Generalized degree of order

Fig. 12. (A) Secondary structure of a TAR RNA analogue where the six residue hairpin loop in wt-TAR (CUGGGA) has been replaced with the stable tetraloop (UUCG). (B) Histogram plots of the generalized degree of order ( ) describing the degree of molecular alignment for the two helices. The large difference in alignment indicates the presence of inter-helical motions.

Fig. 13. Structural dynamics of TAR RNA in response to increasing Mg2+ concentrations. (A) The TAR inter-helical conformation as a function of [Mg] [TAR] stoichiometry. Ribbon representation of the relative orientation of stem I (bottom) and II (top) determined by superimposing stem-specific principal axes. The helix axis of stem II is superimposed for all three conformations along the molecular z direction. (B) The generalized degree of order ( ) for stem I (lower line) and II (upper line), as a function of [Mg] [TAR] stoichiometry. Addition of Mg2+ leads to attenuations in the difference between helix-specific values indicating quenching of inter-helical motions.

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... 

Comparison of these expressions indicates that the activation entropy is related to the steric factor for the reaction. One may interpret the steric factor in terms of the degree of order of molecular configurations required to bring about the reaction, and this viewpoint is generally regarded as more satisfactory from an intellectual viewpoint than is that which regards Ps as an a posteriori correction factor necessary to obtain agreement between theory and experiment. 

The early surface studies described above indicated that compounds were probably being formed with the first cycle and that the deposits had some degree of order. FEED, however, is an averaging technique. A surface can have significant amounts of disorder, relatively small domains, and still give a reasonable FEED pattern. STM was also used in those studies of compound monolayers, however the images collected were generally of very small areas of the deposits—5-15 nm on a side. Those STM studies... 

Most of the studies on polymers such as polyamides in solution are limited because the insolubility of these polymers in common solvents. This fact makes their characterization very difficult [87] The degree of order or crystallinity shown by these polymers caused by intra- and inter- chain interactions affect their solubility and their general properties. 

Transitions of the Cu-Zn Type with Arbitrary Composition.—It is not much harder to discuss the general ease of arbitrary composition than it is the simple case of 50 per cent concentration taken up in the two preceding sections. We assume that there are Nx atoms a, JV(1 — x) 6 s, and we shall limit ourselves to the case where x is less than the same formulas do not hold for x greater than but to get this cast we can merely interchange the names of substances a and b. As before, we let the degree of order be w. Then we assume... 

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