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

Rentería-Baltiérrez, F. Y.; Melo, Martín Édgar Reyes; López-Walle, Beatriz; García-Loera, A. F.; González-González, V.

doi:10.1007/s10973-019-08369-4

Cited by 6 publications

(5 citation statements)

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“…In the case of relaxation phenomena, the fractional order of a fractional integral is an indication of the remaining or preserved energy of a signal passing through a viscoelastic system (partial energy dissipation). 14 Through the application of fractional calculus, two innovative fractional elements have been developed: the spring-pot for mechanical properties and the cap-resistor to describe dielectric behaviors. 27 The cap-resistor (Figure 1a) combines the responses of an electric capacitor and a resistance (Ohm's law) by a differential operator of fractional order a, where 0 ≤ a ≤ 1.…”

Section: Models: Fractional Modelingmentioning

confidence: 99%

“…As depicted in Figure 3, the MFM is characterized by three mechanisms. 14 The first spring-pot, b 1 , is associated with the viscoelastic response observed at a low temperature. The second springpot, b 2 , is associated with the viscoelastic response occurring at a high temperature.…”

Section: Mechanical Fractional Model (Mfm)mentioning

confidence: 99%

“…The mechanical fractional model (MFM) was obtained by substituting the dashpot in the classical Zener model with two spring-pots, and its fractional equation is expressed in eq . As depicted in Figure , the MFM is characterized by three mechanisms . The first spring-pot, b 1 , is associated with the viscoelastic response observed at a low temperature.…”

Section: Models: Fractional Modelingmentioning

confidence: 99%

“…These models extend traditional concepts of derivatives and integrals, which are well-established mathematical operations, to include noninteger orders and therefore makes it possible to take into account the nonlinearities of behavior. In the case of relaxation phenomena, the fractional order of a fractional integral is an indication of the remaining or preserved energy of a signal passing through a viscoelastic system (partial energy dissipation) . Through the application of fractional calculus, two innovative fractional elements have been developed: the spring-pot for mechanical properties and the cap-resistor to describe dielectric behaviors…”

Section: Models: Fractional Modelingmentioning

confidence: 99%

“…Moreover, the temperature-dependent character of structural transitions highlights the correlation between the dynamic response of the polymer and its relaxation time loss during these relaxation processes reflects the rate at which a portion of energy is dissipated as the polymer undergoes structural changes. 14 However, the complicated nature of these relaxation processes makes traditional calculus-based models inadequate for their analysis. 15 Classical models are based on traditional calculus and generally presume that relaxation times remain constant.…”

Section: Introductionmentioning

confidence: 99%

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Correlation between Mechanical and Dielectric Dynamic Behavior Using Fractional Models: Application to Polylactic Acid

Fakraoui,

Arous,

Royaud

et al. 2024

ACS Appl. Polym. Mater.

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The complementarity between mechanical and dielectric properties is crucial, as it facilitates a comprehensive understanding of material behavior, enabling optimal using. This work mainly focuses on the use of broadband dielectric spectroscopy (BDS) and dynamic mechanical analysis (DMA) to investigate the electrical and mechanical aspects of polymer relaxation phenomena. We have opted to conduct experiments on polylactic acid (PLA) due to its well-known use in various applications, attributed to its notable properties and essential relaxation processes. Differential scanning calorimetry (DSC) was used to identify characteristic temperatures for distinguishing different relaxation processes in the polymer. The obtained experimental results were analyzed using the mechanical fractional model (MFM) and the dielectric fractional model (DFM). The fractional model parameters confirm that higher temperatures correlate with increased molecular mobility within macromolecular chains, especially in relaxation processes associated with the glass transition. Subsequently, a fractional calculus approach is employed to investigate the correlation between the complex modulus and complex permittivity of PLA. This correlation model enables the prediction of the real permittivity ε′(T) curve from the real modulus E′(T) data, providing valuable insights into PLA behavior. These results suggest that the correlation model has the potential to predict the dielectric behavior of a polymer based on its mechanical results and vice versa.

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Section: Models: Fractional Modelingmentioning

confidence: 99%

Section: Mechanical Fractional Model (Mfm)mentioning

confidence: 99%

Section: Models: Fractional Modelingmentioning

confidence: 99%

Section: Models: Fractional Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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