Диффузионная модель межфазового потенциала ионоселективных электродов

Представлена модель межфазового потенциала ионоселективных электродов, сочетающая простоту стационарных подходов с возможностью описания динамического отклика ионоселективных электродов, характерной для динамических диффузионных моделей. Получены уравнения, в явном виде описывающие зависимость величины межфазового потенциала потенциометрических сенсоров от времени, наблюдающуюся при работе с высокоселективными электродами в растворах постороннего иона, а также в смешанных растворах, содержащих посторонний и основной ионы, например при определении коэффициентов селективности рекомендуемыми ИЮПАКметодами. Достоинством предложенной модели является минимизация времени вычислений до долей секунды (в отличие от требующего десятков минут численного решения систем дифференциальных уравнений в рамках известных аналогов). Благодаря получению уравнений в аналитическом виде предложенный подход исключает необходимость использования ресурсоемких систем компьютерной алгебры (таких как Wolfram Mathematica) и позволяет оперативно прогнозировать отклик ионоселективных электродов. Высокая прогностическая способность разработанной модели подтверждена сопоставлением результатов расчетов с экспериментальными данными по динамике изменения отклика тетрабутиламмоний- и пикрат-селективных электродов в растворах, содержащих посторонние ионы, и с результатами, полученными в рамках экстракционно-обусловленной динамической диффузионной модели.

1. Никольский, Б. П. Теория стеклянного электрода / Б. П. Никольский // Журнал физичской химии. – 1937. – Т. X, вып. 3. – С. 495–503.

2. Morf, W. E. Computer simulation of ion-selective membrane electrodes and related systems by finite-difference procedures / W. E. Morf, E. Pretsch. N. F. de Rooij // Journal of Electroanalytical Chemistry. – 2007. – Vol. 602, № 1. – P. 43–54. https://doi.org/10.1016/j.jelechem.2006.11.025

3. Egorov, V. V. Application of the interface equilibria-triggered dynamic diffusion model of the boundary potential for the numerical simulation of neutral carrier-based ion-selective electrodes response / V. V. Egorov, A. D. Novakovskii // Analytica Chimica Acta. – 2018. – Vol. 1043. – P. 20–27. https://doi.org/10.1016/j.aca.2018.08.043

4. Egorov, V. V. On the possibilities of potentiometric analysis in presence of small concentrations of highly interfering foreign ions: Ways for reducing the interference / V. V. Egorov, A. D. Novakovskii // Journal of Electroanalytical Chemistry. – 2019. – Vol. 847. – Art. 113234. https://doi.org/10.1016/j.jelechem.2019.113234

5. Lewenstam, A. Application of Nernst-Planck and Poisson equations for interpretation of liquid-junction and membrane potentials in real-time and space domains / A. Lewenstam, T. Sokalski // Electrochemistry Communications. – 2001. – Vol. 3, № 3. – P. 107–112. https://doi.org/10.1016/S1388-2481(01)00110-2

6. Bobacka, J. Potentiometric ion sensors / J. Bobacka, A. Ivaska, A. Lewenstam // Chemical Reviews – 2008. – Vol. 108, № 2. – P. 329–351. https://doi.org/10.1021/cr068100w

7. Morf, W. E. Time-dependent selectivity behavior and dynamic response of silver halide membrane electrodes to interfering ions / W. E. Morf // Analytical Chemistry. – 1983. – Vol. 55, № 7. – P. 1165–1168. https://doi.org/10.1021/ac00258a042

8. Egorov, V. V. A simple dynamic diffusion model of the response of highly selective electrodes: the effect of simulation parameters and boundary conditions on the results of calculations / V. V. Egorov, A. D. Novakovskii, E. A. Zdrachek // Russian Journal of Electrochemistry. – 2018. – Vol. 54, № 4. – P. 381–390. https://doi.org/10.1134/S1023193518040031

9. Novakovskii, A. D. Lipophilicity criteria for ionic components used in liquid-junction-free reference electrodes / A. D. Novakovskii, V. V. Egorov, D. V. Korostik // Analytical Chemistry. – 2025. – Vol. 97, № 12. – P. 6382–6390. https://doi.org/10.1021/acs.analchem.4c04156

