Crystallization crystalline systems

The problems already mentioned at the solvent/vacuum boundary, which always exists regardless of the size of the box of water molecules, led to the definition of so-called periodic boundaries. They can be compared with the unit cell definition of a crystalline system. The unit cell also forms an "endless system without boundaries" when repeated in the three directions of space. Unfortunately, when simulating hquids the situation is not as simple as for a regular crystal, because molecules can diffuse and are in principle able to leave the unit cell. 

Experiments at present are concentrated on sd-metals and Pt-group metals. The sp-metals, on which theories of the double layer have been based, are somewhat disregarded. In some cases the most recent results date back more than 10 years. It would be welcome if double-layer studies could be repeated for some sp-metals, with samples prepared using actual surface procedures. For instance, in the case of Pb, the existing data manifest a discrepancy between the crystalline system and the crystal face sequence of other cases (e.g., Sn and Zn) the determination of EgaQ is still doubtful. For most of sp-metals, there are no recent data on the electron work function. 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

The mixing of nematogenic compounds with chiral solutes has been shown to lead to cholesteric phases without any chemical interactions.147 Milhaud and Michels describe the interactions of multilamellar vesicles formed from dilauryl-phosphotidylcholine (DLPC) with chiral polyene antibiotics amphotericin B (amB) and nystatin (Ny).148 Even at low concentrations of antibiotic (molar ratio of DLPC to antibiotic >130) twisted ribbons are seen to form just as the CD signals start to strengthen. The results support the concept that chiral solutes can induce chiral order in these lyotropic liquid crystalline systems and are consistent with the observations for thermotropic liquid crystal systems. Clearly the lipid membrane can be chirally influenced by the addition of appropriate solutes. 

Radical formation in a mixed crystal system of cytosine monohydrate doped with small amounts of thiocytosine (ca. 0.5%) was investigated on order to gain insight into hole transfer in a well-defined crystalline system.31 Also of interest was whether the protonation state of the thiocytosine radical(s) was the same as that of the cystosine radical(s). Crystals were X-irradiated (ca. 30 kGy) and ESR and ENDOR spectra recorded at ca. 15 K. After irradiation, many types of free radicals were formed. Among these, the low field resonance from a sulfur centered radical (42), with g-tensor (2.132, 2.004, 2.002), was clearly visible. Radical 42 constituted approximately 10% of the total cohort of radicals formed in the crystal and is apparently the only sulfur-centred radical observed in this experiment. Six weakly coupled protons were observed, two of which are shown... 

Nevertheless, the chemical potentials of SE s are frequently used instead of the chemical potentials of (independent) components of a crystalline system. Obviously, a crystal with its given crystal lattice structure is composed of SE s. They are characterized much more specifically than the crystal s chemical components, namely with regard to lattice site and electrical charge. The introduction of these two additional reference structures leads to additional balanced equations or constraints (beside the mass balances) and, therefore, SE s are not independent species in the sense of chemical thermodynamics, as are, for example, ( - 1) chemical components in an n-component system. 

Since the state of a crystal in equilibrium is uniquely defined, the kind and number of its SE s are fully determined. It is therefore the aim of crystal thermodynamics, and particularly of point defect thermodynamics, to calculate the kind and number of all SE s as a function of the chosen independent thermodynamic variables. Several questions arise. Since SE s are not equivalent to the chemical components of a crystalline system, is it expedient to introduce virtual chemical potentials, and how are they related to the component potentials If immobile SE s exist (e.g., the oxygen ions in dense packed oxides), can their virtual chemical potentials be defined only on the basis of local equilibration of the other mobile SE s Since mobile SE s can move in a crystal, what are the internal forces that act upon them to make them drift if thermodynamic potential differences are applied externally Can one use the gradients of the virtual chemical potentials of the SE s for this purpose ... 

