1
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Lemmon MT, Toledo D, Apestigue V, Arruego I, Wolff MJ, Patel P, Guzewich S, Colaprete A, Vicente‐Retortillo Á, Tamppari L, Montmessin F, de la Torre Juarez M, Maki J, McConnochie T, Brown A, Bell JF. Hexagonal Prisms Form in Water-Ice Clouds on Mars, Producing Halo Displays Seen by Perseverance Rover. GEOPHYSICAL RESEARCH LETTERS 2022; 49:e2022GL099776. [PMID: 36245894 PMCID: PMC9539710 DOI: 10.1029/2022gl099776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 08/18/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
Observations by several cameras on the Perseverance rover showed a 22° scattering halo around the Sun over several hours during northern midsummer (solar longitude 142°). Such a halo has not previously been seen beyond Earth. The halo occurred during the aphelion cloud belt season and the cloudiest time yet observed from the Perseverance site. The halo required crystalline water-ice cloud particles in the form of hexagonal columns large enough for refraction to be significant, at least 11 μm in diameter and length. From a possible 40-50 km altitude, and over the 3.3 hr duration of the halo, particles could have fallen 3-12 km, causing downward transport of water and dust. Halo-forming clouds are likely rare due to the high supersaturation of water that is required but may be more common in northern subtropical regions during northern midsummer.
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Affiliation(s)
| | - D. Toledo
- Instituto Nacional de Técnica AerospacialMadridSpain
| | - V. Apestigue
- Instituto Nacional de Técnica AerospacialMadridSpain
| | - I. Arruego
- Instituto Nacional de Técnica AerospacialMadridSpain
| | | | - P. Patel
- Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaCAUSA
- Mullard Space Science LaboratoryUniversity College LondonLondonUK
| | - S. Guzewich
- NASA Goddard Space Flight CenterGreenbeltMDUSA
| | | | | | - L. Tamppari
- Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaCAUSA
| | | | | | - J. Maki
- Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaCAUSA
| | | | - A. Brown
- Plancius ResearchSeverna ParkMDUSA
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2
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Application of the Moment Method for Numerical Simulation of Homogeneous-Heterogeneous Condensation. FLUIDS 2022. [DOI: 10.3390/fluids7020068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
The paper considers the numerical modeling of the processes of homogeneous and heterogeneous condensation and evaporation in multiphase flows using the method of moments. Nonstationary processes of gas dynamics and phase transitions in the two-dimensional plane and axisymmetric regions are described by a general system of equations. The system of equations is expanded by adding two equations. One describes the evolution of the total mass fraction of the condensing substance; the other describes the evolution of the mass fraction of solid particles. An instant wetting model is used to model heterogeneous nucleation. The Gyarmathy model is used for the approximation of the average droplet growth rate. Heterogeneous condensation is modeled based on the distribution function of foreign impurities. An approach to calculating evaporation in the heterogeneous case is proposed. A comparison of the proposed models with a numerical experiment is given. Numerical simulation of homogeneous-heterogeneous condensation in a gas-dynamic ejector is carried out.
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3
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Ganguly S, Barreiro-Lage D, Walsh N, Oostenrijk B, Sorensen SL, Díaz-Tendero S, Gisselbrecht M. The origin of enhanced [Formula: see text] production from photoionized CO 2 clusters. Commun Chem 2022; 5:16. [PMID: 36697591 PMCID: PMC9814840 DOI: 10.1038/s42004-022-00629-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 01/11/2022] [Indexed: 01/28/2023] Open
Abstract
CO2-rich planetary atmospheres are continuously exposed to ionising radiation driving major photochemical processes. In the Martian atmosphere, CO2 clusters are predicted to exist at high altitudes motivating a deeper understanding of their photochemistry. In this joint experimental-theoretical study, we investigate the photoreactions of CO2 clusters (≤2 nm) induced by soft X-ray ionisation. We observe dramatically enhanced production of [Formula: see text] from photoionized CO2 clusters compared to the case of the isolated molecule and identify two relevant reactions. Using quantum chemistry calculations and multi-coincidence mass spectrometry, we pinpoint the origin of this enhancement: A size-dependent structural transition of the clusters from a covalently bonded arrangement to a weakly bonded polyhedral geometry that activates an exothermic reaction producing [Formula: see text]. Our results unambiguously demonstrate that the photochemistry of small clusters/particles will likely have a strong influence on the ion balance in atmospheres.
