Liquid Cristals - Materials Design and Self-Assembly

Liquid Crystals 

CONTENT:

Fluorinated Liquid Crystals: Design of Soft Nanostructures and
Increased Complexity of Self-Assembly by Perfluorinated Segments 

Carsten Tschierske

Liquid Crystalline Crown Ethers 

Martin Kaller and Sabine Laschat

Star-Shaped Mesogens – Hekates: The Most Basic Star Structure
with Three Branches 

Matthias Lehmann

DNA-Based Soft Phases

Tommaso Bellini, Roberto Cerbino, and Giuliano Zanchetta

Polar and Apolar Columnar Phases Made of Bent-Core Mesogens 

N. Vaupoticˇ, D. Pociecha, and E. Gorecka

Spontaneous Achiral Symmetry Breaking in Liquid
Crystalline Phases 

H. Takezoe

Nanoparticles in Liquid Crystals and Liquid Crystalline
Nanoparticles

Oana Stamatoiu, Javad Mirzaei, Xiang Feng, and Torsten Hegmann

Stimuli-Responsive Photoluminescent Liquid Crystals

Shogo Yamane, Kana Tanabe, Yoshimitsu Sagara, and Takashi Kato

Fluorinated Liquid Crystals: Design of SoftNanostructures and Increased Complexity of Self-Assembly by Perfluorinated Segments
Carsten Tschierske

    Abstract The effects of perfluorinated and semiperfluorinated hydrocarbon units
on the self-assembly of rod-like, disc-like, polycatenar, taper- and star-shaped,
dendritic, and bent-core liquid crystalline (LC) materials is reviewed. The influence
of fluorinated segments is analyzed on the basis of their contributions to
the cohesive energy density, molecular shape, conformational flexibility, microsegregation,
space filling, and interface curvature. Though the focus is on recent
progress in the last decade, previous main contributions, general aspects of
perfluorinated organic molecules, and the basics of LC self-assembly are also briefly
discussed to provide a complete overall picture. The main focus is on structureproperty-
relations and the use ofmicro-segregation to tailor mesophasemorphologies.
Especially polyphilic molecules with perfluorinated segments provide new modes
of LC self-assembly, leading to ordered fluids with periodic multi-compartment
structures and enhanced complexity compared to previously known systems.
Keywords Columnar mesophase Cubic mesophase Dendrimer Liquid crystal
Metallomesogen Micro-segregation Organic semiconductor Perfluorinated
molecule Polyphilic molecule Self-assembly

Abbreviations
1D/2D/3D One- two-, three-dimensional
ahex Hexagonal lattice parameter
CED Cohesive energy density
Col Columnar phase
Colhex Hexagonal columnar phase
Colob Oblique columnar phase
Colortho Orthorhombic “columnar” phase
Colrec Rectangular columnar Phase
Colsqu Square columnar phase

Cr Crystalline solid
CubI Spheroidic (micellar) cubic phase
CubV Bicontinuous cubic phase
d Layer periodicity
E Crystalline E phase
G Glassy state
HT High temperature phase
Iso Isotropic liquid
Isore Re-entrant isotropic phase
l Molecular length
LamN Laminated nematic phase
LamSm/cor Correlated laminated smectic phase
LamSm/dis Non-correlated laminated smectic phase
LC Liquid crystal/Liquid crystalline
LT Low temperature phase
M Unknown mesophase
N/N* Nematic phase/Chiral nematic Phase
RF Perfluoroalkyl chain
RH Alkyl chain
RSi Carbosilane chain
SmA Smectic A phase (nontilted smectic phase)
SmAd/SmCd Double layer SmA/SmC phase
SmB Smectic B phase
SmC Smectic C phase (synclinic tilted smectic C phase)
SmC* Chiral (synclinic tilted) smectic C phase
SmCA* Chiral anticlinic tilted (antiferroelectric switching) SmC phase
SmCPA Antiferroelectric switching polar smectic C phase
SmCPF Ferroelectric switching polar smectic C phase
SmCa* Chiral smectic C alpha phase
SmIA* Chiral antiferroelectric switching smectic I phase
SmX Smectic phase with unknown structure
UCST Upper critical solution temperature
XRD X-ray diffraction

