Excluded Volume of Coiled Molecules

Real coiled molecules have an external and internal excluded volume. The external excluded volume results from the volume excluded to other molecules it is intermolecular and its influence disappears at infinite dilution. 

The external excluded volume, however, retains a finite value even at infinite dilution. 

On the other hand, the internal excluded volume results from the finite thickness of the macromolecular chain, and its influence is retained, even at infinite dilution. The internal excluded volume can be formally separated into two components. Repulsive forces lead to a positive excluded volume. Attractive forces, in contrast, tend to reduce the volume occupied by two contacting parts of the chain from the value obtained by the summation of their individual volumes the resulting excluded volume is negative. 

Positive and negative excluded volumes can compensate each other in special cases. The coil then behaves as if it consisted of an infinitely thin chain. Thus, it adopts the unperturbed state, with unperturbed dimensions it is an ideal coil with a Gaussian distribution of the chain end-to-end distances (see Section A4-4). 

Because of the internal excluded volume produced, long-range forces cause either an expansion or a contraction of the molecular coil. This change in dimensions can be formally described by an expansion factor, a/ , with respect to the radii of gyration, Rg  

---