Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids
Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibi...
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MDPI AG
2023-04-01
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| Series: | International Journal of Molecular Sciences |
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| Online Access: | https://www.mdpi.com/1422-0067/24/9/7871 |
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| author | Francesco Rusciano Raffaele Pastore Francesco Greco |
| author_facet | Francesco Rusciano Raffaele Pastore Francesco Greco |
| author_sort | Francesco Rusciano |
| collection | DOAJ |
| description | Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>t</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula>, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≃</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a “universal” evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential. |
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| language | English |
| last_indexed | 2024-03-11T04:16:47Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-09ac3914015e4038a624848f18e56f682023-11-17T23:01:45ZengMDPI AGInternational Journal of Molecular Sciences1661-65961422-00672023-04-01249787110.3390/ijms24097871Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming LiquidsFrancesco Rusciano0Raffaele Pastore1Francesco Greco2Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, ItalyDepartment of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, ItalyDepartment of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, ItalyRecent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>t</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula>, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≃</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a “universal” evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.https://www.mdpi.com/1422-0067/24/9/7871diffusionglass-formerssupercooled liquidsFickian yet non-GaussianBrownian motionBrownian non-Gaussian diffusion |
| spellingShingle | Francesco Rusciano Raffaele Pastore Francesco Greco Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids International Journal of Molecular Sciences diffusion glass-formers supercooled liquids Fickian yet non-Gaussian Brownian motion Brownian non-Gaussian diffusion |
| title | Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids |
| title_full | Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids |
| title_fullStr | Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids |
| title_full_unstemmed | Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids |
| title_short | Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids |
| title_sort | universal evolution of fickian non gaussian diffusion in two and three dimensional glass forming liquids |
| topic | diffusion glass-formers supercooled liquids Fickian yet non-Gaussian Brownian motion Brownian non-Gaussian diffusion |
| url | https://www.mdpi.com/1422-0067/24/9/7871 |
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