1 Introduction
1.1 Liquid Crystal Self-Assembly
Liquid crystals (LC) represent truly fascinating materials in terms of their
properties, their importance for the fundamental understanding of molecular selfassembly,
and their tremendous success in commercial applications [1, 2]. Liquid
crystals can be considered as a state of matter which in a unique way combines
order and mobility. The constituent molecules of LC phases are sufficiently

 

Fig. 1 Organization of rod-like molecules (top) and disc-like molecules (bottom) in LC phases
(for clarity the alkyl chains are not shown in the models of the phase structures). Abbreviations: Iso
isotropic liquid state; N nematic LC phase; SmA smectic A phase, SmC smectic C phase (tilted),
Col columnar phase

disordered to generate softness and even flow properties, yet comprising varying
degrees of ordering depending on the actual type of liquid crystal phase (Fig. 1).
Hence, depending on the rheological properties, liquid crystals can be considered as
anisotropic soft matter or anisotropic fluids with interesting application properties.
Liquid crystalline phases usually occur in a distinct temperature range between the

crystalline solid state (Cr) and the isotropic liquid state (Iso). Therefore, such
phases are also called mesophases, and the compounds that exhibit such behavior
are called mesogens or liquid crystals.
The nematic phase (N) is the least ordered, and hence the most fluid liquid
crystal phase. The order in this type of LC phases is based on a rigid and
anisometric (in most cases rod-shaped or disc-shaped) molecular architecture.
Such molecules tend to minimize the excluded volume between them, and this
leads to long range orientational order. For rod-like molecules the ratio between
molecular length and its broadness determines the stability of the nematic phase
with respect to the isotropic liquid state and the stability rises with increase of this
ratio. In most cases the rigid cores are combined with flexible chains, typically alkyl
chains, which hinder crystallization and in this way retain fluidity despite of the
onset of order.
The combination of rigid and flexible segments in one molecule can lead to
amphiphilicity if these chains are sufficiently long. This gives rise to nano-scale
segregation of the rigid cores and flexible chains which is an important route
to positional long range order, providing layer-like LC structures for rod-like
molecules and columnar aggregates for disc-like molecules; see Fig. 1 [3, 4, 9, 10].
Layer structures (smectic phases, Sm) have a periodicity in only one direction
(the distance d between the layers) and these phases can be further classified
according to the order in the layers. If there is no order or rod-like anisometric
units which adopt an orientation with the director n on average perpendicular to the
layer planes, then the phase is assigned as SmA (Fig. 1). If anisometric units adopt
a uniformly tilted configuration, the phase is assigned as SmC. With increasing
order in the layers additional types of higher ordered smectic phases can arise (e.g.,
SmB, E, G. . .) [11]. Columnar aggregates assemble on a periodic 2D lattice,
leading to columnar phases (Col) [12, 13].
Amphiphilicity is a very general driving force for molecular self-assembly
and, besides the rigid-flexible amphiphiles [14] mentioned above, any other type
of incompatibility can generate long range positional order. The most important are
the polar/apolar incompatibility, leading to polar amphiphilic LC [15–18], and the
incompatibility between hydrocarbons and fluorocarbons (“apolar” amphiphiles),
but the combination of segments with a distinct shape, for example rod-like and
disc-like can also lead to an amphiphilic structure (shape amphiphiles [19, 20]).
Due to the very different kinds of amphiphilicity occurring in LC systems, which
are often combined, it is difficult to describe them theoretically and to make precise
quantitative predictions such as, for example, developed for lyotropic systems [21,
22] and block copolymers [23].

The concept of micro-segregation, (nano-segregation is used synonymously)
developed for these thermotropic LC systems, is based on the approximation that
micro-segregation of the two incompatible components of a binary amphiphile into
two distinct nano-spaces can be related to the ability of macroscopic segregation
(demixing) of two immiscible liquids with molecular structures similar to the two
segments forming the amphiphile [6, 9, 10, 24, 25]. The Gibbs free energy of
mixing of two liquids (DGmix) must be positive (endergonic) for demixing. The free

