Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights

The diffusion process in the molten state at a polymer/polymer interface of symmetrical and model bilayers has been investigated using a small-amplitude oscillatory shear measurement. The polymers employed in this study were poly (vinylidene fluoride) (PVDF) and poly (methyl methacrylate) (PMMA) of varying molecular weights and polydispersities. The measurements were conducted in the linear viscoelastic regime (small deformations) so as to decouple the effect of flow from the diffusion. The focus of this paper has been to investigate the effects of healing time, angular frequency (ω), temperature, and molecular weight on the inter-diffusion and the triggered interphase between the neighboring layers. The kinetics of diffusion, based on the evolution of the apparent diffusion coefficient (D _a) versus the healing time, was experimentally obtained. The transition from the non-Fickian to the normal Fickian region for the inter-diffusion at the interface was clearly observed, qualitatively consistent with the reptation model, but it occurred at a critical time greater than the reptation time (τ _rep). In non-Fickian region, effects of frequency and temperature were studied with regard to the ratio of the apparent diffusion coefficient to the self-diffusion coefficient (D _a/D _s). The D _s determined in the Fickian region was found to be consistent with Graessley’s model as well as with the literatures. And the dependence of the D_s on the frequency agreed well with the Doi–Edwards theory, in particular, scaling as \(D_{\rm s} \sim \omega^{1/2}\) at ω > 1/τ _e and \(D_{\rm s} \sim \omega^{0}\) at ω < 1/τ _rep. Our experimental results also confirmed that the dependence of the D _s on the temperature for PMMA and PVDF can be well described by the Arrhenius law. Moreover, blends of PMMAs have been proposed in order to be able to change the \(\overline M_\emph{w} \). The rheological investigations of these corresponding bilayers rendered it possible to monitor the effect of \(\overline M_\emph{w} \) on the diffusion process. The obtained results gave \(D_{\rm s} \sim \overline M_\emph{w}^{-1}\), thus corroborating some earlier studies and some experimental results recently reported by Time-Resolved Neutron Reflectivity Measurements. Lastly, the thickness of the interphase and its corresponding viscoelastic properties could be theoretically determined as a function of the healing time.