in 10nm-nanochannels. 21 Such devices exhibit a fast response time, since the dynamics of wavelength tuning is limited only by the reorientation dynamics of the small number of LC molecules fitting into a nano cavity. However, the understanding of these effects has remained on a quite qualitative level. 21–27 Theoretical studies on ChLCs in confinement suggest remarkable novel phase behavior for confined systems in comparison to unconfined systems. Depending on the type of restricted geometry the formation of complex patterns of relative arrangements of single-twist and double-twist helices, encompassing long range defect lattices, have been reported. 16,28–30 This sparse knowledge of the phase behavior and dynamics of ChLCs in confinement contrasts the one of achiral mesogens. The miniaturization trends in electronics and optoelectronics, but also the general goal to manipulate and understand matter at the nanoscale has motivated detailed studies of the structural, dynamical and thermodynamical properties of confined and semi-confined achiral mesogens. 31,32 Despite recent experimental advancements to directly probe orientational order parameter profiles in the proximity of planar, solid walls, 33–36 achieving the spatial (and temporal) resolution necessary to rigorously explore these phenomenologies at the nanoscale remains experimentally extremely demanding. Still, it could be revealed that both the collective orientational (I-N) and the translational (Sm-I or Sm-N) transitions are significantly affected by finite size and interfacial (solid-liquid or liquid-liquid) interactions introduced by confining walls 36–44 or the geometrical constraints in nanoporous media. 31,45–64 These studies were partially motivated and/or confirmed by computer simulations of LCs in thin film and pore geometry. 48,65–71 These indicate pronounced spatial heterogeneities, particularly interface-induced molecular layering and radial gradients both in the orientational order and reorientational dynamics in cylindrical channel geometry. 67



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crystalline'

314.9&K&

smec+c'A'

315.3&K&

chiral' 318.4&K& isotrope' nema+c'

Figure 2: Schematic sketch of the cholesteric ester molecule (CE6) along with its liquid crystalline phases and phase transition temperatures in the bulk state. Here, we report optical polarimetry and diffraction experiments on an archetypical chiral mesogen, the chiral ester CE6, see Fig. 2, in the bulk state and embedded into parallel-arrays of cylindrical channels of alumina and silica membranes of different channel sizes. Bulk CE6 exhibits three phase transitions during cooling, 72 an I-N* transition at T1 =318.4 K, a N*SmA transition at T2 =315.3 K and a SmA-Cr transformation at Tc =314.9 K. Moreover, blue phases BP I-BP III have been reported in a quite narrow temperature interval of 0.5 K at the I-N* transition. 73 In order to explore the chiral phases and thermotropic phase transitions of this mesogen we performed temperature-dependent experiments on the optical retardation (linear birefringence), which is sensitive to the collective orientational order. These experiments are complemented by simultaneous experiments of the optical rotation (optical activity), i.e., the rotation of the polarization plane, which is sensitive to helical structures in the molecular condensates. Additional X-ray diffraction experiments allow us to get detailed information on the translational order of the LCs, in particular with regard to the formation of smectic order in the bulk and confined states. Our study aims at fundamental insights on the interplay of molecular chirality, macroscopic, collective chiral substructures and the resulting behavior upon confinement at the nano scale.


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2. EXPERIMENTAL SECTION The cholesteric LC S-(+)-4-(2-methylbutyl)phenyl-4-decyloxybenzoate (CE6) has been purchased from AWAT Ltd. (Warszawa, Poland). A schematic sketch of the molecular structure along with the liquid crystalline mesophases and characteristic transition temperatures in the bulk state can be found in Fig. 2. Porous alumina (pAl2 O3 ) and silica (pSiO2 ) membranes traversed by parallel arrays of cylindrical nanochannels of different diameters were employed as confining hosts. The pAl2 O3 membranes (thickness h =100 µm) were purchased from Smart Membranes GmbH (Halle, Germany). They were fabricated by means of an electrochemical etching process of pure aluminum. In addition to scanning electron microscopy pictures their channel sizes and porosities were determined by volumetric N2 -sorption isotherms measured at T=77 K. These measurements gave the following average channel radii, R: 21.0±2.0 nm (porosity P=24%), 15.5±1.5 nm (P =17%) and 10.0±0.7 nm (P =16%). The pSiO2 membranes were fabricated by oxidation (12 h at T =800 o C under standard atmosphere) of mesoporous silicon. The mesoporous silicon was produced by electrochemical etching of boron doped silicon wafers (resistivity 0.01-0.02 Ω·cm) using an electrolyte mixture of HF(48%):C2 H5 OH (2:3 v/v) and a DC current density of 11-13 mA/cm2 . The etching time was 8 hours. The resulting pSiO2 membranes had a thickness of 340 µm thickness, an average channel radius of 7.0±0.5 nm and a porosity of P = 52%. The native, polar surfaces of pAl2 O3 and pSiO2 membranes favor a tangential anchoring. 47 Thus in nanocylinders an axial orientation of liquid crystalline order is realized. We noticed in preliminary studies that this is not the case for pAl2 O3 -CE6 nanocomposites. They do not show a distinct molecular ordering. Optical tests showed that in the orientationallyordered phases the birefringence is unexpectedly small and its temperature behavior is not reproducible in subsequent temperature circles. This indicated inhomogeneous anchoring conditions. In order to achieve a uniform anchoring two types of polymer coatings, SE130 (dimethylformamid, DMF) or SE-1211 (dimethylacetamid, DMA), which enhance the 7 ACS Paragon Plus Environment


