Liquid Crystals

Abstract

Liquid crystals (GlossaryTerm

LC

s) are nowadays widely used in electro-optical devices (e. g., liquid crystalline displays), for optical visualization of physical influences (heat, IR, high-frequency radiation, pressure, etc.), for nondestructive testing, as well as for thermography.

1 Liquid Crystalline State

Liquid crystals represent an intermediate state of order (mesophase) between crystals and liquids. Crystals have a three-dimensional long-range order of both position and orientation (Fig. 26.1a). Liquids, in contrast, do not show any long-range order (Fig. 26.1b). In plastic crystals (disordered crystals, Fig. 26.1c), the positional order is maintained, but the orientational order is lost. In mesophases, imperfect long-range order is observed, and thus they are situated between crystals and liquids. The reasons for the formation of a mesophase include the molecular shape or a microphase separation of amphiphilic compounds.

Fig. 26.1a–c

Types of states: (a) crystal, (b) isotropic liquid, (c) plastic crystal

At present more than 100000 individual liquid crystals have been synthesized [26.1, 26.2, 26.3, 26.4, 26.5, 26.6] and about 2000 of these liquid crystals have been tested for physical properties and technical applications [26.10, 26.3, 26.7, 26.8, 26.9]. These materials can be classified according to their chemical structures and physical characteristics (Table 26.1).

Generally, molecules of liquid crystalline substances have the following shapes:

• Rod-like molecules, which form calamitic liquid crystals (nematic and smectic phases)

• Disc-like molecules, which form discotic liquid crystals (discoid nematic and discotic phases)

• Amphiphilic compounds, which form layered columnar or cubic phases in the individual state and in solution.

Table 26.1 Classifications of liquid crystals

Fig. 26.2a–g

Types of mesophases: (a) nematic, (b) cholesteric, (c) discoid nematic, (d) smectic A, (e) smectic B, (f) smectic C, (g) discotic

The simplest and most widespread liquid crystalline phase is the nematic phase. The molecules are statistically distributed within the medium, but the long axes are orientated in one direction, the director (Fig. 26.2a). A special class of nematic phase is the cholesteric phase (Fig. 26.2b). Here the orientation of the director does not apply to the whole medium but rather to a virtual layer. Perpendicular to this layer, the director follows a helix with a certain pitch. In the case of the blue phases such a helical structure is formed not only in one but in all three dimensions. Thus, highly complex arrangements, with chiral cubic symmetry in most cases, are generated. Not only rod-like but also disc-like molecules can form nematic phases. The discoid nematic phase is shown in Fig. 26.2c.

Rod-like molecules arranged in layers form smectic phases. They are subdivided into a considerable number of different species. These classifications result from various arrangements of the molecules within the layers and different restrictions of their movement. The smectic A phase, the simplest smectic phase, can be regarded as a two-dimensional liquid. The molecules are arranged normal to the layers (Fig. 26.2d). The smectic B phase can be interpreted as the closest packing of rod-like molecules, so that within a layer each molecule has a hexagonal environment (Fig. 26.2e). The smectic A phase and the smectic C phase are similar, except that in the latter the molecules are tilted within the layers by a tilt angle (Fig. 26.2f). A particular case of smectic C is the chiral smectic C^∗ phase, where the tilt angle varies from layer to layer, forming a helical structure [26.11]. For discussion of other smectic phases, as well as their further subclassification, the reader should consult the references [26.12, 26.13, 26.14, 26.15].

In discotic phases, the disc-like molecules are arranged in columns [26.16, 26.17]. In this group, again various phases are possible, depending on the orientation of the molecules within the columns and the order between the columns. The simplest phase is the hexagonal columnar discotic phase. It can be regarded as a one-dimensional liquid. The columns have a hexagonal order (Fig. 26.2g).

Lyotropic liquid crystals are formed by aggregation of micelles [26.18]. They are multicomponent systems. Normally they consist of an amphiphilic substance and a solvent. In contrast, thermotropic liquid crystals are individual compounds.

Enantiotropic LC phases are formed during both the heating and the cooling process. Monotropic LC phases exist only in the supercooled state below the melting point. Thus, these phases are observed during cooling only.

1.1 Chemical Requirements

A liquid crystalline compound can be divided into the mesogenic group and the side groups. The mesogenic group is subdivided into fragments of rings and bridges. The side groups are subdivided into links and terminal groups.

