Evaluation of Egorov’s Improved Separate Solution Method for Determination of Low Selectivity Coefficients by Numerical SimulationClick to copy article linkArticle link copied!
Abstract
The group of Egorov has recently proposed an elegant method to determine unbiased selectivity coefficients of ion-selective electrodes (Egorov et al. Anal. Chem. 2014, 86, 3693). Once the electrode is exposed to a solution containing only interfering ions, the time-dependent experimental selectivity coefficients are plotted as a function of the inverse fourth root of time and extrapolated to zero. The principal assumption of the approach is the progression of the diffusion layer in the membrane phase with square root of time. This letter critically evaluates the usefulness of this methodology by finite element analysis. The results suggest that the improvement of observed selectivity values are highly significant for an initially uniform distribution of primary ions across the membrane, strongly supporting the methodology. When strong inward ion fluxes of primary ions are present instead, a modification of the method by extrapolation of logarithmic selectivity coefficients appears to give the best results.



Results and Discussion
Figure 1
Figure 1. At time zero, the sample solution is changed to one containing interfering ions only, and the potential is monitored over time, displayed here to show the apparent selectivity coefficient. The curves correspond to different unbiased selectivities in steps of 0.5 orders of magnitude with a membrane containing a primary ion concentration equal to the ion-exchanger concentration (balanced membrane).
Figure 2
Figure 3
Figure 3. Time-dependent membrane concentration profiles (10 min interval shown) relative to the ion-exchange concentration, cRm, for the indicated selectivity and with the data from Figure 1
Figure 4
Figure 4. Confirmation of the key assumption of the approach, δIm(t) = (πDImt)1/2 using the simulated membrane concentration data for the case of best selectivity.
Figure 5
Figure 6
Figure 7
Figure 8
Figure 8. Simulated logarithmic selectivity coefficients for membranes exhiting a strong inward ion flux, using the modified method of extrapolating logarithmic selectivity coefficients (open circles) and the potentials after 10 min experimental time (black circles).
Supporting Information
Derivation of Egorov’s approach, details of simulations, and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.
Terms & Conditions
Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.
Acknowledgment
This work was supported by the Swiss National Science Foundation.
References
This article references 6 other publications.
- 1Bakker, E. Anal. Chem. 1997, 69, 1061– 1069Google Scholar1https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXhslyku7w%253D&md5=4d402be1723fb4176a4ae72033c8ffc5Determination of Unbiased Selectivity Coefficients of Neutral Carrier-Based Cation-Selective ElectrodesBakker, EricAnalytical Chemistry (1997), 69 (6), 1061-1069CODEN: ANCHAM; ISSN:0003-2700. (American Chemical Society)A new procedure for the detn. of selectivity coeffs. of neutral carrier-based cation-selective electrodes is established that avoids exposure to the preferred ion prior to the measurement of discriminated ions. The method is, therefore, unbiased by the presence of preferred ions in the membrane that otherwise could mask the response to discriminated ion solns. It is generally applicable as long as considerations are met and can only be applied once for a given membrane. Careful studies with sodium-, silver-, and calcium-selective electrodes reveal that Nernstian response slopes can now be obtained for even highly discriminated cations. Specifically, a 1,3-bridged calix[4]arene deriv. as introduced by Yamamoto and Shinkai indeed yields an extraordinary sodium selectivity of log KNa,Kpot = -4.9, with potassium showing Nernst response as well. Analogous measurements with two different silver carriers, a bisthioether-functionalized calix[4]arene and methylenebis(diisobutyldithiocarbamate), and the calcium carrier ETH 129 also show extremely high selectivity, which can satisfactorily be correlated to data obtained previously in ion-buffered solns. The new procedure promises to be a valuable addnl. tool for future characterizations of highly selective ion carriers.