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tangential or normal anchoring, respectively, have been used. The corresponding monomers were dissolved in an organic solvent to get 1% solutions in both cases. Initially, the empty matrices of pAl2 O3 were annealed at 200o C for 1 hour to remove adsorbed water from the channel walls. Then they were immersed into the monomer solutions for 24 hours. After removal from the solution, extra bulk solution was removed with a tissue. The infiltrated membrane was then dried at room temperature for 3 hours and at 60o C for 1 hour in order to remove the solvent from the channels. Finally the adsorbed polymer film was thermo-polymerized at 180o C for 40 min. Estimations based on a comparison of the optical birefringence of the samples with and without coating indicated a thickness of the polymer coating of less than 1 nm. The optical polarization investigations combined two types of measurements performed simultaneously on a sample: i) Optical rotation Ψ measurements along the optical axis of the sample. The optical axis is parallel to the long axis of the channels. ii) Optical retardation ∆ measurements at a certain angle (α ∼ 36o ) of incident laser light (λ = 633 nm) with respect to the optical axis, see the sketch in Fig. 3a. The setup is based on polarization modulation employing a photoelastic modulator (PEM) PEM-90 (Hind Instruments), see Fig. 3b, and is similar to the one used for the experiments in Ref. 74 However, in this study only one PEM was used. The modulated intensities, detected by the photodetectors PD1 and PD2 depend on the sample characteristics Ψ and ∆, respectively. They are analyzed for each arm by two lock-in amplifiers, which measure the amplitudes of the first (IΩ ) and second (I2Ω ) harmonics of the modulated light intensity. The optical rotation Ψ and optical retardation ∆ measured simultaneously in the Ψ- and ∆-arm, respectively, are related to the measured intensity amplitudes by simple relations:

Ψ=

1 arctan(kIΩ /I2Ω ), ∆ = arctan(kIΩ /I2Ω ) 2

(1)

where the effective coefficient k = r(2Ω)·J2 (A0 )/(r(Ω)·J1 (A0 )), r(ω) is the frequency response


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optical axis

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0

A2

-arm o

- 45

45 o (b)

PEM

Temperature

controller

controller

reference (

lock-in

PD 2 lock-in lock-in

50 kHz)

Figure 3: High-resolution optical polarimetry setup for simultaneous measurements of the linear and circular birefringence. (a) A membrane with parallel-aligned cylindrical channels acts as an uniaxial, anisotropic medium, whose optical axis is parallel to the long axis of the channels. Embedding of chiral molecules into the channels can result in two types of optical anisotropy: (i) circular birefringence, i.e. a rotation of light polarization, Ψ, and (ii) linear birefringence, i.e. an optical retardation, ∆. These characteristics can be probed independently by polarized light propagating simultaneously parallel and at a final incident angle α with regard to the long channel axis. With a dual optical polarimetry setup, as sketched in section (b), both optical characteristics can be measured in parallel. Here PBS is a polarizing beam splitter, P is a polarizer, A1 and A2 are analyzers, PEM is a photoelastic modulator, M1 and M2 are mirrors, λ/4 is a quarter-wave plate. The modulated light intensities in the Ψ- and the ∆-arm are detected by the photodiodes PD1 and PD2, respectively, and subsequently analyzed by two pairs of lock-in amplifiers. The angular orientations of the optical elements are indicated in the figure.



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function of the photodetector, J1 (A0 ) and J2 (A0 ) are the values of Bessel functions at the amplitude of the PEM retardation A0 . The modulation frequency is Ω/2π=50 kHz and the retardation amplitude A0 =0.383λ. The effective coefficient k was directly determined within the calibration procedure by performing measurements on ethanol samples. The accuracy for both types of measurements was about 0.005o . The light beams in both arms have been directed in such a way, that they intersected at a common spot on the sample. This ensures that both measured characteristics, Ψ and ∆, result from the same chosen local region of the sample. The sample was placed into an optical thermostat operated by a temperature controller (Lakeshore 340) with an accuracy of the temperature control of 0.01 K. In the case of optical polarimetric experiments, the straight cylindrical geometry employed in our experiments has a number of advantages in comparison to nanoporous materials with random pore networks. In composites, a preferred orientational ordering of the guest molecules results in an excess birefringence, ∆n+ , or associated with it an excess retardation, ∆+ ∝ ∆n+ , which can be easily measured in a sample geometry as it is sketched in Fig. 3a and b. Accordingly, the molecular ordering inside the channels can be precisely characterized by means of optical polarimetry techniques. In the case of LCs the orientational order is described by the scalar order parameter S = 12 h3 cos2 φ−1i, where φ is the angle between the characteristic axis of the molecules and a direction of preferred local molecular orientation (the so-called director ~n). The brackets denote here an averaging over all molecules under consideration, whereas the orientation of the director may vary locally depending on anchoring conditions and/or the specifics of the geometrical constraints. Since the wavelength of the light is much larger than the channel size, the measured retardation linearly scales with hSipv , i.e. the order parameter averaged over the channel volume. Particularly, for optically positive calamatic nematic LCs, the axial molecular ordering inside the nanocylinders, originating from a tangential anchoring, results in a positive excess birefringence (or positive retardation). By contrast, the radial or so-called polar molecular arrangements inside the nanocylinders, which can result from normal anchoring, yields a negative birefringence (or


