Location of Chain Ends

Any discussion of the lamellar structure raises the following question where are the chain ends  

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Keller, A., and D. J. Priest. Experiments on the location of chain ends in mono-layer single crystals of 4>olyethylene. J. Macromol. Sci. Phys. B. 2 479-495, 1968. 

One chosen example is about the investigation of the location of chain ends in the lamellar crystal. By selective deuterium labeling on several segments of both ends of an alkene, Ungar et al. were able to identify the locations of chain ends during crystallization [117, 118]. Figure 1.21 shows SANS curves during isothermal... 

The Gaussian function (7) is shown graphically in Fig. 77. The most probable location of one end of the chain relative to the other is at coincidence, i.e., at r = 0. The density, or probability, decreases monotonically with r, exactly as noted above for the one-dimensional case. Equation (7) likewise is unsatisfactory for values of r not much less than the full extension length nl. The extent of this limitation will be discussed presently. 

In the case of linear polymers, the orientation of a chain segment has been shown to depend on its location along the chain. A more rapid orientation of chain ends has been evidenced. 

Finally we should consider the location of the chain ends. On physical groimds it can be argued that a chain with its end near a surface suffers a smaller loss of entropy by virtue of the surface than does a chain with a middle segment at the surface, so that the density of chain ends at the surface should be somewhat enhanced. This picture is supported by simulations for example in the variable density self-consistent mean field study of PDMS of relative molecular mass 3270 already cited, more than 50% of the population of the outermost layer of the polymer consisted of chain ends, even though chain ends represented only 17% of the total mass. On the other hand experimental evidence for chain-end segregation is much more equivocal. The reason for this is that, in order to detect such segregation, it is necessary experimentally to label the end of the chain in some way so that a surface analysis technique may be used to detect an excess of the ends. However, as we shall see in chapter 6, even a very small substitution at the end of a polymer chain may lead it to be... 

High or low molecular weights are also reflected in the concentration of chain ends in the bulk phase. The chain ends often exhibit quite different behaviors from those monomers locating in the middle of polymer chains. In the following are listed the so-called chain-end ejfects. 

The state of the ideal rubber can be specified by the locations of all the junction points, ij, and by fce end-to-end vectors for all tire chains connecting the junction points,. The first postulate of the statistical theory of rubber elasticity is that, in the rest state with no external constraints, the distribution fimction for the set of chain end-to-end vectors is a Gaussian distribution witii a mean-squared end-to-end distance that is proportional to the molecular weight of the chains between jimcnons ... 

The effect of annealing of the crystalline polymer on the chain ends located of the surface can be explained in two different ways. One is that the heat treatment, leading to a thickening of the lamella, would move the surface chain end into the inside of the crystallite. The other explanation would be that the heat treatment results in the exclusion of chain ends from the crystallite. 

The second hypothetical step is the assignment of chain ends to the locations of the cross-linkages within the deformed polymer as is required by Eq. (8.34). The entropy change for the hrst step is given by... 

To establish the existence of possible transfer reactions, a direct method can be used which consists in characterizing molecular groups resulting from tfansfer and which are necessarily located at chain ends. Because of their low proportion, it is necessary to utilize extremely sensitive techniques and, for example, H- or " C-labeled molecules. 

In all arm-first methods a living monofunctional polymer of known length and low polymolecularity serves as a precursor. Subsequently, the active sites located at chain end can be used in one of two different ways ... 

The longest continuous chain that contains the —CH group provides the base name for aldehydes The e ending of the corresponding alkane name is replaced by al and sub stituents are specified m the usual way It is not necessary to specify the location of O... 

We desire to use the probability function derived above, so we recognize that the mass contribution of the volume element located a distance r from an axis through the center of mass is the product of the mass of a chain unit mp times the probability of a chain unit at that location as given by Eq. (1.44). For this purpose, however, it is not the distance from the chain end that matters but, rather, the distance from the center of mass. Therefore we temporarily identify the jth repeat unit as the center of mass and use the index k to count outward toward the chain ends from j. On this basis, Eq. (1.49) may be written as... 

It has been hypothesized that cross-linked polymers would have better mechanical properties if interchain bridges were located at the ends rather than the center of chains. To test this, low molecular weight polyesters were synthesizedf... 

The location of the nitrogen end of the ethanamine chain in the phenanthrene nucleus has been discussed recently by Holmes et and... 

Schopf has also obtained direct evidence for the location of th carbon end of the ethanamine chain by submitting dihydrocodeinoneoximr to a Beckmann rearrangement. This process, the steps in which an illustrated by partial formal for ring III, should provide an aldehydt (XLVc) if the oxime is correctly represented by the Gulland and Robinsoi formula (XLVb) and a ketone (XLVIc) if it has the structure (XLVIb required by the Wieland and Kotake formula. 

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