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The time response of plasmonic sensors due to binary adsorption: analytical versus numerical modeling

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Abstract

In order to allow for multiscale modeling of complex systems, we focus on various approaches to modeling binary adsorption. We consider multiple methods of modeling the temporal response of general plasmonic sensors. We start from the analytical approach. The kinetics of adsorption and desorption is modeled both as a first order reaction and as a second-order reaction. The criteria for their validity and the choice between them in the case of two-component adsorption are established. Due to the nonlinearities of the second-order reactions and the lack of their analytical solutions, computer-aided modeling is considered next, also in multiple ways: the employment of numerical solvers, fitting of experimental results, the stochastic simulation algorithms and the employment of artificial neural networks (ANN). The examples we present illustrate the advantages and disadvantages of the particular approaches. The goal is to aid the concurrent multiscale modeling of adsorption-based devices. Machine learning in ANN performed here is used to estimate the equilibrium values of adsorbed quantities. The obtained results show that to train an ANN for the estimation of the equilibrium adsorption quantities the Levenberg–Marquardt and the Bayesian regularization algorithms are less efficient than the quasi-Newton BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm.

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References

  1. W.J. Thomas, B. Crittenden, Adsorption Technology and Design (Elsevier Science and Technology Books, Amsterdam, 1998)

    Google Scholar 

  2. J. Toth, Adsorption: Theory, Modeling, and Analysis (Marcel Dekker Incorporated, NY, 2002)

    Google Scholar 

  3. A. Dabrowski, Adv. Colloid Interface Sci. 93, 135 (2001)

    Google Scholar 

  4. L. Zhou, Adsorption: Progress in Fundamental and Application Research (World Scientific, Singapore, 2007)

    Google Scholar 

  5. A.B. Dahlin, B. Dielacher, P. Rajendran, K. Sugihara, T. Sannomiya, M. Zenobi-Wong, J. Vörös, Anal. Bioanal. Chem. 402, 1773 (2012)

    Google Scholar 

  6. S.Y. Lagergren, Zur Theorie Der Sogenannten Adsorption Gelöster Stoffe (Kungliga Svenska Vetenskapsakademiens, Hadlingar, 1898)

    Google Scholar 

  7. R.L. Tseng, F.C. Wu, R.S. Juang, J Taiwan Inst. Chem. E 41, 661 (2010)

    Google Scholar 

  8. Y. Liu, L. Shen, Langmuir 24, 11625 (2008)

    Google Scholar 

  9. H. Qiu, L. Lv, B. Pan, Q. Zhang, W. Zhang, Q. Zhang, J. Zhejiang Univ. Sci. A 10, 716 (2009)

    Google Scholar 

  10. W. Stroberg, S. Schnell, Math. Biosci. 287, 3 (2017)

    MathSciNet  Google Scholar 

  11. O. Jakšić, I. Jokić, Z. Jakšić, Ž. Čupić, L. Kolar-nić, Phys. Scr. 2014, 014047 (2014)

    Google Scholar 

  12. F. Amato, J.L. González-Hernández, J. Havel, Talanta 93, 72 (2012)

    Google Scholar 

  13. Y.W. Huang, M.Q. Chen, Q.H. Li, J. Therm. Anal. Calorim. 138(1), 451 (2019)

    Google Scholar 

  14. E. Weinan, Principles of Multiscale Modeling (Cambridge University Press, Cambridge, 2011)

    MATH  Google Scholar 

  15. Z.W. Ulissi, M.T. Tang, J. Xiao, X. Liu, D.A. Torelli, M. Karamad, K. Cummins, C. Hahn, N.S. Lewis, T.F. Jaramillo, K. Chan, J.K. Nørskov, ACS Catal. 7, 6600 (2017)

