Correlation between the mechanical and dielectric responses in polymer films by a fractional calculus approach

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

doi:10.1002/app.49853

Cited by 11 publications

(25 citation statements)

References 21 publications

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“…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. In this way, the correlation model successfully related the mechanical and dielectric properties of polymers.…”

Section: Introductionmentioning

confidence: 94%

“…On the other hand, the relaxation times, mechanical or electrical, for cooperative motions, τ cooperative , is given by the following law in a temperature range T 0 < T < T*. 19 Ä…”

Section: Correlation Between Dielectric and Mechanical Propertiesmentioning

confidence: 99%

“…where τ 0 is a pre-exponential factor with values within the range of 10 −16 s ≤ τ 0 ≤ 10 −13 s; values in the vicinity of the upper limit correspond to molecular vibrational times, and those near to the lower limit may be rationalized as additional entropy contributions. 19 E a is the activation energy corresponding to elementary movements of cooperative mobility. k B is the Boltzmann constant, and T is the absolute temperature.…”

Section: Correlation Between Dielectric and Mechanical Propertiesmentioning

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: Introductionmentioning

confidence: 94%

“…On the other hand, the relaxation times, mechanical or electrical, for cooperative motions, τ cooperative , is given by the following law in a temperature range T 0 < T < T*. 19 Ä…”

Section: Correlation Between Dielectric and Mechanical Propertiesmentioning

confidence: 99%

Section: Correlation Between Dielectric and Mechanical Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Чаще и проще проводить анализ полимеров экспериментальным путем, что, как правило, сопровождается использованием дорогостоящей техники и достаточно масштабного и затратного технологического процесса. Таким образом объясняется актуальность использования неэмпирических методов на основе математических, информационных и химических подходов, а именно их прогностическая функция [2][3][4].…”

Section: Introductionunclassified

Optimization of a Multicomponent Polymer Composition Using a Fuzzy Mathematical Model

Гермашев

Feoktistov

Derbisher

et al. 2022

Applied Mathematics and Control Sciences

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Some aspects of the analysis of polymer composite materials as complex systems are considered. In this case, the system is presented as a combination of one polymer matrix and several active additives. Within the framework of this work, the composition is assumed to be unchanged, and the properties of the composition are controlled by changing the concentration of the ingredients. In work, a mathematical model was developed that calculates the optimal content of components to improve specific properties of the polymer composition. Obtaining such a model is partly hampered by complex interactions between components, but a solution was obtained within the framework of one specific composition. Nevertheless, it was impossible to transfer these results to other compositions in this case, and it was impossible to obtain a general mathematical model for an arbitrary composition. Therefore, to solve this problem, a black-box model was used in this work. The main methods for studying polymer compositions are presented; their systematization is considered according to the principle of controlling properties at different stages of material synthesis. In this work, a variant of controlling the properties of the polymer composition using active additives was used. The urgency of the problem related to the development of methods for assessing the properties and control of the latter by ranking the concentrations of the ingredients of the polymer matrix has been substantiated. As a result, a mathematical model for optimizing the composition of the polymer composition was obtained. It takes into account the positive and the negative influence of the ingredients on the entire composition of the polymer matrix. Also, computational experiments were carried out to find the optimal concentration of active additives in the composition of the polymer composition under conditions of pair interaction of additives. The model is presented and solved using a quadratic programming problem using a specific example. Different cut-off values were used for the content of the ingredients. The results obtained clearly demonstrate the dependence of the properties of a chemical system on the concentration of specific ingredients. Based on the results of two computational experiments under different boundary conditions, the optimal concentration was calculated for the full manifestation of two properties. The paper also presents a vector of further actions, prospects for improving the model, and possible areas of application of this model.

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“…In the literature, an interesting topic is to find the correlation between viscoelastic and dielectric responses [19], both of which can be regarded as intermediate states. The mechanical characterization of viscoelasticity lies between pure elasticity and viscosity, which are the zero-and first-order derivatives of the strain rate.…”

Section: Introductionmentioning

confidence: 99%

Application of Fractional Calculus to Modeling the Non-Linear Behaviors of Ferroelectric Polymer Composites: Viscoelasticity and Dielectricity

Meng

2021

Membranes

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Ferroelectric polymer composites normally show non-linear mechanical and electrical behaviors due to the viscoelastic and dielectric relaxation of polymer matrixes. In this paper, a fractional calculus approach is used to describe the non-linear behavior of ferroelectric polymer composites from both viscoelastic and dielectric perspectives. The fractional elements for viscoelasticity and dielectricity are “spring-pot” and “cap-resistor”, which can capture the intermediate properties between spring and dashpot or capacitor and resistor, respectively. For modeling the viscoelastic deformation, the “spring-pot” equation is directly used as the fractional mechanical model. By contrast, for the dielectricity of ferroelectric polymer composites, which is usually characterized by dielectric constants and dielectric losses, the “cap-resistor” equation is further formulated into the frequency domain by Fourier transform to obtain the fractional order dielectric model. The comparisons with experimental results suggest that the proposed models can well describe the viscoelastic deformation as well as the frequency dependence of the dielectric constant and dielectric loss of ferroelectric polymer composites. It is noted that the fractional order dielectric model needs to be separated into two regions at low and high frequencies due to the polarization effect. Additionally, when the dipole relaxations occur at higher frequencies, the proposed model cannot describe the rise of the dielectric loss curve.

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Correlation between the mechanical and dielectric responses in polymer films by a fractional calculus approach

Cited by 11 publications

References 21 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

Optimization of a Multicomponent Polymer Composition Using a Fuzzy Mathematical Model

Application of Fractional Calculus to Modeling the Non-Linear Behaviors of Ferroelectric Polymer Composites: Viscoelasticity and Dielectricity

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