Long-chain hypothesis

From the mass balance for each monomer type, assuming that long chains are formed (long chain hypothesis or LCH), the monomers are mainly consumed in propagation reactions ... 

For a two-monomer system, the polymerization rates of the two monomers, assuming long-chain hypothesis, are written as... 

Assuming no inflow of polymer into the reactor and the long-chain hypothesis, the steady-state values for DPn and DPw in the absence of LCB = 0) are given by Eq. (83). LCB and reaction with terminal double bonds broaden the MWD significantly [81]. 

Derivation of eqn (1.15) neglect other side-reactions such as transfer to monomer and p-scission (see below). By implementing the so-called long-chain hypothesis ( p CM 2 t CMCR + i cspr) into eqn (1.16) yields a simplified expression for the fraction of MCRs ... 

FAAH was originally purified and cloned from rat liver microsomes and is able to catalyse the hydrolysis of anandamide and 2-AG, in addition to other long-chain fatty acid amides [25]. Studies into the structure and role of this enzyme have generated interest in the potential therapeutic applications of FAAH inhibitors [26-28]. FAAH knock-out mouse brains contained 15-fold higher levels of anandamide than their wild-type counterparts and these animals have also been shown to be more responsive to exogenously administered anandamide [29]. These animals also showed a reduced response to painful stimuli, supporting the hypothesis that FAAH inhibition may provide novel analgesics. Levels of 2-AG were not elevated in the FAAH knock-out animals, apparently due to the existence of alternative metabolic fates for this compound [30]. 

He even proposed the existence of polyvalent atoms producing "sponge or net like" molecular mass in 1878. Towards the end of his career, he advanced the hypothesis that natural organic substances-those most closely associated with life, proteins, starch, and cellulose-may consist of very long chains, and derive their special properties from this structure. 

Experimental verification of Collie s hypothesis came many years later when isotopic hydrogen and carbon (2H, 3H, 13C, and 14C) became available. Tracer studies showed that long-chain fatty acids are made by plants and animals from CH3CO units by successively linking together the carbonyl group of one to the methyl group of another (K. Bloch and F. Lynen, Nobel Prize, 1964). 

An even more remarkable prediction was made by Crick and Watson (1953) of the structure of the vast molecules, such as that of deoxyribonucleic acid (DNA), which are concerned with the maintenance and transference of genetic information. These molecules contain very long chains of nucleotide units linked by covalency bonds. (A nucleotide consists of the residue of a sugar, often ribose or deoxyribose, one of a purine or pyrimidine base, and one of phosphoric acid, bonded together.) The Crick-Watson hypothesis was that the macromolecule consists of two such chains,... 

These equations have remarkable consequences if we add the so-called fixed point hypothesis. For a very long chain we can apply the mapping repeatedly, always rescaling by a factor of A. In the limit of an infinitely long... 

In the hypothesis of long-chain polymerization the distribution function is proportional to the amounts of %-rners, Rx or Px. Accordingly, the moments of discrete distribution for live and dead polymer species may be defined by the relations ... 

The data in Table II demonstrate that the effectiveness for poly (vinyl chloride) stabilization of dibutyltin salts of maleic acid or monoesters of maleic acid is caused by a high rate of reaction with allylic chloride moieties. Thus, it is not necessary to postulate, as has been done several times in the literature, that these compounds are effective because they are dieneophiles and therefore capable of disrupting the long chains of unsaturation responsible for color formation. It is gratifying that the performance of the maleate stabilizers is consistent with the Frye-Horst substitution hypothesis. 

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