On the Apparent Radius of Gyration of Linear Polymers and the Experimental Determination of the Excluded - Volume Parameter

The structure factor for linear polymers in the 0 state is given by the well-known Debye function. In a good solvent the chain is subject to excluded volume; however, the form of the structure factor still closely resembles that of the Debye function. As a result, one is tempted to interpret the structure factor as a Debye function whose argument is scaled by the radius of gyration of the swollen chain. We present here rigorous and numerical arguments which demonstrate that such an interpretation is legitimate only for small values of the argument. An asymptotic expression for the structure factor suggests a method of measuring the value of the excluded-volume variable 2 by experiment.