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Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results. ENTROPY 2019. [PMCID: PMC7514492 DOI: 10.3390/e21121147] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that is valid not only for one-component but generally for multi-component systems. In this analysis, one basic assumption of classical nucleation theory is utilized. In addition, commonly employed in application to crystallization, it is supposed that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)], also relying widely on the standard classical approach in the description of crystal nucleation, holds for multi-component systems as well. The general form of the nucleation theorem derived by us is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, expressions recently developed by us for the curvature dependence of the surface tension, respectively, its dependence on pressure and/or temperature are employed. The basic assumption of classical nucleation theory mentioned above is, however, in general, not true. The bulk and surface properties of the critical crystal clusters may differ considerably from the properties of the evolving macroscopic phases. Such effects can be incorporated into the theoretical description by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem, as derived based on classical nucleation theory, holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.
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Banerjee D, Dutta A, Vimal KK, Kapur GS, Ghosh AK. Correlation of Micro- and Macrostructural Attributes with the Foamability of Modified Polypropylene Using Supercritical CO 2. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b01258] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Debjyoti Banerjee
- Department of Materials Science and Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Anindya Dutta
- Department of Materials Science and Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
| | | | - Gurpreet Singh Kapur
- Petrochemical and Polymer Department, R&D Division, Indian Oil Corporation Ltd., Faridabad 121007, India
| | - Anup K. Ghosh
- Department of Materials Science and Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
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Wyslouzil BE, Wölk J. Overview: Homogeneous nucleation from the vapor phase—The experimental science. J Chem Phys 2016; 145:211702. [DOI: 10.1063/1.4962283] [Citation(s) in RCA: 94] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Barbara E. Wyslouzil
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, USA
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Judith Wölk
- Department of Chemistry, Physical Chemistry, Universität zu Köln, Luxemburger Str. 116, 50939 Köln, Germany
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Noppel M, Vehkamäki H, Winkler PM, Kulmala M, Wagner PE. Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. II. The generalized Laplace, Gibbs-Kelvin, and Young equations and application to nucleation. J Chem Phys 2013; 139:134108. [DOI: 10.1063/1.4822047] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Noppel M, Vehkamäki H, Winkler PM, Kulmala M, Wagner PE. Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. I. Formulation of general equations: electrical surface and line excess quantities. J Chem Phys 2013; 139:134107. [PMID: 24116552 DOI: 10.1063/1.4822046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermodynamics is applied to formulate general equations for internal energies and grand potential for a system consisting of a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. To take into account spontaneous polarization of surface layer molecules we introduce the electrical surface and line excess quantities.
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Affiliation(s)
- M Noppel
- Institute of Physics, University of Tartu, 18 Ülikooli St., 50090 Tartu, Estonia
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Onischuk AA, Vosel SV, Borovkova OV, Baklanov AM, Karasev VV, di Stasio S. Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus. J Chem Phys 2012; 136:224506. [PMID: 22713056 DOI: 10.1063/1.4725535] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.
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Affiliation(s)
- A A Onischuk
- Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, Russia
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Schmelzer JWP, Abyzov AS. Thermodynamic analysis of nucleation in confined space: generalized Gibbs approach. J Chem Phys 2011; 134:054511. [PMID: 21303142 DOI: 10.1063/1.3548870] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
A general thermodynamic analysis of nucleation-growth processes in confined space in initially metastable states of the ambient phase is performed based on the generalized Gibbs approach to the description of heterogeneous systems. In particular, it is shown analytically how the parameters of critical clusters and clusters in stable equilibrium with the ambient phase depend on the volume of the system for initially fixed intensive state parameters of the ambient phase. Qualitatively, the results are shown to be similar independent on the boundary conditions employed. It is demonstrated further that the behavior of systems in confined space is directly related to the kinetics of phase transformation processes in spatially extended systems, when ensembles of clusters are formed. The results of the thermodynamic analysis of cluster formation and growth in a confined space are employed then, in particular, to the derivation of kinetic equations for the description of the process of coarsening or Ostwald ripening. In the analysis of both the nucleation in confined space and the description of Ostwald ripening, no specific assumptions concerning the equations of state of the system under consideration and the number of components both in the ambient and newly evolving phases are made. Consequently, the results are of very general nature and hold always as far as the necessary condition for the possibility of a phase transformation is fulfilled.
