• Ei tuloksia

Calligraphic symbols

A, B , C, D . . . Liquid drop model coefficients F . . . Helmholtz free energy of a population G . . . Gibbs free energy of a population M . . . Number of atoms in a molecule N . . . Number of particles

P . . . Probability R . . . Rotational energy S . . . Entropy

T . . . Translational energy V . . . Vibrational energy Z . . . Zeldovich factor Greek symbols

α . . . Evaporation rate coefficient β . . . Collision rate coefficient ΔG . . . Formation free energy ΔH . . . Latent heat of transition δT . . . Temperature fluctuation ΔL . . . Lindemann index δT . . . Tolman length

ε . . . Lennard-Jones energy parameter ε0 . . . Vacuum permittivity

Γ . . . Gamma function

γ . . . Surface tension of the cluster-vapour interface γsl . . . Solid-liquid surface tension

Λ . . . de Broglie wavelength μ . . . Reduced mass ν . . . Interaction exponent Ω . . . Collision cross section ω . . . Vibrational frequency ρ . . . Density

σ . . . Lennard-Jones distance parameter σr . . . Symmetry number

Θ . . . Normalisation factor for equilibrium cluster distribution Roman symbols

F . . . Force p . . . Momentum

A . . . Interaction coefficient An . . . Surface area of ann-cluster B . . . Impact parameter

b . . . Energy fluctuation as a result of collisions d . . . Sink coefficient

55

drot . . . Rotational degrees of freedom E . . . Energy

Ec . . . Configurational energy F . . . Helmholtz free energy f . . . Distribution function G . . . Gibbs free energy

g . . . Melting point depression coefficient H . . . Hamiltonian

h . . . Planck constant I . . . Flux

i, j, k . . . General indices

Ixx . . . Principal moment of inertia about the x-axis J . . . Nucleation rate

K . . . Transition rate kB . . . Boltzmann constant L . . . Angular momentum m . . . Monomer type mi . . . Mass of particlei N . . . Number density n . . . Cluster size n . . . Critical cluster size P . . . Pressure

Pd . . . Decay probability Pg . . . Growth probability Q . . . Partial charge q . . . Excess energy R . . . Gas constant r . . . Distance or radius S . . . Saturation ratio s . . . Source coefficient T . . . Temperature t . . . Time

Tm . . . Melting temperature U . . . Potential energy Ueff . . . Effective potential V . . . Volume

v . . . Velocity

w . . . Number of carrier gas collisions between the size-changing events Z . . . Partition function of a population

z . . . Partition function erf . . . Error function

References

Almeida, J., Schobesberger, S., K¨urten, A., Ortega, I. K., Kupiainen-M¨att¨a, O., Praplan, A. P., Adamov, A., Amorim, A., Bianchi, F., Breitenlechner, M., et al. (2013). Molecular understanding of sulphuric acid-amine particle nucleation in the atmosphere. Nature, 502(7471):359–363.

Amaya, A. J. and Wyslouzil, B. E. (2018). Ice nucleation rates near 225 K. J. Chem. Phys., 148(8):084501.

Barducci, A., Bussi, G., and Parrinello, M. (2008). Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett., 100(2):020603.

Barrett, J. (1994). Equilibrium and steady-state distributions of vapour clusters in nucleation theory. J. Phys. A: Math. Gen., 27:5053–5068.

Barrett, J., Clement, C., and Ford, I. (1993). Energy fluctuations in homogeneous nucleation theory for aerosols. J. Phys. A: Math. Gen., 26:529–548.

Barrett, J. C. (2011). Note: Cluster temperatures in non-isothermal nucleation.

J. Chem. Phys., 135(9):096101.

Becker, R. and D¨oring, W. (1935). Kinetische Behandlung der Keimbildung in ¨ubers¨attigten ampfen. Ann. Phys. (Leipzig), 24:719–752.

Brus, D., ˇZd´ımal, V., and Smol´ık, J. (2008). Homogeneous nucleation rate measurements in supersaturated water vapor. J. Chem. Phys., 129(17):174501.

