Chain Stretching, Salt Effects and Interchain Ordering

2 Chain Stretching, Salt Effects and Interchain Ordering 

Single neutral polymers in a highly dilute solution have coiled conformations with sizes as described by the scaling laws Eq. (2.35) and (2.83) for a theta solvent and a good solvent, respectively. 

To show this, we ask about the balance between the Coulomb repulsion that expands the chain and the entropic rubber elastic forces acting in opposite direction. For an estimate of the total electrostatic energy stored in a chain with a diameter of the order R, we write 

The expression implies that Coulomb interaction energies of the order / AnsosR) arise from the repulsive interaction between the (iV io) ion pairs in the chain. On the other hand, rubber-elastic entropic forces for a polymer chain with an end-to-end distance R lead to an increase of the free energy to a value 

Note that the chain is not completely stretched. The ratio between R and the contour length Na of the chain amounts to 

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