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Affiliation(s)
- Jürn W P Schmelzer
- Institut für Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany.
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9
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Vosel SV, Onischuk AA, Purtov PA. Response to “Comment on ‘Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: Metal vapor homogeneous nucleation’ ” [J. Chem. Phys. 133, 047101 (2010)]. J Chem Phys 2010. [DOI: 10.1063/1.3469784] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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Wei H, Thompson R, Park C, Chen P. Surface tension of high density polyethylene (HDPE) in supercritical nitrogen: Effect of polymer crystallization. Colloids Surf A Physicochem Eng Asp 2010. [DOI: 10.1016/j.colsurfa.2009.06.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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11
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Vosel SV, Onischuk AA, Purtov PA. Translation-rotation correction factor in the theory of homogeneous nucleation. J Chem Phys 2009; 131:204508. [DOI: 10.1063/1.3258643] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Carreón-Calderón B, Soria A, Romero-Martínez A. Modified Rachford-Rice equations including interfacial contributions and their application to the nucleation process. AIChE J 2009. [DOI: 10.1002/aic.12103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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13
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Carreón-Calderón B, Soria A, Romero-Martínez A. Driving force in first-order phase transitions and its application to gas hydrate nucleation from a single phase. AIChE J 2009. [DOI: 10.1002/aic.11836] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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14
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Schmelzer JWP, Boltachev GS, Baidakov VG. Classical and generalized Gibbs’ approaches and the work of critical cluster formation in nucleation theory. J Chem Phys 2006; 124:194503. [PMID: 16729821 DOI: 10.1063/1.2196412] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts developed long ago by Gibbs are widely employed giving some basic qualitative insights into these processes. However, from a quantitative point of view, the results of such analysis, based on the classical Gibbs approach and involving in addition the capillarity approximation, are often not satisfactory. Some progress can be reached here by the van der Waals and more advanced density functional methods of description of thermodynamically heterogeneous systems having, however, its limitations in application to the interpretation of experimental data as well. Moreover, both mentioned theories--Gibbs' and density functional approaches--lead to partly contradicting each other's results. As shown in preceding papers, by generalizing Gibbs' approach, existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of phase formation processes can be developed. In the present analysis, a comparative analysis of the basic assumptions and predictions of the classical and the generalized Gibbs approaches is given. It is shown, in particular, that--interpreted in terms of the generalized Gibbs approach--the critical cluster as determined via the classical Gibbs approach corresponds not to a saddle but to a ridge point of the appropriate thermodynamic potential hypersurface. By this reason, the classical Gibbs approach (involving the classical capillarity approximation) overestimates as a rule the work of critical cluster formation in nucleation theory and, in general, considerably.
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Affiliation(s)
- Jürn W P Schmelzer
- Institut für Physik der Universität Rostock; Universitätsplatz, 18051 Rostock, Germany.
