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Schmelzer JWP, Tropin TV, Schick C. Effects of Structural Relaxation of Glass-Forming Melts on the Overall Crystallization Kinetics in Cooling and Heating. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1485. [PMID: 37998176 PMCID: PMC10670338 DOI: 10.3390/e25111485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Revised: 10/21/2023] [Accepted: 10/23/2023] [Indexed: 11/25/2023]
Abstract
In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to the current values of pressure and temperature. However, near and below the glass transition temperature, Tg, this condition is commonly not fulfilled. In such cases, in the treatment of crystallization, deviations in the state of the liquid from the respective metastable equilibrium state have to be accounted for when determining the kinetic coefficients governing the crystallization kinetics, the thermodynamic driving force of crystallization, and the surface tension of the aggregates of the newly evolving crystal phase including the surface tension of critical clusters considerably affecting the crystal nucleation rate. These factors may greatly influence the course of the overall crystallization process. A theoretical analysis of the resulting effects is given in the present paper by numerical solutions of the J(ohnson)-M(ehl)-A(vrami)-K(olmogorov) equation employed as the tool to model the overall crystallization kinetics and by analytical estimates of the crystallization peak temperatures in terms of the dependence on cooling and heating rates. The results are shown to be in good agreement with the experimental data. Possible extensions of the theory are anticipated and will be explored in future analysis.
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Affiliation(s)
- Jürn W. P. Schmelzer
- Institut für Physik, Universität Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany;
- Competence Centre CALOR, Faculty of Interdisciplinary Research, University of Rostock, Albert-Einstein-Str. 25, 18051 Rostock, Germany
| | - Timur V. Tropin
- BCMaterials, Basque Center for Materials, Applications and Nanostructures, UPV/EHU Science Park, 48940 Leioa, Spain;
- Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, ul. Joliot-Curie 6, 141980 Dubna, Russia
| | - Christoph Schick
- Institut für Physik, Universität Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany;
- Competence Centre CALOR, Faculty of Interdisciplinary Research, University of Rostock, Albert-Einstein-Str. 25, 18051 Rostock, Germany
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2
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Consiglio AN, Ouyang Y, Powell-Palm MJ, Rubinsky B. An extreme value statistics model of heterogeneous ice nucleation for quantifying the stability of supercooled aqueous systems. J Chem Phys 2023; 159:064511. [PMID: 37565684 DOI: 10.1063/5.0155494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 07/10/2023] [Indexed: 08/12/2023] Open
Abstract
The propensity of water to remain in a metastable liquid state at temperatures below its equilibrium melting point holds significant potential for cryopreserving biological material such as tissues and organs. The benefits conferred are a direct result of progressively reducing metabolic expenditure due to colder temperatures while simultaneously avoiding the irreversible damage caused by the crystallization of ice. Unfortunately, the freezing of water in bulk systems of clinical relevance is dominated by random heterogeneous nucleation initiated by uncharacterized trace impurities, and the marked unpredictability of this behavior has prevented the implementation of supercooling outside of controlled laboratory settings and in volumes larger than a few milliliters. Here, we develop a statistical model that jointly captures both the inherent stochastic nature of nucleation using conventional Poisson statistics as well as the random variability of heterogeneous nucleation catalysis through bivariate extreme value statistics. Individually, these two classes of models cannot account for both the time-dependent nature of nucleation and the sample-to-sample variability associated with heterogeneous catalysis, and traditional extreme value models have only considered variations of the characteristic nucleation temperature. We conduct a series of constant cooling rate and isothermal nucleation experiments with physiological saline solutions and leverage the statistical model to evaluate the natural variability of kinetic and thermodynamic nucleation parameters. By quantifying freezing probability as a function of temperature, supercooled duration, and system volume while accounting for nucleation site variability, this study also provides a basis for the rational design of stable supercooled biopreservation protocols.
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Affiliation(s)
- Anthony N Consiglio
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | - Yu Ouyang
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | - Matthew J Powell-Palm
- J. Mike Walker '66 Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77840, USA
| | - Boris Rubinsky
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
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Sampson CC, Metaxas PJ, Barwood MTJ, Stanwix PL, Johns ML, May EF. Aqueous Solid Formation Kinetics in High-Pressure Methane at Trace Water Concentrations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:4631-4641. [PMID: 36958053 DOI: 10.1021/acs.langmuir.2c03376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Natural gas containing trace amounts of water is frequently liquefied at conditions where aqueous solids are thermodynamically stable. However, no data are available to describe the kinetics of aqueous solid formation at these conditions. Here, we present experimental measurements of both solid formation kinetics and solid-fluid equilibrium for trace concentrations of (12 ± 0.7) ppm water in methane using a stirred, high-pressure apparatus and visual microscopy. Along isochoric pathways with cooling rates around 1 K·min-1, micron-scale aqueous solids were observed to form at subcoolings of (0.3-8.6) K, relative to an average equilibrium melting temperature of (253 ± 1.9) K at (8.9 ± 0.08) MPa; these data are consistent with predicted methane hydrate dissociation conditions within the uncertainty of both the experiment and model. The 36 measured formation events were used to construct a cumulative formation probability distribution, which was then fitted with a model from Classical Nucleation Theory, enabling the extraction of kinetic and thermodynamic nucleation parameters. While the resulting nucleation parameter values were comparable to those published for methane hydrate formation in bulk-water systems, the observed growth kinetics were distinctly different with only a small percentage of the water in the system converting into micron-scale solids over the experimental time scale. These results may help explain how cryogenic heat exchangers in liquefied natural gas facilities can operate for long periods without blockages forming despite being at very high subcoolings for aqueous solids.