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Affiliation(s)
- Smita Ganguly
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - Dario Barreiro-Lage
- Departamento de Química - Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Noelle Walsh
- MAXIV laboratory, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - Bart Oostenrijk
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | | | - Sergio Díaz-Tendero
- Departamento de Química - Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Institute for Advanced Research in Chemical Sciences (IAdChem), Universidad Autónoma de Madrid, 28049 Madrid, Spain
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4
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Both AK, Cheung CL. Growth of carbon dioxide whiskers. RSC Adv 2019; 9:23780-23784. [PMID: 35530633 PMCID: PMC9069459 DOI: 10.1039/c9ra04583j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Accepted: 07/24/2019] [Indexed: 11/21/2022] Open
Abstract
We report the growth of carbon dioxide (CO2) whiskers at low temperatures (−70 °C to −65 °C) and moderate pressure (4.4 to 1.0 bar). Their axial growth was assessed by optical video analysis. The identities of these whiskers were confirmed as CO2 solids by Raman spectroscopy. A vapor–solid growth mechanism was proposed based on the influence of the relative humidity on the growth. Carbon dioxide (CO2) whiskers were reported to grow at low temperatures (−70 °C to −65 °C) and moderate pressure (4.4 to 1.0 bar).![]()
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Affiliation(s)
| | - Chin Li Cheung
- University of Nebraska-Lincoln Lincoln Nebraska 68588 USA
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5
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Plane JMC, Carrillo‐Sanchez JD, Mangan TP, Crismani MMJ, Schneider NM, Määttänen A. Meteoric Metal Chemistry in the Martian Atmosphere. JOURNAL OF GEOPHYSICAL RESEARCH. PLANETS 2018; 123:695-707. [PMID: 29780678 PMCID: PMC5947882 DOI: 10.1002/2017je005510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Revised: 01/17/2018] [Accepted: 01/24/2018] [Indexed: 06/08/2023]
Abstract
Recent measurements by the Imaging Ultraviolet Spectrograph (IUVS) instrument on NASA's Mars Atmosphere and Volatile EvolutioN mission show that a persistent layer of Mg+ ions occurs around 90 km in the Martian atmosphere but that neutral Mg atoms are not detectable. These observations can be satisfactorily modeled with a global meteoric ablation rate of 0.06 t sol-1, out of a cosmic dust input of 2.7 ± 1.6 t sol-1. The absence of detectable Mg at 90 km requires that at least 50% of the ablating Mg atoms ionize through hyperthermal collisions with CO2 molecules. Dissociative recombination of MgO+.(CO2)n cluster ions with electrons to produce MgCO3 directly, rather than MgO, also avoids a buildup of Mg to detectable levels. The meteoric injection rate of Mg, Fe, and other metals-constrained by the IUVS measurements-enables the production rate of metal carbonate molecules (principally MgCO3 and FeCO3) to be determined. These molecules have very large electric dipole moments (11.6 and 9.2 Debye, respectively) and thus form clusters with up to six H2O molecules at temperatures below 150 K. These clusters should then coagulate efficiently, building up metal carbonate-rich ice particles which can act as nucleating particles for the formation of CO2-ice clouds. Observable mesospheric clouds are predicted to occur between 65 and 80 km at temperatures below 95 K and above 85 km at temperatures about 5 K colder.
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Affiliation(s)
| | | | | | - M. M. J. Crismani
- Laboratory for Atmospheric and Space Physics (LASP)University of ColoradoBoulderCOUSA
| | - N. M. Schneider
- Laboratory for Atmospheric and Space Physics (LASP)University of ColoradoBoulderCOUSA
| | - A. Määttänen
- Laboratoire Atmosphères, MilieuxObservations Spatiales (LATMOS)GuyancourtFrance
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6
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Unveiling CO 2 heterogeneous freezing plumes during champagne cork popping. Sci Rep 2017; 7:10938. [PMID: 28912451 PMCID: PMC5599640 DOI: 10.1038/s41598-017-10702-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Accepted: 08/11/2017] [Indexed: 11/15/2022] Open
Abstract
Cork popping from clear transparent bottles of champagne stored at different temperatures (namely, 6, 12, and 20 °C) was filmed through high-speed video imaging in the visible light spectrum. During the cork popping process, a plume mainly composed of gaseous CO2 with traces of water vapour freely expands out of the bottleneck through ambient air. Most interestingly, for the bottles stored at 20 °C, the characteristic grey-white cloud of fog classically observed above the bottlenecks of champagne stored at lower temperatures simply disappeared. It is replaced by a more evanescent plume, surprisingly blue, starting from the bottleneck. We suggest that heterogeneous freezing of CO2 occurs on ice water clusters homogeneously nucleated in the bottlenecks, depending on the saturation ratio experienced by gas-phase CO2 after adiabatic expansion (indeed highly bottle temperature dependent). Moreover, and as observed for the bottles stored at 20 °C, we show that the freezing of only a small portion of all the available CO2 is able to pump the energy released through adiabatic expansion, thus completely inhibiting the condensation of water vapour found in air packages adjacent to the gas volume gushing out of the bottleneck.
