Abstract
In most interpretations of potentiometric ion sensor responses with glass, solid, or liquid/polymer membranes, a model assuming electrochemical equilibrium between the aqueous sample and the membrane is used. This model is often called a phase boundary model to emphasize the importance of ion-exchange processes at the interface. The essence of the phase boundary model is that it accepts electroneutrality and thermodynamic equilibrium, and thus ignores electrochemical migration and the time-dependent effects. For this reason, this model is in conflict with many experimental reports on ion sensors in which both kinetic (time-dependent) discrimination of ions to improve selectivity and non-equilibrium transmembrane ion transport for lowering the detection limits are deliberately used. To respond to the experimental challenges in the author’s groups, we elevated the potentiometric modeling by using the Nernst–Planck–Poisson (NPP) equations system to model the non-equilibrium response. In the NPP model, electroneutrality and steady-state/equilibrium assumptions are abandoned, and thus we access the space and time domain. This approach describes the concentration changes of ions participating in the ion-exchange and transport processes, as well as the electrical potential evolution over space and time, and allows in particular, the inspection of the equilibrium set by the phase boundary models as a special “stationary” case after infinite time. Additionally, directly predicting the selectivity and the low detection limit variability over time and the influence of other parameters, e.g., ion diffusibility, is possible. As a coherent and non-arbitral model, the NPP system facilitates solving the inverse problem, i.e., to optimize the sensor properties and measurement conditions in a customized way via desired target functions and hierarchical genetical strategy modeling. In this way the NPP allows setting the conditions under which the experimentally measured selectivity coefficients are true (unbiased) and the detection limits are optimized.
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References
Morf WE (1981) The principle of ion-selective electrodes and of membrane transport. Akadémiai Kiadó, Budapest
Bobacka J, Ivaska A, Lewenstam A (2008) Chem Rev 108:329
Nernst W (1989) Z Phys Chem 4:165
Guggenheim EA (1929) J Phys Chem 33:842
Guggenheim EA (1930) J Phys Chem 34:758
Nikolskii BP (1937) Acta phys-chim USSR 7:597
Scholz F (2010) J Solid State Electrochem. doi:10.1007/s10008-010-1163-0
Bakker E (2010) J Electroanal Chem 639:1
De Battisti A, Trasatti S (1977) J Electroanal Chem 79:251
Lewenstam A, Bobacka J, Ivaska A (1994) J Electroanal Chem 368:23
Cadogan A, Gao Z, Lewenstam A, Ivaska A, Diamond D (1992) Anal Chem 64:2496
Hulanicki A, Michalska A, Lewenstam A (1994) Talanta 41:323
Bobacka J, Gao Z, Ivaska A, Lewenstam A (1994) J Electroanal Chem 368:33
Gao Z, Bobacka J, Lewenstam A, Ivaska A (1994) Electrochim Acta 39:755
Hulanicki A, Michalska A, Lewenstam A (1994) Electroanalysis 6:604
Migdalski J, Blaz T, Lewenstam A (1996) Anal Chim Acta 322:151
Michalska A, Hulanicki A, Lewenstam A (1997) Microchem J 57:59
Lindfors T, Bobacka J, Lewenstam A (1998) Electrochim Acta 43:3503
Sjoberg P, Bobacka J, Lewenstam A, Ivaska A (1999) Electroanalysis 11:821–824
Migdalski J, Blaz T, Lewenstam A (1999) Anal Chim Acta 395:65
Blaz T, Migdalski J, Lewenstam A (2000) Talanta 52:319
Vazquez M, Bobacka J, Ivaska A, Lewenstam A (2002) Sens Actuators B 82:7
Vazquez M, Danielsson P, Bobacka J, Lewenstam A, Ivaska A (2004) Sens Actuators B 97:182
Buck RP (1968) Anal Chem 40:1432
