Copolymer sequences

Item (2) requires that each event in the addition process be independent of all others. We have consistently assumed this throughout this chapter, beginning with the copolymer composition equation. Until now we have said nothing about testing this assumption. Consideration of copolymer sequence lengths offers this possibility. 

Polymers are classified according to their chemical structures into homopolymers, copolymers, block copolymers, and graft copolymers. In a graft copolymer, sequences of one monomer are grafted onto a backbone of the other monomer and can be represented as follows ... 

The full picture of the factors affecting copolymer sequence distribution and their relative importance still needs lo be filled in. 

Copolymer sequence analysis follows the same procedure. A computer program (HIXCO.TRIAD) was previously written for the two-state B/B model-fitting of triad sequence distributions and applied to (unfractionated) propylene-butylene copolymers and... 

Keywords Biopolymers Copolymer sequences Globules Polymers Sequence design... 

Khalatur, P. G. and Khokhlov, A.R. Computer-Aided Conformation-Dependent Design of Copolymer Sequences. Vol. 195, pp. 1-100. 

A similar technique was applied to the synthesis of AB and ABA block copolymers containing random and alternating copolymer sequences [178-180]. For example poly(St-ra dora-MMA)-hZock-poly(VAc), poly(VAc-hZock-poly(St-ran-dora-MMA)-hZock-poly(VAc), poly(St)-foZoc/c-poly(DiPF-aZMBVE), poly(IBVE-aZf-MAn)-hZock-poly(St)-hZock-poly(IBVE-aZf-MAn), poly(St)-hZock-poly(EA)-random-AA), and poly(St)-hZock-poly(EA-ra dora-AA-random-MMA) were synthesized [178]. 

Moore, J. S. Zimmerman, N. W. Masterpiece copolymer sequences by targeted equilibrium-shifting. Org. Lett. 2000, 2, 915-918. 

If this interpretation is correct it means that the copolymer sequence is far from random. 

Nuclear magnetic resonance spectroscopy of dilute polymer solutions is utilized routinely for analysis of tacticlty, of copolymer sequence distribution, and of polymerization mechanisms. The dynamics of polymer motion in dilute solution has been investigated also by protoni - and by carbon-13 NMR spectroscopy. To a lesser extent the solvent dynamics in the presence of polymer has been studied.Little systematic work has been carried out on the dynamics of both solvent and polymer in the same systan. 

As illustrated in Fig. 24, the addition of ethylene during the living polymerization of propylene resulted in rapid increases in both yield and Mn of the polymers. After the rapid increases which required several minutes, yield and lVln increased by a slower rate, identical with that of the propylene homopolymerization. The propylene content in the resulting polymers attained a minimum value several minutes after the addition of ethylene. These results indicate that the second stage of the polymerization with ethylene was complete within several minutes to afford a diblock copolymer, followed by the third stage of propylene homopolymerization leading to the formation of a triblock copolymer. The 13C NMR spectra of the diblock copolymers showed that the second block was composed of an ethylene-propylene random copolymer sequence. 

There is no doubt that polaronic and bipolaronic charge states can be supported in stable form in small oligomers in solution, or incorporated as part of a copolymer sequence. Enhanced x properties can derive from either N, P or BP states as a function of increased delocalization length, and we anticipate several families of copolymers based on the modeling studies discussed in this paper to become available in the near future to test these proposals. 

C nuclear magnetic resonance spectroscopy can be employed to study changes in copolymer sequence distribution brought about by differences in monomer feed profiles. Sequence distributions characteristic of conventional, staged, and power-feed copolymers are easily distinguishable in a model system of the type described here. 

X length of sliding window along copolymer sequence... 

For a statistical analysis of copolymer sequences, different mathematical techniques are used. For mathematically oriented researchers, a copolymer sequence might be considered as a string of symbols whose correlation structure can be characterized completely by all possible monomer-monomer correlation functions. Since the correlations at long distances are typically small, it is important to use the best possible estimates to measure the correlations, otherwise the error due to a finite sample size can be as large as the correlation value itself. 

In the literature, some computer models describing the evolution of copolymer sequences have been proposed [26,28]. Most of them are based on a stochastic Monte Carlo optimization principle (Metropolis scheme) and aimed at the problems of protein physics. Such optimization algorithms start with arbitrary sequences and proceed by making random substitutions biased to minimize relative potential energy of the initial sequence and/or to maximize the folding rate of the target structure. 

Using a molecular-dynamics-based algorithm, the conformation-dependent evolution of model HP copolymer sequences was simulated [70]. The se-... 

Information complexity of copolymer sequences. A common approach to the analysis of the complexity of a system is to use concepts from information theory and information-theoretic-based techniques. 

In general, the aim here is to find a measure capable of indicating how far copolymer sequences generated during the evolutionary process differ from each other and from random or trivial (degenerate) sequences. It turned out that the usual measures of the degree of complexity (based, e.g., on Shannon s entropy and related characteristics) are nonadequate [70]. To overcome this problem, it was proposed to use the so-called Jensen-Shannon (JS) divergence measure [70]. Let us explain how it can be defined. 

---