energy term can be split into an enthalpic and an entropic contribution according to
DGmix ¼ DHmix–TDSmix. The mixing enthalpy (DHmix) is related to the difference
in cohesive energy density (CED, c) of the two components (A, B), i.e., DHmix ~
(cA-cB). The CED can be calculated from the vaporization enthalpy (DHV) and the
molar volume (Vm) according to c ¼ (DHV RT)/Vm or, alternatively, from the
surface tension (g) and the molar volume by c ¼ g/Vm
1/3. The Hildebrand solubility
parameter (d) [26] is the square root of the cohesive energy density d ¼ c1/2 and
hence these parameters, which are tabulated [27, 28], can be used to estimate
whether two molecules would mix or not. If these two molecules are interconnected
in an amphiphile the degree of incompatibility of the two segments decides whether
nano-scale segregation could takes place. The larger the difference dA dB the
larger the incompatibility and the higher the mesophase stability.1 Segregation
works against the entropy of mixing and hence segregation is favored for larger
molecules because there are less molecules per volume unit and therefore in this
case the influence of the mixing entropy to the entropy term (–TDSmix) is smaller
than for small molecules. As DSmix is positive and coupled with temperature (–T) it
becomes more important at higher temperature. This reduces DGmix and, as soon as
it approaches zero and becomes negative, segregation is lost at the order–disorder
transition temperature, also assigned as clearing temperature in LCs. It should be
pointed out that the mesophase stability is independent from the total value of the
cohesive energy density of the components; this only influences the transition from
the liquid to the gaseous state, i.e., the complete isolation of the molecules (vaporization).
Segregation is the reverse of mixing which is the separation of molecules
by other molecules and this is driven by the difference in cohesive energy density
between the two types of molecules (macroscopic demixing) or the distinct
segments forming an amphiphilic mesogens (micro-segregation). Therefore, the
stability of a positional ordered mesophase increases with growing difference
of solubility parameters (Dd) of the two components which is equivalent to the
difference in CED (Dc). Because it is the difference between the CEDs of the
distinct segments of an amphiphilic mesogens which determines the mesophase
stability and not their absolute values, an increase of mesophase stability can also
be achieved by reducing the CED of one of the incompatible segments of an
amphiphile. This is important for understanding mesophase stabilization by the

fluorophobic effect, as the CED of fluorinated alkyl chain is usually the lowest of all
possible LC building blocks (see Sect. 1.3). Despite the total CED being reduced
(i.e., the attractive forces between the molecules are reduced!) by perfluorination
of the alkyl chains of the mesogens, the difference of the cohesive energy densities
between the segments is increased. Therefore, fluorination usually leads to
mesophase stabilization, as shown in Table 1 for a representative example. Though
these considerations are simplified, they provide a fundamental understanding
of the structure-property relations in nano-segregated LC systems and allow
a comparison of related molecules and the effect of structural variations on the
mesophase stability.
Segregation of the incompatible molecular segments takes place with formation
of distinct nano-compartments organized on a one-dimensional (1D), twodimensional
(2D), or three-dimensional (3D) periodic lattice, separated by interfaces.
These interfaces tend to be minimal in order to reduce the interfacial energy
stored in the system. For amphiphilic molecules without anisometric segments
(flexible amphiphiles) the mesophase type is mainly determined by the relative
volume of the two incompatible segments, as shown in Fig. 2.
Lamellar phases (¼ smectic phases, Sm), composed of stacks of alternating
layers, have flat interfaces between the micro-segregated regions (layers) and these
structures are formed by molecules for which the incompatible segments have
comparable sizes and hence require comparable cross section areas at the interfaces.
If the size of one segment is increased the layers become unstable and a
curvature of the interfaces arises. In this case the layers are replaced by columns,
followed by spheroidic aggregates with increasing interface curvature (Fig. 2) [21].
Self-assembly of circular columns takes place on a hexagonal lattice, leading to
hexagonal columnar phases (Colhex) providing minimized interfaces compared to
non-circular columns forming square (Colsqu), rectangular (Colrec), or oblique
(Colob) 2D lattices [29]. Formation of these non-hexagonal columnar phases
requires additional contribution from the molecular shape.
Self assembly of spheroidic aggregates leads in most cases to micellar cubic
phases (CubI) [30–35], where closed spheroidic aggregates are organized on a cubic
3D lattice (Fig. 2d,e).

