Expansion of chain

In good solvents, the expansion of chains causes an increase of viscosity as described by the following equation ... 

Equation [156] underestimates the ratio of Rh/Rg by about 15% ° when compared with the experimental one at the 6 temperature. Similar calculations can be made for Gaussian chains with other architectures. In real chains, the expansion of chain dimension by exduded-volume effects brings about an expansion of the hydrodynamic radius. ... 

There are two approaches connnonly used to derive an analytical connection between g(i-) and u(r) the Percus-Yevick (PY) equation and the hypemetted chain (FfNC) equation. Both are derived from attempts to fomi fimctional Taylor expansions of different correlation fimctions. These auxiliary correlation functions include ... 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Only a fraction of the chain segments will be present in this spherical shell, but whatever their number is, it will increase with the degree of polymerization n. Therefore, in the volume element associated with the expansion of the coil, the volume fraction of chain segments 0 is proportional to n/dV, or 0 n/a ro dro ... 

As the quinone stabilizer is consumed, the peroxy radicals initiate the addition chain propagation reactions through the formation of styryl radicals. In dilute solutions, the reaction between styrene and fumarate ester foUows an alternating sequence. However, in concentrated resin solutions, the alternating addition reaction is impeded at the onset of the physical gel. The Hquid resin forms an intractable gel when only 2% of the fumarate unsaturation is cross-linked with styrene. The gel is initiated through small micelles (12) that form the nuclei for the expansion of the cross-linked network. 

Temperature also affects production rates but, through its influence on the thermal expansion of water, it also induces changes in the depth of vertical mixing and resistance to wind-stirring processes. Reactions to temperature of other components of the food chain are also important in the regulation of phytoplankton biomass by consumers. Different phytoplankton species, with important morphological differences, are differentiated selectively by the interplay of these factors. " ... 

The quantity b has the dimension of a volume and is known as the excluded volume or the binary cluster integral. The mean force potential is a function of temperature (principally as a result of the soft interactions). For a given solvent or mixture of solvents, there exists a temperature (called the 0-temperature or Te) where the solvent is just poor enough so that the polymer feels an effective repulsion toward the solvent molecules and yet, good enough to balance the expansion of the coil caused by the excluded volume of the polymer chain. Under this condition of perfect balance, all the binary cluster integrals are equal to zero and the chain behaves like an ideal chain. 

The reaction of crotonaldehyde and methyl vinyl ketone with thiophenol in the presence of anhydrous hydrogen chloride effects conjugate addition of thiophenol as well as acetal formation. The resulting j3-phenylthio thioacetals are converted to 1-phenylthio-and 2-phenylthio-1,3-butadiene, respectively, upon reaction with 2 equivalents of copper(I) trifluoromethanesulfonate (Table I). The copper(I)-induced heterolysis of carbon-sulfur bonds has also been used to effect pinacol-type rearrangements of bis(phenyl-thio)methyl carbinols. Thus the addition of bis(phenyl-thio)methyllithium to ketones and aldehydes followed by copper(I)-induced rearrangement results in a one-carbon ring expansion or chain-insertion transformation which gives a-phenylthio ketones. Monothioketals of 1,4-diketones are cyclized to 2,5-disubstituted furans by the action of copper(I) trifluoromethanesulfonate. ... 

The way in which this salt is formed is still not known with any certainty, but it may involve transient formation of a monophosphazene, 03 = NH. It may then be that Cl3P=NH effects expansion of cationic phosphazene chains ... 

The evaluation of the elastic free energy AFei rests on the assumption that the root-mean-square distance between the ends of the chain is distorted by the same factor a representing the linear expansion of the spatial distribution. As in the treatment of the swelling of network... 

There are indications which fall short of definite proof, that a certain amount of chain rearrangement takes place, thus reducing the real chain expansion to values less than expected from elementary models. 

The trimethylsilyl ethers 212 of four-membered 1-alkenyl-1-cyclobutanols rearrange to the ring-expanded 0-mercuriocyclopentanones 213. These can be converted into the a-methylenecyclopentanones 214 through elimination or further expanded by one-carbon atom into cyclohexanones 215 via the Bu3SnH-mediated free radical chain reactions [116]. A similar radical intermediate is suggested to be involved in the ring expansion of a-bromomethyl-fi-keto esters [117]. (Scheme 84)... 

Figure 5.37 APG can be used to label specifically arginine residues in proteins, producing stable, cyclic Schiff base-like bonds with the side-chain guanidino groups. Photoactivation with UV light then causes ring expansion of the phenyl azide group, initiating covalent bond formation with amines.

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