A fractional calculus approach to study mechanical relaxations on hybrid films of Fe₂O₃ nanoparticles and polyvinyl butyral

Abstract

Polymeric hybrid magnetic films composed of iron oxide nanoparticles and polyvinyl butyral (PVB) were synthesized and studied by a fractional calculus approach. Iron oxide nanoparticles were synthesized in situ from a polymeric hybrid precursor composed of Fe⁺² and PVB. These polymeric hybrid magnetic films (PVB/Fe₂O₃) could carry out functions as actuators or sensors in electronic or mechatronic devices. But, for this purpose, it is required a study of the mechanical relaxation processes displayed in the polymer matrix. The synthesis of iron oxide nanoparticles into PVB was confirmed by HRTEM, XRD and FTIR analysis. The main goal of this work is the study of the effect of iron oxide nanoparticles on the α-relaxation for three PVB samples with a different mass average molar mass. Experimental measurements of the complex modulus, $\left( {E^{*} = E^{{\prime }} + iE^{\prime \prime } } \right)$, were obtained by dynamic mechanical analysis (DMA) to identify the α-relaxation for each analyzed sample. Experimental isochronal curves of $E^{\prime }$ and $E^{\prime \prime }$ were compared with theoretical curves of $E^{\prime } \left( T \right)$ and $E^{\prime \prime } \left( T \right)$ computed by the fractional Zener model (FZM). An agreement between experiments and fractional model predictions has been achieved. The effect of fractional parameters ($a$ and $b$) of the FZM was related to molecular motions associated with this relaxation process. The cooperative motions of chains segments were observed in all analyzed samples, and $b > a$; this means that when temperature increases, the molecular mobility (energy dissipation) also increases. The matching between PVB matrix and the Fe₂O₃/PVB films showed that Fe₂O₃ nanoparticles decreases the molecular mobility of PVB; this effect is more pronounced at temperatures above $T_{\text{g}}$.