 

There is a second kind of cubic phases, assigned as bicontinuous cubic phases
(abbreviated as CubV) which can occur at the transition between lamellar and
columnar organization [35, 36]. In these cubic phases the layers develop saddle
splay curvature (see Fig. 2) and adopt the shape of infinite minimal surfaces. Alternatively,
these bicontinuous cubic phases could be considered as resulting from
a branching of columns; these branched columns are interconnected at distinct
nodes to give rise to two interwoven continuous networks (Fig. 2b) [32, 37, 38].
Both descriptions can be regarded as equivalent, one considering the regions of the
alkyl chains and the other the segregated mesogenic cores. Depending on the shape
of the infinite minimal surfaces and on the number of columns interconnected at
each branching point, respectively, quite distinct structures could result which
are again classified according to space group symmetry [29].2 Although there is
3D-long range order in density fluctuations, cubic and other 3D mesophases are still
regarded as liquid crystalline as long as there is no preferred position for individual
molecules, i.e., as long as there is a diffuse wide-angle X-ray scattering.

Whereas formation of nematic phases usually requires a specific rod-like or disclike
molecular shape, this is not the case for mesophases based on nano-segregation
[9, 10]. Any amphiphilic molecule can adopt the mesophase morphologies shown in
Fig. 2a–e, depending on the size ratio of the incompatible units. However, a specific
molecular shape can lead to a preference for a distinct type of self assembly.
Generally, rod-like molecules prefer to be organized in layers as they tend to
avoid the splay occurring in curved aggregates. Disc-like molecules provide curvature
in their molecular structure and therefore preferably form columnar LC phases.
Taper-shaped or cone-like molecules tend to form columnar and micellar cubic
phases with strong interface curvature [31, 35, 39]. However, it is not always the
case that self-assembly of anisometric units and amphiphilic self-assembly enhance
each other. These two modes of self assembly can also be in competition and this
can modify the mesophase morphology. For example, disc-like molecules can,
under certain conditions, organize in layers (lamello-columnar phases) and rodlike
molecules can form ribbons organized on a 2D lattice (assigned as modulated
smectic phases or ribbon phases). Similarly, taper shaped molecules can arrange
antiparallel and form layers (Fig. 2). If this competition provides significantly
strong frustration, it can either lead to disorder (occurrence of isotropic or nematic
phases) [40, 41] or, alternatively, to completely new LC structures [8]. Hence,
competition is a way to new LC phases. Another alternative way to increased
mesophase complexity consists in the combination of more than two incompatible
units, leading to polyphilic LC (see Sect. 7) [8, 10, 42].
Depending on temperature, transitions between distinct types of LC phases can
occur.3 All transitions between various liquid crystal phases with 0D, 1D, or 2D
periodicity (nematic, smectic, and columnar phases) and between these liquid
crystal phases and the isotropic liquid state are reversible with nearly no hysteresis.
However, due to the kinetic nature of crystallization, strong hysteresis can occur for
the transition to solid crystalline phases (overcooling), which allows liquid crystal
phases to be observed below the melting point, and these phases are termed
monotropic (monotropic phases are shown in parenthesis). Some overcooling
could also be found for mesophases with 3D order, namely cubic phases. The
order–disorder transition from the liquid crystalline phases to the isotropic liquid
state (assigned as clearing temperature) is used as a measure of the stability of the
LC phase considered.

Besides molecular shapes and amphiphilicity, chirality also has a large influence
on LC self assembly, leading to series of LC phases with helical superstructures,
reduced symmetry, and chirality induced frustration [43–46].
Also mesogens with more complex shapes, such as, for example, those with
bent aromatic cores (bent-core mesogens [47]), star mesogens [48], or cone-like

molecules are of contemporary interest, together with LC states formed by
biomolecules [49–51], polymers, dendrimers, or network structures (gels,
elastomers) [52–54]. The huge number of possible molecular and supramolecular
structures and the complex relations between molecular shape, nano-scale segregation,
and symmetry of molecular packing leads to a large number of self assembled
LC structures, which is continuously growing.
Due to inherent fluidity these self-organized LC structures have the ability to
change their configuration under the influence of external stimuli (surfaces, electric,
magnetic, and mechanical fields) and to eliminate defects by self-healing. Therefore,
this special state of matter is not only of interest for displays, adaptive optics,
information storage, and nano-patterning – it provides a very general way to
assemble functional molecules/materials into well defined superstructures. This
can be used in technology, and it is an important concept of molecular self assembly
in biosystems [55].

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