Theoretical framework of modeling of ionic EAPs within the Theory of Porous Media

Bluhm, Joachim; Serdas, Serdar; Schröder, Jörg

doi:10.1007/s00419-015-1110-8

Cited by 17 publications

(18 citation statements)

References 39 publications

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“…In order to derive the constitutive relations and the evolution equations, the entropy inequality given in [4] has been considered. The solid phase contains the polymer network ϕ P and the anions ϕ − .…”

Section: Theoretical Modelingmentioning

confidence: 99%

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Modeling the actuation and sensing behavior of an IPMC within the framework of the Theory of Porous Media

Bluhm

Serdas

Schröder

2019

Proc Appl Math and Mech

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Electroactive polymers (EAPs) are considered as smart materials. Therein, a differentiation between an electric and an ionic EAP will be made. In this contribution, in particular the ionic polymer-metal composites (IPMCs) are investigated which belong to the class of the ionic EAPs. These kind of materials act as an actuator and a sensor in variety of applications. The actuation application is given by applying an electrical voltage to the electrodes which instantaneously leads to the relocation of the mobile cations towards the cathode. The sensor application is performed by loading the IPMC mechanically which generates an electrical field. For the prediction of the behavior of this material, the theoretical framework of electrodynamics in combination with the Theory of Porous Media has been taken into account, see [1][2][3]. A numerical example for the 2D sensing behavior is investigated. Theoretical modelingIn general, the structure of an IPMC can be divided into a solid phase ϕ S and an overall fluid phase ϕ F . The solid phase contains the polymer network ϕ P and the anions ϕ − . The overall fluid phase is defined by the constituents of the liquid ϕ L and the mobile cations ϕ + . Attention is paid to the motion functions of both phases, i.e., the solid phase is given by one single motion function (χ S = χ P = χ − ) due to the attachment of the anions to the polymer network. The constituents of the overall fluid phase possess their individual motion function (χ L = χ + ). In order to derive the constitutive relations and the evolution equations, the entropy inequality given in [4] has been considered. The evaluation of the entropy inequality has been performed by neglecting the dynamic effects (x ′′ α = 0) and an isothermal process (Θ α = Θ = const.) is considered. All constituents are assumed to be incompressible (ρ αR = const.). Production terms such asρ α (mass production),ρ α e (charge production),κ α e (electric flux continuity) andm α (moment of momentum) are excluded. The direct production terms of the liquid and the cations are taken into account in order to evaluate the Darcy and the Nernst-Planck equations. The local electric potentials of the constituents are equal (φ α e = φ e ). The influence of the higher order terms such as the gradients of the deformation gradients are neglected. With the given assumptions, the set of field equations and the corresponding constitutive relations are given as below:• Balance of momentum of the mixture • Overall Cauchy stressGauss law for the mixture • Constitutive relation for the electric displacement div d SF e = ρ e d SF e = −ǫ 0 ǫ r grad φ e • Darcy equation • Overall electrical body forceNernst-Planck equation • Overall charge density n F c + m w +S = − D + R Θ { R Θ grad c + m + c + m V + m grad P ρ e = n F F { z + c + m + z − c − m } − c + m M + m b + + z + F c + m grad φ e } • Concentration of the anions

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Section: Theoretical Modelingmentioning

confidence: 99%

“…

Electroactive polymers (EAPs) are considered as smart materials. In order to derive the constitutive relations and the evolution equations, the entropy inequality given in [4] has been considered. In this contribution, in particular the ionic polymer-metal composites (IPMCs) are investigated which belong to the class of the ionic EAPs.

…”

mentioning

confidence: 99%

Modeling the actuation and sensing behavior of an IPMC within the framework of the Theory of Porous Media

Bluhm

Serdas

Schröder

2019

Proc Appl Math and Mech

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“…see [5]. For the evaluation of the above entropy inequality, i.e., deriving constitutive relations and evolution equations, some assumptions will be made.…”

Section: Theoretical Modelingmentioning

confidence: 99%

“…Therein, the Theory of Porous Media (TPM) was used, see [3], while the motion of the liquid and the cations were restricted. In the present contribution, the actuation and sensing behavior of an IPMC is presented within the framework of the TPM, see [5].In order to model the actuation and sensing behavior of an IPMC, the Theory of Porous Media is considered. An IPMC consists of the polymer network ϕ P and the fixed anions ϕ − where both constituents describe the solid phase ϕ S .…”

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confidence: 99%

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Modeling and simulation of electro‐chemomechanical behavior of ionic polymer‐metal composites within the framework of the Theory of Porous Media

Serdas

Bluhm

Schröder

2017

Proc Appl Math and Mech

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Ionic polymer-metal composites (IPMCs) serve as electro-mechanical transducers for actuator and sensor applications, see [1]. Typically, they are sandwiched between two impermeable electrodes comprising the polymer network, the liquid, the fixed anions and the mobile cations. The actuation mechanism takes place by applying an electric potential (voltage) and the mobile cations move towards the cathode. Due to the relocation of the cations (electrostatic and ionic forces), a deformation of the IPMC can be observed. In contrast, the sensing mechanism is performed by applying a mechanical load yielding to a concentration redistribution and generating an electrical potential inside the IPMC. In Leichsenring [2], a parametric study has been carried out for the description of an IPMC. Therein, the Theory of Porous Media (TPM) was used, see [3], while the motion of the liquid and the cations were restricted. In the present contribution, the actuation and sensing behavior of an IPMC is presented within the framework of the TPM, see [5].In order to model the actuation and sensing behavior of an IPMC, the Theory of Porous Media is considered. An IPMC consists of the polymer network ϕ P and the fixed anions ϕ − where both constituents describe the solid phase ϕ S . Furthermore, the overall fluid phase ϕ F contains the liquid ϕ L and the mobile cations ϕ + . Considering the extended balance relations by the electrical quantities within the framework of the TPM, one obtains after some rearrangements the following entropy inequality κ α=1

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Multisensitive Swelling of Hydrogels for Sensor and Actuator Design

et al. 2020

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A main characteristic of hydrogels is their multisensitivity, i.e., the material's capability to respond to multiple stimuli such as temperature, chemical concentration or light. Most modeling approaches to swelling in the literature deal with the monosensitive behavior of hydrogels. Herein, two approaches to the modeling of multisensitive sensors and actuators are proposed: the N‐field method and the trajectory method. They are derived using experimental data of the bisensitive hydrogel [net‐P(AMPS‐co‐NiPAAm)]‐sipn‐PAMPS. It is sensitive to sodium salt concentration and temperature. For the trajectory method, the procedure for the generalized representation of the material behavior is presented. Applying the Temperature Expansion Model, this is implemented in Abaqus and the results of verification simulations are given. The trajectory method is capable of representing the multisensitive behavior of hydrogels. The method is easy to implement in commercial Finite Element tools based on the free‐swelling data of the material. Simulation results of the free swelling are in excellent agreement with the given calibration data. The obtained swelling behavior can be combined with mechanical loads and arbitrary boundary conditions to form more complex setups. The current work allows a deeper understanding of complex multifunctional materials, such as hydrogels, and their application in sensor or actuator devices.

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Theoretical framework of modeling of ionic EAPs within the Theory of Porous Media

Cited by 17 publications

References 39 publications

Modeling the actuation and sensing behavior of an IPMC within the framework of the Theory of Porous Media

Modeling the actuation and sensing behavior of an IPMC within the framework of the Theory of Porous Media

Modeling and simulation of electro‐chemomechanical behavior of ionic polymer‐metal composites within the framework of the Theory of Porous Media

Multisensitive Swelling of Hydrogels for Sensor and Actuator Design

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