Solutions crystallization and

The crystallization process involves a system (which we are interested in) and the surroundings. In terms of the component entropies in this example, we say AS,iSyiSlcm, is the entropy of the solute crystallizing and that A.S liSlllTOimdmgiS I represents the entropy change of the solvent molecules released. 

Triplet-triplet annihilation (TTA), i.e., deactivation of triplet molecules as a result of their interaction, is one of the main pathways of triplet state decay in solutions, crystals and the gas-phase. TTA may become the determining pathway of triplet state deactivation under conditions of high concentrations of triplet-state molecules resulting in particular from powerful laser photoexcitation. 

Although many of the properties of strontia are intermediate between those of lime and baryta, he proved that it is not a combination of the two and that it bears repeated solutions, crystallizations, and precipitations without showing the smallest disposition to a separation of principles (48). Thus it is evident that Dr. Hope foreshadowed in 1793 one of the triads which J. W. Dobereiner pointed out in 1829. 

In addition to these studies on the branched polyethylene, fractions of linear polyethylene prepared by large-scale gel-permeation chromatography are being characterized for certification in the near future. These should be useful for gel-permeation chromatography calibration. We also expect them to be particularly valuable in dilute solution, crystallization, and rheological studies. 

The recent studies of the phase structure of linear polyethylene by refined NMR analyses are reviewed. The phase structure of the polymer in various crystalline forms, including bulk-crystals, solution-crystals and drawn fibers, is discussed in terms of different modes of molecular mobilities in a wide range of temperature. 

In this article we have reviewed our recent work with NMR analysis on various kinds of linear polyethylene samples. It has become evident that the refined NMR analysis gives us much important information on the phase structure of samples in terms of molecular mobility, and establishes that there is no unified phase structure for polymer samples. The phase structure of samples varies over a very wide range, depending strongly on the sort of samples involved as well as on the mode of crystallization or the history of those samples. We should emphasize that there are significant differences in phase structure among the bulk-crystals, the solution-crystals, and the fiber samples, particularly in the conformation of molecular chains in the noncrystalline content. We should not confuse these phase structures with each other. The phase structures are evidently different, sample by sample, as their macroscopic properties also differ one from another. 

Fig. 5.12. Relationship between hardness H of solid solution crystals and composition of aluminium-niobium and aluminium-tantalum alloys after melting at different temperature, and limited solubility curves for tantalum in aluminium.

Raman optical activity has only been measured so far in pure liquids and strong solutions. Crystals and powders are harder to study crystals must be polished and oriented carefully to eliminate artefacts, whereas multiple scattering in powders depolarizes the incident light. It would be of great interest to measure pure rotational, and rotational-vibrational, ROA in gases, but insufficient scattered intensity has so far prevented this. An additional complication in resonance scattering is that circular dichroism of the incident beam can contribute to the measured circular intensity difference. 

With regard to specific properties, we will focus on those that are more relevant to solution crystallization and those that have a direct impact on the quality of the final bulk pharmaceuticals such as purity, form, habit, and size, based upon our own experience. We will leave readers to find other properties, such as miller index for crystal morphology, hardness of crystals, interfacial tension, etc., in other books on crystallization (Mersmann 2001 Mullin 2001), which provide in-depth theoretical discussion on these properties. 

Stress development. Generally, solidification is accompanied by development of in-plane tensile elastic stress. This is because departure of solvent from solution, crystallization and vitrification, consolidation of particulates, colloidal flocculation and coagulation, and the chemical reactions of curing almost always tend to produce shrinkage of the... 

Crystallization operations include the crystallization of an inorganic compound from an aqueous solution (solution crystallization) and the crystallization of an organic compound from a mixture of organic chemicals (melt crystallization). On a large scale, solution... 

Fluidized heds (direct convection), relatively insensitive, solutions, crystals and melts. Inlet temp about 400-500 °C AT = 150-300 °C solids residence or drying time, 30-250 s. Mass air/mass water evaporated = 10-100 evaporation rate = 0.005-0.4 kg water evaporated/s m. Solids holdup 10-30 kg solids/m. ... 

The description of phase equilibria makes use of the partial molar free enthalpies, i, called also chemical potentials. For one-component phase equilibria the same formalism is used, just that the enthalpies, G, can be used directly. The first case treated is the freezing point lowering of component 1 (solvent) due to the presence of a component 2 (solute). It is assumed that there is complete solubility in the liquid phase (solution, s) and no solubility in the crystalline phase (c). The chemical potentials of the solvent in solution, crystals, and in the pure liquid (o) are shown in Fig. 2.26. At equilibrium, ft of component 1 must be equal in both phases as shown by Eq. (1). A similar set of equations can be written for component 2. By subtracting j,i° from both sides of Eq. (1), the more easily discussed mixing (left-hand side, LHS) and crystallization (right-hand side, RHS) are equated as Eq. (2). 

In contrast to the gel formation at these concentrations, it is well known,30 that from more dilute solution, the polymer will precipitate, or crystallize, in the form of isolated lamella-like crystallites. It is theoretically possible to prepare both the lamella-like crystallites and the gels, of the same molecular weight fraction, at the same undercooling. This possibility exists since there is only an imperceptible change between the equilibrium melting temperature for a concentration of about 0.1%, where the platlets form, and the higher concentrations typical of gel formation.24 Hence, a rationale or natural comparison can be made between the thermodynamic properties of the well-known lamella-like crystallites typical of dilute solution crystallization and those of the crystallites involved in the gel formation when both are crystallized at the same temperature. In Table I, a typical set of such data is given. 

Properties of Dilute Solution Crystals and Gels Formed at 86°C, for Polyethylene Fraction Myy, = 4.5 x 10 ... 

Practically all processes in the chemical, petroleum, and related industries require the transfer of energy. Typical examples are the heating and cooling of process streams, phase changes, evaporations, separations (distillations, etc.), solutions, crystallizations, and so on. 

The lamellar thicknesses after solution crystallization and annealing at different temperatures showed a decrease with decreasing syndiotacticity index and annealing temperatures. The long spacings are also critically dependent upon the solvent systems used in solution crystallization. It was postulated that defects might be included, at least to a certain degree, in the crystal lattice. 

The variation of lamellar thickness with crystallization temperature for polyoxymethylene crystallized from a variety of solvents is shown in Fig. 4.19(a). For a given solvent the lamellar thickness is found to increase with increasing crystallization temperature. This behaviour is typical of many crystalline polymers such as polyethylene or polystyrene for which the length of the fold period increases as the crystallization temperature is raised. The different behaviour in the various solvents displayed in Fig. 4.19(a) is again typical of solution crystallization and Fig. 4.19(b) is a plot of the lamellar thickness against the reciprocal of the supercooling AT(= T, — Tc) which gives a master curve of all the data in Fig. 4.19(a). This... 

Since the physical properties of semicrystalline polymers usually depend on crystal modification, the study of the effects of crystallization and processing conditions on the polymorphic behavior is essential to tailor the performance of polymeric materials. Aside from T, crystallization methods (e.g., melt, cold, or solution crystallization), and stress, crystal modifications of polymers can be regulated by many other factors. 

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