10. Mathison, S. Effect of transmembrane electrolyte diffusion on the detection limit of carrier-based potentiometric ion sensors / S. Mathison, E. Bakker // Analytical Chemistry. – 1998. – Vol. 70, № 2. – P. 303–309. https://doi.org/10.1021/ac970690y

11. Large improvement of the lower detection limit of ion-selective polymer membrane electrodes / T. Sokalski, A. Ceresa, T. Zwickl [et al.] // Journal of the American Chemical Society. – 1997. – Vol. 119, № 46. – P. 11347–11348. https://doi.org/10.1021/ja972932h

12. Lowering the detection limit of solvent polymeric ion-selective membrane electrodes. 1. Modeling the influence of steady-state ion fluxes / T. Sokalski, T. Zwickl, E. Bakker [et al.] // Analytical Chemistry. – 1999. – Vol. 71, № 6. – P. 1204–1209. https://doi.org/10.1021/ac980944v

13. Morf, W. E. Memory effects of ion-selective electrodes: Theory and computer simulation of the time-dependent potential response to multiple sample changes / W. E. Morf, E. Pretsch. N. F. de Rooij // Journal of Electroanalytical Chemistry. – 2009. – Vol. 633, № 1. – P. 137–145. https://doi.org/10.1016/j.jelechem.2009.05.004

14. Hulanicki, A. Model for treatment of selectivity coefficients for solid-state ion-selective electrodes / A. Hulanicki, A. Lewenstam // Analytical Chemistry. – 1981. – Vol. 53, № 9. – P. 1401–1405. https://doi.org/10.1021/ac00232a024

15. Time-dependent phenomena in the potential response of ion-selective electrodes treated by the Nernst-Planck-Poisson model. 1. Intramembrane processes and selectivity / P. Lingenfelter, I. Bedlechowicz-Sliwakowska, T. Sokalski [et al.] // Analytical Chemistry. – 2006. – Vol. 78, № 19. – P. 6783–6791. https://doi.org/10.1021/ac060264p

16. Morf, W. E. Time-dependent selectivity behavior and dynamic response of silver halide membrane electrodes to interfering ions / W. E. Morf // Analytical Chemistry. – 1983. – Vol. 55, № 7. – P. 1165–1168. https://doi.org/10.1021/ac00258a042

17. Bakker, E. Evaluation of Egorov’s improved separate solution method for determination of low selectivity coefficients by numerical simulation / E. Bakker // Analytical Chemistry. – 2014. – Vol. 86, № 16. – P. 8021–8024. https://doi.org/10.1021/ac502638s

18. Egorov, V. V. An interface equilibria-triggered time-dependent diffusion model of the boundary potential and its application for the numerical simulation of the ion-selective electrode response in real systems / V. V. Egorov, A. D. Novakovskii, E. A. Zdrachek // Analytical Chemistry. – 2018. – Vol. 90, № 2. – P. 1309–1316. https://doi.org/10.1021/acs.analchem.7b04134

19. Potentiometry at trace levels in confined samples: ion-selective electrodes with subfemtomole detection limits / A. Malon, T. Vigassy, E. Bakker [et al.] // Journal of the American Chemical Society. – 2006. – Vol. 128, № 25. – P. 8154– 8155. https://doi.org/10.1021/ja0625780

20. Bakker, E. Potentiometric sensors for trace-level analysis / E. Bakker, E. Pretsch // Trends in Analytical Chemistry. – 2005. – Vol. 24, № 3. – P. 199–207. https://doi.org/10.1016/j.trac.2005.01.003

21. Bakker, E. Modern potentiometry / E. Bakker, E. Pretsch // Angewandte Chemie International Edition. – 2007. – Vol. 46, № 30. – P. 5660–5668. https://doi.org/10.1002/anie.200605068

22. Bakker, E. The phase-boundary potential model / E. Bakker, P. Bühlmann, E. Pretsch // Talanta. – 2004. – Vol. 63, № 1. – P. 3–20. https://doi.org/10.1016/j.talanta.2003.10.006

