Chain configuration randomly coiled form

As pointed out by Flory (1956b), a crystalline fiber which is cross-linked in this manner differs from one in which the cross-links are introduced at random when the chains have the random-coil configuration In particular, if the cross-linked helices are melted, the resulting random coils (amorphous state) will have a lower entropy than a polymer which is cross-linked in the random-coil configuration. The entropy decrease, A/S, due to the introduction of the cross-links in the crystalline form reflects the restriction on the distribution of cross-links in the randomly coiled form. The value of A(S, according to Flory (1956b), is... 

Fig. 41. Representation of equilibria between helix and random coil forms. The solid lines represent covalent cross-links and the dashed lines side-chain hydrogen bonds. Species C, I, and A- are crystalline (helix), intermediate, and amorphous (random coil) forms, respectively. Forms C and A may also be regarded as native and denatured forms, respectively. In any given protein molecule the native configuration may actually consist of both helical and randomly coiled regions, i.e., the helices may not be perfect (Scheraga, 1960d).

The excimer of poly(2-napAla) showed an intense circular polarization, indicating that the excimer has a skewed chiral configuration. Therefore, the excimer in poly(2-napAla) may be formed not in the randomly coiled part (e.g., at the termini), where no particular excimer configuration is expected, but in the helix part of the polypeptide. Since the interchromophore distance in the helix part (6,0 A) may be too far to form an excimer, a small distortion of the side-chain and/or main-chain will be necessary to form the excimer. 

The assumption that the contraction process is ideally adiabatic, while perhaps not entirely permissible practically, seems indicated by modern theory of the behavior of molecular chains, which pictures these as undergoing, when freed of restraints, a sort of segmental diffusion, much like the adiabatic expansion of an ideal gas into a vacuum (155). In the case of the molecular chain, it diffuses to the most probable, randomly coiled configuration, which is much less asymmetric, hence shorter, than an initially extended chain. Because rubber most nearly presents this ideal behavior, those fibers which develop increased tension (a measure of the tendency toward assumption of the contracted form) when held isometrically under conditions of increasing temperature (favoring the diffusion ) are said to be rubber-like. Most normal elastic solids upon stress are strained from some stable structure and relax as the temperature is raised. 

Fringed Micelles. These are the crystals formed during crystallization from the melt, and they are the most important in terms of melt crystallization measured with DSC. The elements of all three major conformations, the folded-chain lamellae and the extended-chain crystals, and the random coil configuration of the amorphous phase are present in the fringed micelles. In fringed micelles the polymer chains pass through several crystallites and the amorphous portions surrounding these crystallites. 

We assume that each bond between the two monomeric imits of a polymer has a constant length a and that r, is the bond probability. This enables the configuration of a polymer molecule in the form of a flexible random coil to be described in terms of a Markov chain namely, the probability w R) dR that after N displacements the position of the particle lies between R and R + dR can be described by Eqs. (5.5) and (5.6). All we have to do is to change r, to r in Eq. (5.5) and /, to a in Eq. (5.6) and to rewrite the two equations as follows ... 

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