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negative retardation) with an absolute value approximately twice smaller than in the case of axial arrangement. Examples of these distinct orientations have been reported by Chahine et al. . 75 Molecular chirality brings new features to the optical properties among which the circular birefringence, also called optical activity or optical rotation, is a frequently measured quantity. It is used for identification and/or characterization of helical structures in cholesteric or SmC* bulk phases. The chirality of the single molecules already leads to an intrinsic optical activity of the isotropic liquid. Note that this intrinsic activity is only 3 deg/cm, whereas in the cholesteric phase, with a collective chiral order, it is about 104 deg/cm, i.e. it is more than three orders of magnitude larger. 17 Hence, for materials with a long pitch the helical structure in a bulk cell with homogenous helicity can act as an effective polarization rotator, i.e. the light polarization rotates in a synchronous way with the helix like in twisted nematic LC displays. In the nanoporous membranes the helical structures in different channels are expected to form individually, i.e. they are unphased, which on average should give no optical rotation. However, in this case the light propagates in a dielectric medium with a dielectric constant modulated in a spatially periodic manner, which again should result in a rotation of the polarization. Particularly, an analytical approach for the polarized light propagating along the helix axis leads to the so-called de-Vries equation describing the optical rotation: 17,76 πd Ψ=− 4p

n2e − n2o λ0 · n2e + n2o λ

2

1−

λ λ0

2 !−1 (2)

where p is the pitch length, d is sample thickness, no and ne are the ordinary and extraordinary refractive indices, respectively. According to this equation the optical rotation diverges at the characteristic wavelength λ0 = np, where n is the mean refractive index. Below and above λ0 the optical activity of a bulk cholesteric LC is characterized by opposite directions of rotation, i.e. a right-handed and left-handed one or vice-versa. It is obviously a challenging question, whether the de-Vries equation remains valid in the case of nanocomposites with cylindrical channels filled by ChLCs, since this ansatz 11 ACS Paragon Plus Environment


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was developed for one component homogeneous dielectric media. An appropriate effective medium model would have to consider the peculiar geometric arrangement investigated here, the de-Vries equation should allow, however, to get at least qualitiative and semi-quantitative insights in the behavior.

3. RESULTS AND DISCUSSION Optical polarimetry and x-ray diffraction of the bulk liquid crystal The results of polarimetric measurements for bulk CE6 (26 µm-cell, homeotropic alignment) are presented in Fig. 4. At high temperature there is no optical retardation, ∆ and no optical rotation, Ψ detectable. The LC is in the isotropic phase. Upon cooling, there are distinct changes in these quantities at the temperatures T1 and T2 . The changes at T1 are typical of the isotropic-to-cholesteric transition with the formation of collective helical structures. A homogeneous formation of cholesteric structures is incompatible with the homeotropic boundary conditions at the LC-glass interfaces. This results in domain formation and thus in strong light scattering, so that optical retardation and activity measurements are not possible in the shaded areas of Fig. 4. Upon further cooling the light scattering vanishes at the temperature T = T2 ; both the retardation and the optical rotation are measurable again. This corresponds to the cholesteric nematic-to-Smectic A transition. The retardation, and thus the birefringence, are positive (Fig. 4a), whereas the optical activity measured along the optical axis (incident light is perpendicular to the glass cell plates) is negative (Fig. 4b), i.e. it is characterized by a left-handed rotation. These findings indicate a perfect homogeneous alignment of the CE6 molecules in the SmA phase in this thin-film, bulk geometry. The formation of the SmA phase is also clearly observable in complementary X-ray diffraction experiments. In Fig. 5a the intensity of the (001) Bragg peak at a wave vector transfer −1

q(001) = 0.215 Å , is plotted as a function of temperature during cooling and heating scans. 12 ACS Paragon Plus Environment

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T

2

1

0.0

-0.4

SmA

N*

phase

phase

-0.8

I phase

(b)

314

316

318

T [K]

Figure 4: (a) Optical retardation and (b) optical rotation of bulk CE6 in a homeotropic 26 µm-cell. Dash-dot (blue online color) and solid (red online color) curves correspond to cooling and heating runs, respectively. The shaded temperature regions are characterized by large light scattering originating in the formation of cholesteric domains typical of an inhomogeneously oriented cholesteric phase. Thus, the data presented in the temperature range, T2 < T < T1 , are not suitable for a quantitative characterization of the molecular order. By contrast, in the SmA-phase the liquid crystal is perfectly homeotropically oriented. It is characterized by a positive optical birefringence and weak left-handed optical rotation.



