Stretching a Polymer Chain The Entropic Spring

The change in free energy of a polymer chain on increasing the end-to-end distance by dR can be given by 

FIGURE 4.12 The force it takes to stretch out a polymer derives from the associated decrease ita chain entropy. 

The idea here is that as the polymer is stretched to an increasing magnitude of R, there are a decreasing number of conformational states capable of producing that R value. The implied decreased disorder in the system means that the entropy of the chain decreases as the chain is stretched. The entropy of an ideal chain of size R is defined by the formula 

The derivation for this formula is beyond the scope of this book but can be found in Polymer Physics (p. 66) by Rubenstein and Colby.  

If we have the probability of a particular R, we can find the change in entropy associated with stretching the polymer chain to a different R. 

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