Three techniques are commonly used to characterize mesophases: polarizing optical microscopy (POM), differential scanning calorimetry (DSC), and X-ray diffraction (XRD).
Micelle
Reverse micelle Reverse micelle cross-section Micelle cross-section
FIGURE 11 Structures of micelles formed by amphiphilic molecules.Adapted fromCollings and Hird (1997).
3.1. Polarizing Optical Microscopy (POM)
Mesophases can be identified by studying the characteristic pattern (textures, also called defect textures) that are observed when a thin film of a LC is placed between the crossed polarizers of a POM. This method is based on the optical anisotropy and birefringence of LCs. Most LCs are optically uni- axial materials, with the optical axis being defined by the director. An opti- cally anisotropic material is able to change the polarization state of light.
Unpolarized light contains bothx-polarized andy-polarized electric field com- ponents (Fig. 15). When an unpolarized light beam passes a first polarizer, only one electric field component remains and linearly polarized light is
Polar head group
Nonpolar chains Bilayer unit
Water layer
FIGURE 12 Structure of the lamellar lyotropic liquid-crystalline phase.Adapted fromCollings and Hird (1997).
Polar head groups
Water surrounding head groups Nonpolar chains
FIGURE 13 Structure of the hexagonal lyotropic liquid-crystalline phase.Adapted fromColl- ings and Hird (1997).
obtained. When an isotropic material (or no material at all) is present between the two crossed polarizers, the polarization direction of the light beam will not be changed and thex-polarized light beam cannot pass the second polarizer (which is called the “analyzer”).
The situation is totally different when a LC is placed between the crossed polarizers. The first polarizer is oriented so that the direction of the linearly polarized light beam makes an angle other than 0 or 90 with the director of the LC. One can consider this light beam as being composed of light polar- ized along the director and light polarized perpendicular to the director with zero phase difference. In passing through the LC, the two linearly polarized light beams get out of phase and in general emerge as elliptically polarized light. Since the electric field of elliptically polarized light is constantly rotat- ing completely around during each cycle, it is parallel to the polarization axis of the second polarizer twice during each cycle. Therefore, some light will pass through the second polarizer. In general, the introduction of a LC between crossed polarizers causes the field of view to appear bright, whereas the field is dark with no LC between the polarizers. However, there are two
Micelle cross-section Micelle
FIGURE 14 Structure of the cubic lyotropic liquid-crystalline phase.Adapted fromCollings and Hird (1997).
Unpolarized light source
Polarizer Analyzer
No light
Ex Ex
Ey
FIGURE 15 Principle of crossed polarizers.
conditions under which LCs continue to appear black: if the incident linearly polarized light beam has its polarization direction either parallel or perpendic- ular to the director of the LC. There are also several positions in the texture where the brightness at once changes from very bright to black. These points or lines are called disclinations and represent places where the director is undefined, since it points to many directions within an extremely small region. Due to these defects and the symmetry of the phase, each liquid- crystalline phase has a different texture. InFig. 16, the typicalSchlierentex- ture of a nematic phase is shown. Often the textures show many colors because of interference effects. The textures are often diagnostic for a partic- ular mesophase, although it can sometimes be difficult to determine the meso- phase type from the texture alone. Especially the identification of columnar phases can be difficult on the sole basis of optical textures. Isotropic materials only possess one refractive index and cannot change the polarization direction of the incident light beam. Therefore, they appear black between crossed polarizers.
A POM for liquid-crystal studies is equipped with two crossed polarizers and a heating stage (hot stage). One polarizer is placed between the light source and the heating stage (polarizer) and the other is localized between the heating stage and the observer (analyzer). For observing liquid-crystalline phases the polarizers are typically crossed. The heating block of the heating stage is made of silver, because of the high thermal conductivity of this metal.
The temperature of the heating stage can accurately be controlled by an elec- tronic temperature controller, and most heating stages can also be cooled in a controlled way. To observe the texture, a small amount of the LC (typically less than 1 mg) is placed between two microscope cover slips, and the com- pound is transformed into the mesophase by heating it on the heating stage.
