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Transworld Research Network 37/661 (2), Fort P.O. Trivandrum-695 023 Kerala, India Liquid Crystalline Organic Compounds and Polymers as Materials of the XXI Century: From Synthesis to Applications, 2011: 19-52 ISBN: 978-81-7895-523-0 Editors: Agnieszka Iwan and Ewa Schab-Balcerzak 2. An overview of liquid crystals based on Schiff base compounds Shankar B. Rananavare 1 and V.G.K.M. Pisipati 2 1 Department of Chemistry, Portland State University, Portland, OR 97206, USA 2 Liquid Crystal Research Centre, ECE Department, Koneru Lakshmaiah University, Vaddeswaram, 522 502, India Abstract. In the mid sixties, the pioneering research efforts at RCA and Xerox brought attention to possibility of using a relatively unknown class of organic materials, i.e., liquid crystals (LC’s), for modulating electro-optic properties of light for fabricating a revolutionary new flat panel display. Today the flat panel liquid crystal display devices, (LCD’s) have replaced the bulky and power-hungry cathode ray tubes (CRTs) and thus changed the face of the modern office. In this review, we focus on the first class of pure synthetic liquid crystals based on N-(p-n- alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO.m Schiff’s base compounds, where the n and m represent the chain lengths on either side of the rigid core. This homologous series exhibits rich but subtle poly mesomorphism (exhibition of different liquid crystalline phases) as functions of chain length, isotopic substitution of hydrogen with fluorine, insertion of optically active groups and metals. Further, it has been observed that these materials exhibit different clearing temperatures as well as liquid crystal phase modifications depending on the placement and/or the 11 Correspondence/Reprint request: Dr. Shankar B. Rananavare, Department of Chemistry, Portland State University, Portland, OR 97206, USA. E-mail: [email protected]

Transcript of Liquid Crystalline Organic Compounds and Polymers … Iwan.pdf · Transworld Research Network...

Transworld Research Network 37/661 (2), Fort P.O. Trivandrum-695 023 Kerala, India

Liquid Crystalline Organic Compounds and Polymers as Materials of the XXI Century: From Synthesis to Applications, 2011: 19-52 ISBN: 978-81-7895-523-0

Editors: Agnieszka Iwan and Ewa Schab-Balcerzak

2. An overview of liquid crystals based on Schiff base compounds

Shankar B. Rananavare1 and V.G.K.M. Pisipati2

1Department of Chemistry, Portland State University, Portland, OR 97206, USA 2Liquid Crystal Research Centre, ECE Department, Koneru Lakshmaiah

University, Vaddeswaram, 522 502, India

Abstract. In the mid sixties, the pioneering research efforts at RCA and Xerox brought attention to possibility of using a relatively unknown class of organic materials, i.e., liquid crystals (LC’s), for modulating electro-optic properties of light for fabricating a revolutionary new flat panel display. Today the flat panel liquid crystal display devices, (LCD’s) have replaced the bulky and power-hungry cathode ray tubes (CRTs) and thus changed the face of the modern office. In this review, we focus on the first class of pure synthetic liquid crystals based on N-(p-n-alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO.m Schiff’s base compounds, where the n and m represent the chain lengths on either side of the rigid core. This homologous series exhibits rich but subtle poly mesomorphism (exhibition of different liquid crystalline phases) as functions of chain length, isotopic substitution of hydrogen with fluorine, insertion of optically active groups and metals. Further, it has been observed that these materials exhibit different clearing temperatures as well as liquid crystal phase modifications depending on the placement and/or the 11

Correspondence/Reprint request: Dr. Shankar B. Rananavare, Department of Chemistry, Portland State University, Portland, OR 97206, USA. E-mail: [email protected]

Shankar B. Rananavare & V.G.K.M. Pisipati 20

removal of the electronegative oxygen atom on either side of the rigid benzylidene core. That is, these compounds can be identified as nO.m, n.Om, nO.Om and n.m series. In this review, we briefly cover interesting phase variants, the nature of different phase transitions and phase diagrams of the above four series of homologous series. The main focus lies on the nature of isotropic – nematic (IN), nematic - smectic-A, (NA), smectic–A – smectic-C, (AC) and other higher order smectic to smectic phase transformations. In addition, we provide discussions on multi- critical points such as NA tricritical point (TCP) and ACC* Lifshitz point. The occurrence of such multi-critical points permits predictions of physical properties that are important in material optimization for device applications. Finally we conclude with a new class of amphitropic liquid crystals. Introduction

I. Historical perspective Today the use of LCDs is norm than rarity as it was even 10 years ago. The technological breakthroughs that have led to replacement of ubiquitous cathode ray tubes (CRTs) stretch as far as the mid-sixties when the notion of flat panel display that would consume far less power and space appeared in Radio Corporation of America (RCA) labs [1, 2]. Here, the basic idea was to modulate linearly polarized light transmission through an optically anisotropic medium such as nematic liquid crystal by means of applied electric fields. Thus, these liquid crystals acted as voltage controlled optical valve similar to MOSFET (metal oxide semiconductor field effect transistors). Early segmented direct-drive liquid crystal displays [3] found immediate home in calculators due to their low power consumption. To improve upon cumbersome direct drive approach, a matrix addressing scheme was proposed by Alt and Pesko [4] at IBM and was subsequently elegantly implemented [5] in the STN (super twisted nematic) type of devices developed by Scheffer et al [6]. However, the mid-nineties saw a rapid decline in use of STN displays owing to their inability to address larger area displays arising from inter-pixel cross-talk effects. Today, the key to the dominance of LCD technology is its marriage with the classic semiconductor technology through the use of thin film transistors (TFTs) to address individual pixels. TFT based addressing makes it possible design an entirely digital display. The development of thin film transistors for this application traces its origin to back to the legendary Palo Alto Research Center (PARC) at XEROX [7]. As matter of fact, Xerox had an essential prototype of modern digital LCD device incorporating TFTs as early as early eighties. The main technological hurdle, at the time, was the ability to mass-produce thin film transistors on large area substrates. Herein lies the crucial difference in

An overview of liquid crystals based on Schiff base compounds 21

semiconductor and display industry; the former employs die sizes of few square inches while for the latter the die size is in square feet. Early nineties saw a brief but unsuccessful resurgence of interest in the LCD manufacturing [8] in US guided by ARPA (advanced research projects agency) to establish strategic alternatives to Asian manufacturers. The display market still continues to be dominated by Asian electronic giants such as Sony and Sharp. Mid nineties also saw entry of Samsung in this market who now has now established the largest market share in LCD market [9]. To be successful display manufacturer, clearly, requires not only an expertise in liquid crystals cell processing but also requires an expertise in semiconductor manufacturing. Besides information displays, that thrive on high pixel density, liquid crystals have found many wide ranging applications spanning non-linear optical devices [10, 11] to anisotropic solvents in chemistry [12-14]. Displaytech has commercialized fast spatial light modulators using ferroelectric liquid crystals (FLCs) [15, 16]. In addition, Kent system developed an ultrathin newspaper//book using polymer dispersed and cholesteric liquid crystals [17]. It is not too difficult to imagine the future applications of liquid crystals for bottom-up self assembly methods for nanotechnology [14, 18, 19] as the limitations of currently actively pursued self-assembled monolayer (SAM) methods [20] such as high defect density and inability to work over large surface area are fully realized. Although in all fairness, besides LCD displays, the second commercially successful application of liquid crystal based materials from a technological viability perspective is yet to emerge. Therefore, in this review we will focus mainly on materials properties that are useful in developing better displays while noting along the way potential future applications in other areas. II. Display relevant LC properties The fundamental properties of display relevance of the most commonly used nematic liquid crystals are their orientational elasticity and alignability on wide area substrates [21]. To align liquid crystal molecules parallel to surface (the so called homogeneous alignment) rubbed polymer surfaces or grooved surfaces are used; the macroscopic alignability of LC is a result of elastic energy minimization on such surfaces. In the absence of electric and magnetic fields, lying parallel to grooves is preferred on a macroscopic scale. This molecular level alignment can be perturbed, nonlinearly (switching) through application of modest electric field. Interplay of surface and electrically field (controlled alignment due to dielectric constant anisotropy

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(Δε)) permits fabrication of display devices of directionally aligned fluid on length scales of feet! There exists a threshold voltage at which molecular director begins to align with respect to (or normal to) the applied electric field at the Freederick’s transition. For example, a 90 degree twisted nematic LCD cell has a threshold voltage that is fortunately independent of electrode spacing (LC film thickness) and is give by VTh = π [(K11+K33-2K22)/(ε0Δ ε )]1/2; where K11, K33, K22, are elastic constant associated splay, bend and twist distortion of LC director [22] and ε0 is the permittivity of vacuum. The optical transmission through LC cells can be turned on or off by electrically switching molecular alignment with respect to incoming plane polarized light. This can be modeled using extended Jones matrix formalism. For a simple homogenously aligned LC cell the optical path length (~Δn(birefringence)) affecting the device contrast is highly dependent on the viewing angle. This effect was responsible for poor viewing angle characteristics of early LCDs which have been overcome in last two decades using vertical nematic cells and in-plane switching [23, 24]. One of the main limitations of LCD is their relatively low contrast due to light loss in polarizers that affect their bright on state and leakage of light through the off state. Compared to CRTs or LED displays optical switching of the LCDs is slow. In the absence of electric field, pixel switching time scales directly as the viscosity(η) of nematic liquid crystal and inversely as the orientational elastic constant (s), Kii [22]. Geometrically, the switching time, τ, varies as a square of the gap thickness (d), so overall τ~ ηd2/Ki) [22]. Making devices thinner does enhance switching speed but too small thickness lead to degradation of the device contrast which is related to reduction in optical path length. To reduce viscosity, use of fluorinated functional groups [25] as well as chain unsaturation [26] has been explored. These important considerations dictate the materials and device optimization programs. III. Molecular engineering of LCs for flat panel display applications Molecular factors affecting elastic constants, optical birefringence, switching time have been continually explored both theoretically and experimentally. As it turns out many of these fundamental properties of nematic liquid crystals, Δn, Δε , Kii can be related to the degree of molecular orientational order (S=<P2(cos(θ)>, where P2 is a second Legendre polynomial; and θ is the angle describing instantaneous orientation of molecular long axis and the direction of average alignment of molecules, the director ň [21]). Orientational order, S, exhibits a strong temperature

