Crystalline theoretical considerations

For crystalline compounds, they noted that an important factor to consider is the crystal lattice energy. From theoretical considerations and subsequent empirical studies, they discovered that melting point (mp) serves as an excellent proxy for this factor. While this is a significant advance in our understanding of water solubility, it falls short as a means to predict solubility from the chemical structure alone a compound must be made and a mp determined experimentally. 

Ziabicki and Jericki reported the crystallization characteristics of PET as well as a theory of molecular orientation and oriented crystallization [5a], Besides these theoretical considerations, the rate of recrystallization understandably seems to play an important role, particularly in high-speed spinning. Little is known about the crystallinity gradient caused during melt spinning at high take-up speeds. 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

We note here that gel is a coherent solid because its structure is characterized by a polymer network, and hence, the above theoretical considerations on crystalline alloys should be applicable to gels without essential alteration. It is expected that the curious features of the first-order transition of NIPA gels will be explained within the concept of the coherent phase equilibrium if the proper calculation of the coherent energy and the elastic energy of the gel network is made. This may be one of the most interesting unsolved problems related to the phase transitions of gels. 

There is long standing theoretical interest in the question of how this affects the electronic DOS [5.18,28-33], Due to the inapplicability of Bloch s theorem, calculations are extremely difficult. Using Green s function techniques, Ballentine [5.28] could show for liquid metals that distinct deviations from the free-electron-like behaviour may occur whenever v(K) is significantly large at a peak of S(K) (see Fig. 5.2a, c). The width of the so-called pseudo gap may then correspond to 2 n(/C) as in crystalline matter, and the depth to the intensity of S(K), the structural weight. Theoretical considerations by Nicholson and Schwartz [5.30] as well as recent work by Fresard [5.32], Beck et al. [5.33], and Hafner et al. [5.18] could also show the structural effects on the DOS. 

For an experimental check-up of the theoretical considerations about liquid-crystalline elastomers in a mechanical field, Fin-kelmann and coworkers [107, 123] studied, in nematic networks, the evolution of the order parameter and of the transition temperature as a function of the stress. The observed results are in full agreement with the predictions of the Landau-de Gennes theory, since an increasing clearing temperature as well as an increasing order parameter are observed with increasing stress. From their results, it was possible to estimate the crosscoupling coefficient U (see Sec. 3.1.1) between the order parameter and the strain of a nematic elastomer [123]. 

An example of this is syndiotactic poly(propylene). The ir spectrum has a pronounced crystalline band at 868 cm" for the stablest crystalline state. According to theoretical considerations, this band, (see Figure 4-10), is practically entirely due to helical (TTGG) conformations. The band disappears on melting. 

None of the molecular network theories thus far discussed, however, is capable of predicting the course of the orientation of the crystallites which form the junction points of the network. It is only known from experiment (see p. 624) that the orientation of the crystallites runs ahead of that of the non crystalline gel component. From a large experimental material covering cellulose gels of various swelling degree and of different preparation, it was found that there seems to be a uniform relation between the optical orientation factor and that derived from X-rays holding for all cases. This relation, which may be of value, for future theoretical considerations, is shown in Fig. 102. 

Most discussions of surfactants in solution concern themselves with relatively low concentrations so that the system contains what may be called simple surfactant species such as monomers and their basic aggregates or micelles. Before entering into a discussion of micelles, however, it is important to know that although they have been the subject of exhaustive studies and theoretical considerations, they are only one of the several states in which surfactants can exist in solution. A complete understanding of surfactants requires a knowledge of the complete spectrum of possible states of the surfactant, including liquid crystalline phases, which can be important in the stabilization of emulsions and foams, as well in other areas. 

Nevertheless, just as the basic ideas for the understanding of cr>stalline semiconductors were available in the pre-germanium era, very probably most of the present interpretations have a sound foundation and will survive as basic concepts for the future more detailed and better founded work. The recent book on the Electronic Properties in Non-crystalline Materials by Mott and Davis presents an ingenious attempt to correlate the observed electronic effects in disordered solids on the basis of a few concepts derived from some theoretical considerations and generalized with a sharp physical intuition. 

The phenomenological aspects of LCP rheology has been reviewed by the author [2]. More recently [14, 15], further data were obtained to compare the viscosity of the same polymer in the isotropic and liquid crystalline states. As with small molecule LC s, the viscosity of nematic LCP s was found to be lower than that of the isotropic forms. There are other aspects of the LCP rheology which require discussion, but first the evidence from theoretical considerations Is described. 

In 1966, the first reports on the successful syntheses of NF4 salts were published by two research groups, Tolberg etal. [1] and Christe etal. [2]. Previously, it was concluded from theoretical considerations that NF4 could not form crystalline salts [3] or that only the fluoroborate, NF4BF4, might exist at low temperatures. Thus, no other hypothetical salts such as perfluoroammonium perchlorate, -sulfate, and -fluoride were thought to exist [4]. Since the first reports, numerous NF4 salts have been prepared and characterized containing counterions which are derived mainly from perfluorinated Lewis acids. 

Ideally, the solidus should be established for all cases. Except in a few rare situations a complete phase diagram, where both the liquidus and solidus are presented, is not available. Determining the solidus for polymers, even on a compositional basis, is a formidable matter. As theoretical considerations have indicated, the sequence distributions in both phases are actually required for polymers rather than the composition. This makes the task of determining the solidus a very difficult one. Moreover, if a mixed crystalline phase is observed a decision has to be made as to whether it represents an equilibrium or defected state. 

The coupling between the properties of conventional polymer networks and the properties of chiral liquid crystalline phases results in interesting, new opto- and electromechanical effects of the chiral liquid crystalline elastomers, as demonstrated by theoretical considerations and experiments. Knowledge about these new materials is still in its infancy. But the properties analyzed so far for these elastomers indicate promising aspects for application and are the basis for the new syntheses of optimized chiral liquid crystal networks. 

In solution-crystallized polyethylene fractions, Raman spectra have demonstrated that crystalline structure is invariant with molecular mass and that crystallinity is far from complete. The interfadal region is relatively small, as expected from theoretical considerations. Densities of solution-grown crystals of linear polyethylene show that the crystals are 8(C90% crystalline [145 147]. This conclusion is supported by measurements of the enthalpy of fusion, infrared and Raman spectroscopy, and other physical properties [148]. Consequently there is a small but appreciable... 

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