Brus, D., ˇZd´ımal, V., and Uchtmann, H. (2009). Homogeneous nucleation rate measurements in supersaturated water vapor II. J. Chem. Phys., 131(7):074507.

Chen, B., Siepmann, J. I., Oh, K. J., and Klein, M. L. (2001). Aggregation-volume-bias Monte Carlo simulations of vapor-liquid nucleation barriers for Lennard-Jonesium.

J. Chem. Phys., 115(23):10903–10913.

Chesnavich, W. J., Su, T., and Bowers, M. T. (1980). Collisions in a noncentral field: a variational and trajectory investigation of ion–dipole capture.J. Chem. Phys., 72(4):2641–

2655.

Chkonia, G., W¨olk, J., Strey, R., Wedekind, J., and Reguera, D. (2009). Evaluating nucleation rates in direct simulations. J. Chem. Phys., 130:064505.

Courtney, W. G. (1961). Remarks on homogeneous nucleation. J. Chem. Phys., 35:2249.

Duff, K. M. (1966). Non-equilibrium condensation of carbon dioxide in supersonic nozzles.

PhD thesis, Massachusetts Institute of Technology.

57

Dugan Jr, J. V. and Magee, J. L. (1967). Capture collisions between ions and polar molecules.

J. Chem. Phys., 47(9):3103–3112.

Farkas, L. (1927). Keimbildungsgeschwindigkeit in ¨ubers¨attigten D¨ampfen. Z. Physik.

Chem., 125:236–242.

Feder, J., Russell, K., Lothe, J., and Pound, G. (1966). Homogeneous nucleation and growth of droplets in vapours.Adv. Phys., 15(57):111–178.

Ferreira, M., Lukkarinen, J., Nota, A., and Vel´azquez, J. J. (2019). Stationary non-equilibrium solutions for coagulation systems. arXiv preprint arXiv:1909.10608.

Frenkel, J. (1946). Kinetic Theory of Liquids. Oxford University Press, London.

Gibbs, J. W. (1875). On the equlibrium of heterogeneous substances. Trans. Connecticut Acad., 3:108–248, 343–524.

Girshick, S. L. and Chiu, C.-P. (1990). Kinetic nucleation theory: A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor.J. Chem. Phys., 93:1273–1277.

Hale, B. N. and DiMattio, D. J. (2004). Scaling of the nucleation rate and a Monte Carlo discrete sum approach to water cluster free energies of formation. J. Phys. Chem. B, 108:19780–19785.

Hale, B. N. and Plummer, P. L. M. (1974). Molecular model for ice clusters in a supersat-urated vapor. J. Chem. Phys., 61:4012–4019.

Hoare, M. R. and Pal, P. (1975). Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems. Adv. Phys., 24:645–679.

Holten, V., Labetski, D. G., and van Dongen, M. E. H. (2005). Homogeneous nucleation of water between 200 and 240 K: New wave tube data and estimation of the Tolman length.J. Chem. Phys., 123:104505.

Iland, K., Wedekind, J., W¨olk, J., Wagner, P. E., and Strey, R. (2004). Homogeneous nucleation rates of 1-pentanol.J. Chem. Phys., 121(24):12259–12264.

Imry, Y. (1980). Finite-size rounding of a first-order phase transition. Phys. Rev. B., 21(5):2042.

Isenor, M., Escribano, R., Preston, T. C., and Signorell, R. (2013). Predicting the infrared band profiles for CO2cloud particles on Mars. Icarus, 223(1):591–601.

Jen, C. N., McMurry, P. H., and Hanson, D. R. (2014). Stabilization of sulfuric acid dimers by ammonia, methylamine, dimethylamine, and trimethylamine. J. Geophys. Res. Atmos., 119(12):7502–7514.

Jorgensen, W. L., Maxwell, D. S., and Tirado-Rives, J. (1996). Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc., 118(45):11225–11236.