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7
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Dundar E, Boulet P, Wexler C, Firlej L, Llewellyn P, Kuchta B. Heterogeneous melting of methane confined in nano-pores. J Chem Phys 2016; 145:144704. [PMID: 27782515 DOI: 10.1063/1.4964650] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- E. Dundar
- Aix Marseille Université, CNRS, MADIREL (UMR 7246), 13397 Marseille, France
| | - P. Boulet
- Aix Marseille Université, CNRS, MADIREL (UMR 7246), 13397 Marseille, France
| | - C. Wexler
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
| | - L. Firlej
- Laboratoire Charles Coulomb (L2C), UMR5221, Université de Montpellier, 34095 Montpellier, France
| | - Ph. Llewellyn
- Aix Marseille Université, CNRS, MADIREL (UMR 7246), 13397 Marseille, France
| | - B. Kuchta
- Aix Marseille Université, CNRS, MADIREL (UMR 7246), 13397 Marseille, France
- Department of Chemistry, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
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8
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Read PL, Lewis SR, Mulholland DP. The physics of Martian weather and climate: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:125901. [PMID: 26534887 DOI: 10.1088/0034-4885/78/12/125901] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The planet Mars hosts an atmosphere that is perhaps the closest in terms of its meteorology and climate to that of the Earth. But Mars differs from Earth in its greater distance from the Sun, its smaller size, its lack of liquid oceans and its thinner atmosphere, composed mainly of CO(2). These factors give Mars a rather different climate to that of the Earth. In this article we review various aspects of the martian climate system from a physicist's viewpoint, focusing on the processes that control the martian environment and comparing these with corresponding processes on Earth. These include the radiative and thermodynamical processes that determine the surface temperature and vertical structure of the atmosphere, the fluid dynamics of its atmospheric motions, and the key cycles of mineral dust and volatile transport. In many ways, the climate of Mars is as complicated and diverse as that of the Earth, with complex nonlinear feedbacks that affect its response to variations in external forcing. Recent work has shown that the martian climate is anything but static, but is almost certainly in a continual state of transient response to slowly varying insolation associated with cyclic variations in its orbit and rotation. We conclude with a discussion of the physical processes underlying these long- term climate variations on Mars, and an overview of some of the most intriguing outstanding problems that should be a focus for future observational and theoretical studies.
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Affiliation(s)
- P L Read
- Atmospheric, Oceanic & Planetary Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK
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9
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Tanimura S, Park Y, Amaya A, Modak V, Wyslouzil BE. Following heterogeneous nucleation of CO2 on H2O ice nanoparticles with microsecond resolution. RSC Adv 2015. [DOI: 10.1039/c5ra19782a] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Heterogeneous nucleation of CO2 on H2O ice particles in supersonic nozzles.
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Affiliation(s)
- Shinobu Tanimura
- William G. Lowrie Department of Chemical and Biomolecular Engineering
- The Ohio State University
- Columbus
- USA
| | - Yensil Park
- William G. Lowrie Department of Chemical and Biomolecular Engineering
- The Ohio State University
- Columbus
- USA
| | - Andrew Amaya
- William G. Lowrie Department of Chemical and Biomolecular Engineering
- The Ohio State University
- Columbus
- USA
| | - Viraj Modak
- William G. Lowrie Department of Chemical and Biomolecular Engineering
- The Ohio State University
- Columbus
- USA
| | - Barbara E. Wyslouzil
- William G. Lowrie Department of Chemical and Biomolecular Engineering
- The Ohio State University
- Columbus
- USA
- Department of Chemistry
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10
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Maltagliati L, Montmessin F, Fedorova A, Korablev O, Forget F, Bertaux JL. Evidence of Water Vapor in Excess of Saturation in the Atmosphere of Mars. Science 2011; 333:1868-71. [DOI: 10.1126/science.1207957] [Citation(s) in RCA: 107] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- L. Maltagliati
- Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), 78280 Guyancourt, France
| | - F. Montmessin
- Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), 78280 Guyancourt, France
| | - A. Fedorova
- Space Research Institute (IKI), 117997 Moscow, Russia
| | - O. Korablev
- Space Research Institute (IKI), 117997 Moscow, Russia
| | - F. Forget
- Laboratoire de Météorologie Dynamique (LMD), 75252 Paris, France
| | - J.-L. Bertaux
- Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), 78280 Guyancourt, France
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11
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Heavens NG. Planetary science. Sunshine on a cloudy forecast. Science 2011; 333:1832-3. [PMID: 21960617 DOI: 10.1126/science.1212490] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Nicholas G Heavens
- Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853, USA.