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q

2 qi

300

200

100

0

312

313

314

315

316

317

318

Temperature [K]

−1

Figure 5: Integrated X-ray intensity of the (001) Bragg peak at q = 0.215 Å as a function of temperature for (a) the bulk LC, the LC confined in R =21 (b) and 15 nm (c), respectively. The solid lines represent fits according to a (TC − T )2β -scaling. The insets depict the smectic layering peaks of the bulk and of the confined LC. Moreover, schematics of the kinetic scattering geometries are displayed, where qi , qo , and q are the incident wave vector, the scattered wave vector and the wave vector transfer, respectively. Note that q is parallel to the surface normal of the bulk film and to the long axis of the cylindrical channels, respectively.


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It is direct proportional to the square of the smectic order parameter and indicates, in agreement with the literature, 4 a d(001) = 2π/q(001) =2.9 nm. In agreement with the polarimetry measurements the formation and vanishing of the lamellar order is observable at T2 = 314.7 K and the transition is discontinuous, of first order. Note that we do not observe any decrease or vanishing of the optical birefringence in the vicinity of the isotropic-to-cholesteric transition, as would be typical of the formation of blue phases. 73 This is, however, not too surprising, since the homeotropic alignment suppresses these phases in our sample geometry.

Chiral nematic and helical phases of the confined liquid crystal The results of the optical measurements on CE6 embedded in nanocylinders of different diameters are displayed in Fig. 6. For alumina membranes the observed temperature behavior and the phase sequence both critically depend on the surface grafting, i.e. on the type of LC anchoring favored by the polymer coating. For alumina membranes with tangential (homogeneous) anchoring the optical polarimetry data are reminiscent of the bulk behavior. There are two phase transitions at T1 and T2 as indicated by steep increases of the optical retardation. However, the step-like behavior becomes increasingly suppressed with decreasing channel radii. Nevertheless, even for the smallest radii, as in the case of porous silica membranes (R = 7 nm), both phase transitions can be observed. Quite in contrast, for the alumina membranes with normal (homeotropic) anchoring only one phase transition at T = T1 is indicated by a characteristic kink in the temperature behavior of ∆(T ). Interestingly, for the silica membranes the observed phase sequence is independent of the type of anchoring. In both cases a practically identical ∆(T )-behavior is found. The measured temperature dependences of the optical retardation, ∆ and rotation, Ψ are compatible with the following scenario: Above T1 all composites show a small ∆, independent of the wall anchoring type. It can be traced to ”geometrical birefringence”. It results from the aligned channels in the porous membrane and the fact that the refractive index of the 15 ACS Paragon Plus Environment


pAl O 2

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*

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Figure 6: (a),(c),(e),(g) Optical retardation and (b),(d),(f),(h) optical rotation of CE6 confined in cylindrical channels of alumina membranes (thickness h =0.1 mm, panels (a)-(f)) and silica membranes (thickness h =0.35 mm, (g) and (h)) with different channel radii R as indicated in the figures. The measurements for the distinct molecular anchorings, i.e. tangential (polymer wall coating SE-130) and normal (polymer wall coating SE-1211), are labeled by TA and NA, respectively. Dash-dot (blue or green online colors) and solid (red or orange online colors) curves correspond to cooling and heating runs, respectively. Double arrows marked by ∆+ define the excess retardation with respect to the retardation value extrapolated from the paranematic phase, as discussed in the text.


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filling and the guest material are different. Thus, this contribution is not related to any collective orientational order of the LC in the channels, it is a pure geometric effect. 77 The levels of this pure geometrical contribution are marked in the Fig. 6a, c, e and g by the horizontal broken lines, ∆iso (T ). Depending on the wall anchoring types the corresponding ”isotropic value” ∆iso is asymptotically approached from above or below its value. This is exemplified in Fig. 7 for the alumina composite with channel diameter 2R = 42 nm. Here, the excess birefringence, beyond the pure geometric contribution, ∆+ = ∆ − ∆iso , is marked in the temperature range above T1 for both wall graftings. It is positive for the membrane with tangential anchoring and negative for the membrane with normal anchoring. For both wall anchoring types a small excess birefringence is measured far above T1 and it asymptotically approaches zero. This is characteristic of a paranematic state, as known for achiral, calamatic systems. 47,49,61,78 In this paranematic, or more strictly spoken chiral paranematic state (PN∗ ), the core of the channel filling is dominated by molecular disorder (isotropic liquid state), whereas the interface region is characterized by a preferential molecular orientation, giving rise to a small excess birefringence, see the illustration of the PN∗ state in Fig. 1. The paranematic state in the confined system corresponds to the isotropic state of the bulk LC in the sense that for R → ∞ eventually the bulk behavior is reached. In agreement with the different types of wall anchoring, the different signs of the excess birefringence indicate that molecules near the channel walls are oriented preferably either parallel to the long channel axis in the case of tangential anchoring (see Fig. 1a) or perpendicular to it for normal wall anchoring (see Fig. 1d). Hence, one observes two different paranematic molecular configurations, denoted hereafter as PN∗k and PN∗⊥ state, respectively. Below T1 the collective orientational ordering propagates to the core region of the channels. This is indicated by a considerable increase in the absolute value of the measured retardation. The signs for the different wall anchoring types is consistent with the paranematic states. This means that for a favored tangential anchoring the LC molecules are