Wuhrmann HR, Morf WE, Simon W (1973) Helv Chim Acta 56:1011
Lewenstam A (1994) Scand J Clin Lab Invest 54:11
Buck RP, Shepard VR (1974) Anal Chem 46:2097
Koebel M (1974) Anal Chem 46:1559
Hulanicki A, Lewenstam A (1976) Talanta 23:661
Lewenstam A, Sokalski T, Hulanicki A (1985) Talanta 32:531
Hulanicki A, Lewenstam A (1977) Talanta 24:171
Hulanicki A, Sokalski T, Lewenstam A (1988) Microchim Acta 3:119
Lewenstam A, Hulanicki A (1990) Sel Electrode Rev 12:161
Lewenstam A (1991) Sel Electrode Rev 13:129
Hulanicki A, Maj-Zurawska M, Lewenstam A (1979) Anal Chim Acta 107:121
Hulanicki A, Lewandowski R, Lewenstam A (1979) Anal Chim Acta 110:197
Hulanicki A, Krawczynski T, Lewenstam A (1984) Anal Chim Acta 158:343
Maj-Zurawska M, Sokalski T, Hulanicki A (1988) Talanta 35:281
Sokalski T, Maj-Zurawska M, Hulanicki A (1991) Mictrochimica Acta 1:285
Sokalski T, Zwickl T, Bakker E, Pretsch E (1999) Anal Chem 71:1204
Sokalski T, Ceresa A, Fibbioli M, Zwickl T, Bakker E, Pretsch E (1999) Anal Chem 71:1210
Zwickl T, Sokalski T, Pretsch E (1999) Electroanalysis 10–11:673
Buhlmann P, Umezawa Y (1999) Electroanalysis 10–11:687
Mikhelson KN, Lewenstam A (1998) Sens Actuators B 48:344
Mikhelson KN, Lewenstam A (2000) Anal Chem 72:4965
Bakker E, Pretsch E (2005) Trends Anal Chem 25:199
Baucke FGK (2000) Electrochemistry of solid glasses. In: Bach H, Baucke F, Krause D (eds) Electrochemistry of glasses and glass melts, including glass electrodes. Springer, Berlin, pp 35–268
Bakker E, Buhlmann P, Pretsch E (2004) Talanta 63:3
Hulanicki A, Lewenstam A (1981) Anal Chem 53:1401
Lewenstam A, Hulanicki A, Sokalski T (1987) Anal Chem 59:1539
Hulanicki A, Lewenstam A (1982) Talanta 29:661
Morf WE, Pretsch E, de Rooij NF (2008) J Electroanal Chem 614:15
Paczosa-Bator B, Blaz T, Migdalski J, Lewenstam A (2007) Bioelectrochem 71:66
Paczosa-Bator B, Stepien M, Maj-Zurawska M, Lewenstam A (2009) Magnes Res 22:10
Brumleve TR, Buck RP J (1978) Electroanal Chem 90:1
Sokalski T, Lewenstam A (2001) Electrochem Commun 3:107
Sokalski T, Lingenfelter P, Lewenstam A (2003) J Phys Chem B 107:2443
Lingenfelter P, Bedlechowicz-Sliwakowska I, Sokalski T, Maj-Zurawska M, Lewenstam A (2006) Anal Chem 78:6783
Sokalski T, Kucza W, Danielewski M, Lewenstam A (2009) Anal Chem 81:5016
Jasielec JJ, Sokalski T, Filipek R, Lewenstam A (2010) Electrochim Acta 55:6836
Ilcheva L, Cammann K (1985) Fresenius J Anal Chem 320:664
Trojanowicz M, Matuszewski W (1983) Anal Chim Acta 151:77
Fu B, Bakker E, Yun JH, Yang VC, Meyerhoff ME (1994) Anal Chem 66:2250
Maj-Zurawska M, Lewenstam A (1990) Anal Chim Acta 236:331
Lewenstam A, Maj-Zurawska M, Blomqvist N, Öst J (1993) Clin Chem Enzymol Commun 5:95
Saris NE, Mervaala E, Karppanen H, Khawaja JA, Lewenstam A (2000) Clin Chim Acta 294:1
Kucza W, Danielewski M, Lewenstam A (2006) Electrochem Commun 8:416
Paczosa-Bator B, Piech R, Lewenstam A (2010) Talanta 81:1003
Anastasova-Ivanova S, Mattinen U, Radu A, Bobacka J, Lewenstam A, Migdalski J, Danielewski M, Diamond D (2010) Sens Actuators B 146:199
Lewenstam A, Sokalski T, Jasielec J, Kucza W, Filipek R, Wierzba B, Danielewski M (2009) ECS Trans 19:219
Acknowledgements
My colleagues in Turku and Krakow are acknowledged for their enthusiasm and dedicated work. My special thanks are dedicated to docent Tomasz Sokalski.
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Lewenstam, A. Non-equilibrium potentiometry—the very essence. J Solid State Electrochem 15, 15–22 (2011). https://doi.org/10.1007/s10008-010-1199-1
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DOI: https://doi.org/10.1007/s10008-010-1199-1