2 Basics of Thermal Analysis __________________________________________________________________ 166 Fig. 2.102 Fig. 2.101 changes in entropy which are coupled with the disordering are listed. Details about these data are presented in Sect. 5.4. Usually these transitions are first-order transitions (see Sect. 2.5.7). All mesophases, when kept for structural or kinetic reasons from full crystallization on cooling, display in addition a glass transition, as is indicated on the left-hand side of Fig. 2.103. The glass transition leads to a glass 2.5 Phases and Their Transitions __________________________________________________________________ 167 Fig. 2.103 with mesophase order, but without the large-amplitude motion. The recognition of mesophases and mesophase glasses as states of intermediate order and their study by thermal analysis has become of great importance for the understanding of the multitude of materials. The empirical rule of change of the heat capacity when going through a glass transition, is described in Sect. 2.5.6. 2.5.2 Phases of Different Sizes It was noted about 150 years ago that the properties of phases change when their dimensions decrease to the micrometer scale. This observation was first made after the discovery of colloids. Today, such small phases are better called microphases [27]. In microphases, the effect of the surfaces cannot be neglected. Surface free energies and charges (surface potentials) governthe properties and stability (ormeta- stability) of the microphases. Similarly, in Fig. 1.6 it is shown that molecules may be classified into three types, small, large and flexible, and large and rigid. In this section the changes of phase size and molecular size are analyzed briefly. When forming a crystal via nucleation and growth, as described in Sects. 3.5 and 3.6, the linear growth rates in the various crystallographic directions determine the initial, usually metastable, crystal shape. Linear, flexible macromolecules, for example, chain-fold to lamellar crystals with much faster growth in the crystallo- graphic a- and b-directions than in direction c, along the chain direction, as outlined in Fig. 2.104. The folds accumulate in the ab-surface (see Sect. 5.2). By limiting the available material to a few macromolecules, the initial liquid takes the shape of a small droplet with a micrometer diameter, and the crystal is also a microphase, as assumed in the figure. On annealing, the initial, kinetically-determined morphology 2 Basics of Thermal Analysis __________________________________________________________________ 168 Fig. 2.104 (shape) may approach equilibrium, as shown in the sketch at the bottom. The major rearrangement of the molecules within the crystal requires sufficient mobility, as has been observed, for example, in the condis mesophase of polyethylene. The equilibrium crystal must have a minimum of the positive surface free energy. Based on this principle, Wulff devised in 1901 a construction to establish the equilibrium shape (Wulff construction). By drawing normals from a point within the crystal to the various possible surfaces with lengths proportional to the surface free energy, the innermost complete body of these surfaces is the equilibrium shape. The proper volume can be achieved by adjusting the lengths without changing the proportions. The equilibrium polymer crystal should have,thus, its large dimension atright angles to the high energy fold surface ab, as indicated in Fig. 2.104. New properties arise when the molecular sizes increase to the dimensions of the phase, as for example in the case of a typical polyethylene of 500,000 Da. It has a contour length of2.8 m and can easily cross microphase boundaries. This traversing of the surface makes neighboring phases interact strongly, in contrast to the weak interactions by intermolecular forces (see Fig. 1.5). The lower limit of the size of crystals of macromolecules may be as small as 2 nm andmustthenbecalledananophase as displayed in Fig. 2.98. The noncrystalline material surrounding the macromolecular crystals, containing folds, chain ends, noncrystallizable repeating units, and tie molecules, has similarly small phase dimensions. In nanophases the opposing surfaces of a phase area are sufficiently close to interact so that no bulk phase exists anymore. Macromolecules traversing a nanophase will strongly link the surfaces; but even weaker forces, such as caused by polarity at the interface, or by charges in the surface, may bridge nanophases and may give rise to special properties of the nanophases. For characterization, nanophases needa detailed study of composition, physical state, molecular structure, 2.5 Phases and Their Transitions __________________________________________________________________ 169 and molecular motion. The macromolecules can now traverse not only one, but several or many phase domains and influence the macroscopic properties. The limit of nanophases towards smaller sizes occurs at perhaps one nanometer. Two causes exist for this limit: The increasing loss in homogeneity due to the inherent molecular structure and their fluctuations in energy makes the recognition of a homogeneous phase impossible; and for copolymers, the decreasing gain in enthalpy on mixing due to the larger surface contribution relative to the entropy loss on phase separation makes the nanophase unstable compared to a solution. This short summary illustrates that three size-ranges must be considered for each type of phase (macrophases, microphases, and nanophases). In addition, the phase structure may be different for each of the three types of molecules. This leads to a total of nine possible situations for each of the nine condensed phases shown in Fig. 2.103. Of the 81 combinations, 57 have been suggested to be possible at the beginning of Sect. 2.5 [27]. Thermal analysis isthe main technique to distinguish and identify this multitude of different systems. 