Chain-length method

Chain-Length Method of Mishra and Yalkowsky The method of Mishra and Yalkowsky [11] is a modification of Trouton s rule for long-chain hydrocarbons, including alkanes, alkenes, cyclopentanes, cyclohexanes, and alkylbenzenes. The relationship is... 

Grassberger P 1997 Pruned-enriched Rosenbluth method simulations of theta polymers of chain length up to 1,000,000 Phys. Rev. E 56 3682... 

For preparative purposes batch fractionation is often employed. Although fractional crystallization may be included in a list of batch fractionation methods, we shall consider only those methods based on the phase separation of polymer solutions fractional precipitation and coacervate extraction. The general principles for these methods were presented in the last section. In this section we shall develop these ideas more fully with the objective of obtaining a more narrow distribution of molecular weights from a polydisperse system. Note that the final product of fractionation still contains a distribution of chain lengths however, the ratio M /M is smaller than for the unfractionated sample. 

Because the higher alcohols are made by a number of processes and from different raw materials, analytical procedures are designed to yield three kinds of information the carbon chain length distribution, or combining weight, of the alcohols present the purity of the material and the presence of minor impurities and contaminants that would interfere with subsequent use of the product. Analytical methods and characterization of alcohols have been summarized (13). 

Nylon resins are made by numerous methods (53) ranging from ester amidation (54) to the Schotten-Baumann synthesis (55). The most commonly used method for making nylon-6,6 and related resins is the heat-induced condensation of monomeric salt complexes (56). In this process, stoichiometric amounts of diacid and diamine react in water to form salts. Water is removed and further heating converts the carboxylate functions to amide linkages. Chain lengths are controlled by small amounts of monofunctional reagents. The molten finished nylon resin can be dkectly extmded to pellets. 

The properties of polymers depend not only on overall chain length, but also on the degree to which the monomers are ordered along the chain. Different methods of preparation lead to vastly different degrees of ordering. A good example is found in the polymerization of propylene. This polymerizes predominantly head-to-tail , and leads to a stereocenter ( ) at every other atom in the polymer chain. 

Offset couplers may be used to adjust chain tension or chain length when other methods are not feasible. This is done by removing a section of chain having one more pitch than the offset coupler and inserting the coupler in its place. 

Methods for measurement of kp have been reviewed by Stickler,340 41 van Herk Vl and more recently by Beuermann and Buback.343 A largely non critical summary of values of kp and k, obtained by various methods appears in the Polymer Handbook.344 Literature values of kp for a given monomer may span two or more orders of magnitude. The data and methods of measurement have heen critically assessed by IUPAC working parties"45"01 and reliable values for most common monomers are now available. 43 The wide variation in values of kp (and k,) obtained from various studies docs not reflect experimental error but differences in data interpretation and the dependence of kinetic parameters on chain length and polymerization conditions. 

In calculations the moments can be treated as concentrations. Kinetic simulation of radical polymerization to evaluate dispcrsitics typically involves evaluation of the moments rather than the complete distribution. This method of moments is accurate as long as the kinetics are independent of chain length. 

It has been shown that equivalent information can be obtained by analysis of logfnumbcr chain length distribution) plots (the log CLD method)."4" 7 For the case where termination is wholly by disproportionation or chain transfer, it is possible to show that (eq. 6) applies ... 

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