Joswiak, M. N., Duff, N., Doherty, M. F., and Peters, B. (2013). Size-dependent surface free energy and Tolman-corrected droplet nucleation of TIP4P/2005 water. J. Phys. Chem.

Lett., 4(24):4267–4272.

REFERENCES 59 Kaneko, T., Akimoto, T., Yasuoka, K., Mitsutake, A., and Zeng, X. C. (2011). Size-dependent

phase changes in water clusters. J. Chem. Theory Comput., 7(10):3083–3087.

Kuang, C., McMurry, P. H., McCormick, A. V., and Eisele, F. (2008). Dependence of nu-cleation rates on sulfuric acid vapor concentration in diverse atmospheric locations. J.

Geophys. Res. Atmos., 113(D10).

Kulmala, M., Vehkam¨aki, H., Pet¨aj¨a, T., Dal Maso, M., Lauri, A., Kerminen, V.-M., Birmili, W., and McMurry, P. (2004). Formation and growth rates of ultrafine atmospheric particles:

a review of observations. J. Aerosol Sci., 35:143–176.

Kuni, F. M., Grinin, A. P., and Shchekin, A. K. (1998). The microphysical effects in non-isothermal nucleation. Physica A, 252:67–84.

Kurt´en, T., Loukonen, V., Vehkam¨aki, H., and Kulmala, M. (2008). Amines are likely to enhance neutral and ion-induced sulfuric acid-water nucleation in the atmosphere more effectively than ammonia. Atm. Chem. Phys., 8(14):4095–4103.

Landau, L. D. and Lifshitz, E. M. (1980). Statistical Physics. Part 1: Course of Theoretical Physics. Pergamon Press, 3rd edition.

Lee, J. K., Barker, J., and Pound, G. (1974). Surface structure and surface tension: Pertur-bation theory and Monte Carlo calculation. J. Chem. Phys., 60(5):1976–1980.

Lee, J. K., Barker, J. A., and Abraham, F. F. (1973). Theory and Monte Carlo simulations of physical clusters in the imperfect vapor. J. Chem. Phys., 58:3166–3180.

Lettieri, C., Paxson, D., Spakovszky, Z., and Bryanston-Cross, P. (2018). Characterization of nonequilibrium condensation of supercritical carbon dioxide in a de laval nozzle. J. Eng.

Gas Turb. Power, 140(4).

Leyssale, J.-M., Delhommelle, J., and Millot, C. (2005). Molecular simulation of the homo-geneous crystal nucleation of carbon dioxide. J. Chem. Phys., 122(18):184518.

Lippe, M., Szczepaniak, U., Hou, G.-L., Chakrabarty, S., Ferreiro, J. J., Chasovskikh, E., and Signorell, R. (2019). Infrared spectroscopy and mass spectrometry of CO2clusters during nucleation and growth. J. Phys. Chem. A, 123(12):2426–2437.

Lothe, J. and Pound, G. M. (1962). Reconsiderations of nucleation theory. J. Chem. Phys., 36:2080–2085.

Lujiten, C. C. M., Bosschaart, K. J., and van Dongen, M. E. (1997). High pressure nucleation in water/nitrogen systems. J. Chem. Phys., 106:8116–8123.

Maergoiz, A., Nikitin, E., Troe, J., and Ushakov, V. (1996a). Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. I. Ion–dipole capture. J. Chem. Phys., 105(15):6263–6269.

Maergoiz, A., Nikitin, E., Troe, J., and Ushakov, V. (1996b). Classical trajectory and adi-abatic channel study of the transition from adiadi-abatic to sudden capture dynamics. II.

Ion–quadrupole capture. J. Chem. Phys., 105(15):6270–6276.

Maergoiz, A., Nikitin, E., Troe, J., and Ushakov, V. (1996c). Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. III. Dipole–

dipole capture. J. Chem. Phys., 105(15):6277–6284.

Mandelbrot, B. B. (1989). Temperature fluctuation: a well-defined and unavoidable notion.

Physics Today, 42(1):71.