An overview of liquid crystals based on Schiff base compounds 23

dependence near the nematic to isotropic phase transition (to the so called clearing temperature as nematic liquid crystals in bulk are cloudy and become transparent upon undergoing a phase transition into an isotropic phase). From device engineer’s point of view, in addition to having a wide operational temperature range, the clearing temperature must be much higher than room temperature in order to have stable switching performance. Lower temperatures operation of the organic liquid crystals molecules is limited by phase transition into solid or other low symmetry smectic phases. Thus, unlike EL, LED, plasma or field emission displays, the range of operational temperatures of LCDs is narrower and is continually enhanced through strong synthesis efforts and through use of mixtures of liquid crystals. The study of the phase diagram of mixtures of LC focuses on locating the lowest temperature eutectic in mixture of 6-12 compounds! The compositional parameter space has to be large so that the process window, encompassing temperature range, contrast ratio, stable threshold voltage and switching speed, can be optimized. The molecular aspects of phases and phase diagrams of liquid crystals are the primary focus of this review. Although this review focuses on LC materials and properties it should borne in mind that LC-substrate interaction are also of paramount importance for device performance optimization. Use of rubbed polyimide allows the so called planar alignment (molecular long axis lying parallel to surface) while surfactants enable vertical alignment (homeotropic alignment) of molecules with respect to electrodes [21]. Introduction of surface coatings over the electrode also helps to overcome a major issue in device incorporation of liquid crystals: electrolysis/electrochemistry at the electrode-LC interface. During the sixties and seventies chemical degradation issues of liquid crystals were overcome through novel synthetic methods. Schiff’s bases were one of the first pure single component room temperature nematic liquid crystals to be synthesized [27]. Their synthesis involves a simple condensation reaction between an amine and an aldehyde. Typically both the species contain aromatic benzene ring and also alkyl chains connected to the aromatic rings either directly or through an ether linkage. For a variety reasons these interesting class of compounds were quickly replaced by cyano-biphenyls developed by Gray and coworkers [28] for LCD device applications. The cyano-biphenyls have better chemical stability especially with respect to hydrolysis and oxidation. Nevertheless, the ease of synthesis and hence low cost of the Schiff base compounds made them very attractive for the fundamental studies of liquid crystals. These materials have been proving grounds for many spectacular theoretical prediction of new classes of liquid crystals such as ferroelectric liquid crystals [29, 30]. This review therefore focuses on the Schiff base liquid crystals where we discuss

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how the fundamental phases are modulated as a function of molecular architecture, more specifically length of alkyl and alkoxy chain lengths [31] as well as derivatives containing only alkyl chains [32], alkoxy chain length in both segments of molecule [33, 34], in the aldehydic and amine portions of molecules. What is clear is that presence of alkoxy chain [35] creates a distinct tilt of the chain axis along with introduction of significant off- axis dipole moment. IV. Theoretical aspects Molecular level interactions that lead to formation of nematic phases are molecular anisotropy in shape and induced dipolar interactions [21, 36-38]. Onsager developed a statistical mechanical theory [21, 39] based on molecular packing considerations for rod-like molecules. Onsager’s theory has been extremely successful in predicting lyotropic nematic phase made of stiff rod like molecules such as DNA[40-42], peptide/polymers[43, 44] etc. For smaller size molecules, which exhibit thermotropism, molecular field theory of nematic phase was first developed by Mayer-Saupe [36-38]. A deeper molecular level connection to the elastic constants to the mean field potential was developed later [45-47]. Subsequent exposition of mean filed model for lower temperature smectics by McMillan [48, 49] in mid seventies led to the foundation of molecular engineering aspects of liquid crystals. McMillan and de Gennes emphasized coupling of oriental and positional ordering of molecules which leads to interesting crossover in the order of the nematic to smectic A (NA) phase transition from first order to second order through a tricritical point. Our experimental studies [50-52] in eighties verified this basic theoretical picture although the issue of true second order NA transition has been controversial as the nematic order fluctuations lead to a cubic term in the order parameter expansion as was pointed in early seventies [53-55]. Practically, the nature of this transition is important is due to fact that it is common to find nematic phase transforms into a smectic phase at low temperature as opposed to freezing into solid phase. Observed divergence of twist and bend elastic constant as the second order smectic A phase is approached is problematic from device physics point of view as it tends to affect threshold voltage and switching speed of LC devices. Further richness of phase topology of liquid crystals was realized with an introduction of chiral center in alkyl chain portion which Meyer predicted should lead a ferroelectric liquid crystals phase of C2 symmetry. This phase was discovered in Schiff base compounds during seventies [29, 30, 56]. These ferroelectric liquid crystals exhibit net non zero molecular dipole in the plane of smectic liquid crystal layers. Prost developed beautiful theory on

An overview of liquid crystals based on Schiff base compounds 25

liquid crystal structures that emphasized longitudinal dipole moments [57]. However, these theoretical developments were strictly based on Landau or order parameter based description of phases and phase transitions of liquid crystals. Once again these considerations lead us away from molecular features to a more general symmetry arguments as developed by De-Gennes which are beyond the intended focus of this narrow review. The following is the brief outline of the review. We begin with a description of phase behavior in classic Schiff base based liquid crystals [58-60] architectures as illustrated in figure 1. We first consider the phase variants observed as a function of chain length and compare the results with molecular field theoretic predictions. This is followed by a brief discussion of phase transitions that affect display related properties. Thermodynamics of phase transition is developed in light of prevailing theories especially emphasizing the Landau-De Gennes approach. Interesting symmetry arguments that led to prediction and discovery of ferroelectric liquid crystals based on Schiff base molecules are presented next along with our contributions to the field. A new synthetic variation of nO.m series is outlined based on introduction of highly polarizable SF5 group in the alkyl chain that features partial fluorination. Here the goal was to reduce LC viscosity and improve their optical birefringence properties. Finally we give an example, where classical thermotropic (nO.m’s) with lyotropic liquid systems are combined into the so called amphitropic liquid crystals. Results and discussion The molecular structures of the liquid crystals reviewed are shown in Figure 1. 1.0. nO.m compounds Synthesis of these series of molecules is relatively straightforward. Alcoholic solutions of n-alkyl amine and m-alkoxy aldehyde are refluxed in presence of few drops of glacial acetic acid. After couple of hours of refluxing, the reaction mixture is stored overnight in refrigerator to crystallize the product which is filtered and washed with cold alcohol to purify the liquid crystal. 1.1. General comments In the molecular skeleton of nO.m homologous series, there are two electronegative atoms namely oxygen and nitrogen, which lead to non- uniform

Shankar B. Rananavare & V.G.K.M. Pisipati 26

Figure 1. Generic structures of Schiff base liquid crystals.

charge distribution that can be approximated as localized dipoles. It has been noted that molecules with polar alkoxy chain generally give rise to higher NI transition temperatures than one without (n.m series [35], see below) as has also been observed in the cyano-biphenyl series [22]. However, in the present series, magnitude as well as relative location of dipole moments is constant, thus dispersive and steric interactions are modulated by the variation in chain lengths at either terminus of the effectively rod-like molecules. This homologous series exhibits rich mesomorphism as shown in Table 1 below. The observed phases include nematic (N), smectic A (A), smectic C(C), smectic B(B), smectic F (F) and smectic G (G). The alkoxy and alkyl chain numbers are varied from 1 to 18 and 1 to 10, 12, 14, 16 respectively. The richest mesomorphism is exhibited by 5O.6. The salient and interesting features observed from the systematic study presented in Table 1 are [31]: 1. All the phase variants are drawn from the common phase sequence

exhibited by the compound 5O.6, NACBFG (Figure 2) and this is the only compound which exhibits this hexa phases variant,

2. These compounds exhibit twenty one different types of phase sequence variants. These include different types of mono, di, tri, tetra, penta and hexa variants, There are three types of mono variants (N,A, F), five types of di variants (NA, NG, AB, AF, FG), five types tri variants (NAB,

An overview of liquid crystals based on Schiff base compounds 27

NAG, ABF, ABG, AFG), five types of tetra variants (NACB, NACG, NABG, ACBG, ACFG), two types of penta variants (NACFG, NACBG) and one type of hexa variant (NACBFG) totaling twenty one different types of liquid crystalline phase sequence variants,

3. Four different types of phase sequences are exhibited by single compounds viz, NACB by 4O.7, NACBG by 5O.7, NACFG by 5O.5 and NACBFG by 5O.6. The above compounds differ in one alkyl chain number. Addition and subtraction of one alkyl chain to 5O.6 gives two different types of penta phase variants which differ in B and F smectic where both are present in 5O.6,