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Affiliation(s)
- Catherine C Sampson
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
- Future Energy Exports Cooperative Research Centre, 35 Stirling Highway, Perth, Western Australia 6009, Australia
| | - Peter J Metaxas
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
| | - Mark T J Barwood
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
- Future Energy Exports Cooperative Research Centre, 35 Stirling Highway, Perth, Western Australia 6009, Australia
| | - Paul L Stanwix
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
| | - Michael L Johns
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
- Future Energy Exports Cooperative Research Centre, 35 Stirling Highway, Perth, Western Australia 6009, Australia
| | - Eric F May
- Fluid Science & Resources, Department of Chemical Engineering, School of Engineering, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
- Future Energy Exports Cooperative Research Centre, 35 Stirling Highway, Perth, Western Australia 6009, Australia
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Schmelzer JWP, Tropin TV, Abyzov AS. Kinetics of Precipitation Processes at Non-Zero Input Fluxes of Segregating Particles. ENTROPY (BASEL, SWITZERLAND) 2023; 25:329. [PMID: 36832695 PMCID: PMC9955409 DOI: 10.3390/e25020329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2023] [Revised: 02/01/2023] [Accepted: 02/04/2023] [Indexed: 06/18/2023]
Abstract
We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. As shown here, the value of the input flux significantly affects the number of supercritical clusters formed, their growth kinetics, and, in particular, the coarsening behavior in the late stages of the process. The detailed specification of the respective dependencies is the aim of the present analysis, which combines numerical computations with an analytical treatment of the obtained results. In particular, a treatment of the coarsening kinetics is developed, allowing a description of the development of the number of clusters and their average sizes in the late stages of the segregation processes in open systems, which goes beyond the scope of the classical Lifshitz, Slezov and Wagner theory. As is also shown, in its basic ingredients, this approach supplies us with a general tool for the theoretical description of Ostwald ripening in open systems, or systems where the boundary conditions, like temperature or pressure, vary with time. Having this method at one's disposal supplies us with the possibility that conditions can be theoretically tested, leading to cluster size distributions that are most appropriate for desired applications.
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Affiliation(s)
- Jürn W. P. Schmelzer
- Institut für Physik der Universität Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany
- Competence Centre CALOR, Faculty of Interdisciplinary Research, University of Rostock, Albert-Einstein-Str. 25, 18051 Rostock, Germany
| | - Timur V. Tropin
- Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, ul. Joliot-Curie 6, 141980 Dubna, Russia
| | - Alexander S. Abyzov
- National Science Center Kharkov Institute of Physics and Technology, Akademicheskaya Street 1, 61108 Kharkov, Ukraine
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Wu T, Chandran S, Zhang Y, Zheng T, Pfohl T, Xu J, Reiter G. Primary Nucleation in Metastable Solutions of Poly(3-hexylthiophene). Macromolecules 2022. [DOI: 10.1021/acs.macromol.1c02193] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tianyu Wu
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
- Advanced Materials Laboratory of Ministry of Education, Department of Chemical Engineering, Tsinghua University, 100084 Beijing, China
| | | | - Yao Zhang
- Advanced Materials Laboratory of Ministry of Education, Department of Chemical Engineering, Tsinghua University, 100084 Beijing, China
| | - Tianze Zheng
- Advanced Materials Laboratory of Ministry of Education, Department of Chemical Engineering, Tsinghua University, 100084 Beijing, China
| | - Thomas Pfohl
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Jun Xu
- Advanced Materials Laboratory of Ministry of Education, Department of Chemical Engineering, Tsinghua University, 100084 Beijing, China
| | - Günter Reiter
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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Mukhametzyanov T, Schmelzer JW, Yarko E, Abdullin A, Ziganshin M, Sedov I, Schick C. Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL). Polymers (Basel) 2021; 13:polym13213617. [PMID: 34771173 PMCID: PMC8588086 DOI: 10.3390/polym13213617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Revised: 10/15/2021] [Accepted: 10/18/2021] [Indexed: 11/16/2022] Open
Abstract
The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer.
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Affiliation(s)
- Timur Mukhametzyanov
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
- Correspondence: (T.M.); (C.S.); Tel.: +7-903-343-9026 (T.M.); +49-381-498-6880 (C.S.)
| | - Jürn W.P. Schmelzer
- Institute of Physics and Competence Centre CALOR, University of Rostock, Albert-Einstein-Str. 23-24, 18051 Rostock, Germany;
| | - Egor Yarko
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
| | - Albert Abdullin
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
| | - Marat Ziganshin
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
| | - Igor Sedov
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
| | - Christoph Schick
- A. M. Butlerov Chemical Institute, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia; (E.Y.); (A.A.); (M.Z.); (I.S.)
- Institute of Physics and Competence Centre CALOR, University of Rostock, Albert-Einstein-Str. 23-24, 18051 Rostock, Germany;
- Correspondence: (T.M.); (C.S.); Tel.: +7-903-343-9026 (T.M.); +49-381-498-6880 (C.S.)
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