23. Effect of ion transport on the potential response of ionophore-based mem-brane electrodes: a theoretical approach / W. E. Morf, M. Badertscher, T. Zwickl [et al.] // The Journal of Physical Chemistry B. – 1999. – Vol. 103, № 51. – P. 11346– 11356. https://doi.org/10.1021/jp9926443

24. Radu, A. Dynamic diffusion model for tracing the real-time potential response of polymeric membrane ion-selective electrodes / A. Radu, A. J. Meir, E. Bakker // Analytical Chemistry. – 2004. – Vol. 76, № 21. – P. 6402–6409. https://doi.org/10.1021/ac049348t

25. Comparison of different approaches to the description of the detection limit of ion-selective electrodes / J. J. Jasielec, T. Sokalski, R. Filipek [et al.] // Electrochimica Acta. – 2010. – Vol. 55, № 22. – P. 6836–6848. https://doi.org/10.1016/j.electacta.2010.05.083

26. Modeling non equilibrium potentiometry to understand and control selectivity and detection limit / A. Lewenstam, T. Sokalski, J. Jasielec [et al.] // ECS Transactions. – 2009. – Vol. 19, № 6. – P. 219–224. https://doi.org/10.1149/1.3118555

27. Neutral-carrier ion-selective electrodes assessed by the Nernst-Planck-Poisson model / J. J. Jasielec, T. Sokalski, R. Filipek [et al.] // Analytical Chemistry. – 2015. – Vol. 87, № 17. – P. 8665–8672. https://doi.org/10.1021/acs.analchem.5b00065

28. Morf, W. E. The principles of ion-selective electrodes and of membrane transport / W. E. Morf. − New York : Elsevier, 1981. − 433 p.

29. Hulanicki, A. Some properties of ion-selective electrodes based on poly (vinyl chloride) membranes with liquidion-exchanger / A. Hulanicki, R. Lewandowski // Chemia Analityczna. – 1974. – Vol. 19. – P. 53–61.

30. Vigassy, T. Rotating ion-selective membrane electrodes for trace-level measurements / T. Vigassy, R. E. Gyurcsányi, E. Pretsch // Electroanalysis. – 2003. – Vol. 15, № 15–16. – P. 1270–1275. https://doi.org/10.1002/elan.200302818

31. Egorov, V. V. Overcoming of one more pitfall in boundary element calculations with computer simulations of ion-selective electrode response / V. V. Egorov, A. D. Novakovskii // ACS Omega. – 2019. – Vol. 4, № 1. – P. 1617–1622. https://doi.org/10.1021/acsomega.8b02926

32. Description of the effects of non‐ion‐exchange extraction and intra‐membrane interactions on the ion‐selective electrodes response within the interface equilibria‐triggered model / V. V. Egorov, A. D. Novakovskii, F. A. Salih [et al.] // Electroanalysis. – 2020. – Vol. 32, № 4. – P. 674–682. https://doi.org/10.1002/elan.201900647

33. Ion exchanger-based electrodes for determination of highly lipophilic physiologically active amines: Peculiarities of functioning and ways for improving analytical characteristics / F. A. Salih, A. D. Novakovskii, V. A. Zakhvitsevich [et al.] // Electroanalysis. – 2024. – Vol. 36, № 7. – Art. e202300416. https://doi.org/10.1002/elan.202300416

34. Bakker, E. Determination of unbiased selectivity coefficients of neutral carrier-based cation-selective electrodes / E. Bakker // Analytical Chemistry. – 1997. – Vol. 69, № 6. – P. 1061–1069. https://doi.org/10.1021/ac960891m

35. Potentiometric selectivity coefficients of ion-selective electrodes / Y. Umezawa, P. Buhlmann, K. Umezawa [et al.] // Pure and Applied Chemistry. – 2000. – Vol. 72, № 10. – P. 1851–2082. https://doi.org/10.1351/pac200072101851

36. Umezawa, Y. Selectivity coefficients for ion-selective electrodes: recommended methods for reporting values / Y. Umezawa, K. Umezawa, H. Sato // Pure and Applied Chemistry. – 1995. – Vol. 67, № 3. – P. 507–518. https://doi.org/10.1351/PAC199567030507