Necessary relationships copolymers

The purpose of this chapter, therefore, is to describe the basic concepts of the statistical analysis of copolymer sequence distribution. The necessary relationships between various comonomer sequence abundances are introduced, along with simple statistical models based on monomer addition probabilities. The relationships between the statistical models and propagation models based on reactivity ratios are discussed. The use of these models is then illustrated by means of selected examples. Techniques for extracting sequence information from in situ NMR measurements are also described. Finally, the statistical analysis of chemically modified polymers is introduced with examples. 

Copolymer number-average sequence lengths and necessary relationships... 

NMR SPECTROSCOPY OF POLYMERS Table 2.1 Some necessary relationships for copolymers [4]... 

The only exception to the A and B sequence numbers not being the same is for very low molecular weight copolymers. Any particular sequence begins and ends with the opposite unit and the only time that this is not true is for the end units of the copolymer chain, where each end unit is only a part of a diad. If one counts from the second unit of a copolymer chain to the next to last unit of any copolymer chain, the number of A sequences will always equal the number of B sequences. Consequently, a necessary relationship (4,14) for these triads is ... 

Due to higher variety of possible structures, copolymers allow a better control of the HOMO LUMO levels necessary to optimize the EL properties of the PPV, compared to homopolymers. Often the optical and electronic properties in copolymers can be finely tuned by simply changing the feed ratio of comonomers (although the structure-property relationship in these systems is even more complex than in homo-PPV polymers). Using different comonomer units, various PPV-based materials with tuned optical and electronic properties have been prepared. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

To estabhsh relationships between different block copolymer phase diagrams and also to facilitate comparison with theory, it is necessary to specify parameters in addition to yN and/. First, asymmetry of the conformation... 

The evaluation of a and p for application of the above rules is accomplished by examining the spectra of a series of copolymers. The chemical shift difference between AAAAA and BBABB pentads affords a measvire of 2(a + p) and the spectra of polymers with either low or high a contents, where only a few pentads are present in appreciable concentration, can be used for the estimation of a and p. The validity of assignments made this way can be checked by determining whether or not relative pentad concentrations evaluated from the spectra obey necessary n-add relationships [28-30]. 

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