Ciystal models

Fig. 4. Model of the ciystal structure of zeolites X, Y, and the mineral faujasite. At the tight is shown the tetrahedral arrangement of tmncated octahedra surrounding one large cavity. On the left the packing model of zeohte X is shown, containing three types of Na cations.

The dominant mechanism of purification for column ciystallization of sohd-solution systems is reciystallization. The rate of mass transfer resulting from reciystallization is related to the concentrations of the solid phase and free hquid which are in intimate contac t. A model based on height-of-transfer-unit (HTU) concepts representing the composition profQe in the purification sec tion for the high-melting component of a binaiy solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 22-10. The column ciystallizer was operated... 

However, although it allowed a correct description of the current-voltage characteristics, this model presents several inconsistencies. The main one concerns the mechanism of trap-free transport. As noted by Wu and Conwell [1191, the MTR model assumes a transport in delocalized levels, which is at variance with the low trap-free mobility found in 6T and DH6T (0.04 cm2 V-1 s l). Next, the estimated concentrations of traps are rather high as compared to the total density of molecules in the materials (see Table 14-4). Finally, recent measurements on single ciystals [15, 80, 81] show that the trap-free mobility of 6T could be at least ten times higher than that given in Table 14-4. 

I hope that this chapter provides a fitting introduction to the complex task of active pharmaceutical ingredient product design through ciystallization, and most importantly that it will stimulate work and encourage further growth in the application of thermodynamic models and optimization techniques in this area. 

Figure 17. Schematic lepiesentation of a lamellar polyethylene single ciystal. (a) and (b) show enlaiged features of its stnicture in (o) the zigzag conformation of the macromolecular chain inside the crystal in (b) a hypothetical model for the regular folding, drawn according to the calculation reported in ref. 224a.

The small octaazacryptand, 2, is selective for fluoride [44], with extremely high affinity, log Ka = 10-11 in aqueous solution [44-46], As anticipated, the ciystal structure of 2 with fluoride showed the halide to be encapsulated Figure 5) [44], Later theoretical and modeling studies indicated that the small size of the cavity could preclude encapsulation of larger anions [45],... 

Equation (18-31) contains no information about the ciystallizer s influence on the nucleation rate. If the crystallizer is of a mixed-suspension, mixed-product-removal (MSMPR) type, satisfying the criteria for Eq. (18-31), and if the model of Clontz and McCabe is valid, the contribution to the nucleation rate by the circulating pump can be calculated [Bennett, Fiedelman, and Randolph, Chem. Eng. Frog., 69(7), 86(1973)] ... 

Figure 16. Surface structure the (0001) surface of sapphire (a-A Os) from Eng et al. (2000) with permission of the editor of Science, (a) Structure of vacuum-equihbrated diy surface. Al metal atoms sit on the surface, (b) Ideal bulk terminated surface with no relaxation or reconstraction. (c) Model for the wet-equihbrated surface at one atmosphere from surface scattering (ciystal truncation rod) diffraction measurements. Al metal atoms have shifted, the surface is oxygen terminated, and an organized water monolayer is required to accurately describe the observations, (d) Structure of gibbsite or y-Al(OH)3. The relaxed wet-equilibrated sapphire surface is intermediate between this structure and that of the bulk terminated stracture (B).

The crosslinking between PTFE polymer chains and fluorinated-pitch should prevent crystallization of molecules from the molten state. When the crosslinking density is low, the molecules with rather long chain between crosslinking points might ciystallize, where the crystal size would be small and also the ratio of crystalline against amorphous parts would decrease. The DSC results are well explained by above model. 

Roux J, Hovis GL (1996) Thermodynamic mixing models for muscovite-paragonite solutions based on solution calorimetiy and phase equilibrium data. J Petrol 37 1241-1254 Rule AC, Bailey SW (1985) Refinement of the ciystal structure of phengite-2A/i. Clays Clay Minerals 33 403-409... 

Ciystal field model a model used to explain the magnetism and colors of coordination complexes through the splitting of the d orbital energies. (21.6)... 

Ciystallization of PET proceeds in two distinct steps [97], i.e. (1) a fastprimaiy ciystallization which can be described by tire Avrami equation, and (2) a slow secondary ciystallization which can be described by a rate being proportional to tire crystallizable amoi-phous fraction dXc/df = (Xman — Xc)kc, with Xmax being tire maximum crystallinity (mass fraction) [98]. Under SSP conditions, the primary crystallization lasts for a few minutes before it is replaced by secondary crystalhzation. The residence time of tlie polymer in tlie reactor is of the order of hours to days and therefore the second rate equation can be applied for modelling the SSP process. 

Carbohydrates, Recognition of, p. 169 Carbonic Anhydrase Models, p. 178 Carcerands and Hernicarcerands. p. 189 Cation-n Interactions, p. 214 Cavitands, p. 219 Chiral Guest Recognition, p. 236 Classical Descriptions of Inclusion Compounds, p. 253 Classification and Nomenclature of Supramolecular Compounds, p. 261 Clathrate Hydrates, p. 274 Conzplexation of Fullerenes, p. 302 Concepts in Ciystal Engineering, p. 319 Crown Ethers, p. 326 Cryptands, p. 334 Cryptophanes, p. 340 Cyclodextrins, p. 398... 

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