{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T23:38:35Z","timestamp":1783035515283,"version":"3.54.6"},"reference-count":57,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>The two-exponential Sheffield equation of viscosity \u03b7(T) = A1\u00b7T\u00b7[1 + A2\u00b7exp(Hm\/RT)]\u00b7[1 + C\u00b7exp(Hd\/RT)], where A1, A2, Hm, C, and Hm are material-specific constants, is used to analyze the viscous flows of two glass-forming organic materials\u2014salol and \u03b1-phenyl-o-cresol. It is demonstrated that the viscosity equation can be simplified to a four-parameter version: \u03b7(T) = A\u00b7T\u00b7exp(Hm\/RT)]\u00b7[1 + C\u00b7exp(Hd\/RT)]. The Sheffield model gives a correct description of viscosity, with two exact Arrhenius-type asymptotes below and above the glass transition temperature, whereas near the Tg it gives practically the same results as well-known and widely used viscosity equations. It is revealed that the constants of the Sheffield equation are not universal for all temperature ranges and may need to be updated for very high temperatures, where changes occur in melt properties leading to modifications of A and Hm for both salol and \u03b1-phenyl-o-cresol.<\/jats:p>","DOI":"10.3390\/molecules25174029","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T11:22:43Z","timestamp":1599132163000},"page":"4029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On Viscous Flow in Glass-Forming Organic Liquids"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8928-4879","authenticated-orcid":false,"given":"Michael I.","family":"Ojovan","sequence":"first","affiliation":[{"name":"Department of Materials, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK"},{"name":"Department of Radiochemistry, Moscow State University Named after M.V. Lomonosov, Leninskie Gory 1, Bd.3, 119991 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"ref_1","unstructured":"Volf, M.B. (1988). Mathematical Approach to Glass, Elsevier."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6251","DOI":"10.1063\/1.469071","article-title":"Dynamics of glass-forming liquids. I. Temperature-derivative analysis of dielectric relaxation data","volume":"102","author":"Stickel","year":"1995","journal-title":"J. Chem. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1103\/PhysRevE.53.751","article-title":"Fitting of viscosity: Distinguishing the temperature dependences predicted by various models of supercooled liquids","volume":"53","author":"Kivelson","year":"1996","journal-title":"Phys. Rev. E"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.1063\/1.1286035","article-title":"Relaxation in glassforming liquids and amorphous solids","volume":"88","author":"Angell","year":"2000","journal-title":"J. Appl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7619","DOI":"10.1063\/1.1515132","article-title":"Viscosity of silica","volume":"92","author":"Doremus","year":"2002","journal-title":"J. Appl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6135","DOI":"10.1063\/1.1649732","article-title":"Disentangling density and temperature effects in the viscous slowing down of glassforming liquids","volume":"120","author":"Tarjus","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_7","unstructured":"Varshneya, A.K. (2006). Fundamentals of Inorganic Glasses, Society of Glass Technology."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"415107","DOI":"10.1088\/0953-8984\/19\/41\/415107","article-title":"Thermodynamic parameters of bonds in glassy materials from viscosity\u2013temperature relationships","volume":"19","author":"Ojovan","year":"2007","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"19780","DOI":"10.1073\/pnas.0911705106","article-title":"Viscosity of glass-forming liquids","volume":"106","author":"Mauro","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_10","first-page":"143","article-title":"Viscous flow and the viscosity of melts and glasses","volume":"53","author":"Ojovan","year":"2012","journal-title":"Phys. Chem. Glasses"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"032308","DOI":"10.1103\/PhysRevE.90.032308","article-title":"Transition from Arrhenius to non-Arrhenius temperature dependence of structural relaxation time in glass-forming liquids: Continuous versus discontinuous scenario","volume":"90","author":"Popova","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Isayev, A.I. (2016). Encyclopedia of Polymer Blends: Volume 3: Structure, Wiley-VCH. [1st ed.].","DOI":"10.1002\/9783527653966"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jnoncrysol.2016.01.007","article-title":"High-temperature viscosity of many-component glass melts","volume":"437","author":"Hrma","year":"2016","journal-title":"J. Non-Crystalline Solids"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1111\/jace.14678","article-title":"Viscosity of glass-forming systems","volume":"100","author":"Zheng","year":"2016","journal-title":"J. Am. Ceram. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.physb.2017.08.025","article-title":"On relaxation nature of glass transition in amorphous materials","volume":"523","author":"Sanditov","year":"2017","journal-title":"Phys. B Condens. Matter"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"12169","DOI":"10.1016\/j.ceramint.2019.03.121","article-title":"An Avramov-based viscosity model for the SiO2-Al2O3-Na2O-K2O system in a wide temperature range","volume":"45","author":"Starodub","year":"2019","journal-title":"Ceram. Int."