The best textures are observed when the mesophase is formed by cooling of the isotropic liquid. When the compound is thermally unstable at the clearing
FIGURE 16 Schlieren texture of the nematic phase of 4-nonyloxybenzoic acid.
point or even decomposes before the clearing point is reached, the defect tex- ture can only be observed by heating the compound. In that case, it is recom- mended to keep the mesophase some time at a constant temperature so have a good texture developed. The heating or cooling rates of the heating stage can be varied between 0.5 and 10C min1. The fast heating/cooling rates are useful to get an overall impression of the thermal behavior of the compound, whereas the slower rates are used to obtain good textures or to determine the transition temperatures. One can learn to interpret the textures by studying the textures of compounds with known mesophases or to study textbook examples of textures (Demus and Richter, 1978; Dierking, 2003). Besides the determination of phase types, observations by POM can also be used for other purposes in LC research:
(1) to determine the phase transition temperatures of a given material, although not as accurately as by DSC; (2) to observe thermal decomposition of samples;
(3) to check the viscosity of a liquid-crystalline sample (which often supports the identification of a particular type of mesophase); (4) to judge the purity of a compound in a quick way: for a single thermotropic liquid-crystalline material, only one type of phase should be observed at a given temperature and pressure, because theGibbs phase rule(F¼CPþ2, whereFis the variance,Cis the number of components, andPis the number of phases at equilibrium) has to be obeyed; (5) to make estimates of the sample alignment; and (6) to follow voltage-controlled switching processes. Finally, a POM can be used to perform miscibility studies. This phase identification method was very common before the appearance of structural studies using XRD, and is based on the comiscibility of identical types of mesophases shown by different compounds. Pioneering work in this field was performed by Horst Sackmann from the LC group in Halle, Germany (Demus and Richter, 1978; Gray and Goodby, 1984).
3.2. Differential Scanning Calorimetry (DSC)
Phase transitions are accompanied by a change in enthalpy,DH, and thus by a change in entropy, DS (DS¼DH/Ttransition under equilibrium conditions, DG¼0). The magnitude of the entropy change is related to the amount of order that is lost or gained during the transition. In a DSC experiment, the enthalpy changes corresponding to the different phase transitions of a sample are measured by determining the power supplied to (or absorbed by) the sam- ple. The phase transition temperatures can be accurately determined by this method. Phase transitions can be of first or second order. A first-order phase transitionis characterized by a discontinuous jump in the first deriva- tive of the Gibbs free energy (G) in function of the temperature (T),@G(T)/
@T. The enthalpyH, entropyS, and volumeVcan all be defined by appropri-
ate first derivatives of the Gibbs free energy (e.g., DS¼D(@G/@T)) and consequently all these variables change discontinuously at a first-order transi- tion. In a so-calledthermogram, in which the heat flow is plotted as a function of time (t) or temperature (T), first-order phase transitions can be visually
areas). Typical first-order phase transitions are the melting and clearing pro- cess of a LC, but also some mesophase-to-mesophase transitions can be of first order. A second-order phase transitionis characterized by a continuous first derivative of the Gibbs free energy, but a discontinuous second deriva- tive. In this case, the heat capacity Cp will exhibit a discontinuous jump, and results in a step in the baseline of the thermogram. The SmA–SmC tran- sition (with a continuous change of the tilt angle) is a typical example of a second-order transition.
DSC is a widely used technique in the investigation of phase transitions of LCs. There are two types of DSC modules on the market: theheat-flux DSC and the power-compensation DSC. The principle of heat-flux DSC is illu- strated inFig. 17. Heat-flux DSC makes use of one furnace to heat both the sample crucible and an empty reference crucible, which corrects for the heat capacity of the crucible material. Symmetrical heating is achieved by con- structing the furnace from a metal with a high thermal conductivity, such as silver. The temperature is measured at the heat-flux plate, which generates a very controlled heat flow from the furnace surface wall to the sample and ref- erence, and between the two crucibles. When a sampleSand a referenceRare uniformly heated in a furnace and when an exothermic effect takes place in the sample, the temperature of the sample TSwill be higher than that of the reference,TR. In the case of an endothermic effect the temperature of the sam- ple will be lower than that of the reference. The temperature difference DT¼TSTR is recorded against the temperature TR. Because the sample and reference are placed on the heat-flux plate, DT is proportional to the heat-flux difference between the sample and reference. When the sample mass is known and the temperature lag is measured very accurately, the energy of the transition (the enthalpy change) can be calculated. In addition, precise transition temperatures are obtained. However, calibration with a standard compound (e.g., indium, Tm¼156.6C) remains necessary. In a power- compensating DSC, the sample and reference are placed in two different
S R
DT
FIGURE 17 Heat-flux DSC cell. S¼sample, R¼reference.
furnaces. The temperature difference between the sample and the reference is kept at zero (DT¼TSTR¼0) by independent heaters in the sample and ref- erence furnaces (Fig. 18). The small crucibles or sample pans for DSC mea- surements are usually made of aluminum (Tm¼660C), and sealed with a lid. A hole can be pierced into the lid to allow possible decomposition pro- ducts to escape from the crucible, instead of building up an internal pressure, and/or to create a specific atmosphere around the sample (e.g., a helium atmosphere). A few milligrams of sample are needed (e.g., 2 mg if a good resolution of phase transition peaks is required, 5 mg if a good sensi- tivity is required). Typical heating rates for the investigation of liquid- crystalline samples are 2–10C min1. Heating normally occurs under an inert atmosphere, preferentially helium (because of the good thermal conductivity of this gas).