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

Several workers have pointed out that there is a large and growing body of X-ray structural data of transition metal phosphine complexes. Such data can provide real cone angles, which may then be compared to Tolman s cone angles derived from models. Of course this line only applies to crystalline solids. Since the main application of transition metal chemistry is homogeneous catalysis, crystal structure data, though useful, are of limited applicability. Inevitably, cone angles in complexes in solution will be more variable than in crystalline systems. 

Tihe term lyotropic mesomorphism is used to describe the formation of thermodynamically stable liquid crystalline systems through the penetration of a solvent between the molecules of a crystal lattice. In contrast to the thermotropic mesomorphism shown by many pure substances, lyotropic mesomorphism always requires the participation of a solvent. Lyotropically mesomorphous systems, however, are usually as sensitive to changes in temperature as thermotropic systems. So far, lyotropic mesomorphism has been observed almost exclusively in lipid systems containing water. Lipids that show lyotropic mesomorphism frequently... 

The experimental observations could be consistently explained if the general tilt structure (SmCo) inside the layers is assumed. For most bent-core smectics the polar vector is perpendicular to the tilt plane, defined by the layer normal and averaged long axis direction, just as polarization in the ferroelectric rod-like liquid crystalline systems. However, since in the bent-core liquid crystals the polar order is decoupled from the tilt order, the polar director can in general have any direction in space thus it can also have a non-zero component along the layer normal. This can be achieved by a combination of tilting (rotation around the polar director) and leaning (rotation around the direction perpendicular to the polar director) of... 

Despite the tremendous progress made in this field, there is still a severe drawback. The quantum chemistry developed by theoretical chemists tools are primarily suited for isolated molecules in vacuum or in a dilute gas, where intermolecular interactions are negligible. Another class of quantum codes that has been developed mainly by solid-state physicists is suitable for crystalline systems, taking advantage of the periodic boundary conditions. However, most industrially relevant chemical processes, and almost all of biochemistry do not happen in the gas phase or in crystals, but mainly in a liquid phase or sometimes in an amorphous solid phase, where the quantum chemical methods are not suitable. On the one hand, the weak intermolecular forces,... 

After having studied in our laboratory, polymer blends of amorphous polymers poly-c-caprolactone and poly (vinyl chloride) (1,2) (PCL/ PVC), blends with a crystalline component PCL/PVC (3,4), poly(2,6-dimethyl phenylene oxide) (PPO) with isotactic polystyrene (i-PS) (5) and atactic polystyrene (a-PS) with i-PS (6), we have now become involved in the study of a blend in which both polymers crystallize. The system chosen is the poly(1,4-butylene terephthalate)/poly(ethylene terephthalate) (PBT/PET) blend. The crystallization behavior of PBT has been studied extensively in our laboratory (7,8) this polymer has a... 

A typical characteristic of hypersymmetry operations is that they exercise their influence in well-defined discrete domains. These domains do not overlap—they do not even touch each other. The usual hypersymmetry elements lead to point-group properties. This means that no infinite molecular chains could be selected, for example, to which these hypersymmetry operations would apply. They affect, instead, pairs of molecules or very small groups of molecules. Thus, they can really be considered as local point-group operations. These hypersymmetry elements, accordingly, divide the whole crystalline system into numerous small groups of molecules, or transform the crystal space into a layered structure. 

There seems to be even less structural similarity for many other metal halides as the crystalline systems are compared with the molecules in the vapor phase. Aluminum trichloride, e.g., crystallizes in a hexagonal layer structure. Upon melting, and then, upon evaporation at relatively low temperatures, dimeric molecules are formed. At higher temperatures they dissociate into monomers (Figure 9-58) [107], The coordination number decreases from 6 to 4 and then to 3 in this process. However, at closer scrutiny, even the dimeric aluminum trichloride molecules can be derived from the crystal structure. Figure 9-59 shows another representation of crystalline aluminum trichloride which facilitates the identification of the dimeric units. A further example is chromium dichloride illustrated in Figure 9-60. The small oligomers in its vapor have structures [108] that are closely related to the solid structure [109], Correlation between the molecular composition of the vapor and their source crystal has been established for some metal halides [110],... 

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