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12
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Kocifaj M. Approximate analytical scattering phase function dependent on microphysical characteristics of dust particles. APPLIED OPTICS 2011; 50:2493-2499. [PMID: 21673749 DOI: 10.1364/ao.50.002493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The approximate bulk-scattering phase function of a polydisperse system of dust particles is derived in an analytical form. In the theoretical solution, the particle size distribution is modeled by a modified gamma function that can satisfy various media differing in modal radii. Unlike the frequently applied power law, the modified gamma distribution shows no singularity when the particle radius approaches zero. The approximate scattering phase function is related to the parameters of the size distribution function. This is an important advantage compared to the empirical Henyey-Greenstein (HG) approximation, which is a simple function of the average cosine. However, any optimized value of average cosine of the HG function cannot provide the information on particle microphysical characteristics, such as the size distribution function. In this paper, the mapping between average cosine and the parameters of size distribution function is given by a semianalytical expression that is applicable in rapid numerical simulations on various dust populations. In particular, the modal radius and half-width can be quickly estimated using the presented formulas.
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Affiliation(s)
- Miroslav Kocifaj
- ICA, Slovak Academy of Sciences, Dúbravská cesta 9, 845 03 Bratislava, Slovak Republic.
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13
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Phebus BD, Johnson AV, Mar B, Stone BM, Colaprete A, Iraci LT. Water ice nucleation characteristics of JSC Mars-1 regolith simulant under simulated Martian atmospheric conditions. ACTA ACUST UNITED AC 2011. [DOI: 10.1029/2010je003699] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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14
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Pathak J, Michelangeli DV, Komguem L, Whiteway J, Tamppari LK. Simulating Martian boundary layer water ice clouds and the lidar measurements for the Phoenix mission. ACTA ACUST UNITED AC 2008. [DOI: 10.1029/2007je002967] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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15
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Määttänen A, Vehkamäki H, Lauri A, Napari I, Kulmala M. Two-component heterogeneous nucleation kinetics and an application to Mars. J Chem Phys 2007; 127:134710. [PMID: 17919046 DOI: 10.1063/1.2770737] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a two-component heterogeneous nucleation model that includes exact calculation of the Stauffer-type [D. Stauffer, J. Aerosol Sci. 7, 319 (1976)] steady-state kinetic prefactor using the correct heterogeneous Zeldovich factor for a heterogeneous two-component system. The model, and a simplified version of it, is tested by comparing its predictions to experimental data for water-n-propanol nucleating on silver particles. The model is then applied to water-carbon dioxide system in Martian conditions, which has not been modeled before. Using the ideal mixture assumption, the model shows theoretical possibilities for two-component nucleation adjacent to the initial stages of one-component water nucleation, especially with small water vapor amounts. The numbers of carbon dioxide molecules in the critical cluster are small in the case of large water amounts (up to 300 ppm) in the gas phase, but larger when there is very little water vapor (1 ppm).
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Affiliation(s)
- Anni Määttänen
- Division of Atmospheric Sciences, Department of Physical Sciences, University of Helsinki, 00014 Helsinki, Finland.
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16
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Vehkamäki H, Määttänen A, Lauri A, Kulmala M, Winkler P, Vrtala A, Wagner PE. Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters. J Chem Phys 2007; 126:174707. [PMID: 17492879 DOI: 10.1063/1.2723073] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this paper we present a new form of the nucleation theorems applicable to heterogeneous nucleation. These heterogeneous nucleation theorems allow, for the first time, direct determination of properties of nanoclusters formed on pre-existing particles from measured heterogeneous nucleation probabilities. The theorems can be used to analyze the size (first theorem) and the energetics (second theorem) of heterogeneous clusters independent of any specific nucleation model. We apply the first theorem to the study of small water and n-propanol clusters formed at the surface of 8 nm silver particles. According to the experiments the size of the two-component critical clusters is found to be below 90 molecules, and only less than 20 molecules for pure water, less than 300 molecules for pure n-propanol. These values are drastically smaller than the ones predicted by the classical nucleation theory, which clearly indicates that the nucleating clusters are too small to be quantitatively described using a macroscopic theory.
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Affiliation(s)
- Hanna Vehkamäki
- Department of Physical Sciences, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland.
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17
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Lauri A, Zapadinsky E, Vehkamäki H, Kulmala M. Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon. J Chem Phys 2006; 125:164712. [PMID: 17092125 DOI: 10.1063/1.2358343] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.
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Affiliation(s)
- Antti Lauri
- Department of Physical Sciences, University of Helsinki, Finland.
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18
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Zapadinsky E, Lauri A, Kulmala M. The molecular approach to heterogeneous nucleation. J Chem Phys 2005; 122:114709. [PMID: 15836245 DOI: 10.1063/1.1881032] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.
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