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15
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Djikaev Y, Ruckenstein E. Kinetic theory of binary nucleation based on a first passage time analysis. J Chem Phys 2006; 124:124521. [PMID: 16599711 DOI: 10.1063/1.2178317] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The binary classical nucleation theory (BCNT) is based on the Gibbsian thermodynamics and applies the macroscopic concept of surface tension to nanosize clusters. This leads to severe inconsistencies and large discrepancies between theoretical predictions and experimental results regarding the nucleation rate. We present an alternative approach to the kinetics of binary nucleation which avoids the use of classical thermodynamics for clusters. The new approach is an extension to binary mixtures of the kinetic theory previously developed by Narsimhan and Ruckenstein and Ruckenstein and Nowakowski [J. Colloid Interface Sci. 128, 549 (1989); 137, 583 (1990)] for unary nucleation which is based on molecular interactions and in which the rate of emission of molecules from a cluster is determined via a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. The starting master equation is a Fokker-Planck equation for the probability distribution of a surface molecule with respect to its phase coordinates. Owing to the hierarchy of characteristic time scales in the evolution of the molecule, this equation can be reduced to the Smoluchowski equation for the distribution function involving only the spatial coordinates. The new theory is combined with density functional theory methods to determine the density profiles. This is essential for nucleation in binary systems particularly when one of the components is surface active. Knowing these profiles, one can determine the potential fields created by the cluster, its rate of emission of molecules, and the nucleation rate more accurately than by using the uniform density approximation. The new theory is illustrated by numerical calculations for a model binary mixture of Lennard-Jones monomers and rigidly bonded dimers of Lennard-Jones atoms. The amphiphilic character of the dimer component (i.e., its surface activity) is induced by the asymmetry in the interaction between a monomer and the two different sites of a dimer. The inconsistencies of the BCNT are avoided in the new theory.
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Affiliation(s)
- Yuri Djikaev
- Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260, USA.
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16
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Kusaka I. Statistical mechanics of nucleation: incorporating translational and rotational free energy into thermodynamics of a microdroplet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031607. [PMID: 16605537 DOI: 10.1103/physreve.73.031607] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2005] [Indexed: 05/08/2023]
Abstract
Motivated by the original Lothe-Pound prescription, we derive a formula for the replacement partition function that is suitable for vapor to liquid phase nucleation in terms of the classical phase integral. The resulting expression was evaluated for truncated and shifted Lennard-Jones fluids by means of computer simulation. The corresponding Lothe-Pound correction factor, which is to multiply the classical expression for the nucleation rate, decreases significantly with increasing temperature and decreasing cluster size, and is in the range of 10(9)-10(13) for the temperatures and the cluster sizes we studied. This is somewhat smaller than the original estimate of 10(17) by Lothe and Pound.
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Affiliation(s)
- Isamu Kusaka
- The Koffolt Laboratories, The Department of Chemical and Biomolecular Engineering, The Ohio State University, 140 West 19th Avenue, Columbus, Ohio 43210, USA
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17
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Onischuk AA, Purtov PA, Baklanov AM, Karasev VV, Vosel SV. Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: Metal vapor homogeneous nucleation. J Chem Phys 2006; 124:14506. [PMID: 16409040 DOI: 10.1063/1.2140268] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.
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Affiliation(s)
- A A Onischuk
- Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, Russia.
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18
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Li JS, Wilemski G. A structural phase diagram for model aqueous organic nanodroplets. Phys Chem Chem Phys 2006; 8:1266-70. [PMID: 16633606 DOI: 10.1039/b518305g] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Our density functional theory calculations predict that model aqueous organic nanodroplets have either well mixed or core-shell structures, depending on the state of the metastable binary vapor and that, furthermore, there is a broad transition region in the phase diagram where both structures can occur at the same vapor state.
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Affiliation(s)
- Jin-Song Li
- Department of Physics and Cloud and Aerosol Sciences Laboratory, University of Missouri-Rolla, Rolla, Missouri 65409-0640, USA
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Anklam MR, Firoozabadi A. Driving force and composition for multicomponent gas hydrate nucleation from supersaturated aqueous solutions. J Chem Phys 2004; 121:11867-75. [PMID: 15634148 DOI: 10.1063/1.1817999] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The expression for driving force is presented for multicomponent gas hydrate nucleation in an aqueous phase. The derivation includes working equations for predicting the composition of a hydrate nucleus. The results for driving force in multicomponent systems show a significant effect of the composition of the hydrate nucleus. All past work assume a fixed composition based on the three-phase equilibrium point independent of subcooling and supersaturation.
