Degree of ordering

The treatment of such order-disorder phenomena was initiated by Gorsky (1928) and generalized by Bragg and Williams (1934) [5], For simplicity we restrict the discussion to the synnnetrical situation where there are equal amounts of each component (x = 1/2). The lattice is divided into two superlattices a and p, like those in the figure, and a degree of order s is defined such that the mole fraction of component B on superlattice p is (1 +. s)/4 while that on superlattice a is (1 -. s)/4. Conservation conditions then yield the mole fraction of A on the two superlattices... 

The label liquid crystal seems to be a contradiction in tenns since a crystal cannot be liquid. However, tire tenn refers to a phase fonned between a crystal and a liquid, witli a degree of order intennediate between tire molecular disorder of a liquid and tire regular stmcture of a crystal. Wlrat we mean by order here needs to be defined carefully. The most important property of liquid crystal phases is tliat tire molecules have long-range orientational order. For tliis to be possible tire molecules must be anisotropic, whetlier tliis results from a rodlike or disclike shape. 

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

The properties of polymers depend not only on overall chain length, but also on the degree to which the monomers are ordered along the chain. Different methods of preparation lead to vastly different degrees of ordering. A good example is found in the polymerization of propylene. This polymerizes predominantly head-to-tail , and leads to a stereocenter ( ) at every other atom in the polymer chain. 

In what follows the degree of order of the hexagonal phases in Cases 1-6 will be compared to see whether there are basic differences between them. For this purpose the heats of fusion for the hexagonal phases... 

The degree of ordering of the microspheres was estimated by using the radial distribution function g(D) of the P4VP cores of the microspheres (Fig. 11). As previously described, for hexagonal packed spheres, the ratio of the peaks of the distances between the centers of the cores would be For the film at r = 0.5, the... 

Fig. 6. Same as in Fig. 5 but with random fluctuations introduced after the second quench (see text) near the straight APB. at following t (a) too, (b) 500, (c) 1000, and (d) 2000. The grey level varies linearly with the degree of order. from the completely dark for the most disordered region, to the coinplet.ely white for the most Ordered one. 

It should be noted that studying states of order in thermal equilibrium as a function of temperature yields the possibility of measuring the degree of order of a system in values of corresponding equilibrium temperature . This way, the results of residual resistometry are independent of the detailed formalism between state of order and electrical resistivity... 

It will be recalled that in Chapter 7, in dealing with the anions of weak acids, we found that we were able to obtain good qualitative agreement between theory and experiment, if we replaced Jmv by the electrostatic Jti. As has been pointed out more than once, the use of simple electrostatic theory necessarily implies that there is an increment in the degree of order in the solvent subject to the electrostatic field. In the -coefficients of Table 24, however, we have found that for 6 out of the... 

---