4. The dominant phase sequence variants are (≥ 20 compounds which exhibit the same sequence of phases) N (20), F (19), AB (30), FG (25), NAB (19), and ABG (29),

5. For n and m<6, i.e., in the top left corner of the table corresponding to smaller molecular lengths nematic and smectic G phases predominate,

6. For n>10 no nematic is seen while for m>10 nematic phase is observed as long as n<6. As m is varied in this series, the onset of orthogonal smectic-A at 6O.10 quenches the nematic phase for higher homologues,

Table 1. phase variants exhibited by nO.m homologues series.

n/m 1 2 3 4 5 6 7 8 9 10 12 14 161 N N N N N N N2 N N N N N N NA A3 N N NAG NAG N NA N NA N N N4 NA NG NG NABG NABG NAB NACB NAB NAB NAB NAB NAB NAB5 NG NG NG NAG NACFG NACBFG NACBG NABG NAB NAB NAB NAB NA6 NAB NG NAG NABG NABG NABG NAB NABG NA AB ABG AB ABG7 NAB NAB NAB NACG NACG ACFG NACG ACBG ABG AB AB ABG AB8 NAB NAB NABG ABG ABG ACBG ACBG ABG ABG ABF AB ABG AB9 NAB AB AB AFG ABG ACFG ACBG ACFG ACBG ACBG ABG ABG AB10 NA ABG AB ABG ABG ACFG ABG ACFG ACBG ACFG AFG FG AFG11 A AB ABG AB ABG AFG AFG AFG ACBG AFG FG FG FG12 A AB AB ABG ABG ABG AFG AFG FG AFG FG FG FG13 A AB AB ABG ABG AB AB AF FG F FG FG FG14 A AB ABG AB ABG ABG AB F F F F FG FG15 AB AB ABG ABG ABG FG F F F F FG FG16 AB AB AB F F F F FG F FG FG FG18 AB AB AB F F FG FG F F F F FG

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Figure 2. nO.m Phase sequence variant tree. 7. The 5O.m homologues are unique as all phase variants exhibited by

nO.m compounds happen to be subset of their phase variants. This argument further derives support from the largest phase variant, NACBFG exhibited by 5O.6. This is depicted in the Figure 2,

8. The dominant single phase variants N and F are concentrated on the top right and down right portion of the table respectively. Mono-variant A phase is less prominent,

9. The phase variants with tilted phases, C and F are concentrated in the middle of the table, For n and m> 10, only tilted smectic mesophases F and/or G are observed.

10. The smectic-G phase is distributed throughout, 11. Like the single mono variants, N and F, the di phase variants AB and FG

are equally populated among the nO.m compounds, 12. Even though the AB sequence is distributed on the left down and right up

positions of the table while the FG is more concentrated on the down right of the table,

13. Orthogonal smectic phases, A and B are dominant compared to the tilted C and F phases,

An overview of liquid crystals based on Schiff base compounds 29

14. With the increase of alkoxy chain number the onset single phase variant smectic-F is observed with the small number of alkyl chain length. The minimum n and m numbers required for the manifestation single phase variant F are 13 and 10 respectively, while the onset smectic-F from isotropic melted with smectic-G occurred with the n and m values equal to 10 and 14 respectively,

15. The twenty one different phase sequence variants and their degeneracy in nO.m compounds are – N (20), A(5), F (19), NA (7), NG (6), AB (30), AF(2), FG (24), NAB (19), NAG (4), ABG (29), ABF (1), AFG(10), NACB (1), NACG (3), NABG (8), ACBG (8), ACFG (6), NACBG (1), NACFG (1), NACBFG (1) and

16. Most of the phase transitions in all the compounds are enantiotropic except in few cases and the clearing temperatures are < 100oC.

1.2. Specific comments

1.2.1. Nematic phase The early molecular theory of nematic phase, due to Meier-Saupe [36-38] introduces an induced dipole-induced dipole type interaction (having 1/r6 dependence) between smaller size nematogens. In addition, this interaction defines the orientational ordering in terms of second Legendre polynomial (S=<P2(cos(θ)>=<3cos2(θ)-1>/2)) in orientation (θ) of molecules with respect to the direction of average molecular alignment, the nematic director. For most of the nO.m compounds, this interaction should be essentially constant, as the polarizable portions of molecule C-O, C=N and aryl groups are fixed leading to a relatively constant TNI≈70-90˚C for most of the homologous series except for very small size molecules (n<2). It should be noted (see below) that generally a presence of longitudinal dipole moment (μL) on the molecular long axis (see below) leads to higher TNI. For example 5CB vs. 5OCB (pentyl vs. pentoxy chain attached to cyano-biphenyl group) differ in their respective clearing temperatures (TNI) by 35C, with the latter having the higher clearing temperature [22]. The odd and even chain effect predicted by Mercelja is also observed in variation of NI transition temperature [61]. Nematic phase disappears more rapidly with increase in the alkoxy chain length (n) than the alkyl chain length (m). 1.2.2. Smectic A phase For fixed n (or m) variation in the alkyl chain length m (n) leads to a reduction in the nematic phase extent and also to the appearance of an

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orthogonal smectic A phase. In Smectic A phase molecules exhibit positional ordering that can be described as a one dimensional mass density wave, i.e., tendency to form layers. This propensity is consistent with the McMillan’s model of the smectic A phase [48]. McMillan described the positional ordering in terms of average values of Fourier component describing crystallographic positional order. Lowest order component for Smectic A phase is <Cos(2πz/d>, where d is the layer thickness. This positional order disappears at the nematic to smectic A (NA) phase transition. This transition is perhaps most the celebrated phase transition in liquid crystal research as it can be either first or second order. It is possible to realize even higher order NA phase transition, beyond first or second order, a tricritical phase transition (see below). Both McMillan and De Gennes pointed out that the nematic to smectic A phase transition can go through a tricritical point driven by the coupling of nematic and smectic order parameters and their fluctuations [21]. McMillan designated a simple criterion based on the ratio of TNA/TNI, now commonly referred to as the McMillan ratio (M). When M is less than 0.88 his mean field theory predicts a second order NA transition while for larger values it is first order thus defining at tricritical point at M=0.88. McMillan also predicted dependence of M with molecular layer thickness scaled with respect to the rigid core which is shown in Figure 3.

Figure 3. McMillan parameter M as a function of dimensionless measure of layer thickness (l).

An overview of liquid crystals based on Schiff base compounds 31

Our extensive DSC and ESR and X-ray results for nO.m series are summarized in Table 2 below where we outline the M value as well as the nature of the NA transition. Tricritical value of M for the nO.m series is 0.95-0.96 (see Table 2), but in general the value appears to depend on a given LC homologous series. For liquid crystals of cyano-biphenyl homologous series, which have longitudinal dipole along the molecular long axis, compound 9CB is close to the tricritical NA point and it exhibits a MTCP value of 0.994. This value is significantly higher than the McMillan’s prediction. Similarly, different values of MTCP have been reported for other LC series [53]. To gain further molecular level insight, setting the coupling coefficient between nematic and smectic order parameters to be inversely proportional to the longitudinal molecular dipole moment; we find that MTCP~1-K/ μ2

L [62]. Although it should be noted that the increase in the alkoxy chain length affects the order of the NA transition more strongly than increase m the alkyl chain length. Our systematic study of the layer thickness in the smectic A phase revealed that the incremental increase in d spacing is smaller for alkoxy chain than alkyl chain [63]. It implies that the alkoxy chain is tiled with respect to the central rigid benzylidene core of the molecule. For all the molecules at or above n value of 6, only a first order NA transition is observed. For highly asymmetric chain length differences, i.e., m-n>5, the smectic A phase may exhibit interdigitation [64]. High degree of interdigitation appears to suppress the formation of phases with hexatic ordering, perhaps due to enhanced in-plane packing disorder. See for example a disappearance of smectic B phase in 5O.m (B phase disappears after m>15) and nO.1 (B phase disappears after n>9) series. Similarly, tilted hexatic phases like F or C phases do not appear in this region. Table 2. Nematic-Smectic A (NA transition in nO.m series: the McMillan ratio M and the order of transition.

n/m 4 5 6 7 8 4 4O.4

M=0.916 II order

4O.5 M=0.898 II order

4.O.6 M=0.936 II order

4.O7 M=0.925 II order

4O.8 M=0.956 II order

5 5O.4 M=0.951 II order

5O.5 M=0.930 II order

5O.6 M=0.966 I order

5O.7 M=0.956 II order

5O.8 M=0.979 II order

6 6O.4 M=0.976 I order

6O.5 M=0.972 I order

6O.6 M=0.990 I order

6O.7 M=0.990 I order

6O.8 M=0.956 I order

7 7O.4 M=0.994 I order

7O.5 M=0.990 I order

7O.6 M=1.0 No nem.

7O.7 M=0.997 I order

7O.8 M=1.0 No nem.

