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Gheribi AE. Unveiling the Microscopic Origin of Ion Transference Numbers in Molten Salt Systems: A Kinetic Theory Approach to an Accurate "Golden Rule". ACS OMEGA 2025; 10:10272-10282. [PMID: 40124059 PMCID: PMC11923847 DOI: 10.1021/acsomega.4c09587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/25/2024] [Revised: 01/31/2025] [Accepted: 02/05/2025] [Indexed: 03/25/2025]
Abstract
In recent years, there has been a renewed interest in accurately quantifying the ion's transference number within molten salts. Surprisingly, despite efforts to address the severe lack of experimental data, there is still no reliable theoretical framework that establishes a clear link between the transference number and simulated phase trajectories through atomistic simulations or a dependable theoretical relationship for precise estimation. In general, overcoming limitations in both experimental and fundamental aspects, transference numbers are typically estimated by either considering the Nernst-Einstein (NE) approximation or employing the so-called "golden rules". However, it is worth noting that neither the Nernst-Einstein approximation nor the "golden rules" provide a truly accurate prediction. This work concentrates on establishing a robust theoretical framework to accurately define transference number boundaries and averages within molten salt systems. This is achieved by integrating principles from kinetic theory with an in-depth exploration of the electronic structure and local ordering of molten salts. Unlike prevailing theoretical approaches that are heavily reliant on Einstein's concept of ion mobility, which correlate with self-diffusion, the proposed theoretical framework is fundamentally grounded in the inherent mobility of ions. In summary, the introduction of this original "golden rule" showcases robust predictive capabilities, effectively addressing the scarcity of diverse observations gleaned from various experimental sources in the literature. Finally, the proposed formalism is extended to complex molten salts through a microscopic consideration of the impact of the cation associated with the anion upon its diffusional cross-section. Based on this, the cationic transference number of all divalent metal halide molten salts is predicted to be very close to that reported in the literature.
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Affiliation(s)
- Aïmen E. Gheribi
- Department of Mechanical,
Industrial and Aerospace Engineering, Concordia
University, 1455 De Maisonneuve Blvd. W, Montreal, Quebec H3G 1M8, Canada
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Uzoma PC, Ding X, Wen X, Zhang L, Penkov OV, Hu H. A wear-resistant silicon nano-spherical AFM probe for robust nanotribological studies. Phys Chem Chem Phys 2022; 24:23849-23857. [PMID: 36165057 DOI: 10.1039/d2cp03150g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Nanoscale wear can severely limit the performance of tips used in atomic force microscopy, especially in contact and lateral mode operations. Hence, we investigated the mechanical and tribological properties of a newly invented nano-spherical silicon tip produced via swelling of single-crystal silicon using helium ion dosing to ascertain its reliability for AFM operations. The nanoindentation test proved that the modulus of elasticity of the nano-spheres tends to increase with the diameter of the spheres at 0.5 mN contact force. However, at 10 mN higher contact force, the elastic modulus was stable at ∼160 GPa irrespective of the sphere diameter. The SEM images confirmed the durability of the tip after 10 000 cycles of sliding on a silicon wafer and quartz surfaces. There was no damage on the tip and the wear debris was suggested to be from the localized wear on the counter wafer surface. Also, the in situ AFM pull-off force test indicated that the geometry of the tip remained unaltered during the wear test. The Si/SiO2 tribology study showed a decrease in coefficient of friction as velocity and sliding cycles increased which was attributed to the tribochemical reactions occurring at the Si/SiO2 interfaces. These results indicate that the new nano-spherical AFM tip has advantages in nanoscale tribology measurement.
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Affiliation(s)
- Paul C Uzoma
- ZJU-UIUC Institute, International Campus, Zhejiang University, Haining, 314400, China.
| | - Xiaolei Ding
- ZJU-UIUC Institute, International Campus, Zhejiang University, Haining, 314400, China.
| | - Xiaolei Wen
- Center for Micro and Nanoscale Research and Fabrication, University of Science and Technology of China, Hefei, 230026, China
| | - Lansheng Zhang
- ZJU-UIUC Institute, International Campus, Zhejiang University, Haining, 314400, China.
| | - Oleksiy V Penkov
- ZJU-UIUC Institute, International Campus, Zhejiang University, Haining, 314400, China. .,Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Huan Hu
- ZJU-UIUC Institute, International Campus, Zhejiang University, Haining, 314400, China. .,State Key laboratory of Fluidic Power & Mechatronic Systems, Zhejiang University, Hangzhou, China.,Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
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