},{"key":"ref_17","unstructured":"Sturm, K.G. (Preprint, 2020). Microscopic-Phenomenological Model of Glass Transition and Molecular Translation in Liquids III.5 Viscosity Behavior and Glass Transition of Silicate Reference Glasses, Preprint."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zheng, Q., Zheng, J., Solvang, M., Yue, Y., and Mauro, J.C. (2020). Determining the liquidus viscosity of glass-forming liquids through differential scanning calorimetry. J. Am. Ceram. Soc.","DOI":"10.1111\/jace.17363"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chen, C., Zeng, H., Deng, Y., Yan, J., Jiang, Y., Chen, G., Zu, Q., and Sun, L. (2020). A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation. Appl. Sci., 10.","DOI":"10.3390\/app10020428"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"033134","DOI":"10.1103\/PhysRevResearch.2.033134","article-title":"Atomic-scale expressions for viscosity and fragile-strong behavior in metal alloys based on the Zwanzig-Mountain formula","volume":"2","author":"Chevallard","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"225501","DOI":"10.1103\/PhysRevLett.124.225501","article-title":"Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids","volume":"124","author":"Tong","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","first-page":"100034","article-title":"Fragile-to-strong transitions in glass forming liquids","volume":"4","author":"Lucas","year":"2019","journal-title":"J. Non-Cryst. Solids X"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1063\/1.1670321","article-title":"Inadequacies of Viscosity Theories for B2O3","volume":"49","author":"Macedo","year":"1968","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1080\/13642818708208532","article-title":"The viscosity of vitreous silicon dioxide","volume":"56","author":"Mott","year":"1987","journal-title":"Philos. Mag. B"},{"key":"ref_25","first-page":"138","article-title":"The flow of glass","volume":"33","author":"Douglas","year":"1949","journal-title":"J. Soc. Glass Tech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.matlet.2016.07.006","article-title":"On limitations of the viscosity versus temperature plot for glass-forming substances","volume":"182","author":"Fecht","year":"2016","journal-title":"Mater. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3803","DOI":"10.1063\/1.1647260","article-title":"Viscosity of network liquids within Doremus approach","volume":"95","author":"Ojovan","year":"2004","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"11507","DOI":"10.1088\/0953-8984\/18\/50\/007","article-title":"Topologically disordered systems at the glass transition","volume":"18","author":"Ojovan","year":"2006","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"eaba3747","DOI":"10.1126\/sciadv.aba3747","article-title":"Minimal quantum viscosity from fundamental physical constants","volume":"6","author":"Trachenko","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1111\/ijag.12045","article-title":"Thermodynamic Parameters of Bonds in Glassy Materials from Shear Viscosity Coefficient Data","volume":"5","author":"Ojovan","year":"2014","journal-title":"Int. J. Appl. Glas. Sci."},{"key":"ref_31","unstructured":"Karlsson, S. (2019, January 9\u201312). The viscosity effect of TiO2 on soda-lime-silicate bearing glass. Proceedings of the 4th Workshop on Glass and Entropy and 9th Otto Schott Colloquium, Jena, Germany."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.13036\/17533546.60.4.016","article-title":"The viscosity of Bi2O3\u2013B2O3\u2013SiO2 glasses and melts","volume":"60","author":"Shilov","year":"2019","journal-title":"Glas. Technol. Eur. J. Glas. Sci. Technol. Part A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2317","DOI":"10.1021\/j100660a023","article-title":"Viscous flow in simple organic liquids","volume":"76","author":"Laughlin","year":"1972","journal-title":"J. Phys. Chem."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1063\/1.3061720","article-title":"Introduction to Solid State Physics","volume":"7","author":"Kittel","year":"1954","journal-title":"Phys. Today"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"R703","DOI":"10.1088\/0953-8984\/14\/23\/201","article-title":"Heterogeneous dynamics in liquids: Fluctuations in space and time","volume":"14","author":"Richert","year":"2002","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mysen, B., and Richet, P. (2019). Silicate Glasses and Melts, Elsevier.","DOI":"10.1016\/B978-0-444-63708-6.00005-3"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3639","DOI":"10.1063\/1.1680531","article-title":"High-temperature flow behavior of glass-forming liquids: A free-volume interpretation","volume":"59","author":"Cukierman","year":"1973","journal-title":"J. Chem. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3701","DOI":"10.1021\/ja01619a008","article-title":"The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids","volume":"77","author":"Williams","year":"1955","journal-title":"J. Am. Chem. Soc."