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Affiliation(s)
- Mark R Anklam
- Department of Chemical Engineering, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803, USA
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Siripurapu S, Coughlan JA, Spontak RJ, Khan SA. Surface-Constrained Foaming of Polymer Thin Films with Supercritical Carbon Dioxide. Macromolecules 2004. [DOI: 10.1021/ma0484983] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Srinivas Siripurapu
- Departments of Chemical & Biomolecular Engineering and Materials Science & Engineering, North Carolina State University, Raleigh, North Carolina 27695
| | - John A. Coughlan
- Departments of Chemical & Biomolecular Engineering and Materials Science & Engineering, North Carolina State University, Raleigh, North Carolina 27695
| | - Richard J. Spontak
- Departments of Chemical & Biomolecular Engineering and Materials Science & Engineering, North Carolina State University, Raleigh, North Carolina 27695
| | - Saad A. Khan
- Departments of Chemical & Biomolecular Engineering and Materials Science & Engineering, North Carolina State University, Raleigh, North Carolina 27695
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Djikaev YS, Napari I, Laaksonen A. On the closure conjectures for the Gibbsian approximation model of a binary droplet. J Chem Phys 2004; 120:9752-62. [PMID: 15267991 DOI: 10.1063/1.1698575] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within the framework of Gibbsian thermodynamics, a binary droplet is regarded to consist of a uniform interior and dividing surface. The properties of the droplet interior are those of the bulk liquid solution, but the dividing surface is a fictitious phase whose chemical potentials cannot be rigorously determined. The state of the nucleus interior and free energy of nucleus formation can be found without knowing the surface chemical potentials, but the latter are still needed to determine the state of the whole nucleus (including the dividing surface) and develop the kinetics of nucleation. Thus it is necessary to recur to additional conjectures in order to build a complete, thermodynamic, and kinetic theory of nucleation within the framework of the Gibbsian approximation. Here we consider and analyze the problem of closing the Gibbsian approximation droplet model. We identify micro- and Gamma-closure conjectures concerning the surface chemical potentials and excess surface coverages, respectively, for the droplet surface of tension. With these two closure conjectures, the Gibbsian approximation model of a binary droplet becomes complete so that one can determine both the surface and internal characteristics of the whole nucleus and develop the kinetic theory, based on this model. Theoretical results are illustrated by numerical evaluations for binary nucleation in a water-methanol vapor mixture at T=298.15 K. Numerical results show a striking increase in the droplet surface tension with decreasing droplet size at constant overall droplet composition. A comparison of the Gibbsian approximation with density functional calculations for a model surfactant system indicate that the excess surface coverages from the Gibbsian approximation are accurate enough for large droplets and droplets that are not too concentrated with respect to the solute.
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Affiliation(s)
- Y S Djikaev
- NASA Ames Research Center, MS 245-4, Moffett Field, California 94035, USA.