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Figure 7: Optical retardation vs. temperature in the vicinity of the paranematic-tocholesteric phase transition point, T1 , measured in CE6 confined in alumina membranes (R =21 nm). Depending on the wall anchoring the excess birefringence, ∆+ exhibits different signs both in the paranematic phase (T > T1 ) and in the confined cholesteric phase (T > T2 ), which indicates different molecular orderings denoted as P Nk∗ and Nk∗ or P N⊥∗ and N⊥∗ , respectively. See Fig. 1 for illustrations of the corresponding molecular arrangements.


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oriented on average nearly parallel to the long channel axis. The chirality of the CE6 molecules, on the other hand, is expected to result in relative twists. Since the channel sizes are several times smaller than the pitch of the helix in the bulk state, one expects that the twist axis is perpendicular to the long channel axis. Hence, the corresponding chiral configuration will develop along the long channel axis. Having no geometrical restriction in this direction, the corresponding helical structures may be quite long, e.g. on the order of the wavelengths of visible light or even larger. An illustration of the expected chiral configuration can be found in Fig. 1b. It corresponds to a double-twist cylinder, one of the basic structural units of the blue phase with cubic lattice. 15,16 In the following, we will refer to this configuration as N∗k , see Fig. 1. The temperature behavior of the optical activity can be considered as an indirect, but very strong argument of the existence of this peculiar chiral molecular N∗k configuration, see Figs. 6b, d and f. In the PN∗k phase (T > T1 ) the optical rotation is small and does not exceed the experimental resolution. The molecular structure in this state is dominated by orientational disorder. Accordingly, the optical activity in this region is of intrinsic molecular origin. Thus it is similarly small as in the isotropic bulk phase (see Fig. 4), except for the additional contribution of the ordered interface layer. The transition to the N∗k phase is characterized by a strong rising of the left-handed optical activity and a negative optical retardation. This can be attributed to a reorganization of the disordered isotropic molecular configuration into an collectively ordered one with a long periodic helical structure aligned along the cylindrical axis. This conclusion is in a semi-quantitative manner also corroborated by the de Vries equation (see Eq. 2), which relates an anomalous rising of the optical activity in cholesterics to the formation of helical structures, in particular in the case where the light wavelengths are close to the helical pitch. The continuous change in the optical birefringence indicates a gradual formation of the confined cholesteric state. However, for larger pore diameters than explored here one expects a discontinuous, bulk-like behavior, as for example found in simulation studies on cholesteric colloidal particles confined in slit-like pores. 9



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Confined chiral nematic state as a function of channel diameter and wall anchoring A comparison of the optical rotatory power of the cholesteric LC embedded in membranes of different channel sizes gives additional interesting insight with regard to the molecular ordering in geometrical confinement. In order to make a consistent comparison, the measured optical rotation has to be normalized to the density of chiral molecules in each case, which results in the normalized specific rotation, Ψn = Ψ/(P · d), where P is the porosity and d the sample thickness. In Fig. 8 Ψn is plotted for the alumina membranes with different channel sizes and coatings. For tangential wall anchoring the decrease in channel diameter leads to a substantial reduction in the normalized specific rotation. The strongest changes are evidently observed in the intermediate confined cholesteric phase, Nk∗ . The magnitude drops about four times, if one compares e.g. the membranes with R = 21 nm to the ones with R = 10 nm, see also the inset in Fig. 8. This behavior could originate in wall roughness, 49 which results in orientational disorder in the interface region. Since the corresponding optical activity contribution is of the order of the intrinsic molecular activity, it is neglegibley small. The rotatory power is rather dominated by the core region of the channel filling and should scale with its relative volume. Thus, the normalized specific optical rotation Ψn is expected to be proportional to (1−l/R)2 , where l is the effective thickness of the disordered, near-interface layer. In the inset of Fig. 8 we display Ψn , measured in the N∗k phase at T =315 K (solid squares), vs. the average channel radius R, and fits by the function f (R) = Ψn0 (1 − l0 /R)2 (solid lines). For the fit parameters Ψn0 =-620 deg/mm and l0 =4.7 nm, we indeed achieve a reasonable agreement between our model and the observed behavior. For small channel diameters (R ≤10 nm) the discrepancy between the experiment and the model is evident. This indicates alternative mechanisms resulting in a faster reduction of Ψn during decreasing R than captured within our model ansatz. One of them originates in the geometrical constraint. In the N∗k phase the helical structure described by the double20 ACS Paragon Plus Environment