Many other types of liquid crystalline compounds exist besides those with rod-like molecules, e. g., compounds with disc-shaped, banana-shaped, and bowl-shaped molecules [26.10, 26.19, 26.20, 26.21]. However, over 80% of all liquid crystals have a rod-like form, i. e., the molecule shown in Fig. 26.3.

Fig. 26.3

Structure of a calamitic mesogenic compound

1.2 Physical Properties of Liquid Crystals

The order parameter $S=0.5\cdot(3\langle\cos^{2}\Theta\rangle-1)$ characterizes the long-range order of molecules in a mesophase, where Θ is the momentary angle between the long axis of the molecule and the director. In an ideal crystal the order parameter S equals 1 and it equals 0 in an isotropic liquid. In a nematic phase the order parameter lies in the range between 0.5–0.7.

One of the most useful properties for the application of liquid crystals is the anisotropy of their refractive index $\Updelta n=n_{\text{e}}-n_{\text{o}}$, where n_e is the extraordinary and n_o is the ordinary refractive index. For nematics, n_e corresponds to n_∥ and $n_{\text{o}}=n_{\bot}$. n_⊥ means that the vibration vector of plane-polarized light is perpendicular to the optical axis, i. e., the director, while for n_∥ the vibration vector of plane-polarized light is parallel to the director. For the majority of LC the value of Δn is positive, but cholesteryl substituted compounds are optically negative (Δn < 0). On increasing the wavelength, Δn usually decreases. For homologues Δn decreases as the length of alkyl chains increases.

The orientation of molecules in an electric field is determined by the sign of the dielectric anisotropy ($\Updelta\varepsilon=\varepsilon_{\parallel}-\varepsilon_{\bot}$); ε_∥ and ε_⊥ are the dielectric constants measured parallel and perpendicular to the director. Some nematic LC can change the sign of Δε, depending upon the frequency of the applied field.

The majority of mesogens are diamagnetic. The diamagnetic anisotropy (Δχ) characterizes the behavior of LC under the influence of a magnetic field; $\Updelta\chi=\chi_{\parallel}-\chi_{\bot}$, where χ_∥ and χ_⊥ are the diamagnetic susceptibilities parallel and perpendicular to the director.

The basic methods for the determination of phase transition temperatures (T^tr) are GlossaryTerm

DSC

(differential scanning calorimetry), GlossaryTerm

DTA

(differential thermal analysis), and polarization microscopy. Every method has its advantages and restrictions. DSC allows one to determine the enthalpies of phase transitions (ΔH^tr). Microscopy allows one both to determine the phase transition temperatures and to identify the type of mesophase. DTA gives reliable results for melting temperatures of LC having solid-state polymorphism and of LC mixtures. The differences in T^tr that can be found in publications by different authors arise from different measurement techniques and the presence of impurities. We have selected the data with the higher T^tr values in such cases.

The temperature dependence of density (ρ) is practically linear, with the exception of jumps near phase transitions. The volume changes are 3–9%, 0.1–0.4%, and 0.01–0.2% for the crystal–mesophase, nematic–isotropic, and smectic A–nematic transitions, respectively.

The kinematic (ν) and dynamic (η) viscosities can be determined by a capillary viscometer of the Ubbelohde or Ostwald type ($\nu=\eta/\rho$).

The surface tension (γ_LV) influences the angle between the surface and the nematic phase director. It plays an important role in the selection of coatings for the creation of homeotropic alignment (where the molecules are perpendicular to the cell surfaces) or planar alignment (where the molecules are parallel to the surfaces) of LC. The Friedel–Creagh–Kmetz rule states that if γ_L (energy of LC–surface interaction) > γ_S (solid surface energy), then a homeotropic alignment is induced; otherwise, a parallel alignment is induced.

1.3 Applications

The main requirements of LC materials (GlossaryTerm

LCM

) for electro-optics are high clearing (T^N-Is) and low melting temperatures, i. e., a wide temperature range of definite liquid crystalline phases, and a low viscosity for reducing the switching time of electro-optical effects. Wide usage of LCM in displays has become possible since the discovery of mesogenic cyanobiphenyls. At present, a great number of homologous series of LC are synthesized for display application purposes [26.22, 26.23, 26.24, 26.25, 26.26]. Phenylcyclohexane- and bicyclohexane-substituted LC are used as components in LCM; they have low viscosity and, accordingly, fast switching. Fluorinated three-ring LC containing two cyclohexane rings and a phenyl ring are used in LCM with high dielectric anisotropy, which are used at low voltages. For the application of LCM as a material in LC displays, many properties have to correspond to rigid specifications. For this reason LCM consists typically of 7 to 15 components. Sometimes LCM contain nonmesogenic additives, e. g., to reduce the viscosity of the mixture.