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We have studied the order of the NA transition as function of n and m using ESR [51, 52, 65, 66], optical birefringence [50], X-ray [67] and DSC [51, 68] techniques. 1.2.2.1. Nematic-Smectic A phase (NA) transition As discussed early on, this is one of the most intriguing liquid crystal phase transitions where first manifestation of solid-like positional order (one dimensional) appears. The transition is an example of 1D melting/freezing. We still do not have a satisfactory theoretical picture of the nature of this transition. De Gennes and McMillan pointed out the possibility of having both first or second order transitions while Lubensky [54] and Anisimov [55] asserted that the director fluctuations make this transition always first order due to the presence of cubic term in the order parameter expansion for the Landau free energy. An important consequence of the second order nature of this transition is the divergence of spatial fluctuation in order parameter. The effect can be probed by analyzing the X-ray scattering line shape of oriented samples. Anisotropic coherence lengths and their temperature dependence have been investigated over orders of magnitudes in reduced temperature (t). Such studies revealed that many compounds do show a second order NA transition as reflected in diverging coherence lengths both parallel and perpendicular to the smectic layer normal [53, 69, 70]. The twist and bend elastic constants depend on the coherence length; so the occurrence of second order NA transitions near the room temperature is not desirable for display device applications of LCs. Diverging elastic constants increase the threshold voltage for the device switching. This makes pixel addressing difficult. Furthermore, extreme susceptibility of coherence lengths, hence the elastic constants to the variation in temperature are also undesirable. Lower NA transition temperatures, i.e. smaller values of M, are realized by using lower chain homologues and selecting molecular structure with smaller longitudinal dipole moments. This valuable guidance for synthesis became only available after development of molecular field theories for nematic and smectic phases. 1.2.2.1.1. ESR studies. To further investigate how the orientational order parameter varies in the mixture of compounds (4O.6 and 6O.4) that exhibit first and second order NA transition, we employed electron spin resonance technique. Here, ESR active nitroxide radical in very small concentration was dissolved in liquid crystals. Detailed analysis of ESR line shape provided information on molecular ordering and dynamics near phase transitions [51, 52]. The orientational order parameter, S, and its enhancement in the

An overview of liquid crystals based on Schiff base compounds 33

smectic A phase as predicted by McMillan and De Gennes is observed [51, 52]. By looking at disappearance of discontinuity in S at the first order NA transition we measured the critical exponent for this secondary order parameter (ΔS~|TTCP-TNA |β2

, with β2≈1) consistent with the prediction of a tricritical point. When the data in table 2 is analyzed, it turns out that the conjugate field variable for the secondary order parameter, i.e. discontinuity in S at the NA transition, is M. Interestingly, the entire nematic order parameter versus temperature data can be placed on a single universal curve if the a new reduced temperature variable is defined as │ (TNI-T)/ (T*NI-T*NA) │; i.e., scaling the temperature deviation by the effective nematic phase extent defined as difference between hypothetical second order NI and NA phase transitions. Furthermore, the phase topology as a function of order parameter S with respect to M establishes the similarity of this phase transition to the super-fluid to normal fluid phase transition observed in the mixtures of Helium isotopes (3He+4He). This was pointed out by de Gennes by noting the similar symmetry of the order parameters for these two transitions, which is a complex two component vector (ψ=│ψ│e(-iφ)) [21]. The ESR probe orientational order parameter measurements of S have now been confirmed by direct order parameter measurement through optical birefringence [50]. Our studies also explore quasi-critical dynamics near the NI and NA phase transitions [51, 65, 66] in nO.m compounds. At the NI transition, the orientational fluctuations give rise to divergence in EPR spin probe linewidth given by a mean field like exponent (w~ξ~~│T-TNI│1/2 here w refers to homogeneous linewidth of EPR spin label undergoing rapid molecular reorientation, yet experiencing slow dynamic fluctuation modes of the nematic orientational order. At the NA transition, probe expulsion from LC core to alkyl region in layered smectics couples orientational fluctuation of probe with the smectic order parameter. It leads to a slower linewidth divergence (w~ξ1/2~~│T-TNI│1/3). This latter observation is consistent with the De Gennes super-fluid analogy where coherence length is predicted to diverge with 2/3 power-law exponent. 1.2.2.1.2. X-ray studies. Our unpublished data as well as other data from literature pertaining to the critical exponents associated with coherence length (ξ) in directions parallel (ν⎜⎜) and perpendicular (ν⊥) to smectic layer and X-ray quasi Bragg peak intensities (γ) for nO.m homologous series are presented in Table 3. These results are in good agreement with compilation of results provided by Garland et al [53]. Away from the tricritical NA point the results are consistent with a 3D-XY model while for tricritical and weakly first order NA transition the exponents correspond to the mean field values.

Shankar B. Rananavare & V.G.K.M. Pisipati 34

Table 3. Critical exponents determined from X-ray studies; definitions:

; ; ;ν νγ ξ ξΠ ⊥− −−Π ⊥

−∝ ∼ ∼ = NA

NA

T TI t t t tT

Liquid crystal M Γ υ|| υ⊥ Reference4O.8 0.958 1.31 0.70 0.57 [69] 4O.7 0.926 1.46 0.78 0.65 [70] 4O.6 0.936 -- 0.64±0.09 0.46±0.06 [67] 6O.4 0.976 -- 0.43±0.08 0.4±0.1 “ Tricritical 4O.6:6O.4 mixture (81:19 w/w) 0.955 -- 0.60±0.05 0.55±0.05 “ 3D-X-Y 1.32 0.67 0.67 [53] Tricritical (Theory) 0.87 1 0.5 0.5 [53]

1.2.3. Smectic B phase Given that the observed molecular tilts of smectic F and G phases are small, formation of crystalline B phase appears to be a general rule than exception. Smectic B phase that is commonly observed in nO.m compounds tends to be of crystalline variety with a saturated hexatic order parameter. An interesting consequence, as remarked before, is that when there is significant interdigitation this phase is quenched. Generally in nO.m compounds this phase melts into either Smectic A or smectic C phase and it freezes into a tilted smectic G phase. This phase is almost like a three dimensional crystal, melting or freezing through strong first order transitions. In 2D monolayer, however this transition can be potentially second order of the type predicted by Kosterlitz –Thouless [71]. 1.2.4. The smectic C phase This tilted phase is mainly observed in the central region of Table 1, where n ≈ m ≈ 6. In this region, the molecules should be more or less straight and have lateral dipole moment components. Observation of smectic C phase is also consistent with the McMillan’s model [49]. In the McMillan’s mean field model [49], the transition to smectic C phase ( as opposed to C1 and C2 phases ) from smectic A is governed by transverse dipoles (TAC ~μ2

2 where μ2 is the molecular dipole away from the center of mass (CM), presumably corresponding to the dipole moment associated with the alkoxy group (1.15D)). Formation of non-ferroelectric smectic C phases requires 2 μ2

2> μ12

An overview of liquid crystals based on Schiff base compounds 35

where μ1 is a dipole moment at the center of mass of the molecule corresponding to the dipole moment of Schiff base C-N group, ≈1.57D [49]. According to McMillan “The structural factors favoring the smectic C phase relative to smectic A phase are: (i) approximate center of symmetry; (ii) large outboard parallel dipole moments; (iii) zigzag (trans) gross shape of molecules.” Thus when n and m differ by large number (⎜n-m⎜> 3) approximate center of molecular symmetry is lost leading to suppression of the smectic C phase. When n ≈ m for small m (<4) it may be more difficult to maintain the zigzag or trans shape of the molecule, due internal segmental rotation around carbon bonds in the alkyl chains. While for large n, but with n≈m, an incipient in-plane hexatic order might lead to the smectic F phase directly as described below. Chu and McMillan [72] have described a Landau theory for the NAC multicritical point and it suggests a possibility of direct transition from nematic into smectic C phase which is not observed in the nO.m series (but see below). Chen and Lubensky [73] have described the NAC multicritical point as a Lifshitz point [74, 75] where one of the Lifshitz invariants vanishes. X-ray diffraction studies of Birgenau et al [76] do indeed observe Lifshitz point like fluctuations in nematic phase as smectic C phase is approached, although experimentally the N-C transition always appears to be a first order transition. Given that the nO.m. series does not exhibit a direct nematic to smectic C phase transition, we will not discuss here the NAC multicritical point. 1.2.4.1. Smectic A to smectic C (AC) phase transition. In nO.m series, smectic C phase is reached by cooling from the Smectic A phase. This phase transition in this series tends to be a weakly first order and appears to be close to a tricritical point. This finding is consistent with calorimetric studies of Garland et al [21, 77]. What is typically observed is a mean field behavior with unusually large sixth order term for the Landau expansion. Most of our studies have been performed with low temperature resolution hence we were unable to corroborate MIT work for all the AC transitions in this series. This is especially true for compounds such as 10O.8 which appears to exhibit a weakly first order AC transition [63]. This AC transition has become very important in understanding behavior ferroelectric liquid crystals which are realized by doping smectic C phase with chiral solutes. The order parameter for this transition is a complex order parameter similar to NA transition (θ=│θ│e(-iφ)) [21, 78, 79], where θ is a molecular tilt angle with respect to layer normal and phi φ the azimuthal angle, also called as phase angle. Above the AC phase transition, in smectic A phase the fluctuation in the magnitude of tilt angle dominate while below the transition, the phase fluctuation dominate. The latter are called as the Goldstone modes.

