Correlations between chain ends

Fisher and Hiley8 calculated mean square end-to-end distances ((rN - r0)2 in terms of the parameter w = exp( — PJ) by using data published by Orr. The 

A better definition of the Flory temperature Te is given in Chapter 14. 

The calculations have been made for values of w belonging to the interval 0 and 2.5. For large values of N, we expect to find for RN a relation of the form 

The chains being rather short, the exponents vN(w) fluctuate strongly with the parity of N. Fisher and Hiley8 remedied this defect by using the values 

It appears that, for a simple cubic lattice, there exists a value wF = 1.48 0.06 for which v(w) = 1/2, which indicates that, in this case, the chain is Brownian (see Fig. 4.7). The corresponding temperature is given by the equality 

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Asymptotic properties of correlations between chain ends Fisher s result... 

Thus, the probability law associated with the correlations between chain ends is Gaussian. In particular, the exponent v has the value v = 1/2 and we find... 

The hydrolytic depolymerisation of PETP in stirred potassium hydroxide solution was investigated. It was found that the depolymerisation reaction rate in a KOH solution was much more rapid than that in a neutral water solution. The correlation between the yield of product and the conversion of PETP showed that the main alkaline hydrolysis of PETP linkages was through a mechanism of chain-end scission. The result of kinetic analysis showed that the reaction rate was first order with respect to the concentration of KOH and to the concentration of PETP solids, respectively. This indicated that the ester linkages in PETP were hydrolysed sequentially. The activation energy for the depolymerisation of solid PETP in a KOH solution was 69 kJ/mol and the Arrhenius constant was 419 L/min/sq cm. 21 refs. 

A correlation has been reported between the photooxidizability of several PVC samples and the number of long-chain ends in these polymers (45). The mechanistic significance of this result is rather uncertain, as the authors (45) do not state how the number of long-chain ends was varied. Nevertheless, it is perhaps worth noting that, in the absence of added chain-transfer agents, a major fraction of the long-chain ends should consist of allylic chloride groups (46,47). 

Simulation programs for the ESR line shapes of peroxy radicals for specific models of dynamics have been developed for the study of oxidative degradation of polymers due to ionizing radiation [66]. The motional mechanism of the peroxy radicals, ROO, was deduced by simulation of the temperature dependence of the spectra, and a correlation between dynamics and reactivity has been established. In general, peroxy radicals at the chain ends are less stable and more reactive. This approach has been extended to protiated polymers, for instance polyethylene and polypropylene (PP) [67],... 

It is not possible to give here a detailed account of, nor to take issue with, every aspect of the interpretation which the authors give to their results. Their main conclusion is that the inverse correlation between DP and conductivity proves that the principal chain breaking reaction must be a bimolecular termination between free cations at the growing end of the chain and free anions in the solution. However, the arguments which lead to... 

Detailed analysis of defect configurations in the cylinder phase and of their evolution allowed us to conclude that representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or of classical disclinations with incorporated alternative, non-bulk structures with planar symmetry. Further, block copolymers show a strong correlation between the defect structure and chain mobility on both short- and long-term time scales. 

N is the number of skeletal bonds in one chain and k is the Boltzmann constant while b is the mean skeletal bond. The mean square end-to-end distance, Nb2, is also referred to as the square of the Gaussian correlation length between the chain ends, o(N) it reflects the effect of linkage of chemical units. The previous relationship between the force f and the extension r is extended to any real chain submitted to a small elongation provided the correlation length, o(N), includes the stiffness property of the polymer o(N)2= A.KNb2 XK is referred to as a persistence length. The related reduction of entropy is expressed as ... 

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