- 2Sokalski, T.; Ceresa, A.; Zwickl, T.; Pretsch, E. J. Am. Chem. Soc. 1997, 119, 11347– 11348Google Scholar2https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXnsVSrs78%253D&md5=2b1797fa6136c454cc0986e3657112bbLarge improvement of the lower detection limit of ion-selective polymer membrane electrodesSokalski, Tomasz; Ceresa, Alan; Zwickl, Titus; Pretsch, ErnoeJournal of the American Chemical Society (1997), 119 (46), 11347-11348CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)The lower detection limit of ion-selective polymer membrane electrodes (ISEs) of typically 10-6 M is improved by a factor of ≥ 106 so that measurements down to the picomolar range are made possible. This is achieved by using a complexing agent that reduces the primary ion activity to a low level, together with a salt of a discriminated interfering ion as internal electrolyte. The thus generated concn. gradient of primary ions in the membrane lowers the detection limit and yields improved selectivities towards strongly discriminated ions so that ISEs are now usable for trace analyses in environmental and biol. samples.
- 3Ceresa, A.; Bakker, E.; Hattendorf, B.; Gunther, D.; Pretsch, E. Anal. Chem. 2001, 73, 343– 351Google ScholarThere is no corresponding record for this reference.
- 4Egorov, V. V.; Zdrachek, E. A.; Nazarov, V. A. Anal. Chem. 2014, 86, 3693– 3696Google ScholarThere is no corresponding record for this reference.
- 5Morf, W. E.; Pretsch, E.; De Rooij, N. F. J. Electroanal. Chem. 2007, 602, 43– 54Google Scholar5https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXis1GktbY%253D&md5=accdfd054e68d3a638a9264772a2d1b8Computer simulation of ion-selective membrane electrodes and related systems by finite-difference proceduresMorf, W. E.; Pretsch, E.; De Rooij, N. F.Journal of Electroanalytical Chemistry (2007), 602 (1), 43-54CODEN: JECHES ISSN:. (Elsevier B.V.)A simple but powerful numerical simulation for analyzing the electrochem. behavior of ion-selective membranes and liq. junctions is presented. The computer modeling makes use of a finite-difference procedure in the space and time domains, which can be easily processed (e.g., with MS Excel software) without the need for complex math. evaluations. It leads to convincing results on the dynamic evolution of concn. profiles, potentials, and fluxes in the studied systems. The treatment accounts for influences of convection, flow, or stirring in the sample soln. that act on the boundary diffusion layer and it is even capable of including the effects of an electrolyte flow through the whole system. To minimize the no. of arbitrary parameters, interfacial reactions are assumed to be near local equil., and space-charge influences are considered via phase-boundary potential differences. The applicability of the computer simulation is demonstrated for different ion-selective membranes as well as for liq. junctions. The numerical results are in excellent agreement with exptl. data.
- 6Peper, S.; Ceresa, A.; Bakker, E.; Pretsch, E. Anal. Chem. 2001, 73, 3768– 3775Google ScholarThere is no corresponding record for this reference.
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Abstract
Figure 1
Figure 1. At time zero, the sample solution is changed to one containing interfering ions only, and the potential is monitored over time, displayed here to show the apparent selectivity coefficient. The curves correspond to different unbiased selectivities in steps of 0.5 orders of magnitude with a membrane containing a primary ion concentration equal to the ion-exchanger concentration (balanced membrane).
Figure 2
Figure 3
Figure 3. Time-dependent membrane concentration profiles (10 min interval shown) relative to the ion-exchange concentration, cRm, for the indicated selectivity and with the data from Figure 1
Figure 4
Figure 4. Confirmation of the key assumption of the approach, δIm(t) = (πDImt)1/2 using the simulated membrane concentration data for the case of best selectivity.
Figure 5
Figure 6
Figure 7
Figure 8
Figure 8. Simulated logarithmic selectivity coefficients for membranes exhiting a strong inward ion flux, using the modified method of extrapolating logarithmic selectivity coefficients (open circles) and the potentials after 10 min experimental time (black circles).
References
This article references 6 other publications.
