Simulation of flux during electro-membrane extraction based on the Nernst–Planck equation

Gjelstad, Astrid; Rasmussen, Knut; Pedersen‐Bjergaard, Stig

doi:10.1016/j.chroma.2007.08.057

Cited by 213 publications

(124 citation statements)

References 23 publications

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“…This has been verified experimentally in several EME papers, 10,20,[23][24][25]27,29,[31][32][33][34] where recoveries have been found to increase with increasing voltage up to a certain level. The latter point out that extraction is limited by other factors than the voltage at high voltages, and deviations from Eq.…”

Section: Performance Of Emementioning

confidence: 62%

“…(1), the ion balance and the temperature also affect the flux of analyte in EME. This has also been verified experimentally, 34 but both parameters are not very powerful in optimization of EME.…”

Section: Performance Of Emementioning

confidence: 76%

“…EME therefore provides very fast extractions as compared to HF-LPME. 20,34 The principal reason for this is that analytes are transferred by electro-kinetic migration across the SLM in EME as compared to passive diffusion in HF-LPME. The consumption of organic solvent is low, and typically only 10 to 20 μl of solvent is used per Fig.…”

Section: Performance Of Emementioning

confidence: 99%

“…25 7 Theoretical Understanding and Optimization of EME EME has also been discussed from a theoretical point of view. 34 The theoretical model, which was based on a modification of the Nernst-Planck equation, described how the potential difference across the SLM (Δf), the ion balance across the SLM (χ), and the absolute temperature (T) influenced the flux of a charged analyte (Ji) through the SLM by the following equation:…”

Section: Performance Of Emementioning

confidence: 99%

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Electromembrane Extraction from Biological Fluids

et al. 2011

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Section: Performance Of Emementioning

confidence: 62%

Section: Performance Of Emementioning

confidence: 76%

Section: Performance Of Emementioning

confidence: 99%

Section: Performance Of Emementioning

confidence: 99%

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Electromembrane Extraction from Biological Fluids

et al. 2011

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“…Note that Eq. 8 reduces to a form of Nernst-Planck's flux equation 16 for σ = 0 and to the stress-limited diffusion 17,18 for φ = 0.…”

Section: Physical Modelmentioning

confidence: 99%

Field-Limited Migration of Li-Ions in Li-Ion Battery

Yang

2014

ECS Electrochemistry Letters

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The migration of Li-ions in lithium-ion battery cannot be simply described by Fick's second law; the interactions among ionic migration, field, and stress need to be taken into account when analyzing the migration of Li-ions. Using the theory of thermal activation process, the flux for ionic migration under concurrent action of electric field and mechanical stress is found to be a nonlinear function of the gradient of electric potential and the gradient of stress. Electric field can either accelerate or retard the growth of the lithiation layer, depending on polarity of the field. Si-based materials have attracted great interest for possible use as anode materials due to high specific capacity of Si (3580 mAh/g). However, the specific volume change of Si during electrochemical cycling can reach to ∼400%, 2 which can lead to catastrophic failure of lithium-ion battery (LIB). Low-dimensional Si-structures have been studied in rechargeable LIBs 3-7 to improve the cyclic performance and structural durability of Si-based anodes. The results from the studies 3-7 have demonstrated that low-dimensional Si-structures have the potential to offer high reversible capacity and long service life.Ariel et al. 8 observed that the ability to store and deliver charge for electrochemical cells consisting of LiCoO 2 (cathode)/SiO 2 /Si(anode) was inversely proportional to current density. Zhou et al. 9 suggested that the driving force for Li-migration was the gradient of electric potential and the concentration gradient of Li ions. Recently, Liu et al. 10 noted that electric field accelerated the migration of the reaction front during the lithiation of Si nanowires. They pointed out that the quantitative information about the effects of electrical field on both Li diffusion and interface reaction was not available at the moment of their study. 10The theory of thermal activation process 11 has been applied to study diffusion in solids. 12 The purpose of this work is to analyze electromechanical effect on the lithium migration, using the theory of thermal activation process. We consider the lithium migration under concurrent action of electric field and mechanical stress as a thermal activation process and derive an expression for the flux of ions. Physical ModelConsider a system, which consists of an electric anode, an alloy layer, and electrolyte, as shown in Fig. 1. The alloy layer is bounded by an anode-alloy interface and an alloy-electrolyte interface, as demonstrated by Liu et al. 10 for the lithiation of Si nanowires. Due to the large diffusivity of Li-ions, it is believed that the migration of Li-ions through the alloy layer and the reaction of Li-ions with the atoms of active materials to form Li-compound at the anode-alloy interface determine the growth of the alloy layer.According to the theory of thermal activation process, 11 the probability of an ion moving from a stable state to another stable state is determined by the vibration frequency and the energetic fraction of ions which depends on the energy barrier, Q, betw...

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