Shankar B. Rananavare & V.G.K.M. Pisipati 36

In ferroelectric materials the switching involves change of φ by 180 degrees, which can occur in microseconds, a much faster response than millisecond switching speeds commonly found for the nematic based LCDs. Therefore, studies of phase transition and switching dynamics in chiral smectic C as well as bent-core liquid crystals have come under intense scrutiny for their potential display applications. An Achilles heel of these devices based on chiral smectics or smectics in general is the ability to realize defect free alignment over a large area. This is much more challenging than nematic LCs owing to low free energy of focal conic defects which are difficult to anneal away, requiring higher temperature realignment process. 1.2.5. The smectic F phase The smectic F is characterized by in-plane hexatic order. In our studies [63, 80] of few representative nO.m compounds, we noted that both F and C phases exhibit relatively small molecular tilt angles. This is again consistent with the notion that the F phase is reached either from isotropic, or Smectic A or Smectic C phase, which (in nO.m series) have either have no tilt or very small tilt angles. De Gennes and Prost describe this phase transition from C-F as a transition without change in symmetry, i.e. hexatic bond orientational order in the smectic planes varies continuously across the transition [81-83]. Theoretically this is very intriguing transition in that it is believed to be similar to Kosterlitz -Thouless transition [71] in 2D for thin films. The lower temperature transition from the smectic F phase is mostly to smectic G phase or in some instances directly into a solid crystal phase. In this respect, the low temperature transition represents a 2D freezing whereas the interlayer smectic order becomes long range. We found that the intensity of the Bragg peaks increases upon cooling from an istropic to F phase following a power-law behavior. Invariably this transition is weakly first order. Simple molecular mean field theory for either F or G phase does not exist. But a cursory look at the Table 1 indicates that the phase is prevalent in bottom right section, where n and m values are large. The conditions for the occurrence of F phase are therefore very similar to the smectic C phase as discussed above. The primary difference between them is the magnitude hexatic bond orientational order parameter, just as the difference between liquid and gas phases is the magnitude of density of the two phases. It would be interesting to study the C-F transition in thin films and bulk to see if they follow the same trend as TB9 based compounds which also have Schiff base linkage [83]. Finally just as in the case of smectic C phase, the F is not present on the off-diagonal region (bottom left and top right regions). Here the hydrocarbon chain

An overview of liquid crystals based on Schiff base compounds 37

length differential |m-n| is large, presumably leading to interdigitation and suppression of the smectic F phase. 1.2.6. Smectic G phase

Smectic G phase is almost always the lowest temperature mesomorphic phase found in nO.m series. It can be induced in binary mixtures of mesogenic molecule exhibiting strong intermolecular hydrogen bonding [84, 85]. The hydrogen bonding interaction is directional and allows only fixed number of orientational sites for hydrogen bond formation. This presumably enhances the positional ordering i.e. crystallinity, which is the hallmark of the smectic G phase. Therefore, it is more aptly described as 3D pseudo-crystalline phase. Consistent with this finding is the X-ray study of Noh et al who observed that the F-G transition is first order. Although a 3D crystal, elastic constants in Smectic G phase tend to be smaller [83]. These authors noted diffuse scattering with coherence length approaching few hundred nanometers along the direction of the director. Our studies of smectic G phase in 10O.8 and 10O.14 also found that the nature of the transition from hexatic F phase to G is first order [63]. Interestingly, Bragg peaks showed power-law increase in the peak intensity upon cooling into the smectic G phase indicating development of a long range crystalline order parallel to layer normal as the in-plane hexatic order saturates. Early NMR studies of 5O.7 and the mixtures of 5O.6 and 9O.4. due to Doane et al established that the hydrocarbon chains maintain at least some degree of mobility in this phase [86] with high degree molecular ordering. 2. nO.Om series

2.1. General comments This series [34] has been recently attracting greater attention. Phase variants observed in this series are shown in Table 4 (see below). Interestingly, the phase variants are not symmetrically disposed along n=m diagonal although having two alkoxy chains confers a pseudo center of inversion to these class of molecules. Replacement of alky group with alkoxy group seems to have increased propensity for appearance of nematic phases in all the compounds except the few located in the right bottom corner. Galewski et al report that most of these transitions are first order as indicated by thermal calorimetric studies. It would be interesting to study the orientational ordering either through birefringence or magnetic resonance lineshape studies near NA transitions in case of compounds that exhibit the transition.

Shankar B. Rananavare & V.G.K.M. Pisipati 38

The compound showing largest phase variants is 10O.O5, exhibiting NACIG. Another striking feature of the phase diagram is the complete disappearance of the smectic F phase. The reasons for this phenomenon are not well understood at the moment. The hexatic smectic F phase is replaced with another similar hexatic phase, the smectic I phase. As both the chain lengths are increased the tendency to transform directly from isotropic phase to the smectic C is phase is noted. One significant difference compared to nO.m series is the propensity of nematic to smectic C phase transition as compared to the NA phase transition. Furthermore, neither smectic A, nor Smectic B or smectic G phases are as prevalent. 2.2. Specific comments 2.2.1. Nematic phase Presence of polarizable alkoxy group in both chains improves the appearance of nematic phase for a large region of nXm matrix as can be seen in Table 4. Furthermore, these multiple longitudinal dipoles appear to increase the TNI to above 100C or so, approximately 30-40 degrees above the

Table 4. Phase variants in nO.Om series.

n/m 1 2 3 4 5 6 7 8 9 10 12 1 N N N N N N N N N N N 2 N N N N N N N N N N N 3 N N N N N N N N N N 4 N N N N N N N N N NC NC 5 N N N N* -* N N NC NC NC NC 6 N N N N N N NC NC NC NCI NACI 7 N N N NC NC NC NC NCI NCI NCI NCI 8 N N N NCI NCIG NCIG NCI NC NC NCI CI 9 N NACB NACB NACI NCIG NCIG NCI NCI C C CI 10 N NAB NACB NACB NACIG NACIG CI CI CI C CI 12 N N`AB NAB NACB ACB ACB CI CI CI CI C

*Our extensive studies on 4O.Om and 5O.Om series have shown that the compound 4O.O5 exhibits no liquid crystalline phases while 5O.O5 exhibits a narrow range nematic phase.

An overview of liquid crystals based on Schiff base compounds 39

clearing temperatures commonly found in the nO.m series. This is consistent with the Maier-Saupe theory [36-38, 87] results:

24.55 / ( )C BT U k f μ≈ ∝

where μ is the induced molecular dipole moment. The importance of these types of molecules is that they allow a design of Schiff base liquid crystals with a much wider nematic phase range than was accessible with the nO.m series alone. Thus, mixtures of these molecules with high NI transition temperature with those Schiff base molecules that have much lower transition temperature such as n.m series discussed below would be useful. Such mixtures allow careful studies of critical phenomena of crossover from a 3D-XY model to the tricritical point in a chemically similar set of molecules. 2.2.2. Smectic A phase Unlike the nO.m series (Table 1) this phase is only observed in the bottom left portion of the table 4 and altogether there are only 11 instances of the compounds exhibiting the NA transition. In Figure 4 we plot M, the McMillan ratio vs. the sum n+m corresponding to total alkyl chain length by realizing that the molecules in this homologous series are effectively centro-symmetric. Clearly, as McMillan predicted, an increase in M occurs as a function of size of the molecule. A similar plot for nO.m series, showing much higher scatter appears in Figure 4 (right side)1. It should be noted that an even-odd effect [61] in hydrocarbon chain length on the NI transition temperature does make the scatter bit high but qualitatively the results are consistent with the McMillan’s model for the smectic A phase as discussed before. Careful studies of orientational order parameter discontinuities (ΔS) or critical exponents at the NA transition are yet to be performed. It would be interesting to know whether this homologous series exhibits a TCP and the corresponding value of M and how it compares with MTCP (≈ 0.95) for the nO.m series. Empirical prediction based on nCB and nOCB series would be that the corresponding value of MTCP would be higher. A compound 9O.O2 does exhibit M=0.92 and shows a weak or no peak in DSC is likely to be the best candidate for the study of a second order NA phase transition. Coincidently this M value is similar to the one exhibited by 4O.7 (with n+m=11) (M=0.925) which displays a second order NA phase transition. Note, the slopes of M vs n+m (≈ 0.0135) are also comparable, across these two series.

1Although if M is plotted as a function n much better quality linear fit is observed of this series

Shankar B. Rananavare & V.G.K.M. Pisipati 40

Figure 4. Variation of the McMillan parameter M in nO.Om and nO.m series. 2.2.3. Smectic C phase Given the (almost) center of symmetry of these molecules, the observed preponderance of smectic C phase should be taken as a further confirmation of the McMillan’s model of the smectic C phase (see above). It would be interesting to investigate the critical behavior at N-C phase transition as both McMillan and De Gennes models predict a divergence of all three elastic constants at this transition. Blending mixtures [34, 88] with compounds exhibiting NA transition would also permit studies of the NAC multicritical point [44, 76, 89], for example, compounds like 10O.O6 with 6O.O10. Advantage is that chemically similar molecules of similar dimensions should be more compatible and presumably form ideal solutions. This was not possible with nO.m series as no compounds in that series exhibits a NC transition. Another interesting possibility would be to mix a tricritical NA mixture with a compound exhibiting NC transition, to see how or if phase topology changes and bears resemblance to the classic Lifshitz point topology. Similarly it would be worthwhile to establish the nature of AC transition whether it exhibits mean field behavior with large sixth order term or not. 3.0. n.m compounds and 4.0. n.Om series Few studies of these homologous series [35] have been reported. For n.m series the LC transition temperatures are significantly suppressed along with the diversity LC phases. A comparison of phase variants appear below.

An overview of liquid crystals based on Schiff base compounds 41

Table 5. Comparison of phase variants in nO.m, n.Om, nO.Om and n.m homologous series [35].

Compound Phase variant Transition temperatures (OC) 1O.5 N I—62.6—N—39.7--K 1.O5 Non-liquid crystalline nature. 1O.O5 N I—92.1—N—83.5--K 1.5 Liquid crystal below room temp. 2O.5 N I—90.4—N—63.3--K 2.O5 Non-liquid crystalline nature. 2O.O5 N I—119.3—N—88.5--K 2.5 Liquid crystal below room temp. 5O.5 NACFG I—77.8—N—54.5—A—53.1—C—49.9—

F—47.0—G—28.0--K 5.O5 NG I—76.8—N—51.6—G—40.7--K 5O.O5 N I—109.1--N 5.5 NG I—40.8—N—23.9--G 1.O16 Non-liquid crystalline nature.

