Chain Configuration

In polymers made of dis-symmetric monomers, such as, for example, poly(propylene), the stmcture may be irregular and constitutional isomerism can occur as shown in figure C2.1.1(a ). The succession of the relative configurations of the asymmetric centres can also vary between stretches of the chain. Configuration isomerism is characterized by the succession of dyads which are named either meso, if the two asymmetric centres have the same relative configurations, or racemo if the configurations differ (figure C2.1.1(b )). A polymer is called isotactic if it contains only one type of dyad and syndiotactic if the dyad sequence strictly alternates between the meso and racemo fonns. 

The Alexander model and its descendants impose strong restrictions on the allowed chain configurations within the tethered assembly. The equilibrium state thus found is subject to constraints and may not attain the true minimum free energy of the constraint-free system. In particular, the Alexander model constrains the segment density to be uniform and all the chain ends to be at the same distance from the grafting surface. Related treatments of curved systems retain only the second... 

Chart V. Choice of parent in branched-chain monosaccharides. In the first names given for examples 1,3 and 4, side-chain configuration is specified by use of R and S. This approach is generally preferred in all but the simplest cases, as less open to misinterpretation. 

FIGURE 7 Tyrosine-derived poly(iminocarbonates) used to evaluate the effect of various side chain configurations on the physicomechan-ical properties of the resulting polymers. 

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Let us now take the average over all chain configurations. Indicating this average by the bar superscript, we have... 

Equation (10) directs attention to a number of important characteristics of the molecular expansion factor a. In the first place, it is predicted to increase slowly with molecular weight (assuming t/ i(1 — 0/T) >0) and without limit even when the molecular weight becomes very large. Thus, the root-mean-square end-to-end distance of the molecule should increase more rapidly than in proportion to the square root of the molecular weight. This follows from the theory of random chain configuration according to which the unperturbed root-mean-square end- o-end distance is proportional to (Chap. X), whereas /r = ay/rl. 

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