The main electro-optic effects in liquid crystals are described in [26.27, 26.28, 26.29]. In the twist structure, the molecules are parallel to the cell surfaces and the angle between the boundary directors is 90^∘. In the S-effect (Frederics effect), a planar structure is transformed to a homeotropic one, and in the B-effect, a homeotropic structure is transformed to a planar one. In the twist-effect (or twisted nematic, GlossaryTerm

TN

effect) a twist structure turns into a homeotropic one. The disadvantage of the TN effect is the necessity to use polarizers. The dynamic scattering mode depends on the influence of an electrical current on the orientation of the molecules. At a high enough voltage, transparent nematic cells becomes turbid. A disadvantage of this effect is that the lower the voltage, the longer the switching time. One of the modern uses of this effect is the application of the dynamic scattering mode for data storage. After the applied voltage is switched off, the mode of the planar cell does not return to its initial state. The cell can be stored in the turbid state for a long time (from some minutes to some months).

The host–guest effect results from a reorientation of dye dopants (1–2% in the LC matrix) in an electric field. In this case the wavelength of maximum absorption of light is shifted and the color of the LC cell changes.

The sign of the dielectric anisotropy of an LCM determines the type of electro-optical effect. LCM with Δε > 0 are used for TN, GlossaryTerm

STN

(supertwisted nematic), and GlossaryTerm

TFT

(thin film transistor) effects. LCM with low negative values of Δε have been formerly used for the dynamic scattering mode. Now LCM with negative anisotropy Δε are utilized for GlossaryTerm

MVA-TFT

(multidomain vertical alignment thin film transistor) displays. The higher the value of Δε > 0, the smaller is the working voltage. The MVA-TFT and GlossaryTerm

IPS

(in-plane-switching) technologies provide the possibility of improving the viewing angles of displays for television [26.28, 26.29, 26.30, 26.31, 26.32].

Electric current leads to degradation of an LCM and reduces the lifetime of the display. Impurities influence the stability of the material and accelerate electrodegradation. Therefore, a multistage purification (e. g., recrystallization and column chromatography) to remove conducting impurities (intermediate products, water, and CO₂) is necessary. Usually the specific conductivity of an LCM is lower than $E-11{-}E-12\,{\mathrm{Cm/cm}}$ and corresponds to the intrinsic conductivity.

The elastic constants (K_i) determine the switching time of the electro-optical effects. The elastic constant K₁ corresponds to the S-effect, K₃ to the B-effect, K₂ to the TN effect; here K₁ corresponds to splaying, K₂ to twisting, K₃ to bending.

Cholesteryl compounds were the first materials that found application in thermography. A huge number of other applications exist, where the chemical and physical requirements are totally different. These applications include reflectors, temperature measurement with thermochromic materials, nonlinear optics, polymer materials, self-assembled monolayers, GlossaryTerm

LB

(Langmuir–Blodgett) films, and the use of liquid crystals in template synthesis of porous materials, drug delivery, and many more.

1.4 List of Abbreviations

Cr, Cr^′:

Crystalline phases

S:

Smectic

A, B, C, E, F, G, H:

Specific smectic mesophases

C*:

Chiral smectic C (ferroelectric)

D:

Discotic

Dh, Dho, Dhd:

Hexagonal columnar discotic (ordered or disordered)

Dr, Dt:

Rectangular, tilted columnar discotic

N:

Nematic

N*:

Cholesteric

Is:

Isotropic

Examples:

Cr 95.0 C 99.0 N 107.5 Is:

Crystals melt at 95^∘C, smectic C transforms to nematic at 99^∘C and to isotropic liquid at 107.5^∘C

Cr^′ 5.0 Cr 67.3 (N 30.3) Is:

Crystals melt at 67.3^∘C. Compound has a monotropic nematic phase on cooling below 30.3^∘C and polymorphism (solid–solid transition) at 5^∘C

T ^tr :

Temperatures of phase transitions

T ^N-Is :

Temperature of nematic–isotropic transition (in kelvin)

(extra):

Data were extrapolated from 10–20 wt% solution in nematic mixture

dec:

Substance decomposes on heating

Relative temperatures (e. g., T = 0.977T^N-Is) are assumed to be in kelvin only. Inverse temperatures are always given in 1∕kelvin (e. g., $1000/T=2.4$).