1O.O16 Non-liquid crystalline nature.

1.16 Non-liquid crystalline nature. 2O.16A A I—70.1—A—52.2--K 2.O16 Non-liquid crystalline nature. 2O.O16 Non-liquid crystalline nature. 2.16 Non-liquid crystalline nature. 4O.16B NAB I—69.2—N—68.5—A—51.3--B 4O.O16 Non-liquid crystalline nature. 4.16 A I—38.1—A—35.0--K 5O.1664 NA I—68.8—N—67.4—A—55.1--K 5.O16 AB I—79.2—N—72.3—A—51.3--K 5O.O16 N I—87.4—N—87.0--K 5.16 A I—52.9—A—40.2--K 8O.16 C AB I—75.5—A—71.5—B 8.O16 Non-liquid crystalline nature. 8O.O16 Non-liquid crystalline nature.

8.16 Non-liquid crystalline nature. A P.A. Kumar, M.L.N. Madhu Mohan and V.G.K.M. Pisipati, Liq.Cryst., 27, 727 (2000). B N.V.S.Rao, D.M. Potukuchi and V.G.K.M. Pisipati, Mol.Cryst.Liq.Cryst., 196, 71 (1991). CM.Jitendranath, C.G.Rama Rao, M.Srinivasulu and Venkata G.K.M.Pisipati Mol.Cryst.Liq. Cryst., 366, 47 (2001).

Shankar B. Rananavare & V.G.K.M. Pisipati 42

The majority of the present benzylidene aniline compounds exhibit nematic phase except 1.O5 and 2.O5. The presence of oxygen atom on both sides of the benzylidene aniline (1O.O5 and 2O.O5 compounds) and the removal of oxygen from both sides of the compounds (1.5 and 2.5) results in significant changes in melting and clearing temperatures, and their liquid-crystalline nature. As discussed before the molecular dipoles due C-O groups lead nO.Om compounds exhibit their nematic phase at highest temperature, while compounds lacking such polar groups viz, n.m series, exhibits overall lower clearing temperatures. The take home lesson from these synthetic experiments is that molecules of high and low clearing temperatures, that are needed for wide operational range of LCDs, can be synthesized using this strategy of introduction or removal of oxygen in the alky chain region flanking the mesogenic core of the liquid crystal molecules. The n.Om series also illustrates important effect of the reversal of central linkage with respect to the rigid core regions of the molecule (CH=N or N=CH). It shows that in 5O.5 and 5.O5), small and insignificant changes occur on the clearing temperatures as well as melting temperature. However, the variety of LC phases they exhibit is found to be drastically different. In conclusion, the experimental studies of these classic systems illustrates the extent of success of mean field theories as well as challenges in establishing refinement of theoretical models to predict the phase variants. It is clear that besides the molecular shape and mean/induced dipoles, the effects of relative orientations and spacing of functional group dipole moments is very important and need to be investigated theoretically to have better predictability of phase variants. 5.0. Other variations Introduction of a chiral functional group or geometric variation in molecular architecture of nO.m has led to discovery of new liquid crystals such as ferroelectric [29, 30, 56] or bent core liquid crystals [90]. In addition, to improve device switching speeds by reducing viscosity (molecular friction) through introduction of fluorinated chain has also been pursued. This is a very large area of active research and here we focus on few selected molecular structural variants that we have investigated [91, 92]/synthesized [62]. In addition, we present studies of classic thermotropic nO.m of series molecules mixed with traditional surfactant based liquid crystals [93-95]. The so called amphitropic liquid crystals are still in the early stages of development especially with respect to their potential applications in lithography or so called bottom up approach in assembling nanostructures.

An overview of liquid crystals based on Schiff base compounds 43

5.1. Chiral centers and ferroelectric liquid crystals The prediction and discovery of the first ferroelectric liquid crystals by Meyer et al provided a first technologically significant, new class of liquid crystals based on Schiff base architecture [29, 30]. Here the molecules, arranged in smectic C phase have a chiral center attached to them which reduces the overall symmetry of smectic C phase from C2h to C2. Along the C2 axis, in the plane of layer, a non-vanishing component of polarization is generated. The coupling of tilt (primary order parameter) and polarization has been included in the Landau model for the smectic A-chiral C(C*) transition [96]. The direction of the polarization vector can be rapidly changed through application of an electric field. In the bulk, the ferroelectric smectic C* phase exhibits a helical modulation of polarization in direction normal to smectic layers. Switching entails rotation of molecules along the cone of the fixed tilt angle. The switching time ( / . ,τ γ= P E where γ is rotational viscosity, P the polarization and E is the in-plane applied electric field [78]) is at least three orders of magnitude shorter than typical milliseconds switching times observed in nematic liquid crystal based devices. Unlike nematics, which do not have any positional order, the smectic C* phase has positional, orientational as well as hexatic bond orientational order. Following the analogy to dilute magnetism, we [91, 92] investigated ferroelectric phase behavior in a mixture of chiral nO.m, p-(n-decyloxy-benzylidene)-p-amino-(2-methylbutyl) cinnamate (DOMBABC [79]) and an achiral 10O.8 molecule to probe if the ferroelectric phase persists to low concentrations of the chiral molecule. The temperature composition phase diagram appears in Figure 5.

Figure 5. Temperature composition phase diagram of DOBAMBC and 10O.8 mixtures.

Shankar B. Rananavare & V.G.K.M. Pisipati 44

Surprisingly, the observed the chiral-achiral phase transitions appear at finite and significant concentration of DOMBABC (chiral molecule). This finding is contrary to what would be expected based on results of induction of cholesteric phases by chiral solutes in the nematic phase. The smectic C* phase disappears at about 36% dopant (chiral molecule) concentration! The total phase diagram shows remarkable topology similar to a Lifshitz point as predicted by Michaelson et al [74, 75, 97]. At the ACC* Lifshitz point, induced by concentration, pitch length diverges and polarization disappears with power laws that can be rationalized in terms of disappearance of Lifshitz invariants. Nonetheless, the precise chemico-physical principle behind this phenomenon remains to be uncovered. Similar ACC* Lifshitz points have been observed as a function of the helix unwinding fields such as electric, magnetic and confining geometries (so called surface stabilized FLCs discovered by Clark and Lager wall [98]). A fundamental difference between these results and our results lies in that in these studies of mixtures chiral and achiral LCs we observe a simultaneous disappearance of switchable polarization and helical pitch modulation. 5.2. SF5 based nO.m liquid crystals Search for ever increasing polarization (dipole moment per unit area) lead to discovery of anti-ferroelectric phases in the early nineties [99, 100]. Similarly if the molecule is bent, banana-like, then the breakdown of axial symmetry can lead to ferroelectric phases that do not have a local chiral group as was discovered in mid nineties [90]. In the late nineties, in pursuit of higher longitudinal dipole moments to realize the exotic devil staircase type structures in the electric switching led one of us to conjecture that perhaps a highly polarizable and highly polar group such as SF5 might allow one to create such a phase. The structure of the synthesized nO.m, analogs is shown in Fig. 6: In these compounds we observe monotropic liquid crystals which when mixed produce a stable nematic phase [62]. More interestingly, these compounds exhibit remarkably high values of McMillan parameter and yet exhibit a second order NA phase transition. This is similar to result observed in compound, N-p-cyano-benzylidene-p-octyloxy-aniline CBOOA [101], which has an axial cyano group in addition to the benzylidene group in structure. Despite its M=0.934 it exhibits a second order NA transition implying a higher value for its MTCP. These SF5-based compounds also feature per-fluorinated alkyl chains, but not the alkoxy chains. Our expectation was that the longitudinal dipole moment might give rise to longitudinal ferroelectric order. Single crystal analysis revealed that the

An overview of liquid crystals based on Schiff base compounds 45

Figure 6. SF5 based partially fluorinated nO.ms.

Figure 7. Ball-stick model of single crystal SF5 based 7O.2. fluorocarbon and the hydrocarbon chains mixed, leading to a formation of longitudinal and in-plane anti-ferroelectric order as shown in Fig. 7. We also explored possibility of bent core liquid crystals with meta location of amine groups without success perhaps due to limited range of n and m variations.

Shankar B. Rananavare & V.G.K.M. Pisipati 46

5.3. Amphitropic liquid crystals In past we have extensively investigated how bilayer smectic A phase of lyotropic, surfactant-based systems interacts with additives, such as water and hydrocarbons [102-105]. Here the main effect is an increased interlayer spacing as a function of additive concentration till a phase boundary is reached. In cases where additive gets embedded in the layered structure significant changes in molecular orientational ordering in bilayers [106, 107] have been noted. It was therefore of interest if a nematic forming nO.m compound could be dispersed using surfactant and to examine the resulting model ternary phase diagram of such a system. Most common surfactants such as anionic SDS (sodium dodecyl sulfate), cationic CTAB (cetyl tetra-ammonium bromide) or nonionic Brij 30 (C12H25(EO)4OH) molecules exhibited formation of milky emulsions. In these emulsions water droplets tend to form pearl garland-like chains [108-110] are believed to be important for chemo-responsive configurable assemblies [110]. We focused exclusively on a nonionic Triton analog surfactant which exhibited rich phase mesomorphism with MBBA (1O.4) as shown in figure 8 below [111]. The surfactant is sparingly soluble in the nematic phase;

Figure 8. (Left) A partial three component phase diagram of MBBA, Triton X114 and water is shown. Multiphase coexistences as viewed between crossed polarizers (right). Note the inverted test tube in the bottom right portion of the figure corresponding to an isolated critical point between lamellar LCs. L2 and L3 are lamellar LCs, I is an isotropic phase. Shaded triangular region shows coexistence of three phases, I+L2+L3.