In a thermogram, the heat flow (@Q/@t, in mW) is plotted as a function of time (t) or temperature (T). The enthalpy changeDHassociated with a certain transition corresponds to the integral of the DSC curve with respect to time (peak area). According to the commonly used definition in LC research, the heat flow It has a positive value forendothermic transitions (in which heat is absorbed by the sample), and a negative value forexothermic transitions (in which heat is released by the sample). Enthalpy changes between succes- sive liquid-crystalline phases or between a liquid-crystalline phase and the isotropic liquid are typically quite small, around 0.5–10 kJ mol1. Mesophase-to-mesophase transitions are sometimes not even detectable by DSC. The enthalpy change between a crystalline phase and a liquid- crystalline phase is usually quite large, in the range 10–80 kJ mol1. However, the DH values strongly depend on the types of solid and liquid-crystalline phases. Large enthalpy changes correspond to large changes of molecular organization in the sample. The change in entropy can be deter- mined by dividing the enthalpy change DH by the transition temperature, Ttransition (expressed in Kelvin): DS¼DH/Ttransition. DSC is strictly comple- mentary to optical microscopy. Sometimes a phase transition is accompanied by only a very small textural change, which might be overlooked by the observer. On the other hand, not all textural changes result from phase changes. Enthalpy and entropy values can give an indication of the type of mesophase. An example of DSC trace is given inSection 4(Figure 30).
T sensor
S R
FIGURE 18 Power-compensation DSC cell. S¼sample, R¼reference.
XRD is the most powerful experimental technique to determine the structure of liquid-crystalline phases (Seddon, 1998; Templer, 1998). X-rays interact with the electron cloud of the material. The various scattered wavelets from the different atomic sites combine and undergo constructive or destructive interference, depending on the relative phases of the different wavelets, thus on their path difference. This can be expressed by Bragg’s law:
nl¼2dsiny: ð1Þ
As shown inFig. 19, this expression states that X-rays reflected by succes- sive atomic planes separated by a distancedinterfere constructively when the path difference between them is an integer multiple (n) of the wavelengthl.
Note that the diffraction angle is often expressed in degrees 2y. The XRD is typically recorded between 1<2y<40, so that that the region of interest is positioned between the true small-angle region that is of interest for poly- mer scientists (SAXS; small-angle X-ray scattering) and the wide-angle region in which powder diffractograms are recorded for phase identification.
The positions of the diffraction peaks are reciprocally related to the separa- tions between molecules (or groups of molecules), in other words, the smaller thed spacing, the larger is the diffraction angle 2y.
The XRD pattern of a mesophase gives several types of information, depending on the angular region investigated. In general, two regions are
Diffraction
Incident Beam
Q = ( ki - ks ) ks
ks ki
ki ki
peak n
qn qn
2q
FIGURE 19 Diffraction from parallel planes (top), and definition of the scattering vector!Q (bottom).
examined in the pattern, the small-angle region and the wide-angle region.
The small-angle diffraction maxima are due to intermolecular interferences along the director in case of rod-like molecules (calamitic mesogens) or along a direction perpendicular to the director in case of disk-like molecules (disco- tic mesogens), and correspond to long distances (tens of A˚). Periodic distances d in the structure, such as the interlayer spacing, are calculated from these maxima by applying Bragg’s law. In general, thisdvalue corresponds roughly to the molecular length in rod-like compounds and to the molecular diameter in disk-like compounds. The sharpness of the peaks is related to the extent to which the atomic layers extend periodically over large distances. The ratio of the Bragg peak positions reveals the long-range organization of the phase. The wide-angle maxima are due to intermolecular interferences in the direction perpendicular to the director in the case of calamitics or along the director in the case of discotics, and correspond to short distances (3–6 A˚). These dis- tances correspond roughly to the molecular width in the case of calamitic compounds and to the molecular thickness in the case of discotic compounds.