2.5.3 Mesophases The term mesophase, introduced in Sect. 2.5.1, was first coined in 1922 by Friedel to describe mainly liquid crystals which are known since 1888. They are related to liquids, but maintain a certain degree of orientational order, as shown schematically in Fig. 2.105. A list of characteristic properties of liquid crystals is given in the left column of Fig. 2.107, below. In the examples shown in Fig. 2.105, the liquid crystalline order is due to an elongated, rod-like or flat, board or disk-like segment of the molecules, the mesogen. The left example in Fig. 2.105 is a two-dimensional representation of a nematic liquid crystal (Gk. =, thread, from the thread-like interference patterns of nematic liquid crystals under thepolarizingmicroscope). The nematic phase shows orientation of the mesogens in only one direction. The right example is a macromolecular smectic liquid crystal (Gk. );, soap). In this case the limited orientationalorder is in twodimensions. The example isof a polymer that has a mesogen included in the otherwise flexible chain. Forexample, CH 2 -sequences can link the mesogens and providing the mobility needed to give a liquid-crystalline character. A typical example of a mesogen is shown at the bottom of Fig. 2.105. The orientation in the liquid crystals gives rise to the birefringence and its high mobility allows the use of liquid crystals in display devices. Soaps and lipids are alsoliquidcrystals. Thesemolecules consist of two parts that would be phase-separated, if not connected by strong bonds. In the pure state these molecules arrange such that the junction between their two incompatible segments form an interface ( | ) between two phase areas, for example, in sodium stearate, a soap: Na +  OOC( | )(CH 2 ) 16 CH 3 , and in lipids as seen in Fig. 2.106. The domain size of these phases is about one nanometer in the direction of the molecule, i.e., they are nanophases. On crystallization, the molecules of the liquid crystals have to pack closely, which is not always possible for more complicated structures, so that glasses are common low-temperature phases for such molecules. For the soaps and lipids, a nanophase-separation remains in the crystals. Sometimes the two types of nanophases within the overall crystal undergo separate phase transitions. 2 Basics of Thermal Analysis __________________________________________________________________ 170 Fig. 2.106 Fig. 2.105 Plastic crystals are more closely related to the classical crystals. They have full positional order as shown in the sketch in Fig. 2.105. The plastic crystal consist, however, of molecules (their mesogens) that are almost spherical and can start to rotate within the crystal ata given transition temperature. Figure 2.107 contains a list of typical properties of plastic crystals and allows a comparison to liquid crystals. The plastic crystalline state was first recognized in the 1930's. Most plastic crystals 2.5 Phases and Their Transitions __________________________________________________________________ 171 Fig. 2.107 have a cubic crystal structure. Due to the rotation of the molecules in the crystal, their actual symmetry is averaged to a sphere, eliminating both the birefringence and causing an entropy of fusion similar to the metals and noble gases which have spherical motifs (see Sects. 5.4 and 5.5). Cubic crystals have also many slip planes and with rotating, weakly bound molecules, the crystals easily deform, they are plastic. Metals with similar crystal structures and spherical motifs, but stronger bonding, still show ductility, but no plastic-crystal behavior. Both liquid and plastic crystals show conformational mobility and disorder if the basic molecule is flexible, i.e., can change to different conformational isomers. Conformationally disordered crystals (condis crystals) were discovered in the 1980’s. They show positional and orientational order, but are partially or fully conformationally mobile. The condis crystals complete the comparison of mesophases in Figs. 2.103 and 2.107. Linear, flexible molecules can show chain mobility that leaves the position and orientation of the molecule unchanged, but introduces large-amplitude conformational motion about the chain axis. Again, the symmetry of the molecule is in this case increased. Condis crystals have often a hexagonal, columnar crystal structure. Typical examples of condis crystals are the high-temperature phase of polyethylene, polytetrafluoroethylene, trans-1,4- polybutadiene, and the low-temperature phases of soaps, lipids and other liquid- crystal