},{"key":"ref_39","unstructured":"Nemilov, S.V. (1995). Thermodynamic and Kinetic Aspects of the Vitreous State, CRC Press."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1134\/S1087659613060084","article-title":"Maxwell equation and classical theories of glass transition as a basis for direct calculation of viscosity at glass transition temperture","volume":"39","author":"Nemilov","year":"2013","journal-title":"Glas. Phys. Chem."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"21885","DOI":"10.1039\/C5CP03651H","article-title":"Unveiling the relationships among the viscosity equations of glass liquids and colloidal suspensions for obtaining universal equations with the generic free volume concept","volume":"17","author":"Hao","year":"2015","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1140\/epje\/i2015-15091-6","article-title":"The Modified VFT law of glass former materials under pressure: Part II: Relation with the equation of state","volume":"38","author":"Rault","year":"2015","journal-title":"Eur. Phys. J. E"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1557\/opl.2015.44","article-title":"About activation energy of viscous flow of glasses and melts","volume":"1757","author":"Ojovan","year":"2015","journal-title":"Mater. Res. Soc. Symp. Proc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1134\/S108765960701004X","article-title":"Problems of compatibility of the values of glass transition temperatures published in the world literature","volume":"33","author":"Mazurin","year":"2007","journal-title":"Glas. Phys. Chem."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"411914","DOI":"10.1016\/j.physb.2019.411914","article-title":"Glass transition criterion and plastic deformation of glass","volume":"582","author":"Sanditov","year":"2020","journal-title":"Phys. B Condens. Matter"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Mauro, J.C., and Smedskjaer, M.M. (2014). Statistical mechanics of glass. J. Non-Cryst. Solids, 41\u201353.","DOI":"10.1016\/j.jnoncrysol.2014.04.009"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"411895","DOI":"10.1016\/j.physb.2019.411895","article-title":"Homogeneous nucleation of phase transformations in supercooled water","volume":"579","author":"Tournier","year":"2020","journal-title":"Phys. B Condens. Matter"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.chemphys.2019.02.006","article-title":"First-order transitions in glasses and melts induced by solid siperclusters nucleated and melted by homogeneous nucleation instead of surface melting","volume":"524","author":"Tournier","year":"2019","journal-title":"Chem. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3186","DOI":"10.1021\/acs.jpcb.0c00214","article-title":"Revealing Structural Changes at Glass Transition via Radial Distribution Functions","volume":"124","author":"Ojovan","year":"2020","journal-title":"J. Phys. Chem. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1126\/science.aaf3182","article-title":"Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers","volume":"352","author":"Albert","year":"2016","journal-title":"Science"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.jnoncrysol.2010.06.041","article-title":"Observing the twinkling fractal nature of the glass transition","volume":"357","author":"Stanzione","year":"2011","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"A1","DOI":"10.1016\/j.physb.2016.10.037","article-title":"Topological phase transitions","volume":"505","author":"Continentino","year":"2017","journal-title":"Phys. B Condens. Matter"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1063\/1.1677987","article-title":"Configurational Excitations in Condensed Matter, and the \u201cBond Lattice\u2019\u2019 Model for the Liquid-Glass Transition","volume":"57","author":"Angell","year":"1972","journal-title":"J. Chem. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"205504","DOI":"10.1103\/PhysRevLett.110.205504","article-title":"Elementary Excitations and Crossover Phenomenon in Liquids","volume":"110","author":"Iwashita","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.jnoncrysol.2013.10.016","article-title":"Ordering and structural changes at the glass\u2013liquid transition","volume":"382","author":"Ojovan","year":"2013","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Nemilov, S.V. (2018). On the Possibility of Calculating Entropy, Free Energy, and Enthalpy of Vitreous Substances. Entropy, 20.","DOI":"10.3390\/e20030187"},{"key":"ref_57","unstructured":"Cassar, D.R., Santos, G.G., and Zanotto, E.D. (2020). Designing optical glasses by machine learning coupled with genetic algorithms. arXiv."}],"container-title":["Molecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1420-3049\/25\/17\/4029\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:06:32Z","timestamp":1760177192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1420-3049\/25\/17\/4029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,3]]},"references-count":57,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["molecules25174029"],"URL":"https:\/\/doi.org\/10.3390\/molecules25174029","relation":{},"ISSN":["1420-3049"],"issn-type":[{"value":"1420-3049","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,3]]}}}