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de Bruijn R, Michels JJ, van der Schoot P. Transient nucleation driven by solvent evaporation. J Chem Phys 2024; 160:084505. [PMID: 38415833 DOI: 10.1063/5.0186395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 01/31/2024] [Indexed: 02/29/2024] Open
Abstract
We theoretically investigate homogeneous crystal nucleation in a solution containing a solute and a volatile solvent. The solvent evaporates from the solution, thereby continuously increasing the concentration of the solute. We view it as an idealized model for the far-out-of-equilibrium conditions present during the liquid-state manufacturing of organic electronic devices. Our model is based on classical nucleation theory, taking the solvent to be a source of the transient conditions in which the solute drops out of the solution. Other than that, the solvent is not directly involved in the nucleation process itself. We approximately solve the kinetic master equations using a combination of Laplace transforms and singular perturbation theory, providing an analytical expression for the nucleation flux. Our results predict that (i) the nucleation flux lags slightly behind a commonly used quasi-steady-state approximation. This effect is governed by two counteracting effects originating from solvent evaporation: while a faster evaporation rate results in an increasingly larger influence of the lag time on the nucleation flux, this lag time itself is found to decrease with increasing evaporation rate. Moreover, we find that (ii) the nucleation flux and the quasi-steady-state nucleation flux are never identical, except trivially in the stationary limit, and (iii) the initial induction period of the nucleation flux, which we characterize as a generalized induction time, decreases weakly with the evaporation rate. This indicates that the relevant time scale for nucleation also decreases with an increasing evaporation rate. Our analytical theory compares favorably with results from a numerical evaluation of the governing kinetic equations.
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Affiliation(s)
- René de Bruijn
- Department of Applied Physics and Science Education, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Jasper J Michels
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Paul van der Schoot
- Department of Applied Physics and Science Education, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Richard D, Speck T. Classical nucleation theory for the crystallization kinetics in sheared liquids. Phys Rev E 2019; 99:062801. [PMID: 31330660 DOI: 10.1103/physreve.99.062801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Indexed: 06/10/2023]
Abstract
While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds of particles.
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Affiliation(s)
- David Richard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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Arango-Restrepo A, Barragán D, Rubi JM. Self-assembling outside equilibrium: emergence of structures mediated by dissipation. Phys Chem Chem Phys 2019; 21:17475-17493. [DOI: 10.1039/c9cp01088b] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.
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Affiliation(s)
- A. Arango-Restrepo
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
| | - D. Barragán
- Escuela de Química
- Facultad de Ciencias
- Universidad Nacional de Colombia
- Medellín
- Colombia
| | - J. M. Rubi
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
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Schremb M, Campbell JM, Christenson HK, Tropea C. Ice Layer Spreading along a Solid Substrate during Solidification of Supercooled Water: Experiments and Modeling. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:4870-4877. [PMID: 28459594 DOI: 10.1021/acs.langmuir.7b00930] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The thermal influence of a solid wall on the solidification of a sessile supercooled water drop is experimentally investigated. The velocity of the initial ice layer propagating along the solid substrate prior to dendritic solidification is determined from videos captured using a high-speed video system. Experiments are performed for varying substrate materials and liquid supercooling. In contrast to recent studies at moderate supercooling, in the case of metallic substrates only a weak influence of the substrate's thermal properties on the ice layer velocity is observed. Using the analytical solution of the two-phase Stefan problem, a semiempirical model for the ice layer velocity is developed. The experimental data are well described for all supercooling levels in the entire diffusion limited solidification regime. For higher supercooling, the model overestimates the freezing velocity due to kinetic effects during molecular attachment at the solid-liquid interface, which are not accounted for in the model. The experimental findings of the present work offer a new perspective on the design of anti-icing systems.
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Affiliation(s)
- Markus Schremb
- Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt , Darmstadt, Germany
| | - James M Campbell
- School of Physics and Astronomy, University of Leeds , Leeds, United Kingdom
| | - Hugo K Christenson
- School of Physics and Astronomy, University of Leeds , Leeds, United Kingdom
| | - Cameron Tropea
- Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt , Darmstadt, Germany
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Palberg T, Wette P, Herlach DM. Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres. Phys Rev E 2016; 93:022601. [PMID: 26986371 DOI: 10.1103/physreve.93.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2015] [Indexed: 06/05/2023]
Abstract
The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.
