Polymer full-contour length

A polymer stretched out to its full contour length is only one of the myriad conformations possible for a polymer at temperatures above Tg, or if the polymer is entirely crystalline. The chain length is expressed statistically as the RMS distance, which is only a fraction of the contour length. 

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

The exponent a is a measure of the interaction of the solvent and polymer. It is a function of the shape of the polymer coil in a solution, and usually has a value between 0.5 (for a randomly coiled polymer in a 0 solvent) and 0.8 (when the polymer coils expand in good solvents). The a value is 0 for spheres, about 1 for semicoils, and is between 1.8 and 2.0 for a rigid polymer chain extended to its full contour length. The proportionality constant K is characteristic of the polymer and solvent. The constants K and a are the intercept and slope, respectively, of a plot of log [ 7] versus log Af of a series of fractionated polymer samples. Viscosity average molecular weights he between those of the corresponding... 

Contour length the fully extended length of a polymer chain, equal to the product of the length of each repeat unit (/) times the number of units) (or mers, n), thus the product nl is the full contour length. 

Although the Wiener integral formulation for the distribution functions of flexible polymer chains rests upon general considerations of random walks and Brownian motion, it is easily introduced, heuristically, through the concept of an equivalent chain. In this section, only those flexible polymer chains are considered which are composed of equivalent gaussian links. Here L is the maximum contour length of the real chain at full extension, and (R ) for the equivalent chain is taken to be that for the real chain. Thus we have... 

We now pull the two ends of the skeletal linear chain to its full extension (Fig. 1.5). In a vinyl polymer, the chain is in Vi-trans conformation. The distance between the ends is called the contour length. The contour length (L ) is proportional to DP or the molecular weight of the polymer. In solution, this fully stretched conformation is highly unlikely. The chain is rather crumpled and takes a conformation of a random coil. 

An elegant statistical mechanical approach to the dimensions of flexible polymers was developed by Landau and Lifschitz [4], who considered a long, flexible thread of contour length L and positive bending energy (Jxm in SI units). The lowest energy state is when the thread is straight, but thermal fluctuations allow it to bend and wobble in a complex way that tends to shrink below the full... 

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