The more order is present in the short-range organization of the molecules, the sharper are the peaks in the wide-angle region. Each type of mesophase gives a characteristic diffraction pattern.
Diffuse peaks are observed in both the small-angle and the wide-angle region of the X-ray pattern of the nematic phase. The broad signal in the wide-angle region corresponds to the average lateral separations of the close- packed molecules and to the short-range order of the molten alkyl chains.
The signal in the small-angle region, with distances of the order of the molecu- lar length, corresponds tocybotactic groups(i.e., local smectic ordering), a con- sequence of the molecular anisotropy and amphipathic character of the molecule. In many cases, the diffraction pattern of the isotropic phase is very similar to that of the nematic phase. However, a nematic phase can be aligned by an external magnetic field. This is not the case for the isotropic phase. The alignment of the nematic phase in a magnetic field can be observed by XRD if a 2D detector is used.Lamellar structuresare characterized by the layer period- icityd. In the small-angle region, the XRD pattern consists of sharp reflections with reciprocal spacings in the ratio 1, 2, 3,. . .are observed, corresponding to the indexation (00l)¼(001), (002), (003),. . .The higher order reflections have much lower intensities than the first order reflection (001). In the wide-angle region of the X-ray pattern, a broad signal is observed at ca. 4.5 A˚, corresponding to the liquid-like order of the molten aliphatic chains. To get a better understanding of the molecular packing in smectic phases, it is necessary to consider the molecular area,AM, and to compare it with the cross-sectional area of the rigid core of the molecules Acore and the cross-sectional area of the aliphatic chains of the molecules Achains. In general, if at the interface between the rigid core and the aliphatic chains, the cross-sectional area of the chains is similar to that of the core, a nontilted SmA phase is obtained. However, if the cross-sectional area of the chains is greater
than that of the core, the cores must tilt in order to fill space efficiently and a SmC phase is obtained. Thus, as a rule of thumb, there must be a balance between the molecular area and the cross-sectional area of the aliphatic chains:
AMAchains.Figure 20shows a schematic representation of the cross-sectional area of the rigid cores in the SmA (AcoreAchainsAM) and SmC (Acore<AchainsAM) phase. The molecular area AM can directly be deduced from the molecular volumeVmoland the layer thicknessd by the formula:
AM¼Vmol
d : ð2Þ
The rigid part, build up by the rigid cores of two molecules, can be consid- ered as a cylindrical unit with molecular areaAM. In this case,
AM¼2Vmol
d : ð3Þ
In general, for a cylindrical unit build up by the rigid cores ofNmolecules, the molecular area AM is related to the layer thicknessd and the molecular volumeVmolas follows:
AM¼NVmol
d : ð4Þ
AcoreªAM
AM d
FIGURE 20 Schematic representation of the molecular area in the SmA phase (top) and the SmC phase (bottom).AMis the molecular area,Acoreis the cross-sectional area of the rigid core of the molecules, anddis the layer thickness.
A comparison of the molecular lengthLwith the layer thicknessdalso pro- vides useful information about the molecular packing.Lcan be determined via molecular modeling (computer calculations) or can be obtained from XRD on a single crystal (although this provides information about the molecular structure in the crystalline state).Figure 21shows a schematic representation of different lamellar arrangements. In case (A) ofFig. 21, there is one rigid core per cylindri- cal unit and the molecules are nontilted. In case (B) ofFig. 21, there is one rigid core per cylindrical unit and the molecules are tilted within the layers to compen- sate the cross-sectional area of the aliphatic chains. In case (C) ofFig. 21, there is one rigid core per cylindrical unit and the molecules are nontilted. In addition, the aliphatic chains are interdigitated. Finally in case (D) ofFig. 21, there are two rigid cores per cylindrical unit and the molecules are nontilted.
From a geometrical point of view, thecolumnar structuresare character- ized mainly by two parameters: the columnar cross sectionSand the stacking periodicity along the columnar axish(Fig. 22). Knowledge of these two struc- tural parameters permits the interpretation of the molecular packing inside the columns and a better understanding of the influence of this packing on the 2D arrangement of the columns, and, therefore on the mesophase symmetry. The periodicityh, the columnar cross sectionS, and the molecular volumeVmolare linked analytically through the relation:
L
L L
d = L d < L
d < L d ª 2L
d L d
A B
C D
d
d
FIGURE 21 Schematic representation of different lamellar arrangements;dis the layer thick- ness,Nis the number of molecules per cylindrical unit, andL is the molecular length. The description of the different structures can be found in the text.