A non-ideal solution theory for the mechanics and electrochemistry of charged membranes

Boldini, Alain; Porfiri, Maurizio

doi:10.1038/s41524-022-00827-2

Cited by 5 publications

(14 citation statements)

References 50 publications

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“…Several other details could improve the modelling capability, including (i) a further improvement of the mobility matrix governing the species fluxes [40], (ii) a mechanical law for the membrane that describes its behaviour beyond hyperelasticity, thus enabling stresses in the BLs to relax [53], (iii) accounting for a so far missing enthalpic contribution in the free energy of mixing [54], (iv) the analysis of the membrane small-scale behaviour [55], (v) the implementation of nonideal behaviours in the species interactions [56].…”

Section: Open Issuesmentioning

confidence: 99%

Electrochemo-poromechanics of ionic polymer metal composites: identification of the model parameters

Bardella,

Panteghini

2023

Smart Mater. Struct.

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We propose a procedure to identify the parameters of a model for the multiphysics response of ionic polymer metal composites (IPMCs). Aiming at computational efficiency and accuracy, the procedure combines analytical structural mechanics and fully-coupled electrochemo-poromechanics, additionally resorting to an evolutionary algorithm. Specifically, we consider the finite-deformation electrochemo-poromechanical theory recently developed by our group, which couples the linear momentum balance, the mass balances of solvent and mobile ions, and the Gauss law. Remarkably, the theory constitutively accounts for the cross-diffusion of solvent and mobile ions. This, in conjunction with a generalized finite element implementation that we have recently proposed, allows us to accurately capture the boundary layers of ions and solvent concentrations occurring at the membrane-electrode interfaces, which govern the IPMC behaviour in actuation and short-circuit sensing. Thus, we can explore the IPMC behaviour under external actions consistent with applications and obtain accurate predictions with a reasonable computational cost for wide ranges of model parameters. We focus on experimental data from the literature that are concerned with Nafion-Pt IPMCs of variable membrane thickness and subjected to peak voltage drop across the electrodes ranging from 2 to 3.5 V (under alternating current). Importantly, the considered tests deal with both the tip displacement of cantilever IPMCs and the blocking force of propped-cantilever IPMCs. Overall, the adopted theory and the proposed procedure allow unprecedented agreement between predictions and experimental data, thus marking a step forward in the IPMC characterisation.

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Section: Open Issuesmentioning

confidence: 99%

Electrochemo-poromechanics of ionic polymer metal composites: identification of the model parameters

Bardella,

Panteghini

2023

Smart Mater. Struct.

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“…Then, for single electrolyte solutions, the transport number through ideal anion exchangers (positively charged membranes with total exclusion of cations) is t − = 1, while t + = 1 in the case of ideal cation exchangers (negatively charged membranes with total exclusions of anions); when membrane co-ions are not totally excluded, the transport number of the counter ion in the membrane presents lower values. The determination of ion transport numbers in the membrane allows us to estimate the membrane’s permselectivity, which is a significant characteristic of membranes used in water treatment or the characterization of biological membranes [ 18 ]. Expressions of anionic/cationic permselectivity, P(−)/P(+), are as follows [ 2 ]:

where t − /t + indicate the anion/cation transport number in the membrane, and

correspond to the anion/cation transport number in the solution.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The presence of fixed charges on the surfaces and bulk structures of membranes used in traditional filtration separation processes (Microfiltration, Ultrafiltration, Nanofiltration and Reverse Osmosis) is a significant factor, since it affects the transport of electrolyte solutions and ions/charged particles [ 1 , 2 , 3 ]. Moreover, nowadays, charged membranes have great importance in other applications, such as fuel cells, electrodialysis, ions/organic compound recovery, power generation, food industry, microfluids (nanoporous membranes), analytical and biochemical sensors, etc., as well as models used to understand biological membranes behavior [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ].…”

Section: Introductionmentioning

confidence: 99%

Electrochemical Characterization of Charged Membranes from Different Materials and Structures via Membrane Potential Analysis

Romero,

Gelde,

Benavente

2023

Membranes

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Electrochemical characterization of positively and negatively charged membranes is performed by analyzing membrane potential values on the basis of the Teorell–Meyer–Sievers (TMS) model. This analysis allows the separate estimation of Donnan (interfacial effects) and diffusion (differences in ions transport through the membrane) contributions, and it permits the evaluation of the membrane’s effective fixed charge concentration and the transport number of the ions in the membrane. Typical ion-exchange commercial membranes (AMX, Ionics or Nafion) are analyzed, though other experimental and commercial membranes, which are derived from different materials and have diverse structures (dense, swollen or nanoporous structures), are also considered. Moreover, for some membranes, changes associated with different modifications and other effects (concentration gradient or level, solution stirring, etc.) are also analyzed.

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“…14 Here, we propose a purely continuum model for steric effects, 15 based on the hypothesis of incompressibility of individual components of the electrolyte solution. 16,17 We demonstrate that our formulation is equivalent to models of steric effects derived from statistical mechanics considerations, and can naturally account for ions and solvent molecules of arbitrary sizes. Further, we show how our model can shed light on the behavior of actuators with ionic liquid solvents, that is, where only cations and anions are present in an electroactive polymer.…”

Section: Introductionmentioning

confidence: 96%

What are steric effects? A purely continuum model

Boldini

Porfiri

2023

Electroactive Polymer Actuators and Devices (EAPAD) XXV

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In electrolyte solutions, the application of an external voltage elicits a series of complex microscopic phenomena. When there is no charge transfer between solution and electrodes (non-Faradaic processes), an extremely thin electric double layer is formed on each of the electrodes, screening the bulk of the solution from the external electric field. In the simplest double layer models, the volume of ions in the solution is neglected. For relatively small voltage values, one can easily reach values of concentrations in the double layers over the physical packing limit. To address this issue, steric effects associated with the finite volume of ions are introduced, toward limiting the maximum concentration in the double layers. These effects are often introduced at a microscopic scale, through modifications of the entropy of mixing. However, the macroscopic interpretation of these models remains elusive. Here, we propose a purely continuum model of steric effects in electrolyte solutions. We show that including steric effects at a microscopic scale is equivalent to requiring that each constituent of the solution is incompressible at a macroscopic level. Incidentally, the macroscopic model easily extends steric effects to multiple ions of different sizes, a challenging task for microscopic models. We highlight the consequences of our model on electrolyte solutions and ionic membranes. In particular, we show how our model constitutes a simple mathematical formulation for actuators with ionic liquid solvents. Our effort supports the creation of physics-based models of ionic actuators, facilitating their mathematical description.

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A non-ideal solution theory for the mechanics and electrochemistry of charged membranes

Cited by 5 publications

References 50 publications

Electrochemo-poromechanics of ionic polymer metal composites: identification of the model parameters

Electrochemo-poromechanics of ionic polymer metal composites: identification of the model parameters

Electrochemical Characterization of Charged Membranes from Different Materials and Structures via Membrane Potential Analysis

What are steric effects? A purely continuum model

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