    Google Scholar 

  16. J.L. González-Hernández, M.M. Canedo, S. Encinar, J. Math. Chem. 51, 1634 (2013)

    MathSciNet  Google Scholar 

  17. J.L. González-Hernández, M.M. Canedo, S. Encinar, MATCH Commun. Math. Comput. Chem. 79, 619 (2018)

    MathSciNet  Google Scholar 

  18. V.S.R.P. Kumar, K.A. Malla, B. Yerra, K.S. Rao, Appl. Water Sci. 9, 44 (2019)

    ADS  Google Scholar 

  19. M.R. Fagundes-Klen, P. Ferri, T.D. Martins, C.R.G. Tavares, E.A. Silva, Biochem. Eng. J. 34, 136 (2007)

    Google Scholar 

  20. R. Anderson, J. Rodgers, E. Argueta, A. Biong, D.A. Gómez-Gualdrón, Chem. Mater. 30, 6325 (2018)

    Google Scholar 

  21. B. Gezer, U. Kose, D. Zubov, O. Deperlioglu, P. Vasant, Wirel. Netw. (2019). https://doi.org/10.1007/s11276-019-02035-1

    Article  Google Scholar 

  22. M. Ghaedi, M. Roosta, A.M. Ghaedi, A. Ostovan, I. Tyagi, S. Agarwal, V.K. Gupta, Res. Chem. Intermed. 44, 2929 (2018)

    Google Scholar 

  23. S. Ullah, M.A. Assiri, A.G. Al-Sehemi, M.A. Bustam, M. Sagir, F.A. Abdulkareem, M.R. Raza, M. Ayoub, A. Irfan, Int. J. Environ. Res. 14, 43 (2020)

    Google Scholar 

  24. H. Barki, L. Khaouane, S. Hanini, Kem. u Ind. 68, 289 (2019)

    Google Scholar 

  25. O.M. Jakšić, Z.S. Jakšić, Ž.D. Čupić, D.V. Randjelović, L.Z. Kolar-Anić, Sens. Actuators B Chem. 190, 419 (2014)

    Google Scholar 

  26. O. Jakšić, Ž. Čupić, Z. Jakšić, D. Randjelović, L. Kolar-Anić, Russ. J. Phys. Chem. A 87, 2134 (2013)

    Google Scholar 

  27. O.M. Jakšić, D.V. Randjelović, Z.S. Jakšić, Ž.D. Čupić, L.Z. Kolar-Anić, Chem. Eng. Res. Des. 92, 91 (2014)

    Google Scholar 

  28. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 1985)