- 1Bakker, E. Anal. Chem. 1997, 69, 1061– 10691https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXhslyku7w%253D&md5=4d402be1723fb4176a4ae72033c8ffc5Determination of Unbiased Selectivity Coefficients of Neutral Carrier-Based Cation-Selective ElectrodesBakker, EricAnalytical Chemistry (1997), 69 (6), 1061-1069CODEN: ANCHAM; ISSN:0003-2700. (American Chemical Society)A new procedure for the detn. of selectivity coeffs. of neutral carrier-based cation-selective electrodes is established that avoids exposure to the preferred ion prior to the measurement of discriminated ions. The method is, therefore, unbiased by the presence of preferred ions in the membrane that otherwise could mask the response to discriminated ion solns. It is generally applicable as long as considerations are met and can only be applied once for a given membrane. Careful studies with sodium-, silver-, and calcium-selective electrodes reveal that Nernstian response slopes can now be obtained for even highly discriminated cations. Specifically, a 1,3-bridged calix[4]arene deriv. as introduced by Yamamoto and Shinkai indeed yields an extraordinary sodium selectivity of log KNa,Kpot = -4.9, with potassium showing Nernst response as well. Analogous measurements with two different silver carriers, a bisthioether-functionalized calix[4]arene and methylenebis(diisobutyldithiocarbamate), and the calcium carrier ETH 129 also show extremely high selectivity, which can satisfactorily be correlated to data obtained previously in ion-buffered solns. The new procedure promises to be a valuable addnl. tool for future characterizations of highly selective ion carriers.
- 2Sokalski, T.; Ceresa, A.; Zwickl, T.; Pretsch, E. J. Am. Chem. Soc. 1997, 119, 11347– 113482https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXnsVSrs78%253D&md5=2b1797fa6136c454cc0986e3657112bbLarge improvement of the lower detection limit of ion-selective polymer membrane electrodesSokalski, Tomasz; Ceresa, Alan; Zwickl, Titus; Pretsch, ErnoeJournal of the American Chemical Society (1997), 119 (46), 11347-11348CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)The lower detection limit of ion-selective polymer membrane electrodes (ISEs) of typically 10-6 M is improved by a factor of ≥ 106 so that measurements down to the picomolar range are made possible. This is achieved by using a complexing agent that reduces the primary ion activity to a low level, together with a salt of a discriminated interfering ion as internal electrolyte. The thus generated concn. gradient of primary ions in the membrane lowers the detection limit and yields improved selectivities towards strongly discriminated ions so that ISEs are now usable for trace analyses in environmental and biol. samples.
- 3Ceresa, A.; Bakker, E.; Hattendorf, B.; Gunther, D.; Pretsch, E. Anal. Chem. 2001, 73, 343– 351There is no corresponding record for this reference.
- 4Egorov, V. V.; Zdrachek, E. A.; Nazarov, V. A. Anal. Chem. 2014, 86, 3693– 3696There is no corresponding record for this reference.
- 5Morf, W. E.; Pretsch, E.; De Rooij, N. F. J. Electroanal. Chem. 2007, 602, 43– 545https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXis1GktbY%253D&md5=accdfd054e68d3a638a9264772a2d1b8Computer simulation of ion-selective membrane electrodes and related systems by finite-difference proceduresMorf, W. E.; Pretsch, E.; De Rooij, N. F.Journal of Electroanalytical Chemistry (2007), 602 (1), 43-54CODEN: JECHES ISSN:. (Elsevier B.V.)A simple but powerful numerical simulation for analyzing the electrochem. behavior of ion-selective membranes and liq. junctions is presented. The computer modeling makes use of a finite-difference procedure in the space and time domains, which can be easily processed (e.g., with MS Excel software) without the need for complex math. evaluations. It leads to convincing results on the dynamic evolution of concn. profiles, potentials, and fluxes in the studied systems. The treatment accounts for influences of convection, flow, or stirring in the sample soln. that act on the boundary diffusion layer and it is even capable of including the effects of an electrolyte flow through the whole system. To minimize the no. of arbitrary parameters, interfacial reactions are assumed to be near local equil., and space-charge influences are considered via phase-boundary potential differences. The applicability of the computer simulation is demonstrated for different ion-selective membranes as well as for liq. junctions. The numerical results are in excellent agreement with exptl. data.
- 6Peper, S.; Ceresa, A.; Bakker, E.; Pretsch, E. Anal. Chem. 2001, 73, 3768– 3775There is no corresponding record for this reference.
Supporting Information
Supporting Information
Derivation of Egorov’s approach, details of simulations, and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.
Terms & Conditions
Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.