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Figure 8: Normalized specific rotation, Ψn vs. T measured in cylindrical nanochannels with different channel radii and tangential (TA) and normal (NA) molecular wall anchorings, respectively. The inset shows Ψn as a function of channel radius R in the confined nematic phases. Solid symbols are experimental data points taken at T =308 K (in the N⊥∗ -phase) and T =315 K (in the Nk∗ -phase). Solid curves are best fits by the function f (R) = Ψn0 (1−l0 /R)2 with the fit-parameters: Ψn0 =400 deg, l0 =5.5 nm (N⊥∗ ) and Ψn0 =-620 deg, l0 =4.7 nm (Nk∗ ).



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twist cylinder is the reason for large optical activity. The cylindrical shape of the channels acts as ordering geometric field forcing an orientation of the molecules along the channel axis in the interface region. In Landau-de Gennes free energy approache 79,80 this ordering field is in agreement with experiments 47,49 and considered to be proportional to the inverse channel radius R−1 . Such a geometric field acts against the natural twisting of the chiral molecules in the direction perpendicular to the long channel axis. Decreasing the twist causes a reduction in the amplitude of the spatial modulation of the dielectric constant as well as an elongation of the helix pitch p. Hence, both effects result in a reduction of the optical activity with a scaling behavior, which evidently differs from the simple model outlined above. A further reduction of the normalized optical rotation is expected in nanoporous silica membranes, which have the smallest radius, R = 7 nm. Unfortunately, these types of samples are not suitable for reliable and precise characterization of the optical activity. This is caused by the strain birefringence along the optical axis. It appears as a residual thermal effect in the preparation of nanoporous silica, particularly during the oxidation of porous silicon to porous silica at high temperatures. Nevertheless, we can conclude that the optical activity in the case of silica nanocomposites is of the order of the strain birefringence or less. The normalized specific rotation does not exceed 5-10 deg/mm. It is at least two orders of the magnitude smaller compared to the Ψn -value in the alumina nanocomposites with tangential anchoring (R =21 nm).

Interplay of chiral nematic and chiral smectic phases of the confined liquid crystals The second phase transition at T = T2 is observed only for tangential anchoring. Its origin is assumed to be the same as in the bulk, i.e. below T2 the confined SmA-phase forms. In absence of a geometrical restriction along the long channel axis the smectic layers can freely develop with the stacking direction along the long channel axis, as is depicted in Fig. 1c. The observed temperature behavior of the linear and circular birefringence appears 22 ACS Paragon Plus Environment

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to be consistent with a formation of such a confined, aligned SmA structure. Particularly, the transition from the N∗k -phase to SmA-phase exhibits an evident increase of the optical retardation accompanied by a considerable decrease of the optical rotation. The formation of layers destroys the long-range chiral structure existing in the confined cholesteric N∗k phase. Thus at the same time (i) the twisting of molecules with the twist axis perpendicular to the long channel axis and (ii) the helical structural modulation along the channel axis disappear. Process (i) leads to a step-like rise of the optical retardation observed at cooling in the vicinity of T2 , since all molecules become practically parallel to the channel axis. Process (ii) reduces the optical activity substantially. However, because of the collective orientational order of the molecules in the SmA phase the optical rotation is substantially larger than in the isotropic phase, where it originates from the intrinsic chirality of the single-molecule. Note that the optical activity in the SmA phase has the same sign as in the bulk samples, i.e. it is left-handed. These conclusions based on the optical experiments are supported by temperature-dependent X-ray diffraction. In Fig. 5(b) and (c) the intensity of the (001) Bragg peak is plotted for two characteristic channel diameters. It increases in the proximity of T2 in accordance with the conclusions derived from the optical experiments outlined above. In particular, a comparison of the bulk behavior (panel a) and the confined state (panel b and c) highlights the continuous, gradual evolution of the smectic layering in the confined LC, in strong contrast to the discontinuous bulk behavior. This observation is in good agreement with a variety of experiments on the smectic-tonematic transition in confined geometry and can be traced to pure geometrical confinement effects as well as quenched disorder QD, i.e. the influence of static randomness, most prominently the channel wall roughness and the channel diameter variations. 49,81 Various realizations of this phenomology could be achieved by confining LCs in geometrically disordered porous materials or gels in the past. 45,75,82 In principle, the geometric restriction introduces two forms of random-field disorder in LCs: random orientational fields that couple to the



