Statistical structure

Chul, M Phillips, R McCarthy, M, Measurement of the Porous Microstructure of Hydrogels by Nuclear Magnetic Resonance, Journal of Colloid and Interface Science 174, 336, 1995. Cohen, Y Ramon, O Kopeknan, IJ Mizrahi, S, Characterization of Inhomogeneous Polyacrylamide Hydrogels, Journal of Polymer Science Part B Polymer Physics 30, 1055, 1992. Cohen Addad, JP, NMR and Statistical Structures of Gels. In The Physical Properties of Polymeric Gels Cohen Addad, JP, ed. Wiley Chichester, UK, 1996 39. 

Dendritic polymers, the fourth major architectural class of macromolecules, can be divided into three subclasses. These subclasses may be visualized according to the degree of structural perfection attained, namely (1) hyperbranched polymers (statistical structures, Chapter 7), (2) dendrigraft polymers (semi-controlled structures, reviewed in this chapter) and (3) dendrimers (controlled structures, Chapter 1). 

Similarly, AHu°(W — W + E) is of opposite sign to the expected structural hydration contribution of E (28). There does not seem to be too much specificity in the interactions involving U which probably acts as a statistical structure breaker the local U-W interactions are probably not too different from the W-W ones, but the long-range ordering is destroyed. Schrier et al. (28) have interpreted the Bue parameters in terms of a destructure overlap cosphere model. Since... 

Magnetic resonance spectroscopy has a considerable history of being applied to the issue of coal structure. However, as a historical beginning, the structural types in coal were first determined by means of statistical structural analysis (Francis, 1961). One of the first methods to supersede the statistical methods was based on proton (XH) magnetic resonance, which provided a quantitative distribution of the hydrogen types in coal (Brown and Ladner, 1960 Bartle, 1988 Maciel et al., 1993). 

Figure 3. Fiber diffraction from a statistically disordered fiber of the sodium salt of poly d(GC) poly d(GC). The molecules in this structure form an unusual left-handed DNA duplex in which the dinucleotide pCpG is the molecular asymmetric unit. The unit cell is trigonal with a = b = 1.91 nm c = 4.35 nm. The space group is probably P226s. The molecular symmetry is itself 226s, and the statistical structure arises from a random choice of a molecular diad to a point along a particular direction.

Kreulen reported that Rasa coal was a humic coal and contained no sapropelites, waxes, or resins (4). He noted that Rasa coal exhibits dual character, i.e., it exhibits both low- and high-rank characteristics. Chemical tests indicated that a small amount of the sulfur present is in side chains, and a large amount occurs in ring structures. Using a statistical structural analysis method based on density, van Krevelen computed that 59% of the carbon in Rasa coal is aromatic (4). 

The statistical structural model for the gelation behavior of cyanate-epoxide polyreactions was described by Bauer [69] using the cascade formalism, according to the approach by Dusek [70], which had been previously applied for the polycyclotri-merization of acetylene derivatives. 

From a conceptual viewpoint the primary theoretiotl problem yet to be solved is the stress transfer mechanism in polymer solids. As noted earlier, polymers have statistical structures v4ien in the glassy state and a rather broad spectrum of order-disorder when in the crystalline state. Detailed analysis of stress transfer throi a glassy structure requires comprehensive analysis of chain conformation in the (nonequilibrium) glass which in turn requires an imderstanding of both the intramolecular and intermolecular energetics. 

It is noted that attempts to apply composites theory to the materials investigated have not been entirely successful. While upper and lower bounds on, e g., moduli can be established there is little quantitative ediction of the impact strei th or fracture toughness parameters of the composites. Hence, the systems cannot be considered as optimized, for example, with regard to impact strength versus particle size, shape, or distribution or matrix-particle adhesion. The complexity is, of course, due to the statistical structure of the dispersed phase and the resultant uncertainties in the calculations of local stress fields, which in turn imply uncertainty in the local mode of yielding or rate of yielding. 

There is no ideal system of polysaccharide classification [3]. The best system should be that based on chemical structure. However, because of their polymolecularity, which limits descriptions to statistical structures in many cases, and the great variety of structures, classifying polysaccharides in this way has limitations. Combinations of the following categories are used [3] ... 

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