Crystallization phase space

Compound Ref. Crystal Phase Space group Z Dihedral angle between the phenyl ringsV° Selected intermolecular distances [A]... 

Crystal, phase Space group Lattice constants Magnetic properties Reference... 

In contrast to the single molecule case, Monte Carlo methods tend to be rather less efficient than molecular dynamics in sampling phase space for a bulk fluid. Consequently, most of the bulk simulations of liquid crystals described in Sect. 5.1 use molecular dynamics simulation methods. 

The compounds crystallise in noncentrosymmetric space groups namely PI, P2i, C2, and P2i2i2i (but with priority of P2i) due to the chirality of the molecules. Most of the compounds have a tilted layer structure in the crystalline state. The tilt angle of the long molecular axes with respect to the layer normal in the crystal phase of the compounds is also presented in Table 18. Some compounds show larger tilt angles in the crystalline state than in the smectic phase. In the following only the crystal structures of some selected chiral liquid crystals will be discussed. 

The structure of the alkaline-earth metal compound CayC6o (for y < 5) follows the same space group Fm3m as for the heavy (M = K, Rb and Cs) alkali metal MxC6o compounds (x < 3) [27] and the Ca ions occupy both tetrahedral and octahedral sites. Because of the smaller size of the calcium ion, the octahedral sites can accommodate multiple Ca ions, and it is believed that up to three Ca ions can be accommodated in a single octahedral site [27]. Ba6C(jo and Sr6C60, in contrast, exhibit different crystal phases, such as the A15 and other bcc phases [28, 59],... 

In a perfect crystal at 0 K all atoms are ordered in a regular uniform way and the translational symmetry is therefore perfect. The entropy is thus zero. In order to become perfectly crystalline at absolute zero, the system in question must be able to explore its entire phase space the system must be in internal thermodynamic equilibrium. Thus the third law of thermodynamics does not apply to substances that are not in internal thermodynamic equilibrium, such as glasses and glassy crystals. Such non-ergodic states do have a finite entropy at the absolute zero, called zero-point entropy or residual entropy at 0 K. 

The equilibrium in these systems above the cloud point then involves monomer-micelle equilibrium in the dilute phase and monomer in the dilute phase in equilibrium with the coacervate phase. Prediction o-f the distribution of surfactant component between phases involves modeling of both of these equilibrium processes (98). It should be kept in mind that the region under discussion here involves only a small fraction of the total phase space in the nonionic surfactant—water system (105). Other compositions may involve more than two equilibrium phases, liquid crystals, or other structures. As the temperature or surfactant composition or concentration is varied, these regions may be encroached upon, something that the surfactant technologist must be wary of when working with nonionic surfactant systems. 

Occasionally, long-range disorder and/or different phases may coexist within a crystalline material. Arrangement of molecules in the different regions will necessarily be different in at least some respects. One of the earliest reports of invocation of this phenomenon involves the photodimerization of anthracene in the crystalline state [219]. In the crystal structure of anthracene, the faces of no molecules are separated by <4 A. Yet upon irradiation, a dimer is readily formed. Thomas, Jones, and co-workers used electron microscopy to reveal the coexistence inside normal anthracene crystals of regions of a metastable phase. In the minor phase (space group PI), the C9- -C9. distance is 4.2 A, whereas in the stable crystal it is 4.5 A. The dimerization is proposed to originate in the minor phase of the crystal. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

At 6 A resolution, Type I crystals phased from derivatives prepared by soaking in PtCl2-, p-chloromercuribenzenesulfonic acid (PCMBS) and p-acetoxymercurianiline (PAMA) and using all the data within a 6 A sphere in reciprocal space. 

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