Residual disorder

For most substances, the Third Law and statistical calculations of the entropy of the ideal gas are in agreement, but there are exceptions, some of which are summarized in Table 4.2. The difference results from residual entropy, So, left in the solid at 0 Kelvin because of disorder so that St - So calculated from Cp/TdT is less than the St calculated from statistical methods. In carbon monoxide the residual disorder results from a random arrangement of the CO molecules in the solid. Complete order in the solid can be represented schematically (in two-dimensions) by... 

Three groups of disordered proteins have been assembled, with the groups defined by the experimental method used to characterize the lack of ordered structure. Because the focus has been on long regions of disorder, an identified disordered protein or region was not included in these groups if it failed to contain 40 or more consecutive residues. Disordered regions from otherwise ordered proteins as well as wholly disordered proteins were identified. Table I summarizes the collection of sequences in this database. 

S 0 (2 98 K) for N2O, as experimentally determined from Cp/T measurements is some 6 JK-1 mol smaller than the spectroscopically derived result. This residual entropy arises from the fact that the true crystal lattice contains units arranged both as NNO as well as ONN close to the absolute zero of temperature. This residual disorder therefore contrasts with the perfectly ordered arrangement of either NNO NNO or ONN ONN which would satisfy requirements of perfect order at 0 K. 

Isotopic disorders (e.g. in solid chlorine atoms 35C1 and 37C1 isotopes can arise) and nuclear spin degeneracy (ortho and para hydrogen) are two rather less important factors which can also give rise to residual disorder in solids at 0 K. 

The structure of mMIPS also contains a 30 residue disordered region about the active site that corresponds closely to the disordered region identified in yMIPS (Norman et al., 2002). This region corresponds to yMIP s a 14, a 15, and pi5. 

Parak and collaborators (Hartmann et al., 1987 Parak et al., 1987) carried out X-ray structure analyses for metmyoglobin at temperatures of 80—300 K. One hundred sixty water molecules, more than one-third of the water in the crystals, were included in the refinement. The disorder is higher for water that for protein atoms (Fig. 31). Reduction in temperature partially freezes out the disorder for the water, as for the protein. The residual disorder at low temperature has been understood to represent conformational substates or a distribution of conformations, frozen in at low temperature and in mobile equilibrium at high temperature. 

The smallest conceivable conjugated monocyclic diene is 1,3-cyclobutadiene. Several complexes involving cyclobutadiene are known. The compound itself is unstable and has not been studied by structural methods. It will therefore not be included in the present discussion. 1,3-Cyclobutadiene has, however, been isolated in argon matrices, and it has been established that the molecule has symmetry. For the tetra-tert-butyl derivative an envelope conformation (twist angle 7°) was found by X-ray methods, however the distances in the ring were obviously too similar for an antiaromatic system [1.464(3) and 1.483(3) A]. A redetermination at even lower temperatures gave more reasonable results (1.441 and 1.527 A) and a further analysis of the anisotropic parameters revealed that some residual disorder is still responsible for some equilibration and distances of 1.34 and 1.60 A were assumed to be the correct ones. ... 

C. Landron, A. Douy, and D. Bazin, From liquid to solid residual disorder in the local environment of oxygen-coordinated zirconium, Phys. Status Solidi B, 184, 299-307 (1994). 

The modeling of Prosa et al. [228] only reflects the overall average structure of the PA3T chain. The persistence of diffuse scattering features, even in well-ordered films, suggests a high degree of residual disorder. The simulations of Corish and Morton-Blake [243,244] also result in pronounced disorder in... 

Lang et al. have analyzed the tail of the density of states using optical (photocurrent) and electrical (LET) methods [221]. They considered various existing models that describe the tail of the density of states and they concluded that their observation is consistent with the presence of some residual disorder which is not due to impurities (they used ultrapure crystals). The band tails are similar to those observed in amorphous inorganic solid, in agreement with the model of [172] which predicts that, from the electronic point of view, the pentacene crystal at room temperature can be seen as a disordered material. 

---