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nematic director and random positional fields that couple to the smectic order. Both the second order nematic-to-smectic A and normal-superconducting transitions can be mapped onto each other. Since both can be described by a complex order parameter representing the amplitude and phase of a sinusoidal-varying smectic mass density wave or a macroscopic wave function, respectively, they fall in the universality class of the 3D XY model. However, as was pointed out first by de Gennes, the coupling between nematic (Q) and smectic (η) order parameters actually excludes the N-SmA transition from that class. Conversely, increasing the strength of isotropic QD can gradually shift the character of the N-SmA transition from tricritical back to 3D XY universality. The quasi long-range smectic order is replaced by short-ranged, static fluctuations over an extended T -range and the transition is continuous, as observed here. Whereas QD usually results in a downward-shift of the smectic-A-to-isotropic transition, 83 we observe a shift of the transition to higher temperatures. Moreover, the exponent β characterizing the continuous evolution of the smectic order parameter (I(q) ∝ η 2 ∝ (TC − T )2β ) increases with decreasing channel diameter, i.e. β =0.26 and 0.14 for R=25 nm and 15 nm, respectively. This suggests that the cylindrical channel geometry and the collective alignment of the molecules along the long cylindrical axis favor the establishment of the smectic phase. Moreover, the β’s are significantly smaller than the one expected in the frame of the undisturbed 3D XY model, i.e. β = 0.36, a value which was considered as the limit observed for nanoconfined achiral 8CB under QD. 82,84,85 Our values are rather comparable to temperature scalings observed for 8CB in aerogels or porous Silicon (pSi). 81 The observation of a low value for a continuous transition is in fact not unusual, and is observed in the case of dilute antiferromagnets or disordered ferroelectrics, 86 which are prototypical realizations of the 3D random field Ising model (3DRFIM). The cholesteric LC CE6 embedded into the alumina membranes with normal anchoring is characterized by only one transition before solidification. It exhibits a negative excess birefringence (see Figs. 6a, c and e), which saturates well below T1 for larger channel diameters


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(2R = 42 or 31 nm). An important feature of the confined cholesteric phase is the optical activity (see Figs. 6b, d and f) accompanying the orientational order. Its substantial increase below T1 suggests that the molecular ordering is characterized by a helical structure developing along the long channel axis. Amazingly, this optical rotation is positive (right-handed) for all the alumina membranes with normal type of anchoring, i.e. it is characterized by an opposite direction for the rotation of light polarization compared to the membranes with tangential wall anchoring. The reasons herefore can be manifold. Referring to the de Vries Equation, see Eq. 2 in Methods, opposite directions for optical rotation may be due to the pitch length, p, which depend on anchoring conditions, or the ordered chiral configuration may be larger or smaller compared to the normalized wavelength of the light, i.e. λ/n value. Another reason could be different directions of molecular twisting, which may depend on anchoring conditions and thus result in both right- and left-handed helical structures. Optical polarimetry obviously cannot answer which type of helical structure is realized in each particular case. In alumina membranes with tangential anchoring the normalized specific rotation Ψn , versus the average channel radius R of the confined cholesteric phase N∗⊥ exhibits a trend similar to the N∗k phase. However, the reduction of the absolute value is not as strong as in the N∗⊥ -phase. Remarkably, it is described in an excellent manner by f (R) = Ψn0 (1 − l0 /R)2 with the fit parameters Ψn0 =400 deg/mm and l0 =5.5 nm (see Fig. 8). This suggests that for normal anchoring the role of the geometric ordering field is irrelevant. Accordingly, the reduction of the optical rotatory power with decreasing channel diameter can be well explained by our simple disordered-interface model. The thickness of the disordered layer equals to ∼ 5.5 nm. For the membranes with normal anchoring, the absolute value of the excess retardation in the nearly saturated regime, i.e. far below T1 , is less than half of the saturated excess retardation measured in the SmA phase. This indicates an axial type of ordering. Accordingly, for the ChLC CE6 embedded into the porous alumina membranes with normal anchoring in principle two distinct structures are equally possible: chiral polar [N∗⊥ (1)] or



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chiral escaped radial [N∗⊥ (2)], as sketched in Figs. 1e and f, respectively. Both configurations yield negative excess birefringence. Simple averaging shows that a perfect (fully saturated) N∗⊥ (1)-structure is characterized by an excess optical retardation, which exactly equals half of the retardation of the fully saturated axial configuration (e.g. saturated SmA structure in Fig. 1c). The equality ∆+ (N∗⊥ (1)) = − 12 ∆+ (SmA*) should hold in this case. By contrast, for the N∗⊥ (2)-state an inequality is expected instead, i.e. ∆+ (N∗⊥ (2)) < − 12 ∆+ (SmA*). Since in our system the inequality is indeed fulfilled, we conclude that rather type (2) than (1) is realized in the nanocylinders with normal LC anchoring. Note, however, that for channels with diameters larger than the cholesteric pitch of bulk CE6, and thus for channel diameters on the order of micrometers, the formation of radially-aligned, confined helices could be possible, even for normal wall anchoring. After all, at some characteristic diameter a transition towards the bulk behavior is expected. Moreover, depending on the commensurability of the pitch of the radially-aligned helices with R geometrically induced winding transitions could occur as a function of R variation for this anchoring condition. 9 The absence of the SmA phase in the case of normal anchoring is not too surprising. The curved interface of the cylindrical channel wall results in splay deformations and corresponding deformations of the smectic layers. This rises the energy of the SmA phase. Our experiments indicate that upon cooling in channels with 42 nm diameter or less the chiral nematic, high-temperature phase remains energetically more favorable below T1 .

