Polymeric Materials Are Elastic

Rubber is elastic, and gooey liquids such as raw eggs are viscoelastic, because polymer molecules have many conformations of nearly equal energy. Stretching the polymer chains lowers their conformational entropy. The chain retract to regain entropy. The entropy is also lowered when polymers become compact, as w hen proteins fold or when DNA becomes encapsulated within virus heads. The simplest molecular description of polymer elasticity is the random-flight model. 

We consider a polymer chain to be a cormected sequence of N rigid vectors, each of length b. For now, each vector represents a chemical bond, but starting on page 612 we consider other situations in which each vector can represent a virtual bond, a collection of more than one chemical bond. 

There are different ways to characterize the size of a polymer chain. The contour length L is the total stretched-out length of the chain. 

For any vector, you can always consider the x, y, and z components individually. The X component of the end-to-end vector is 

Because the mean value of the end-to-end vector is zero ((rv = 0), (r ) doesn t contain useful information about the size of the molecule. The rman square end-to-end length (r-) or (r ) is a more useful measure of molecular size. It is related to the radius of gyration Rg by = r )l6 for a linear chain [1]. We won t prove that relationship here. The radius of g ration, which is alway s positive, is a measure of the radial dispersion of the monomers. We use (r ) instead of Rg because the math is simpler. 

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To understand why polymeric materials are elastic, you need to know more than just the first and second moments, (r> = 0 and (r-) = Nb you need the full distribution function of the end-to-end lengths. 

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