Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models
Using a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei <i>N</i>(<i>t</i>) vs. time <i>t</i>—from archetypical experiments on the electrod...
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MDPI AG
2023-12-01
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| author | Viktoria Kleshtanova Vassil V. Ivanov Feyzim Hodzhaoglu Jose Emilio Prieto Vesselin Tonchev |
| author_facet | Viktoria Kleshtanova Vassil V. Ivanov Feyzim Hodzhaoglu Jose Emilio Prieto Vesselin Tonchev |
| author_sort | Viktoria Kleshtanova |
| collection | DOAJ |
| description | Using a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei <i>N</i>(<i>t</i>) vs. time <i>t</i>—from archetypical experiments on the electrodeposition of mercury on platinum by I. Markov and E. Stoycheva, to obtain two scales: <i>N</i><sub>max</sub> and <i>τ</i>. The universal character of the studied phenomenon was revealed when replotting the original data as <i>α</i> ≡ <i>N</i>(<i>t</i>)/<i>N</i><sub>max</sub> vs. <i>t</i>/<i>τ</i>. Yet the simplest model, the recently introduced <i>α</i><sub>21</sub> model which is aimed to describe diffusion-limited growth in 2D, <i>α</i><sub>21</sub> = tanh<sup>2</sup>(2<i>t</i>/<i>τ</i><sub>21</sub>), fits all datasets with an <i>R</i><sup>2</sup> ≥ 0.989. This can be rationalized by attracting the non-classical notion of two-step nucleation—the nuclei form in a metastable phase which, in this case, grows on the electrode surface. Beyond the universality, we find the dependence of the two obtained scales on the overvoltage, which is increased systematically from 83 to 88 mV to generate the six <i>N</i>(<i>t</i>) datasets for each of the two electrode types—planar and hemispherical. Surprisingly, for one of them, the planar electrode, there is a discontinuity in the dependence—an almost horizontal jump from 85 to 86 mV, while for the hemispherical electrode, <i>τ</i> decreases smoothly. |
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| language | English |
| last_indexed | 2024-03-08T20:53:18Z |
| publishDate | 2023-12-01 |
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| spelling | doaj.art-fda211c62d2a4ff7b032be9d4c142a7f2023-12-22T14:02:00ZengMDPI AGCrystals2073-43522023-12-011312169010.3390/cryst13121690Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth ModelsViktoria Kleshtanova0Vassil V. Ivanov1Feyzim Hodzhaoglu2Jose Emilio Prieto3Vesselin Tonchev4Faculty of Physics, Sofia University, 1164 Sofia, BulgariaFaculty of Physics, Sofia University, 1164 Sofia, BulgariaInstitute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaInstituto de Química Física Blas Cabrera (IQF), CSIC, 28006 Madrid, SpainFaculty of Physics, Sofia University, 1164 Sofia, BulgariaUsing a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei <i>N</i>(<i>t</i>) vs. time <i>t</i>—from archetypical experiments on the electrodeposition of mercury on platinum by I. Markov and E. Stoycheva, to obtain two scales: <i>N</i><sub>max</sub> and <i>τ</i>. The universal character of the studied phenomenon was revealed when replotting the original data as <i>α</i> ≡ <i>N</i>(<i>t</i>)/<i>N</i><sub>max</sub> vs. <i>t</i>/<i>τ</i>. Yet the simplest model, the recently introduced <i>α</i><sub>21</sub> model which is aimed to describe diffusion-limited growth in 2D, <i>α</i><sub>21</sub> = tanh<sup>2</sup>(2<i>t</i>/<i>τ</i><sub>21</sub>), fits all datasets with an <i>R</i><sup>2</sup> ≥ 0.989. This can be rationalized by attracting the non-classical notion of two-step nucleation—the nuclei form in a metastable phase which, in this case, grows on the electrode surface. Beyond the universality, we find the dependence of the two obtained scales on the overvoltage, which is increased systematically from 83 to 88 mV to generate the six <i>N</i>(<i>t</i>) datasets for each of the two electrode types—planar and hemispherical. Surprisingly, for one of them, the planar electrode, there is a discontinuity in the dependence—an almost horizontal jump from 85 to 86 mV, while for the hemispherical electrode, <i>τ</i> decreases smoothly.https://www.mdpi.com/2073-4352/13/12/1690heterogeneous nucleationelectrodeposition<i>N</i>(<i>t</i>)-curves<i>α</i><sub>21</sub> modelRichards modelmodel of Johnson–Mehl–Avrami–Kolmogorov (JMAKn) |
| spellingShingle | Viktoria Kleshtanova Vassil V. Ivanov Feyzim Hodzhaoglu Jose Emilio Prieto Vesselin Tonchev Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models Crystals heterogeneous nucleation electrodeposition <i>N</i>(<i>t</i>)-curves <i>α</i><sub>21</sub> model Richards model model of Johnson–Mehl–Avrami–Kolmogorov (JMAKn) |
| title | Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models |
| title_full | Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models |
| title_fullStr | Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models |
| title_full_unstemmed | Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models |
| title_short | Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models |
| title_sort | heterogeneous substrates modify non classical nucleation pathways reanalysis of kinetic data from the electrodeposition of mercury on platinum using hierarchy of sigmoid growth models |
| topic | heterogeneous nucleation electrodeposition <i>N</i>(<i>t</i>)-curves <i>α</i><sub>21</sub> model Richards model model of Johnson–Mehl–Avrami–Kolmogorov (JMAKn) |
| url | https://www.mdpi.com/2073-4352/13/12/1690 |
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