vestichИзвестия Национальной академии наук Беларуси. Серия химических наукProceedings of the National Academy of Sciences of Belarus, Chemical Series1561-83312524-2342The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8331-2026-62-3-200-214vestich-1028Research ArticleАНАЛИТИЧЕСКАЯ ХИМИЯANALYTICAL CHEMISTRYДиффузионная модель межфазового потенциала ионоселективных электродовDiffusion model of the phase-boundary potential of ion-selective electrodesНоваковскийА. Д.NovakovskiiA. D.

Новаковский Андрей Дмитриевич − кандидат химических наук, доцент, старший научный сотрудник

ул. Ленинградская, 14, 220006, Минск 

Novakovskii Andrei D. − Ph. D. (Chemistry), Associate Professor, Senior Researcher

14, Leningradskaya Str., 220030, Minsk

navakouski@bsu.byЕгоровВ. В.EgorovV. V.

Егоров Владимир Владимирович – доктор химических наук, профессор, главный научный сотрудник

ул. Ленинградская, 14, 220006, Минск

Egorov Vladimir V. − Dr. Sci. (Chemistry), Professor, Chief Researcher

14, Leningradskaya Str., 220030, Minsk

egorvv@bsu.byБелорусский государственный университет ; Научно-исследовательский институт физико-химических проблем Белорусского государственного университетаБеларусьResearch Institute for Physical Chemical Problems of the Belarusian State UniversityBelarus202629082026623200214Copyright © Новаковский А.Д., Егоров В.В., 20262026Новаковский А.Д., Егоров В.В.Novakovskii A.D., Egorov V.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestichem.belnauka.by/jour/article/view/1028

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.

A model of the phase-boundary potential of ion-selective electrodes is presented, combining the simplicity of steady-state approaches with the ability to describe the dynamic response characteristic of dynamic diffusion models. Within the framework of the proposed model, equations were obtained that explicitly describe the dependence of the phase-boundary potential of potentiometric sensors on time, observed when working with highly selective electrodes in solutions of foreign ions, as well as in mixed solutions containing foreign and primary ions, in particular, when determining the selectivity coefficients using the methods recommended by IUPAC. An advantage of the proposed model is the minimization of computational time to fractions of a second (in contrast to the numerical solution of systems of differential equations within known analogs, which requires tens of minutes). By obtaining equations in analytical form, the proposed approach eliminates the need for resource-intensive computer algebra systems (such as Wolfram Mathematica) and enables the rapid calculation of the response of ion-selective electrodes. The high predictive ability of the developed model is confirmed by comparing the calculation results with experimental data on the dynamics of changes in the response of tetrabutylammonium- and picrateselective electrodes in solutions containing foreign ions, and with the results obtained within the framework of the interface-equilibria-triggered dynamic diffusion model.

математическое моделированиединамические диффузионные моделиионоселективные электродыкоэффициенты селективностимежфазовый потенциалmathematical modelingdynamic diffusion modelsion-selective electrodesselectivity coefficientsphaseboundary potentialРабота выполнена при финансовой поддержке Государственной программы научных иссле­ дований «Химические процессы и технологии» (НИР 2.1.01.04).The authors thank the “Chemical processes and technologies no. 2.1.01.04” State research program.ReferencesНикольский, Б. П. Теория стеклянного электрода / Б. П. Никольский // Журнал физичской химии. – 1937. – Т. X, вып. 3. – С. 495–503.Nikol’skii B. P. Glass Electrode Theory. Zhurnal fizicheskoi khimii = Russian Journal of Physical Chemistry, 1937, vol. 3, pp. 495–503 (in Russian).Morf, W. E. Computer simulation of ion-selective membrane electrodes and related systems by finite-difference procedures / W. E. Morf, E. Pretsch. N. 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The authors declare that there are no conflicts of interest present.