forming, flexible molecules. Figure 2.108 illustrates the chemical structure and a thermal analysis curve of a typical small molecule with liquid-crystal and condis-crystal phases, OOBPD. The mesogen is the rigid bisoxybenzalphenylenediamine. Two flexible octyl groups enable conformational disorder by rotation about theC CandOC bonds. The letter N represents thenematic phase, letters C,I, G’, and H’the increasingly better ordered smectic phases, and K designates condis phases. Note that phase K 3 has still not 2 Basics of Thermal Analysis __________________________________________________________________ 172 Fig. 2.108 Fig. 2.109 reached the heat capacity expected for the solid crystalline or glassy state indicated by the thin, bottom line (vibration-only crystalline heat capacity, see Sect. 2.3). Since no further crystallization occurs, a glass transition is expected and is seen in thermal analysis at about 350 K. More details about this compound are given in Sect. 5.5.4. Fullerene, C 60 , is an example of a molecule with a plastic-crystal phase. Its structure is given in Fig. 2.109 together with the other two allotropes of carbon, 2.5 Phases and Their Transitions __________________________________________________________________ 173 Fig. 2.110 Fig. 2.111 diamond and graphite. Its calorimetry is discussed in Sect. 4.2.7 (see also Figs. 2.39–41). Figure 2.110 is a thermal analysis trace (DSC, see Sect. 4.3). The transition starts rather broad and then becomes sharp as full rotation becomes possible. More details about this transition are available through 13 C nuclear magnetic resonance experiments. Figure 2.111 is a recording of the spin-lattice relaxation time T 1 . It is a measure of the rotation of the molecule. Three models 2 Basics of Thermal Analysis __________________________________________________________________ 174 Fig. 2.112 were fitted to the data: (1) molecular motion about the five-fold symmetry axis C 5 (see Sect. 5.1.5 for a discussion of symmetry), (2) motion about the incomplete, six- fold axis, C 6 , and (3) full rotation. Since there is no change in heat capacity (entropy) in the lowest temperature region of Fig. 2.111, motion (1) must be a jump between indistinguishable states of lower energy and longer residence time. This agrees with the symmetry axis C 5 , best seen in Fig. 5.37. Themechanism (2) is energetically only slightly more difficult, but the symmetry is incomplete and produces disorder, i.e., the entropy (heat capacity) increases. Stage (3), finally, leads orientational disorder. Polytetrafluoroethylene and trans-1,4-polybutadiene are twoexamples of macro- molecular condis crystals. The heat capacity of polytetrafluoroethylene is shown in Fig. 2.63, that of trans-1,4-polybutadiene is illustrated in Fig. 2.112. Both polymers have two endothermic transitions. At low temperature they showan endotherm at the disordering temperature, T d , on going from the crystal to the condis phase, then they ultimately melt at T i (isotropization temperature). In Fig. 2.112 the motion of trans- 1,4-polybutadiene is characterized with 1 H solid-state NMR, using the line width of the signal as a measure of mobility. The line width can be modeled quantitatively in terms of its second moment (G 2 ). The first narrowing is due to the glass transition of the not-crystallized, amorphous fraction of the semicrystalline polymer, the second, due to the conformational mobility gained at T d , the third to final melting (isotro- pization) at T i . Figure 2.113 indicates with an entropy plot that only the trans isomer of the 1,4- butadienes displays a stable mesophase. The crystals of the cis isomer have a more helical structure which packs less well in the crystal and needs much more space to rotate into a conformationally disordered structure. As a result of this different structure, the cis polymer melts at a lower temperature, and in one step. 2.5 Phases and Their Transitions __________________________________________________________________ 175 Fig. 2.113 2.5.4 Mesophase Glasses All mesophases have some large-amplitude type of motion. On cooling the mesophases have two paths to the solid state as seen in Fig. 2.103. Either the mesophase orders to the crystal state, or the large-amplitude motion changes to the corresponding vibrations without change of order. In the second case there is no entropy of transitionto the solid state (see Sect. 2.5.6),only the heat capacity changes to the vibration-only case, discussed in Sect. 2.3. The mesophase glass differs from the amorphous glass by possessing the order of the mobile mesophase. Each mesophase, thus, has a corresponding glass, as was discussed in Sect. 2.5.1 and shown in Fig. 2.103. Liquid crystal glasses were seen already in the 1930’s [28]. Liquid crystals are quite similar to the liquids in their mobility, their glass transition is similar to the glass transition of an amorphous liquid. Figure 2.114 shows a special example. The monomer of the chosen polymer, acryloyloxybenzoic acid, does not have a liquid crystalline phase. On polymerization, an amorphous liquid results that changes with time to a liquid crystal on dimerization of the oxybenzoic acid side-group via hydrogen bonds. The thermal analysis of Fig. 2.114 shows in its upper trace a sample quenched to the amorphous glass before ordering. A normal glass transitionoccurs on heating,followed by ordering to the liquid crystal at T o . On the second cooling, the LC glass is formed, which, on reheating (bottom trace) shows a glass transition of similar magnitude, but at higher temperature because of the dimerization. Glass transitions also have been observed for plastic crystals and condis crystals. Depending on the degree of cooperation necessary between neighboring molecules, narrow or broad glass transition regions result. For some additional information, see Sect. 5.5. [...]