Confined blued phases Optical measurements showed no hints for the existence of blue phases, typical of the bulk state of CE6. 13,73,87 Their appearance in nanocylinders should result in a decrease of the absolute birefringence in the proximity of the PN∗k -N∗k or PN∗⊥ -N∗⊥ transitions. However, the absence of blue phases in nanoconfinement is easily understandable. The blue phases represent mesoscopic regions composed of translationally ordered double-twist cylinders with 26 ACS Paragon Plus Environment

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defects at their mutual contacts. These structures have lattice periods of several hundred nanometers. It is quite obvious, that in the confined geometry (with channel diameters of 42 nm or less), they cannot form in an undisturbed manner or are completely suppressed. In this respect it is interesting to mention that recent molecular dynamics simulations explored in detail the phase behaviour of chiral mesogens, in particular blue phases in cylindrical confinement. 15,16 Depending on the anchoring and the aspect ratio of channel diameter to typical mesogen size an impressive variety of disclination-line structures were reported for the first time. The formation of one of the basic building blocks of the blue phases, i.e. the double-twist helix in the channels, inferred from our experiment, is in good agreement with these simulations for the case, where the double-twist helix just fits into the mesochannel. As a consequence no defects, in particular disclination-lines, arise. For larger channel diameters, however, where the channels can accommodate two or even more double-twist helices, complex disclination-line patterns are predicted by the simulations, in particular structures where helical disclination lines wrap around the channel’s long axes. Such structures, which have also been reported by Fukuda and Zumer in slit-channels with tangential anchoring, 28 could possibly exist in alumina and silica channels with larger channel diameters than examined here.

4. SUMMARY AND CONCLUSIONS Linear and circular optical birefringence measurements in combination with X-ray diffraction experiments allowed us to gain detailed insights in the phase behavior of a nano-confined ChLC. The thermotropic behavior of the nano-confined ChLC deviates significantly from the bulk and is very sensitive to the wall anchoring: There is no isotropic liquid state for the confined LC. By contrast, depending on the wall anchoring a paranematic phase with a radial or axial arrangement of the LC molecules in the pore wall proximity is indicated by a final optical birefringence of distinct positive and negative sign, respectively. For normal



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anchoring a radial-escape structure evolves upon cooling. The phase transition to the smectic phase is completely suppressed. For tangential anchoring, a large optical activity indicates a continuous paranematic-to-cholesteric transition with double-twist helices aligned parallel to the long axes of the cylinders. Upon cooling, these helical structures, known as basic building blocks of blue ChLC phases, transform in a continuous manner to a cylinder-aligned smectic A phase. The crystalline low-temperature phase of confined CE6 has not been addressed in this study. For tangential anchoring one may expect a highly-textured crystalline structure reminiscent of the bulk one, since this anchoring is compatible with the formation of crystalline layers, typical of the bulk state, along the long channel axis. By contrast, for normal anchoring the radial constraints are rather incompatible with this structure. The cylindrical boundary would result in highly curved, radially-aligned crystalline lamellae. Note, however, that also the crystallization kinetics, most prominently the selection of fast crystallization directions by the cylindrical confinement (Bridgman growth) can be decisive for the crystalline structure in confined geometries, rather than pure anchoring constraints. 32,88–91 In fact, this can result in macroscopic layer rearrangements with regard to the channel axis between smectic and crystalline phases in LCs. 75 Therefore, we believe that a detailed exploration of the confined crystalline phase of CE6 would be particularly interesting in the future. We hope that our study will also stimulate theoretical studies, which have provided important insights on the phase behavior of confined LCs in the past. 16,48,65–71,92 In particular, it would be very helpful for a full quantitative understanding of the experiments provided here and for the design of optical materials based on ChLC/mesoporous hybrids, if also optical properties (linear and circular birefringence) could be calculated within such simulations. We believe that the chiral phase behavior and the strong alignment of the mesophases with regard to the channel orientation is of great potential both for fundamental studies of collective chiral phases at the nanoscale and for the large range of applications employing


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self-assembled, macroscopically aligned chiral molecular phases. For the future, it would be of fundamental and technological interest to study this ChLC in tubular channels of larger diameter and in planar nanoconfined geometry, where simulations suggests the existence of blue phases 16 and other long range defect lattices. 28–30

Acknowledgement This work was supported by the Polish National Science Centre (NCN) under the project ”Molecular Structure and Dynamics of Liquid Crystals Based Nanocomposites” (Decision no. DEC-2012/05/B/ST3/02782). The faculty of Electrical Engineering at Czestochowa University of Technology funded the research by Grant No. BS/PB-3-303-304/11. The German research foundation (DFG) contributed to the research by the Grant No. Hu850/5 and within the collaborative research initiative "Tailor-made Multi-Scale Materials Systems" (project B7), Hamburg.

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10 nm

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Chiral Phases of a Confined Cholesteric Liquid Crystal: Anchoring

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