    Google Scholar 

  29. D.T. Gillespie, A. Hellander, L.R. Petzold, J. Chem. Phys. 138, 170901 (2013)

    ADS  Google Scholar 

  30. D.T. Gillespie, J. Phys. Chem. 81, 2340 (1977)

    Google Scholar 

  31. D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)

    ADS  MathSciNet  Google Scholar 

  32. D.T. Gillespie, J. Chem. Phys. 115, 1716 (2001)

    ADS  Google Scholar 

  33. S. Lampoudi, D.T. Gillespie, L.R. Petzold, J. Chem. Phys. 130, 094104 (2009)

    ADS  Google Scholar 

  34. D.T. Gillespie, J. Chem. Phys. 113, 297 (2000)

    ADS  Google Scholar 

  35. D.T. Gillespie, J. Phys. Chem. A 106, 5063 (2002)

    Google Scholar 

  36. D.T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007)

    ADS  Google Scholar 

  37. H. Li, Y. Cao, L.R. Petzold, D.T. Gillespie, Biotechnol. Prog. 24, 56 (2008)

    Google Scholar 

  38. D.D. Do, Adsorption Analysis: Equilibria and Kinetics (Imperial College Press, London, 1998)

    Google Scholar 

  39. S. Maier, Plasmonics. Fundamentals and Applications (Springer, Berlin, 2007)

    Google Scholar 

  40. A. Felinger, J. Chromatogr. A 1184, 20 (2008)

    Google Scholar 

  41. L.S. Jung, C.T. Campbell, T.M. Chinowsky, M.N. Mar, S.S. Yee, Langmuir 14, 5636 (1998)

    Google Scholar 

  42. C.L. Byard, X. Han, S.B. Mendes, Anal. Chem. 84, 9762 (2012)

    Google Scholar 

  43. R. Wood, Philos. Mag. 4, 396 (1902)

    Google Scholar 

  44. H. Raether, Springer Tracts Mod. Phys. 111, 1 (1988)

    Google Scholar 

  45. E. Kretschmann, H. Raether, Z. Naturforsch. 23, 2135 (1968)

    ADS  Google Scholar 

  46. M.S. Mehand, G. De Crescenzo, B. Srinivasan, J. Mol. Recognit. 25, 208 (2012)

    Google Scholar 

  47. M.S. Mehand, B. Srinivasan, G. De Crescenzo, Sci. Rep. 5, 1 (2015)

    Google Scholar 

  48. O. Jakšić, Mendeley Data http://dx.doi.org/10.17632/R9YT6TJZNJ.1 (2018)

  49. O. Jakšić, Mendeley Data http://dx.doi.org/10.17632/w78xsxmg8d.1 (2019)

  50. O. Jakšić, Mendeley Data http://dx.doi.org/10.17632/pwsc2jgwzk.1 (2019)

  51. O. Jakšić, Harvard Dataverse V4. https://doi.org/10.7910/DVN/5VYJ5O (2018)

  52. G. Freiling, G. Jank, H. Abou-Kandil, Linear Algebra Appl. 241–243, 291 (1996)

    Google Scholar 

  53. M.A. Lohe, J. Math. Phys. 60, 072701 (2019)

    ADS  MathSciNet  Google Scholar 

  54. J.A. Samath, N. Selvaraju, I.J.C.A. Int, J. Comput. Appl. 1, 48 (2010)

    Google Scholar 

  55. T.C. Choy, Effective Medium Theory: Principles and Applications (Oxford University Press, Oxford, 2016)

    Google Scholar 

  56. G. Canziani, W. Zhang, D. Cines, A. Rux, S. Willis, G. Cohen, R. Eisenberg, I. Chaiken, Methods 19, 253 (1999)

    Google Scholar 

  57. O.M. Jakšić, Z. Jakšić, M.B. Rašljić, L.Z. Kolar-Anić, Adv. Math. Phys. 2019, 1 (2019)

    Google Scholar 

  58. T. Stanković, N. Dalarsson, and O. Jakšić, in 4th Symposium Mathematical Applications 24. i 25. Maj 2013, 99 (2014)

  59. M. Holmes, fits(f,xd,yd,p0,n,m) (MATLAB Cent. File Exch. Retr. March 31 2020) https://www.mathworks.com/matlabcentral/fileexchange/72113-fits-f-xd-yd-p0-n-m

  60. O. Jakšić, Mendeley Data http://dx.doi.org/10.17632/gfv2vzpx3p.1 (2020)

  61. D. Jenkins, G. Peterson, Mendeley Data http://dx.doi.org/10.17632/n3s9f96jwp.1 (2011)

  62. O. Jakšić, Mendeley Data http://dx.doi.org/10.17632/2jdnx2pfys.1 (2020)

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Acknowledgements

This work is a part of the research funded by the Serbian Ministry of Education, Science and Technological Development.

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Authors and Affiliations

  1. Centre of Microelectronic Technologies, Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, 11000, Belgrade, Serbia

    Olga Jakšić, Ivana Jokić, Zoran Jakšić, Ivana Mladenović, Katarina Radulović & Miloš Frantlović

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  1. Olga Jakšić
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Correspondence to Olga Jakšić.

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Jakšić, O., Jokić, I., Jakšić, Z. et al. The time response of plasmonic sensors due to binary adsorption: analytical versus numerical modeling. Appl. Phys. A 126, 342 (2020). https://doi.org/10.1007/s00339-020-03524-3

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