... transitions are easily determined by thermal analysis (the operation) Recently it has become possible by simulation on supercomputers to establish the link from the microscopic thermal motion of macromolecules to the macroscopic thermal analysis By solving the equation of motion, one can produce a detailed movie of molecular motion (see Sect 1.3 .4, Fig 1 .47 ) At high temperature, conformational disorder... to be largest because of the large disorder in this dilute state The crystal, on the other hand, because of its order, should have the smallest entropy; in fact, the third law of thermodynamics sets the 178 2 Basics of Thermal Analysis Fig 2.116 entropy of an ideal, equilibrium crystal equal to zero at the absolute zero of temperature (Sect 2.2 .4) The free enthalpy,... Poly(oxy-2,6-dimethyl-1 ,4- phenylene) (PPO™, General Electric) has a Tg of 48 2 K and a Tm of 580 K (ratio 1.20), sufficiently low that on partial crystallization, Tg increases due to strain caused by the small crystals, and Tm decreases because of the small size of the crystals, so that Tg may exceed Tm (see the rigid amorphous fraction of PPO in Sect 6.2.2) Similar closeness of Tg and Tm is observed... picosecond time scale (see Sect 5.3 .4) The meaning of the word transition is not specific In Fig 2.115 a dictionary definition is listed, which states: Transition means just a passing from one condition to another The basic transitions of interest to thermal analysis are described in the classification scheme of Fig 2.103 In the bottom half of Fig 2.115 the properties of the condensed phases are reviewed... after a typical polymer There is a jump in the heat capacity, but there is no indication of a heat of transition If there is no heat of transition, there can also be no entropy of transition The increase in heat capacity Cp always occurs over a temperature range of 5 to 20 K, and the jump is often 11 J K 1 mol 1 of mobile units in the liquid This means, for a monatomic liquid the decrease in heat capacity... derivative of G is equal 182 2 Basics of Thermal Analysis Fig 2.119 to Cp/T, as shown in Fig 2.119 This condition is superficially fulfilled in a glass transition at a fixed time scale, but the time-dependence of Tg indicates that the transition should not be considered an equilibrium transition To discuss melting and evaporation, one can make use of the schematic drawing of. .. Basics of Thermal Analysis Fig 2.1 14 2.5.5 Thermodynamics and Motion Thermodynamics and motion can be used as a base for an operational definition of the solid state A solid is a phase below its glass- or melting-transition temperature where the molecular motion is almost completely restricted to small-amplitude vibrations Both transitions are easily determined by thermal. .. reason for the often observed increase in heat capacity at glass and disordering transitions is the need of additional potential energy to create the increased volume for the large-amplitude motion The macroscopic, thermodynamic description of states is achieved through their major functions and variables of state listed in Fig 2.116 One can deduce from the microscopic picture of the states of matter that... stable The change of state is connected with a change in the slope of G—i.e., the transition must be of first order The system changes states with a discontinuity in entropy as well as enthalpy Increasing the temperature further, the limit of stability of the liquid is reached at the boiling temperature Tb Here again, on going from the liquid to the gas there is a change in the slope of G, so that it... enthalpy of evaporation To describe the thermodynamic equilibrium behavior at the transition, one can write the boxed equations in Fig 2.119 Inspection of these equations shows that thermometry, discussed in Sect 4. 1, can give a characterization of a material if there is information on either the heats or entropies of transition Some help for interpretation comes from the fact that related materials . recognition of mesophases and mesophase glasses as states of intermediate order and their study by thermal analysis has become of great importance for the understanding of the multitude of materials. . experiments. Figure 2.111 is a recording of the spin-lattice relaxation time T 1 . It is a measure of the rotation of the molecule. Three models 2 Basics of Thermal Analysis __________________________________________________________________ 1 74 Fig another. The basic transitions of interest to thermal analysis are described in the classification scheme of Fig. 2.103. In the bottom half of Fig. 2.115 the properties of the condensed phases arereviewedandtheir