Disorder linear

Asymmetrical Peaks are rarely found in WAXS from polymers, but they are ubiquitous in the MAXS of liquid crystalline polymers. For asymmetrical peaks in isotropic patterns it is best to determine the peak position from the maximum of the peak, if peak asymmetry is a result of linear or planar disorder. Linear disorder means that the crystals are more or less one-dimensional (a tower of unit cells). Planar disorder means that the crystallites are made from only very few layers of unit cells (cf. Guinier [6] Chap. 7). 

Tilgner, A., H.P Trommsdorff, J.M. Zeigler, and R.M. Hochstrasser. 1992. Polyfdi-normalhexyl-silane) in solid-solutions-experimental and theoretical-studies of electronic excitations of a disordered linear-chain. J Chem Phys 96 781. 

The localization / delocalization behavior of exeitons is illustrated in Figs. 1 and 2 for a disordered linear chain of N=100 molecules eoupled through long-range dipolar interactions. For a given realization of the disorder, the average number of sites covered by the excitation is represented by segments eentered around the mean exciton position for weak disorder (cr/F = 0.01) or for rel-... 

SHINOZUKA, M., Structural Response Variability, accepted for publication in the Journal of Engineering Mechanics, ASCE, 1986. SOON6, T.T. and B06DAN0FF, J.L., On the Natural Frequencies of a Disordered Linear Chain of N Degrees of Freedom, internationa. Journal of Mechanical Science, Vol. 5, No. 3, (1963), pp.237-265. S00N6, T.T. and B06DAN0FF, J.L., On the Impulsive Admittance and Frequency Response of a Disordered Linear Chain of N Degrees of Freedom, international Journal of Mechanical Science, Vol. 6, No. 3, (1964), pp.225-237. 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Using this strategy, constmction of multilayer films of - O. fim thickness by self-assembly of methyl 23-ttichlorosilyltticosanoate (MTST) on siUcon substrates has been demonstrated (Fig. 9) (165). The linear relationship between the film thickness and the layer number showed a slope of 3.5 nm /layer. Filipsometry data, absorbance intensities, and dichroic ratios for the multilayers all suggest that the samples were composed of distinct monolayers. However, ir data indicated that there maybe more tilting or disordering of the alkyl chains in the seven-layer sample than for the monolayer samples. 

It must be pointed out that deviations from such a simple relationship do occur. For example, since random copolymerisation tends to promote disorder, reduce molecular packing and also reduce the interchain forces of attraction, the Tg of copolymers is often lower than would be predicted by the linear relationship. Examples are also known where the Tg of the copolymer is higher than predicted. This could occur where hydrogen bonding or dipole attraction is possible between dissimilar comonomer residues in the chain but not between similar residues, i.e. special interchain forces exist with the copolymers. 

With block copolymers two types of effect have been observed. In some instances a transition corresponding to each block is observable whilst in other cases a single transition is observed, usually close to that predicted by a linear relationship even where random copolymers show large deviations. This is because the blocks reduce both the contacts between dissimilar comonomer residues and also the disorder of the molecules which occurs in random copolymer systems. 

Linear N2 molecules adsorbed on graphite show a transition from a high-temperature phase with orientational disorder to a low-temperature phase with herringbone ordering of the orientational degrees of freedom (see Sec. lie and Fig. 11). 

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. 

For long (infinite) /am.v-polyacclylene chains, the treatment of quantum lattice fluctuations is very complicated, because many lattice degrees of freedom couple in a non-linear way to the lowest electronic transitions. We have recently shown that for chains of up to 70 CH units, the amount of relevant lattice degrees of freedom reduces to only one or two, which makes it possible to calculate the low-energy part of the absorption spectrum in an essentially exact way [681. It remains a challenge to study models in which both disorder and the lattice quantum dynamics are considered. 

Linear polymers when heated sufficiently undergo transition from solid to liquid, that is, they melt. Liquids are characterised in general by greater disorder than solids and by substantially increased molecular mobility. 

X-ray diffraction patterns from dendrimers tend to lack sharp features and are similar to those from amorphous linear polymers. This suggests a molecular arrangement in dendrimers that is fairly disordered. There is also the problem that these molecules can exist in a large number of energetically equivalent conformations and that in solution there can be rapid interchange between these conformations. This contributes to the overall amorphous structure of dendrimers. 

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