https://doi.org/10.1351/goldbook.12265
Equation relating intrinsic viscosity, \(\eta\), and molar mass, \(M\), to the mean-square radius of gyration, with \[[\eta]M = \mathit{\Phi}^{\prime}\!\lt\!s^{2}\!\gt^{3/2}\] where \(\mathit{\Phi}^{\prime}\) is a parameter the value of which depends on the molar-mass distribution, macromolecular constitution, and chain expansion.
Notes:
- \([\eta]M/N_{\rm{A}}\), where \(N_{\rm{A}}\) is the Avogadro constant, is the equivalent hydrodynamic volume in viscous flow, \(V_{\eta}\), with \(V_{\eta} = 4\uppi r_{\eta}^{3}/3\), Hence, the Flory–Fox equation is consistent with the Kirkwood–Riseman theory and the Flory–Fox assumption. (See Notes to Kirkwood–Riseman theory and Flory–Fox assumption.)
- For a solution in the theta state, \(\mathit{\Phi}^{\prime}\) is denoted \(\mathit{\Phi}_{\uptheta}^{\prime}\) and its value is given by the Kirkwood–Riseman theory, with \(\mathit{\Phi}_{\uptheta}^{\prime} = \pu{4.22E22 mol-1}\).
- The Flory–Fox equation is sometimes written in terms of \(\lt\!r^{2}\!\gt\), the mean-square end-to-end distance, instead of \(\lt\!s^{2}\!\gt\), with \[[\eta]M = \mathit{\Phi} \lt\!r^{2}\!\gt^{3/2}\] where \(\mathit{\Phi} = \mathit{\Phi}^{\prime}/6^{3/2}\). The latter equality assumes that \(\lt\!r^{2}\!\gt = 6\!\lt\!s^{2}\!\gt\), which is only exactly true in the theta state. In this case, \[[\eta]M = \mathit{\Phi}_{\theta}\!\lt\!r^{2}\!\gt^{3/2}\] where \(\mathit{\Phi}_{\theta} = \mathit{\Phi}_{\theta}/6^{3/2} = \pu{2.87E21 mol-1}\).
- \(\mathit{\Phi}\) is known as the viscosity function or the Flory function.