Finally, we characterize the relaxation time of the conjugated polymer solution using the extensional retardance measurements. Estimating the relaxation time of our materials is useful as it provides a quantitative measure of the required strain rate necessary to overcome the relaxation of the material. This is described by the Weissenberg number which is a dimensionless value that compares the extensional strain rate of a material versus its relaxation time, ̇ . If relaxation is purely orientational, such as for rods, this dimensionless quantity is also sometimes referred to as the Péclet number. When the strain rate overcomes the relaxation of the material ( ̇ ) orientational ordering can occur through extension and/or alignment. Therefore, a value above the critical value of is necessary to achieve orientational ordering. More precisely, studies on flow-induced alignment and extension of macromolecules have found the critical to range from 0.5 to 1 . To characterize the critical , we subject the solution shown in Figure with exponential fits starting ~10 μm after the solution has already entered the outlet channel. The relaxation times from the decay constants are then plotted against the extensional strain rate for all concentrations in Figure . Interestingly, we find that for all conditions, the relaxation time is not constant but closely follows the inverse relation ⁄ which indicates a value of is followed in all cases (as shown by the dashed line corresponding to exactly ⁄ , or ). As the relaxation time decreases with increasing strain rate this indicates that the material becomes more difficult to align at higher extensional strain rates. This general trend can potentially be explained by a couple of effects. The first is the presence of polydispersity in the fibril aggregates' size. As the extensional strain rate increases, more and more of the shorter fibrils become aligned. Since shorter fibrils have shorter relaxation times the ensemble average relaxation time measured by the retardance decreases. The second is related to the orientation dependence of rotational diffusion related to the tube model described by Doi and Edwards , although the interactions here may be due to hydrodynamic interactions as opposed to entanglements considering the concentrations are just below or at the overlap concentration. As the fibril aggregates align they become less interacting with each other as the volume around a fibril for which neighboring fibrils do not intersect increases. As a result the fibrils are more freely able to rotate and so the rotational diffusion coefficient becomes a function of the fibrils' orientation distribution function. Therefore, as fibrils become more aligned at higher strain rates the rotational diffusion coefficient increases and the orientational relaxation time decreases. This behavior has been observed experimentally by H kansson et al. where cellulose nanofibrils exhibited a higher resistance to alignment at stronger extensional flows. The spatial decays are converted to temporal decays using the centerline velocity. (C) The relaxation time from the temporal decay constant is plotted against the extensional strain rate which closely follows .