Electrolytes and electrolyte transport -
Similarly net chloride flux occurred mainly by solvent drag. Conversely water flow does not modify the large potassium absorption along the concentration gradient and only slightly affects the flux of calcium.
This driving force seemed to be the main one since J Ca is close to zero when these is no gradient. This observation supports the hypothesis that the variations of net Ca absorption during the laying cycle is due to a modification of concentration of soluble calcium in the contents of the intestine.
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As the sulfate ions are the only anions in this system, their amount reflects the total amount of dissolved ions with respect to the charge. Similar to the sodium ions, in the steady state the net sulfate ion transport equals zero so that the copper ions as the only electrochemical active ion type constitute the total net current.
The electric-field and diffusion-driven ion transport of the copper ions point in the same direction from the anode to the cathode. From the measurements graphed in Fig.
In addition to the data graphed in Fig. Figure 4 shows the mean of these measurements with the standard variation as the statistic error of the experiments. Moreover, Fig. The four different parameterizations are characterized by the following features:. The first case is modeled with a constant parameterization, resembling previously reported models in the literature 36 , 37 , 38 , 39 , 40 , The values of Fig.
When the concentration of copper ions near the cathode is thinning out, their local conductivity, diffusion coefficient and transfer number increase with reference to Fig.
By neglecting these concentration dependencies, the current is up to a Na 2 SO 4 concentration of 0.
At higher Na 2 SO 4 concentrations, the decrease of the conductivity, diffusion coefficients and cation transfer number becomes significant so that the model with the constant parameterization overestimates the limited current.
In the second case, the model is parameterized with the individual concentration dependencies of CuSO 4 and Na 2 SO 4 respectively, without taking their interaction into account. Thus, the molar conductivity, diffusivity and cation transport number of the CuSO 4 component decreases towards higher CuSO 4 concentrations, whereas it is not affected by the Na 2 SO 4 concentration.
Likewise, the properties of the Na 2 SO 4 component are influenced by its concentration and do not interact with the CuSO 4 component. The modeled data is overestimating the measured limited current. At Na 2 SO 4 concentrations below 0. As expected from the Debye—Hückel theory, the interaction of the ions is expected to decrease the molar conductivity and diffusion coefficients, explaining the modeled overestimation of the limited currents.
In the third parametrization scenario, the parameters of the CuSO 4 and Na 2 SO 4 components are calculated as a function of the total concentration of sulfate ions, assuming that the interaction between the sulfate ions and the different cations is equal.
However, this parametrization underestimates the measured limited current. Thus, the assumption that the ions influence one another in the same amount does not hold valid.
Figure 1 showed a more pronounced concentration dependence of molar conductivity, diffusion coefficient and transfer number of CuSO 4 than those of Na 2 SO 4. Thus, the ion—ion interactions in CuSO 4 are different from that in Na 2 SO 4 and the influence of the different components on one another is therefore also not that easy to describe.
The fourth case describes a concentration-dependent parameterization that displays a mixture between the second and third approach. Thus, an interaction between the different ion types is partly included, however, to a smaller extent than that between the ions of the same type. Using this parameterization, a good fit of modeled and measured data is obtained.
Measured black lines with scatter and error bars and modeled colored lines limited currents densities for a CuSO 4 concentration of 0. The four different parameterization scenarios for the model are discussed in the text.
The measured data is recorded with a voltage of 0. A Linear increment of the x-axis. B Square root spacing of the x-axis to more clearly resolve the limited current densities at small concentrations.
The scenarios discussed above are based on the experimental data on binary electrolytes and do not represent a physicochemical approach to characterize the ion—ion interactions in mixed ion systems.
Based on these data, however, the ion—ion interaction is shown to crucially impact the ion transport in supporting electrolytes and the related limited currents. In the literature 53 , the Debye—Hückel theory based physicochemical models that are used to describe the complex interaction between the ions are non-trivial and typically do not exactly describe the concentration dependence of the electrolyte parameters.
However, using such approaches a physicochemical description of the ion—ion interactions for the electrolyte parameterization may be possible. Theoretical works to address the prediction of the ion—ion interaction in multi-ion systems have to follow and may lead to more precise parameterization procedures as the presented approaches that is based on the experimental data of binary electrolytic solutions.
Thus far, measured and modeled data showed that limited currents decrease towards higher concentrations of the inert ions. In the following, the modeled limited currents are modeled under a variation of the electrolyte parameters, aiming to display the physicochemical relations that are described by the differential equations of the transport model.
Hereto, two cases are considered, a polar solvent in which the salts are dissolved and an ionic liquid or ionic melt. The first case resembles the above discussed CuSO 4 —Na 2 SO 4 system, where water displayed the polar solvent.
A simplified test system is considered in the following, in order to focus on the physicochemical interactions of the transport mechanisms rather than the complex parameterization that is discussed above. The test system is characterized by the following properties: 1 The electrolyte is comprised by two different salts, with two different types of cations denoted as C1 and C2 and one type of anion denoted as A.
