Application of fractional calculus in the mechanical and dielectric correlation model of hybrid polymer films with different average molecular weight matrices

Rentería-Baltiérrez, F. Y.; Melo, Martín Édgar Reyes; Puente-Córdova, Jesús Gabino; López-Walle, Beatriz

doi:10.1007/s00289-022-04365-1

Cited by 10 publications

(14 citation statements)

References 15 publications

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“…On the other hand, electric fields directly influence molecular groups possessing dipole moments which are reorienting in the electric field during the measurements. Despite these distinctions, the temperature-dependent behavior of dielectric relaxation, as inferred from mechanical results, demonstrates a noteworthy correspondence . In both cases, orientational relaxation is observed.…”

Section: Discussion On the Correlation Between Dielectric And Mechani...mentioning

confidence: 87%

“…Despite these distinctions, the temperature-dependent behavior of dielectric relaxation, as inferred from mechanical results, demonstrates a noteworthy correspondence. 18 In both cases, orientational relaxation is observed. Notably, dielectric measurements offer greater selectivity and a broader frequency range, which enhance the interpretability of the results.…”

Section: Discussion On the Correlation Between Dielectric And Mechani...mentioning

confidence: 94%

“…The correlation model relates the relative permittivity to the elastic modulus and its temperature dependence. In recent research, Renteri ́a-Baltieŕrez et al employed a fractional correlation model to establish a connection between the mechanical and dielectric responses of α-relaxation in polyvinyl butyral 18 and polystyrene. 19 The results showed that the parameters from the fractional models demonstrated a direct proportionality between the temperature and molecular mobility.…”

Section: Introductionmentioning

confidence: 99%

“…It is well-known that both mechanical and dielectric experiments highlighted a similar temperature dependence for the α relaxation, although there were differences in the corresponding relaxation times. 18 Linking both properties to improve polymer film performance in the context of structural relaxation in polymer samples is a challenging task. However, using fractional models, a more accurate description of the mechanical and electrical properties of the polymers was achieved.…”

Section: Introductionmentioning

confidence: 99%

“…They contribute to enhancing our understanding and description of the material behavior under various loads and conditions. It is well-known that both mechanical and dielectric experiments highlighted a similar temperature dependence for the α relaxation, although there were differences in the corresponding relaxation times . Linking both properties to improve polymer film performance in the context of structural relaxation in polymer samples is a challenging task.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Discussion On the Correlation Between Dielectric And Mechani...mentioning

confidence: 87%

Section: Discussion On the Correlation Between Dielectric And Mechani...mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Comparative Study of the Viscoelastic Behavior on PLA Filaments, a Fractional Calculus Approach

Puente-Córdova,

Segura-Méndez

2023

Complex Systems and Their Applications

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An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations

Kumar

2022

Int. J. Appl. Comput. Math

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Fractional order systems of delay differential equations are very advantageous in analyzing the dynamics of various fields such as population dynamics, neural networking, ecology, and physiology. The aim of this paper is to present an implicit numerical scheme along with its error analysis to solve a fractional-order system of delay differential equations. The proposed method is an extension of the L1 numerical scheme and has the error estimate of , where h denotes the step size. Further, we solve various non-trivial examples using the proposed method and compare the results with those obtained by some other established methods such as the fractional Adams method and the three-term new predictor–corrector method. We observe that the proposed method is more accurate as compared to the fractional Adams method and the new predictor–corrector method. Moreover, it converges for very small values of the order of fractional derivative.

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Application of fractional calculus in the mechanical and dielectric correlation model of hybrid polymer films with different average molecular weight matrices

Cited by 10 publications

References 15 publications

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

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

Comparative Study of the Viscoelastic Behavior on PLA Filaments, a Fractional Calculus Approach

An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations

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