Some data are given for the supercooled mesophase (T < T_melting).

CAS-RN:

registration number of the Chemical Abstract Service (CAS).

Common names are historical names, and trade names of BDH, Licristal® Merck, and Hoffmann-La Roche [26.22, 26.23, 26.25].

Δn :

Anisotropy of the refractive index (n_e − n_o)

Δε :

Dielectric anisotropy

ΔH^tr :

Enthalpies of phase transitions (kJ ∕ mol)

C _p :

Heat capacity at constant pressure (J ∕ (mol K))

v :

Sound velocity (m ∕ s)

p :

Helix pitch (for N* phase)

P _s :

Spontaneous polarization (for ferroelectric LC) (nC ∕ cm²)

D :

Diffusion coefficient (m² ∕ s)

C₆H₁₂ :

Cyclohexane

1.5 Conversion Factors

Molar weight:

$${\mathrm{1}}\,{\mathrm{g/mol}}={\mathrm{1\times 10^{-3}}}\,{\mathrm{kg/mol}}$$

Temperatures of phase transitions:

$$T({\mathrm{{}^{\circ}\mathrm{C}}})=T\,({\mathrm{K}})-273.15$$

Density:

$${\mathrm{1}}\,{\mathrm{g/cm^{3}}}={\mathrm{1\times 10^{3}}}\,{\mathrm{kg/m^{3}}}$$

Dynamic viscosity η:

$$\begin{aligned}\displaystyle{\mathrm{1}}\,{\mathrm{mPa{\,}s}}&\displaystyle={\mathrm{1\times 10^{-3}}}\,{\mathrm{Pa{\,}s}}={\mathrm{1}}\,{\mathrm{cP}}\\ \displaystyle&\displaystyle\qquad\quad\text{(centi-Poise)}\end{aligned}$$

Kinematic viscosity $\nu=\eta/\rho$:

$$\begin{aligned}\displaystyle{\mathrm{1}}\,{\mathrm{mm^{2}/s}}&\displaystyle={\mathrm{1\times 10^{-6}}}\,{\mathrm{m^{2}/s}}={\mathrm{1}}\,{\mathrm{cSt}}\\ \displaystyle&\displaystyle\qquad\quad\text{(centi-Stokes)}\end{aligned}$$

Thermal conductivity:

$${\mathrm{1}}\,{\mathrm{W/(m{\,}K)}}={\mathrm{1\times 10^{-2}}}\,{\mathrm{W/(cm{\,}K)}}$$

Diamagnetic anisotropy Δχ:

$${\mathrm{1}}\,{\mathrm{m^{3}/kg}}={\mathrm{1\times 10^{3}}}\,{\mathrm{cm^{3}/g}}\quad\text{(CGS unit)}$$

Dipole moment:

$$\begin{aligned}\displaystyle{\mathrm{1}}\,{\mathrm{D}}\,\text{(Debye)}&\displaystyle={\mathrm{3.33564\times 10^{-30}}}\,{\mathrm{C{\,}m}}\\ \displaystyle&\displaystyle\qquad\quad\text{(Coulomb meter)}\end{aligned}$$

2 Physical Properties of the Most Common Liquid Crystalline Substances

The compounds are arranged in the tables on the basis of the number and priority of fragments. The order principles for mesogenic groups are the number of rings and bridges, and the priority of rings, bridges, and side groups.

Priority of rings: benzene > cyclohexane > heterocycles > halogen-substituted benzenes.

Priority of bridges: $\mathrm{C_{\mathit{n}}H_{\mathit{m}}}> \mathrm{CH}{=}\mathrm{N}> \mathrm{N}{=}\mathrm{N}> \mathrm{N}{=}\mathrm{N}(\mathrm{O})> \mathrm{COO}$.

Homologues are arranged in order of increasing number of carbon atoms in the alkyl chains.

We have attempted to include all of the most common liquid crystals, from the traditional model substances (e. g., 5CB, MBBA, and PAA) to substances used in modern applications.

Table 26.2 Acids

Table 26.3 Two-ring systems without bridges

Table 26.4 Two-ring systems with bridges

Table 26.5 Three- and four-ring systems

Table 26.6 Ferroelectric liquid crystals

Table 26.7 Cholesteryl (cholest-5-ene) substituted mesogens

Table 26.8 Discotic liquid crystals

Table 26.9 Liquid crystal salts

3 Physical Properties of Some Liquid Crystalline Mixtures

Table 26.10 Nematic mixtures

Table 26.11 Ferroelectric mixtures