One of these parameters of the supporting salt that is constituted of C2 and A are varied, while the other remain constant. Figure 3 showed, that the net concentration of all ions at the cathode in the system decreases near the cathode. However, in the case of ionic liquids or salt melts, the depletion of the ions at an electrode means that the entire electrolyte vanishes whereas it concentrates at another electrode.
For the test system with the ionic liquid an encapsulated volume is considered such as in a battery. As both salts in the test system have the same type of anions and the same density, only the positions of the cations can change whereas the concentration of the anions is constant over the entire electrolyte.
Hence, the differential equations that describe the anion transport are neglected and deleted from the source code. Figure 5 A shows the modeled concentration gradients of the test system with a polar solvent.
Despite the different parameterization, a similar shape of the concentration gradients compared to Fig. Figure 5 B graphs the limited currents that are obtained under the parameter variation of the electrolyte with the polar solvent.
With a negligible concentration or conductivity of the inert cations C2, the same limited current as in the case of the unsupported electrolyte is reached. Thus, in this case the conduction of C1 has a minor impact on its net transport.
In the case of a variation factor of unity equal properties of inert and active salt , the limited current is 1. A Concentration gradients obtained for the polar solvent. B Parameter variation for the polar solvent.
The variation factor on the x-axis is multiplied to either the concentration, molar conductivity or diffusion coefficient of the supporting salt. C,D Same as A and B but for an ionic liquid, where the ion displacement is confined as described in the text in more detail.
In binary diluted electrolytes the conductivity does not influence the limited current, as the entire current is anyway carried by the ions However, as here defined by the conductivity ratio Eq.
The conductivity is shared between the different types of ions. When the conductivity of the inert ion C2 type becomes much larger than that of the active ion C1, the ion C1 is mainly transported by the driving force of the concentration gradient as the conduction is mainly done by C2.
The limited current increases towards higher values of the diffusion coefficient of the inert salt. In this case, a depletion of ions at the cathode is avoided, from which also the limited current benefits. Figure 5 C shows the concentration gradient modeled for an ionic liquid.
In this case, the amount of anions is constant over the distance see discussion above. Figure 5 D shows the modeled limited currents for the ionic liquid scenario. Without the supporting salt, the limited current is infinite as the boundary condition of the constant anion concentration does not allow a concentration gradient.
With small additions of the supporting electrolyte, the supporting salt accumulates at the cathode and high concentration gradients of C1 over small distance close to the cathode result, for which the limited currents are orders of magnitude higher than those in the case of the polar solvent.
However, the aim of this article is to conclude physicochemical relations that are applicable to a wider scope and which are independent of the parameterization of the presented model system.
With the knowledge that the limited current decreases with the amount of supporting ions, the addition of inert ions displays a compromise between an increased conductivity and a decreased limited current.
When the electrolyte is mechanically mixed by convectional forces, the concentration gradients formed by the electrochemical current are partly equilibrated. Thus, the diffusion-limited currents in such flowing electrolytes is larger than in the case of static electrolytes.
Causes for such convection can be found in: i Macroscopic density difference, where the gravitational force leads to shear forces. ii Bubble formation and ascending bubbles.
iii Mechanical mixing of the electrolyte by stirring or pumping. In ionic liquids, the electrode is always in contact with the electrolyte, which reduces with reference to Fig. However, high viscosities typically cause smaller diffusion coefficients and conductivities of the active ion types in ionic liquids than that those of solvent based electrolytes.
As a result, limited currents can display a severe limitation for electrochemical devices and processes that operate with ionic liquids.
Further studies have to follow to experimentally examine limited currents in ionic liquids. This study examined the ion conduction, current-driven concentration gradients and related limited currents in supporting electrolytes.
A computational model is developed to describe the ion transport and the related spatiotemporal ion concentrations in electrolytes with three ion types. This model is equipped with different concentration-dependent parameterization scenarios and evaluated with measured limited currents of CuSO 4 —Na 2 SO 4 electrolytes.
The comparison of measured and modeled data shows that a complex concentration-dependent parameterization of the interaction between the different ion types in supporting electrolytes is required to adequately model the ion transport. A computational study on the variation of the electrolyte parameters reveals the ion transport mechanisms and the interplay of electric-field and diffusion-driven ion motion.
The similarities and differences of the ion transport in supporting electrolytes and ionic liquids is examined with the computational model, showing the impact of electrolyte parameters on limited currents. All data of the computational model generated or analysed during this study are included in this published article and its supporting information as it can be calculated and reproduced with the provided source code.
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Acta 54 , — Danilov, D. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.
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Comments: 16 pages, 9 figures Subjects: Chemical Physics physics. chem-ph ; Soft Condensed Matter cond-mat. soft ; Computational Physics physics.
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