An overview of liquid crystals based on Schiff base compounds 47

however, very small amounts dissolved in the nematic phase of MBBA lead to destruction the nematic phase. The NI phase transition is very rapidly quenched at low concentration of surfactant. Even where a small amount of surfactant is present in the nematic phase the maximum amount of water it accommodates is even smaller <0.5%. We rationalize the instability of nematic phase in presence of inverse micellar structures to creation of axial +1 type of defects compensated by creation of corresponding –1 type of defect in the surrounding nematic phase. As more water and surfactant are added, the deformation elastic energy associated with micellar structures drives the transition from the nematic phase containing micelles to an isotropic phase. Note that the dimensions of micelles are comparable to the core dimensions of defects found in nematics [87]. This proposed mechanism borrows from the well understood mechanism of homeotropic alignment of nematic liquid crystals by surfactant derivatized surfaces. In the lamellar region of the phase diagram there appears an extension towards water corner in a manner reminiscent of nonionic surfactant-benzene- water phase diagrams [105, 112]. A noteworthy feature of this ternary phase diagram is a three phase region where two lamellar phases of different densities coexist with an isotropic phase as shown in above (top right portion of) figure 8. Following the two lamellar phase coexistences into a single phase lamellar region we were able to locate a critical point where the bulk viscosity diverges. More studies are needed to establish the nature of this critical divergence. The remarkable features of the phase diagram are:

1. The nematic phase of MBBA is completely quenched with very small addition of surfactant molecules;

2. We find that the lamellar phase accommodates small amount of MBBA but does not lead to formation of a nematic microemulsion;

3. Interestingly, we find a novel three phase region where two lamellar phases coexist with an isotropic phase.

4. Along the side of the Gibbs triangle, which shows coexistence of lamellar phases, the viscosity exhibits dramatic divergence hinting a formation of an isolated critical point. At this concentration, the system has 80% water and yet it does not flow freely but forms a birefringent gel. Away from this region, the lamellar phase L1 as well as coexisting lamellar phases (L2 and L3) and I phases flow freely.

More details of the work will be published elsewhere. However, the general area of phase behavior of surfactants and the classic thermotropic liquid crystals remains mysterious and poorly investigated. One deficiency of nO.ms for this application is that they tend to hydrolyze over time.

Shankar B. Rananavare & V.G.K.M. Pisipati 48

Summary and future prospects The classic nO.m series has provided a novel platform for development of modern liquid crystal physics and chemistry. Some of the key achievements are: the discovery of new classes of liquid crystals such as ferroelectric and bent core liquid crystals. The potential of these mesogen in polymeric systems as well as their incorporation in amphitropic liquid crystals should be contemplated. Such materials will provide a suitable medium for aligning nanowire and nanotubes. Once alignment is achieved and locked these materials are relatively easy to chemically degrade. In general, the use of liquid crystals for lithographic application is an area that has received no attention but holds potential of improving resist sensitivity as well as providing novel non linear optic material of controllable birefringence for immersion lithography. Acknowledgements It is a great pleasure to acknowledge many stimulating discussion with Professor Jack Freed at Cornell University. Professor Anthony J Ward provided a careful review of the manuscript. Financial support was provided to SBR from National Institute of Health grant No. HL 54209 and to VGKMP by Department of Science and Technology, New Delhi, India through the grant No.SR/S2/CMP-0071/2008. References 1. H. Kawamoto, Proceedings of the IEEE 2002, 90, 460. 2. R. Williams, The Journal of Chemical Physics 1963, 39, 384. 3. M. Schadt, W. Helfrich, Applied Physics Letters 1971, 18, 127. 4. P. M. Alt, P. Pleshko, Electron Devices, IEEE Transactions on 1974, 21, 146. 5. T. J. Scheffer, B. Clifton, D. Prince, A. R. Conner, Displays 1993, 14, 74. 6. T. Scheffer, J. R. Nehring, Annual Review of Materials Science 1997, 27, 555. 7. J. A. McDonald, Microelectronics Journal 1994, 25, xvii. 8. http://business.highbeam.com/industry-reports/equipment/special-industry-

machinery-not-elsewhere-classified. 9. http://www.samsung.com/ae/news/newsRead.do?news_seq=19410&gltype=local

news. 10. T. Larsen, A. Bjarklev, D. Hermann, J. Broeng, Opt. Express 2003, 11, 2589. 11. F. Simoni, Nonlinear optical properties of liquid crystals and polymer dispersed

liquid crystals, Vol. 2, World Scientific, New York, 1997. 12. C. Aroulanda, V. Boucard, F. Guibé, J. Courtieu, D. Merlet, Chemistry – A

European Journal 2003, 9, 4536. 13. R. Yamamoto, Physical Review Letters 2001, 87, 075502.

An overview of liquid crystals based on Schiff base compounds 49

14. M. D. Lynch, D. L. Patrick, Nano Letters 2002, 2, 1197. 15. L. K. Cotter, T. J. Drabik, R. J. Dillon, M. A. Handschy, Opt. Lett. 1990, 15, 291. 16. Y. W. Zhang, M., O'Callaghan M. J., Walker, C. M., Thurmes W, Ferroelectrics

2006, 344, 11. 17. J. W. Doane, A. Khan Cholesteric liquid crystals for flexible displays, chapter 17

pg 332, Wiley, Hoboken, NJ 07030, 2005. 18. M. Shimomura, T. Sawadaishi, Current Opinion in Colloid & Interface Science

2001, 6, 11. 19. B. D. Gates, Nat. Nano., 2010, 5, 484. 20. J. C. Love, L. A. Estroff, J. K. Kriebel, R. G. Nuzzo, G. M. Whitesides, Chemical

Reviews 2005, 105, 1103. 21. P. G. De Gennes, P. J., Prost The physics of liquid crystals, Vol. 83, second

edition ed., Clarendon Press, Oxford Science Publications, Oxford, 1993. 22. I.C. Khoo, S.T. Wu, Optics and nonlinear optics of liquid crystals, Chapt. 2,, Vol.

1, World Scientific, River Edge, NJ 07661, 1993. 23. R. Lu, X. Zhu, S. T. Wu, Q. Hong, T.X. Wu, Journal of Display Technology

2005, 1, 3. 24. M. Koden, in http://sharp-world.com/corporate/info/rd/tj2/pdf/12.pdf, Sharp

Technology. 25. P. Detlef, T. Kazuaki, Journal of Materials Chemistry 2004, 14, 1219. 26. G. Gauza, C. H. Wen, B. Wu, S. T. Wu, A. Spadlo, R. Dabrowski, Liquid

Crystals 2006, 33, 705. 27. H. Kelker, B. Scheurle, Angewandte Chemie International Edition in English

1969, 8, 884. 28. G. W. Gray, K. J. Harrison, J. A. Nash, Electronics Letters 1973, 9, 130. 29. R. B. Meyer, Ferroelectrics 1980, 28, 319 30. R. B. Meyer, L. Libert, I. Strzeleck, P. Keller, J. Phys. (Paris) Lett 1975, 36 69. 31. V. Pisipati, Zeitschrift Fur Naturforschung Section a-a Journal of Physical

Sciences 2003, 58, 661. 32. N. Ajeetha, V. Pisipati, Zeitschrift Fur Naturforschung Section a-a Journal of

Physical Sciences 2005, 60, 207. 33. K. Fakruddin, R. J. Kumar, P. V. D. Prasad, V. Pisipati, Molecular Crystals and

Liquid Crystals 2009, 511, 1616. 34. J. Godzwon, M. J. Sienkowska, Z. Galewski, Acta Physica Polonica A 2008, 113,

1145. 35. N. Ajeetha, D. M. Potukuchi, V. Pisipati, Phase Transitions 2005, 78, 369. 36. W. Maier, A. Saupe, Z. Naturforsch 1958, 13A, 554. 37. W. Maier, A. Saupe, Z. Naturforsch 1959, 14A, 882. 38. W. Maier, A. S. Z., Z. Naturforsch, 1960, 15A, 287. 39. L. Onsager, Ann. N. Y. Acad. Sci. 1949, 51, 627. 40. M. Nakata, G. Zanchetta, B. D. Chapman, C. D. Jones, J. O. Cross, R. Pindak, T.

Bellini, N. A. Clark, Science 2007, 318, 1276. 41. H.-S. Park, S.-W. Kang, L. Tortora, Y. Nastishin, D. Finotello, S. Kumar, O. D.

Lavrentovich, The Journal of Physical Chemistry B 2008, 112, 16307. 42. G. Zanchetta, et al., Journal of Physics: Condensed Matter 2008, 20, 494214.