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Schmelzer JWP, Gokhman AR, Fokin VM. Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach. J Colloid Interface Sci 2004; 272:109-33. [PMID: 14985029 DOI: 10.1016/j.jcis.2003.08.038] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2003] [Accepted: 08/21/2003] [Indexed: 11/17/2022]
Abstract
In the theoretical description of nucleation-growth processes, currently Gibbs's classical thermodynamic theory of heterogeneous systems is predominantly employed for the description of the properties of the clusters. However, Gibbs's approach does not make it possible to describe, in general, the properties of critical clusters (determining the rate of nucleation) in a sufficiently correct way. Moreover, Gibbs's approach is restricted by its applicability to thermodynamic equilibrium states exclusively. For this reason, it does not give a theoretically founded prescription for a determination of the possible states of clusters of sub- and supercritical sizes in dependence on supersaturation and size of the clusters. In order to overcome these shortcomings, in recent years a generalization of Gibbs's classical approach has been developed and employed for the description of nucleation processes. This generalization of Gibbs' classical method leads, for a variety of different applications, to dependencies of the work of critical cluster formation on supersaturation, which are qualitatively and widely even quantitatively in agreement with density-functional computations. The theoretical methods and results are summarized in the first part of the present paper. They are then extended for the first time to a description of processes of growth of single clusters and ensembles of clusters. In order to fulfill this task, a new method for determination of the parameters of sub- and supercritical clusters is developed. It turns out as the result of the analysis that a variety of thermodynamic and kinetic parameters, determining cluster growth, become dependent on cluster size as well. The results are illustrated for a model system (segregation in regular solutions) and applied to the interpretation of experimental results on segregation processes in solutions and crystallization processes in glass-forming melts. It is shown that the newly developed approach resolves a variety of problems in the interpretation of experimental data on the kinetics of phase formation processes which could not be given a satisfactory explanation so far.
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Affiliation(s)
- Jürn W P Schmelzer
- Fachbereich Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany.
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Kashchiev D. Multicomponent nucleation: Thermodynamically consistent description of the nucleation work. J Chem Phys 2004; 120:3749-58. [PMID: 15268538 DOI: 10.1063/1.1643711] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A thermodynamically consistent formula is derived for the nucleation work in multicomponent homogeneous nucleation. The derivation relies on the conservative dividing surface which defines the nucleus as having specific surface energy equal to the specific surface energy sigma0 of the interface between the macroscopically large new and old phases at coexistence. Expressions are given for the radius of the nucleus defined by the conservative dividing surface and by the surface of tension. As a side result, the curvature dependence of the surface tension sigmaT of the nucleus defined by the surface of tension is also determined. The analysis is valid for nuclei of any size, i.e., for nucleation in the whole range of conditions between the binodal and the spinodal of the metastable old phase provided the inequality sigmaT < or = sigma0 is satisfied. It is found that under the conditions of validity of the analysis the nucleation rate is higher than the nucleation rate given by the classical nucleation theory. The general results are applied to nucleation of unary liquids or solids in binary gaseous, liquid or solid mixtures.
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Affiliation(s)
- Dimo Kashchiev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, ul. Acad. G Bonchev 11, Sofia 1113
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Li H, Lee LJ, Tomasko DL. Effect of Carbon Dioxide on the Interfacial Tension of Polymer Melts. Ind Eng Chem Res 2003. [DOI: 10.1021/ie034092n] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hongbo Li
- Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
| | - L. James Lee
- Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
| | - David L. Tomasko
- Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
