Liquid crystals Monodisperse particles

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

Micron-size monodisperse polymeric microspheres are used in a wide variety of applications, such as toners, instrument calibration standards, column packing materials for chromatography, spacers for liquid crystal displays, and biomedical and biochemical analysis [1-3]. Because of the commercial and scientific interest in these particles, research into their preparation has been active... 

The sol-gel method is also used to make very fine spherical particles of oxides. By structuring the solvent with surface-active solutes, other forms can also be realized during condensation of the monomeric reactant molecules to form a solid particle. Figure 8.16 shows that normal or inverse micelles or liquid crystals (liquids having long-distance order) can be formed in such solutes. Micelles are small domains in a liquid that are bounded by a layer of surface-active molecules. In these domains the solid is condensed and the microstructure of the precipitated solid is affected by the micelle boundaries. Monodisperse colloidal metal particles (as model catalyst) have been made in solvents that have been structured with surfactants. In the concentration domains where liquid crystals obtain highly porous crystalline oxides can be condensed. After calcination such solids can attain specific surface areas up to 1000 m /g. Micro-organisms use structured solutions when they precipitate calcite, hematite and silica particles. 

Lattice Dynamics of Icosahedral Alpha-Boron Under Pressure. Physical Review Letters, Vol. 78, No. 4, (January 1997), pp. 693-696, ISSN 0031-9007 Wang, Y.L. Gai, L. Xia, Y.N. (2005). Monodisperse Spherical Colloids of Pb and Their Use as Chemical Templates to Produce Hollow Particles. Advanced Materials, Vol. 17, No. 4, (February 2005), pp. 473-477, ISSN 0935-9648 Wang, Z.K. Shimizu, Y. Sasaki, T. Kawaguchi, K. Kimura, IC Koshizaki, N. (2003). Catalyst-Free Fabrication of Single Crystalline Boron Nanobelts by Laser Ablation. Chemical Physics Letters, Vol. 368, No. 5-6, Qanuary 2003), pp. 663-667, ISSN 0009-2614 Wagner, R.S. Ellis, W. C. (1964). Vapor-Liquid-Solid Mechanism of Single Crystal Growth. 

In these simulations, we computed the crystal-nucleation barrier and the structure of the critical nucleus, as a function of both polydispersity and supersaturation. As in the case of monodisperse suspensions [32], we find that all critical nuclei have a randomly-stacked close-packed structure. During crystallization, size-fractionation occurs [52, 53] the particles that make up the critical nucleus are on average larger, and the polydispersity is lower, than those in the metastable liquid, as is shown in Figs. 14 and 15. 

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