Pauling relationship

M.R. Paxton and D.R. Paul, Relationship Between Structure and Transport Properties for Polymers with Aromatic Backbones, in Polymeric Gas Separation Membranes, D.R. Paul and Y.P. Yampol skii (eds), CRC Press, Boca Raton, FL, pp. 83-154 (1994). 

The concept of a bond order or bond index can be particularly useful in the description of transition structures, where bonds are being broken and formed and the bond order can provide a measure of the extent of reaction at different bonds. It has been suggested that the parameter in the Pauling relationship (1.26) should be 0.6 for bond orders... 

The value of c must be determined separately for each system but it does not vary much. The Pauling relationship can be derived from the properties of the Morse function [46]. Bond number conservation seems to apply quite generally to reaction paths involving bond breaking and bond formation in a system of three collinear atoms, and thus to 5N2-type reactions at tetrahedral-ly coordinated Cd, Sn, Si, Ge, Al, and B [47] although not at C. 

M.R. Pixton, D.R. Paul, Relationship between structure and transport prop-... 

Pauling relationship (c) determine Pb(IV) by allowing it to oxidize 1 and titrating I2 formed with thiosulfate (or heat with HCl, pass CI2 into Kl(aq), and titrate I2 formed against thiosulfate). 

Brown and Cudby [6] and Randall [7] have analyzed the C-spectra of a series of propylene-butene-1 copolymers prepared using an isospecific catalyst system. The enchainment of the monomer units was essentially isotactic and head-tail. Resonances observed for the homopolymers, assignments made previously by Fish and Dannenberg [78], the Grant-Paul relationships and variations in resonance intensity with copolymer composition were used to make assignments for the resonances of methine, methylene and methyl carbon atoms. Triad and some tetrad sequence distribution measured from the spectra were consistent with Bernoullian distributions over the entire range of copolymer compositions examined. 

The primary structure of a peptide is its ammo acid sequence We also speak of the secondary structure of a peptide that is the conformational relationship of nearest neighbor ammo acids with respect to each other On the basis of X ray crystallographic studies and careful examination of molecular models Linus Pauling and Robert B Corey of the California Institute of Technology showed that certain peptide conformations were more stable than others Two arrangements the a helix and the (5 sheet, stand out as... 

To these ancient identities was added in due course the historical Jesus.It was the apostle Paul who established the dehnitive Christian dogma concerning the nature of Christ. His account recalls the role of the ancient Iranian and Jewish Saviour figure (although the exact relationship to the pagan elements is the subject of serious contention on the part of Christian theology). 

Figure 3-4. Dimensions of a fully extended polypeptide chain. The four atoms of the peptide bond (colored blue) are coplanar. The unshaded atoms are the a-carbon atom, the a-hydrogen atom, and the a-R group of the particular amino acid. Free rotation can occur about the bonds that connect the a-carbon with the a-nitrogen and with the a-carbonyl carbon (blue arrows). The extended polypeptide chain is thus a semirigid structure with two-thirds of the atoms of the backbone held in a fixed planar relationship one to another. The distance between adjacent a-carbon atoms is 0.36 nm (3.6 A). The interatomic distances and bond angles, which are not equivalent, are also shown. (Redrawn and reproduced, with permission, from Pauling L, Corey LP, Branson PIR The structure of proteins Two hydrogen-bonded helical configurations of the polypeptide chain. Proc Natl Acad Sci U S A 1951 37 205.)...

XRD on battery materials can be classified as powder dififaction, a technique developed by Peter Debye and Paul Scherrer. In powder dififaction the material consists of microscopic crystals oriented at random in all directions. If one passes a monochromatic beam of X-rays through a fiat thin powder electrode, a fraction of the particles will be oriented to satisfy the Bragg relation for a given set of planes. Another group will be oriented so that the Bragg relationship is satisfied for another set of planes, and so on. In this method, cones of reflected and transmitted radiation are produced (Fig. 27.2). X-ray diffraction patterns can be recorded by intercepting a... 

Now the use of molecular psychiatry of ascorbic acid in schizophrenia by Linus Pauling and others, where there seems to be some relationship to dopamine neurons, and finding that dopamine-dopaminergie neurons or receptors are present in twice the normal amount, makes this an intriguing... 

EPA. 1976. Effect of hydrogen sulfide on fish and invertebrates, Part II—Hydrogen sulfide determination and relationship between pH and sulfide toxicity. Report to the U.S. Environmental Protection Agency, Environmental Research Lab, Duluth, MN, by Broderius SJ, Smith LL Jr., University of Minnesota, Department of Entomology, Fisheries, and Wildlife, St. Paul, MN. 

Grant and Paul Chemical Shifts. The technique of obtaining branch content information from NMR for polymers utilizes an empirical relationship given by Grant and Paul [29,79,80]. The Grant and Paul empirical relationship [29,79,80] can be used to calculate the values of the chemical shifts for carbon atoms in the vicinity of a branch point in a hydrocarbon polymer. The empirical relationship was obtained from NMR studies on alkanes. The chemical shift of any carbon atom in a 13C-NMR can be decomposed as a sum of contributions from its nearest five neighboring carbon atoms. The value of the chemical shift for any carbon atom C, is given as,... 

This empirical relationship cannot be used without accounting for some correction terms, which take into account the molecular geometry of the bonded neighbors. This is especially essential when calculating the chemical shift of a branch point carbon atom. These correction terms were given by Grant and Paul to be as follows [29,80]. 

In 1992, Paul and Van Alstyne reported on the processes that occur after tissue disruption in different species of the calcified green seaweed Halimeda [56]. After wounding, these algae transform their major secondary metabolite, the his-enoylacetate diterpene halimedatetraacetate (48), into halimedatrial (50) and epihalimedatrial (51). The structural relationship between the educt and the reaction products suggests that the transformation occurs by a combination of solvolysis and hydrolysis reactions as indicated in Scheme 14 [108]. 

It will be noted that there is a factor of approximately 105 between successive dissociation constants. This relationship exists between the equilibrium constants for numerous polyprotic acids, and it is sometimes known as Pauling s rule. This rule is also obeyed by sulfurous acid, for which ffj = 1.2 X 10 2 and K2 = 1 X 10 7. 

FIGURE 1. The relationships between the methyl deviation, 5(CH3— Z), and Pauling electronegativity of the bonded Z atom in various homologous functional group series, CH3—(CH2)m—Z. See References 17b and 18... 

We have shown19 that there are separate but nearly parallel linear relationships between the methyl deviations, 6(CH3—Z), of methyl substituted species CH3—Z and the electronegativity of the atom in Z bonded to carbon for functionality in the second row of the periodic table (Z = —OH, —NH2, —CH3, —B<) and in the third row of the periodic table (Z = —Cl, —SH, —Al<). If the methyl deviations for CII3B1 and (CH3)4Ge, both containing fourth-row atoms, are now calculated and the results plotted versus the Pauling electronegativity, the two new points fall on the line established by the third-row series (Figure 1). 

Now the bond ionicity must be related in some manner to the electronegativity xA (the ability of atom A to gain and hold electrons). Pauling originally postulated a relationship of the form31... 

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