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Noppel M, Vehkamäki H, Kulmala M. Reversible work of the formation of a layer of a new phase on a spherical charged conductor within a uniform multicomponent macroscopic mother phase. J Chem Phys 2003. [DOI: 10.1063/1.1620499] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schmelzer JWP, Baidakov VG, Boltachev GS. Kinetics of boiling in binary liquid–gas solutions: Comparison of different approaches. J Chem Phys 2003. [DOI: 10.1063/1.1602066] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Reguera D, Reiss H. Nucleation in confined ideal binary mixtures: The Renninger–Wilemski problem revisited. J Chem Phys 2003. [DOI: 10.1063/1.1579685] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Noppel M, Vehkamäki H, Kulmala M. An improved model for hydrate formation in sulfuric acid–water nucleation. J Chem Phys 2002. [DOI: 10.1063/1.1423333] [Citation(s) in RCA: 97] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Schmelzer JWP, Baidakov VG. Kinetics of Condensation and Boiling: Comparison of Different Approaches. J Phys Chem B 2001. [DOI: 10.1021/jp010943y] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jürn W. P. Schmelzer
- Fachbereich Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany, and Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, 620219 Ekaterinburg, Russia
| | - Vladimir G. Baidakov
- Fachbereich Physik der Universität Rostock, Universitätsplatz, 18051 Rostock, Germany, and Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, 620219 Ekaterinburg, Russia
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Kusaka I, Oxtoby DW. A Monte Carlo simulation of nucleation in amphiphilic solution. J Chem Phys 2001. [DOI: 10.1063/1.1392358] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Djikaev YS, Bowles R, Reiss H, Hämeri K, Laaksonen A, Väkevä M. Theory of Size Dependent Deliquescence of Nanoparticles: Relation to Heterogeneous Nucleation and Comparison with Experiments. J Phys Chem B 2001. [DOI: 10.1021/jp010537e] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Y. S. Djikaev
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095
| | - R. Bowles
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095
| | - H. Reiss
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095
| | - K. Hämeri
- Finnish Institute of Occupational Health, Laajaniityntie 1, FIN-01620 Vantaa, Finland
| | - A. Laaksonen
- Department of Applied Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland
| | - M. Väkevä
- Department of Physics, University of Helsinki, P.O. Box 9, FIN-00014 Helsinki, Finland
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Kusaka I. Comment on “Reversible work of formation of an embryo of a new phase within a uniform macroscopic mother phase” [J. Chem. Phys. 108, 5498 (1998)]. J Chem Phys 1999. [DOI: 10.1063/1.479667] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Debenedetti PG, Reiss H. Response to “Comment on ‘Reversible work of formation of an embryo of a new phase within a uniform macroscopic mother phase’ ” [J. Chem. Phys. 111, 3769 (1999)]. J Chem Phys 1999. [DOI: 10.1063/1.479668] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Laaksonen A, McGraw R, Vehkamäki H. Liquid-drop formalism and free-energy surfaces in binary homogeneous nucleation theory. J Chem Phys 1999. [DOI: 10.1063/1.479470] [Citation(s) in RCA: 71] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Li JS, Nishioka K. Direction of the steady state nucleation flux in the whole size space for binary systems. J Chem Phys 1999. [DOI: 10.1063/1.478486] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Noppel M. Binary nucleation of water–sulfuric acid system: A reexamination of the classical hydrates interaction model. J Chem Phys 1998. [DOI: 10.1063/1.477575] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Debenedetti PG, Reiss H. Reversible work of formation of an embryo of a new phase within a uniform macroscopic mother phase. J Chem Phys 1998. [DOI: 10.1063/1.475938] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kulmala M, Laaksonen A, Pirjola L. Parameterizations for sulfuric acid/water nucleation rates. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/97jd03718] [Citation(s) in RCA: 333] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Li JS, Nishioka K, Maksimov IL. Theory of the kinetic critical nucleus in binary systems. J Chem Phys 1997. [DOI: 10.1063/1.474407] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Nishioka K. Kinetic and thermodynamic definitions of the critical nucleus in nucleation theory. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:3263-3265. [PMID: 9963782 DOI: 10.1103/physreve.52.3263] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Guilleumas M, Pi M, Barranco M, Jezek DM, Navarro J. Nucleation in supersaturated solutions of 3He in 4He at negative pressures. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:1210-1214. [PMID: 9980701 DOI: 10.1103/physrevb.52.1210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Laaksonen A, Oxtoby DW. Gas–liquid nucleation of nonideal binary mixtures. I. A density functional study. J Chem Phys 1995. [DOI: 10.1063/1.469312] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Nishioka K, Fujita K. Transient nucleation in binary vapor of water and sulfuric acid. J Chem Phys 1994. [DOI: 10.1063/1.466969] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Laaksonen A, Kulmala M, Wagner PE. On the cluster compositions in the classical binary nucleation theory. J Chem Phys 1993. [DOI: 10.1063/1.465827] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Nishioka K, Mori A. Thermodynamic formula for the reversible work of forming a noncritical cluster from the vapor in multicomponent systems. J Chem Phys 1992. [DOI: 10.1063/1.463674] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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