Disorder-order transitions

Order-disorder transitions are examples of a second-order transformation. An order-parameter can be assigned that goes from one for a perfectly ordered state to zero for a completely random state, i.e., a solid solution. Using a technique similar to the Curie-Weiss model for ferromagnetism (see Chapter 25), it can be shown that the order parameter goes from 1 at low temperatures to 0 at the transition temperature and the system then becomes a solid solution again. 

A theoretical treatment of order-disorder phenomena in molecular crystals has been developed by Pople and Karasz. The theory considered disorder in both the positions and orientations of the molecules and it was assumed that each molecule could take up one or two orientations on the normal, a-, and the interstitial, ]8-, sites of the two-lattice model proposed by Lennard-Jones and Devonshire in their treatment of the melting of inert gas crystals. The theory introduced a single non-dimensional parameter, v- related to the relative energy barriers for the 

Conference on Plastic Crystals and Rotation in the Solid State, J. Phys. and Chem. Solids, 1961,18, 1-92. 

Westrum, jun., and J. P. McCullough, Thermodynamics of Crystals in Physics and Chemistry of the Organic Solid State, eds. D. Fox, M. M. Labes, and A. Weiss-berger. Interscience, New York, 1963, Vol. 1, Chap. 1. 

Conference on Mouvements et Changements de Phase dans les Solides Moleculaires, J. Chim. phys., 1966, 63, 9-205. 

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Onsager L 1944 Orystal statistics I. A two-dimensional model with an order-disorder transition Phys. Rev. 65 117... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

Thermal stahility. Yor applications of LB films, temperature stability is an important parameter. Different teclmiques have been employed to study tliis property for mono- and multilayers of arachidate LB films. In general, an increase in temperature is connected witli a confonnational disorder in tire films and above 390 K tire order present in tire films seems to vanish completely [45, 46 and 45] However, a comprehensive picture for order-disorder transitions in mono- and multilayer systems cannot be given. Nevertlieless, some general properties are found in all systems [47]. Gauche confonnations mostly reside at tire ends of tire chains at room temperature, but are also present inside tire... 

Ocko B M, Wang X J and Wandlowski Th 1997 Bromide adsorption on Ag(OOI) A potential induced two-dimensional Ising order-disorder transition Phys. Rev. Lett. 79 1511-14... 

The ability of XPD and AED to measure the short-range order of materials on a very short time scale opens the door for surface order—disorder transition studies, such as the surface solid-to- liquid transition temperature, as has already been done for Pb and Ge. In the caseofbulkGe, a melting temperature of 1210 K was found. While monitoring core-level XPD photoelectron azimuthal scans as a function of increasing temperature, the surface was found to show an order—disorder temperature 160° below that of the bulk. 

Tanner, L.E, and Leamy, H.J. (1974) The microstructure of order-disorder transitions, in Order-Disorder Transformations in Alloys, ed. Warlimont, H. (Springer, Berlin) p. 180. 

Figure 6.10. Dilatotneuic record of a sample of a Ni-AI-Fe alloy in the neighbourhood of an order-disorder transition temperature (Cahn ei al. 1987).

In another study Milehev and Landau [27] investigated in detail the transition from a disordered state of a polydisperse polymer melt to an ordered (liquid erystalline) state, whieh oeeurs in systems of GM when the ehains are eonsidered as semiflexible. It turns out that in two dimensions this order-disorder transition is a eontinuous seeond-order transformation whereas in 3d the simulational results show a diseontinuous first-order transformation. Comprehensive finite-size analysis [27] has established... 

The ternary Ge halides, MGeX3 (M = Rb, Cs X = Cl, Br, I) are polymorphic with various distorted perovskite-like (p. 963) structures which reflect the influence of the nonbonding pair of electrons on the Ge" centre. Thus, at room temperature, rhombohedral CsGel3 has three Ge-I at 275 pm and three at 327 pm whereas in the high-temperature cubic form (above 277°C) there are six Ge-I distances at 320 pm as a result of position changes of the Ge atoms (reversible order-disorder transition). Again, RbGel3 has a lemon-yellow, orthorhombic form below —92° an intermediate, bordeaux-red orthorhombic perovskite form (—92° to —52°) a black rhombohedral form (—52° to —29°) and... 

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

Iodine monobromide forms an intercalate with limiting composition CsIjBrj-j (C9) when natural graphite is used. Higher stages CgljcBri-x and C,2ljBr, x have also been shown to exist (C9). An order-disorder transition within IBr layers occurs at -60°C (CIO). 

Fig. 19 Raman spectra of the torsional and external vibrations of pSg at two different temperatures showing the dramatic change due to the order-disorder transition, after [146]. Spectral resolution was 0.75 cm ...

There are few reports on block-copolymeric TPE (namely, polyurethane, EVA, SBS, poly (styrene-fo-butyl acrylate) (PSBA))-clay nanocomposites also [196-199]. Choi et al. [196] studied the effect of the silicate layers in the nanocomposites on the order-disorder transition temperature of... 

FIGURE 5.17 Temperature versus G —the shear storage modulus at a frequency of 1.6 Hz for diblock copolymer poly(ethylene propylene)-poly(ethylethylene) (PEP-PEE). The order-disorder transition (ODT) calculated to be 291°C 1°C. (From Rosedale, J.H. and Bates, F.S., Macromolecules, 23, 2329, 1990. With permission of American Chemical Society.)... 

LeiblerL., Theory of microphase separation in block copolymers. Macromolecules, 13, 1602, 1980. Eoerster S., Khandpur A.K., Zhao J., Bates E.S., Hamley I.W., Ryan A.J., and Bras W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules, 21, 6922, 1994. 

Hashimoto T., Order disorder transition in block copolymers. Thermoplastic Elastomers A Comprehensive Review (Legge N.R., Holden G., and Schroeder H.E., eds.), Hanser Publishers, Munich, 1987. Bianchi U. and Pedemonte E., Morphology of styrene butadiene styrene copolymer. Polymer, 11, 268, 1970. 

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