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Affiliation(s)
- Thomas Palberg
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
| | - Patrick Wette
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51147 Köln, Germany
- Space Administration, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 53227 Bonn, Germany
| | - Dieter M Herlach
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51147 Köln, Germany
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Schweizer M, Sagis LMC. Systematic coarse-graining in nucleation theory. J Chem Phys 2015; 143:074503. [DOI: 10.1063/1.4927338] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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Malila J, McGraw R, Laaksonen A, Lehtinen KEJ. Communication: Kinetics of scavenging of small, nucleating clusters: First nucleation theorem and sum rules. J Chem Phys 2015; 142:011102. [DOI: 10.1063/1.4905213] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jussi Malila
- Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
| | - Robert McGraw
- Biological, Environmental & Climate Sciences Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Ari Laaksonen
- Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
- Finnish Meteorological Institute, Climate Research, P.O. Box 503, 00101 Helsinki, Finland
| | - Kari E. J. Lehtinen
- Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
- Finnish Meteorological Institute, Atmospheric Research Centre of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
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ter Horst JH, Bedeaux D, Kjelstrup S. The role of temperature in nucleation processes. J Chem Phys 2011; 134:054703. [PMID: 21303148 DOI: 10.1063/1.3544689] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Heat and mass transfers are coupled processes, also in nucleation. In principle, a nucleating cluster would have a different temperature compared to the surrounding supersaturated old phase because of the heat release involved with attaching molecules to the cluster. In turn a difference in temperature across the cluster surface is a driving force for the mass transfer to and from the cluster. This coupling of forces in nonisothermal nucleation is described using mesoscopic nonequilibrium thermodynamics, emphasizing measurable heat effects. An expression was obtained for the nonisothermal nucleation rate in a one-component system, in the case where a temperature difference exists between a cluster distribution and the condensed phase. The temperature is chosen as a function of the cluster size only, while the temperature of the condensed phase is held constant by a bath. The generally accepted expression for isothermal stationary nucleation is contained as a limiting case of the nonisothermal stationary nucleation rate. The equations for heat and mass transport were solved for stationary nucleation with the given cluster distribution and with the temperature controlled at the boundaries. A factor was defined for these conditions, determined by the heat conductivity of the surrounding phase and the phase transition enthalpy, to predict the deviation between isothermal and nonisothermal nucleation. For the stationary state described, the factor appears to give small deviations, even for primary nucleation of droplets in vapor, making the nonisothermal rate smaller than the isothermal one. The set of equations may lead to larger and different thermal effects under different boundary conditions, however.
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Affiliation(s)
- J H ter Horst
- Process & Energy Laboratory, Delft University of Technology, Leeghwaterstraat 44, 2628CA Delft, The Netherlands.
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Rosner DE, Arias-Zugasti M. Coupling between homogeneous rate processes and fluid deformation rate: Brownian particle coagulation in a rapidly dilating solvent. AIChE J 2011. [DOI: 10.1002/aic.12277] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Su ZQ, Chen XN, Yu ZZ, Zhang L. Morphological distribution of polymeric nucleating agents in injection-molded isotactic polypropylene plates and its influence on nucleating efficiency. J Appl Polym Sci 2008. [DOI: 10.1002/app.29098] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Abstract
Concepts of everyday use such as energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and the general rules that the macroscopic properties of systems at equilibrium follow. Outside equilibrium and away from macroscopic regimes, most of those rules cannot be applied directly. Here we present recent developments that extend the applicability of thermodynamic concepts deep into mesoscopic and irreversible regimes. We show how the probabilistic interpretation of thermodynamics together with probability conservation laws can be used to obtain Fokker-Planck equations for the relevant degrees of freedom. This approach provides a systematic method to obtain the stochastic dynamics of a system directly from its equilibrium properties. A wide variety of situations can be studied in this way, including many that were thought to be out of reach of thermodynamic theories, such as nonlinear transport in the presence of potential barriers, activated processes, slow relaxation phenomena, and basic processes in biomolecules, such as translocation and stretching.
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Affiliation(s)
- D Reguera
- Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 1, 08028-Barcelona, Spain
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Reguera D, Rubı́ JM. Homogeneous nucleation in inhomogeneous media. II. Nucleation in a shear flow. J Chem Phys 2003. [DOI: 10.1063/1.1614777] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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