Shankar B. Rananavare & V.G.K.M. Pisipati 50

43. S. Bucak, C. Cenker, I. Nasir, U. Olsson, M. Zackrisson, Langmuir 2009, 25, 4262.

44. Z. Y. Chen, Macromolecules 1994, 27, 2073. 45. L. R. Evangelista, I. Hibler, H. Mukai, Physical Review E 1998, 58, 3245. 46. J. Nehring, A. Saupe, The Journal of Chemical Physics 1971, 54, 337. 47. J. Nehring, A. Saupe, The Journal of Chemical Physics 1972, 56, 5527. 48. W. L. McMillan, Physical Review A 1971, 4, 1238. 49. W. L. McMillan, Physical Review A 1973, 8, 1921. 50. V. G. K. M. Pisipati, P. V. D. Prasad, Molecular Crystals and Liquid Crystals

2009, 506, 13. 51. S. B. Rananavare, V. G. K. M. Pisipati, J. H. Freed, Liquid Crystals 1988, 3, 957. 52. S. B. Rananvare, V. G. K. M. Pisipati, J. H. Freed, Chemical Physics Letters

1987, 140, 255. 53. C. W. Garland, G. Nounesis, Physical Review E 1994, 49, 2964. 54. B. I. Halperin, T. C. Lubensky, S.-k. Ma, Physical Review Letters 1974, 32, 292. 55. M. A. Anisimov, Mol. Cryst. Liq. Cryst. 1988, 162A, 1. 56. R. B. Meyer, Molecular Crystals and Liquid Crystals 1977, 40, 33 57. P. Barois, J. Pommier, J. Prost, Phase Transitions: A Multinational Journal 1991,

33, 183 58. D. Demus, S. Diele, S. Grande, H. Sackmann, Advances in Liquid Crystals 1983,

6, 1. 59. H. Sackmann, D. Demus, Molecular Crystals and Liquid Crystals 1973, 21, 239. 60. A. Wiegeleben, L. Richter, J. Deresch, D. Demus, Molecular Crystals and Liquid

Crystals 1980, 59, 329. 61. Marcelja, S. The Journal of Chemical Physics 1974, 60, 3599. 62. J. A. Smith, R. A. DiStasio, N. A. Hannah, R. W. Winter, T. J. R. Weakley, G. L.

Gard, S. B. Rananavare, The Journal of Physical Chemistry B 2004, 108, 19940. 63. V. G. K. M. Pispati, S. B. Rananavare, Molecular Crystals and Liquid Crystals

Science and Technology. Section A. Molecular Crystals and Liquid Crystals 1994, 238, 207

64. V. G. K. M. Pisipati, S. B. Rananavare, Liquid Crystals 1993, 13, 757. 65. J. H. Freed, A. Nayeem, S. B. Rananavare, in Molecular Dynamics of Liquid

Crystals, Vol. 431 (Ed.: G. R. Luckhurst, C. A. Veracini), 1994, pp. 335. 66. A. Nayeem, S. B. Rananavare, V. S. S. Sastry, J. H. Freed, The Journal of

Chemical Physics 1992, 96, 3912. 67. S. B. Rananavare, R. C. Creapau, V. G. K. M. Pisipati, J. H. Freed, 1988. 68. V. G. K.M. Pisipati, S.B. Rananavare, J.H. Freed, Molecular Crystals and Liquid

Crystals 1987, 4, 181. 69. R. J. Birgeneau, C. W. Garland, G. B. Kasting, B. M. Ocko, Physical Review A

1981, 24, 2624. 70. C. W. Garland, M. Meichle, B. M. Ocko, A. R. Kortan, C. R. Safinya, L. J. Yu, J.

D. Litster, R. J. Birgeneau, Physical Review A 1983, 27, 3234. 71. J. M. Kosterlitz, D. J. Thouless, Journal of Physics C: Solid State Physics 1973,

6, 1181. 72. K. C. Chu, W. L. McMillan, Physical Review A 1977, 15, 1181.

An overview of liquid crystals based on Schiff base compounds 51

73. J.-h. Chen, T. C. Lubensky, Physical Review A 1976, 14, 1202. 74. A. Michelson, Physical Review Letters 1977, 39, 464. 75. A. Michelson, Physics Letters A 1977, 60, 29. 76. C. R. Safinya, R. J. Birgeneau, J. D. Litster, M. E. Neubert, Physical Review

Letters 1981, 47, 668. 77. R. J. Birgeneau, C. W. Garland, A. R. Kortan, J. D. Litster, M. Meichle, B. M.

Ocko, C. Rosenblatt, L. J. Yu, J. Goodby, Physical Review A 1983, 27, 1251. 78. Carlsson, T. Zeks, B., Filipic, C., Levstik, A., Blinc, R. Blinc, Molecular Crystals

and Liquid Crystals Incorporating Nonlinear Optics 1988, 163, 11 79. S. Dumrongrattana, C. C. Huang, G. Nounesis, S. C. Lien, J. M. Viner, Physical

Review A 1986, 34, 5010. 80. P. B. Rao, N. V. S. Rao, V. G. K. M. Pisipati, Molecular Crystals and Liquid

Crystals 1991, 206, 9 81. A. Aharony, R. J. Birgeneau, J. D. Brock, J. D. Litster, Physical Review Letters

1986, 57, 1012. 82. J. D. Brock, A. Aharony, R. J. Birgeneau, K. W. Evans-Lutterodt, J. D. Litster, P.

M. Horn, G. B. Stephenson, A. R. Tajbakhsh, Physical Review Letters 1986, 57, 98.

83. D. Y. Noh, J. D. Brock, J. D. Litster, R. J. Birgeneau, J. W. Goodby, Physical Review B 1989, 40, 4920.

84. R. Suriyakala, V. G. K. M. Pisipati, Phase Transitions: A Multinational Journal 2004, 77, 281

85. P. Swathi, S. S. Sastry, P. A. Kumar, V. G. K. M. Pisipati, Molecular Crystals and Liquid Crystals 2001, 365, 523.

86. M. J. Vaz, Z. Yaniv, R. Y. Dong, J. W. Doane, Journal of Magnetic Resonance (1969) 1985, 62, 461.

87. S. Chandrasekhar, Liquid Crystals, pg. 41, 2 nd ed., Cambridge University Press, Cambridge, 1992.

88. J. Godzwon, M. J. Sienkowska, Z. Galewski, Journal of Molecular Structure 2007, 844-845, 259.

89. L. J. Martnez-Miranda, A. R. Kortan, R. J. Birgeneau, Physical Review A 1987, 36, 2372.

90. T. Niori, T. Sekine, J. Watanabe, T. Furukawa, H. Takezoe, Journal of Materials Chemistry 1996, 6, 1231.

91. S. B. Rananavare, V. G. Pisipati, E. W. Wong, in Liquid Crystal Materials, Devices, and Applications III, Vol. 2175, 1 ed., SPIE, San Jose, CA, USA, 1994, pp. 108.

92. S. B. Rananavare, V. G. K. M. Pisipati, E. W. Wong, Physical Review Letters 1994, 72, 3558.

93. G. S. Attard, S. Fuller, O. Howell, G. J. T. Tiddy, Langmuir 2000, 16, 8712. 94. D. Blunk, N. Bongartz, C. Stubenrauch, V. Gärtner, Langmuir 2009, 25, 7872. 95. S. Fuller, N. N. Shinde, G. J. T. Tiddy, G. S. Attard, O. Howell, Langmuir 1996,

12, 1117. 96. T. Carlsson, B. Zeks, A. Levstik, C. Filipic, I. Levstik, R. Blinc, Physical Review

A 1987, 36, 1484.

Shankar B. Rananavare & V.G.K.M. Pisipati 52

97. I. Musevic, B. Zeks, R. Blinc, T. Rasing, P. Wyder, Physical Review Letters 1982, 48, 192.

98. N. A. Clark, S. T. Lagerwall, Applied Physics Letters 1980, 36, 899. 99. H. Takezoe, E. Gorecka, M. Ccaronepiccaron, Reviews of Modern Physics,

82, 897. 100. A. D. L. Chandani, E. Gorecka, Y. Ouchi,. H. Takezoe, A. Fukuda, Jpn. J.

Appl. Phys 1989, 28, L1265. 101. J. Als-Nielsen, R. J. Birgeneau, M. Kaplan, J. D. Litster, C. R. Safinya, Physical

Review Letters 1977, 39, 352. 102. S. B. Rananavare, A. J. I. Ward, D. W. Osborne, S. E. Friberg, H. Kaiser, The

Journal of Physical Chemistry 1988, 92, 5181. 103. A. J. I. Ward, S. E. Friberg, D. W. Larsen, S. B. Rananavare, The Journal of

Physical Chemistry 1984, 88, 826. 104. A. J. I. Ward, S. E. Friberg, D. W. Larsen, S. B. Rananavare, Langmuir 1985,

1, 24. 105. A. J. I. Ward, S. B. Rananavare, S. E. Friberg, Langmuir 1986, 2, 373. 106. E. Meirovitch, E. T. Samulski, A. Leed, H. A. Scheraga, S. Rananavare, G.

Nemethy, J. H. Freed, The Journal of Physical Chemistry 1987, 91, 4840. 107. S. E. Friberg, S. B. Rananavare, D. W. Osborne, Journal of Colloid and Interface

Science 1986, 109, 487. 108. P. Poulin, H. Stark, T. C. Lubensky, D. A. Weitz, Science 1997, 275, 1770. 109. T. C. Lubensky, D. Pettey, N. Currier, H. Stark, Physical Review E 1998,

57, 610. 110. G. M. Koenig, I.-H. Lin, N. L. Abbott, Proceedings of the National Academy of

Sciences 2010, 107, 3998. 111. S. B. Rananavare, M. Silverberg, E. W. Wong, C. W. Sheeleigh, Oregon Graduate

Institute, 1992. 112. H. Christenson, S. E. Friberg, D. W. Larsen, The Journal of Physical Chemistry

1980, 84, 3633.