Manka, A., Bergmann, D., Ghosh, D., Strey, R., and W¨olk, J. (2007). Preliminary results on homogeneous nucleation of water: A novel measurement technique using the two-valve expansion chamber. InNucleation and Atmospheric Aerosols, pages 260–264. Springer.

Manka, A., Pathak, H., Tanimura, S., W¨olk, J., Strey, R., and Wyslouzil, B. E. (2012). Freezing water in no-man’s land. Phys. Chem. Chem. Phys., 14(13):4505–4516.

Manka, A. A., Brus, D., Hyv¨arinen, A.-P., Lihavainen, H., W¨olk, J., and Strey, R. (2010).

Homogeneous water nucleation in a laminar flow diffusion chamber. J. Chem. Phys., 132(24):244505.

Maxwell, J. C. (1873). Molecules. Nature, 8(204):437–441.

McClurg, R. B. and Flagan, R. C. (1998). Critical comparison of droplet models in homo-geneous nucleation theory. J. Coll. Interface. Sci., 201(2):194–199.

McFee, R. (1973). On fluctuations of temperature in small systems.Am. J. Phys., 41(2):230–

234.

Mcgrath, M. J., Olenius, T., Ortega, I., Loukonen, V., Paasonen, P., Kurt´en, T., Kulmala, M., and Vehkam¨aki, H. (2012). Atmospheric cluster dynamics code: a flexible method for solution of the birth-death equations. Atmos. Chem. Phys., 12(5):2345–2355.

Merikanto, J., Spracklen, D. V., Mann, G. W., Pickering, S. J., and Carslaw, K. S. (2009).

Impact of nucleation on global CCN. Atmos. Chem. Phys., 9:8601–8616.

Merikanto, J., Vehkam¨aki, H., and Zapadinsky, E. (2004). Monte carlo simulations of critical cluster sizes and nucleation rates of water. J. Chem. Phys., 121(2):914–24.

Mikheev, V. B., Irving, P. M., Laulainen, N. S., Barlow, S. E., and Pervukhin, V. V. (2002).

Laboratory measurement of water nucleation using a laminar flow tube reactor.J. Chem.

Phys., 116(24):10772–10786.

Miller, R. C., Anderson, R. J., Kassner Jr, J., and Hagen, D. E. (1983). Homogeneous nucleation rate measurements for water over a wide range of temperature and nucleation rate. J. Chem. Phys., 78(6):3204–3211.

Neal, C. M., Starace, A. K., and Jarrold, M. F. (2007). Melting transitions in aluminum clusters: The role of partially melted intermediates. Phys. Rev. B., 76(5):054113.

Nos´e, S. (1984). A molecular dynamics method for simulations in the canonical ensemble.

Mol. Phys., 52(2):255–268.

Oh, K. J. and Zeng, X, C. (2000). A small-system ensemble Monte Carlo simulation of supersaturated vapor: Evaluation of barrier to nucleation. J. Chem. Phys., 112:294–300.

REFERENCES 61 Ostwald, W. (1897). Studien ¨uber die Bildung und Umwandlung fester K¨orper. 1.

Abhand-lung ¨Ubers¨attigung und ¨Uberkaltung.Z. Physik. Chem. (Leipzig), 22:289–330.

Pawlow, P. (1909). ¨Uber die Abh¨angigkeit des Schmelzpunktes von der Oberfl¨achenenergie eines festen K¨orpers. Z. Physik. Chem., 65(1):1–35.

Plummer, P. L. M. and Hale, B. N. (1972). Molecular model for prenucleation water clusters.

J. Chem. Phys., 56:4329.

Potoff, J. J. and Siepmann, J. I. (2001). Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen. AIChE J., 47(7):1676–1682.

Reguera, D. and Rub´ı, J. (2001). Nonequilibrium translational-rotational effects in nucle-ation. J. Chem. Phys., 115(15):7100–7106.

Reiss, H., Kegel, W. K., and Katz, J. I. (1997). Resolution of the problems of replacement free energy, 1/S, and internal consistency in nucleation theory by consideration of the length scale for mixing entropy. Phys. Rev. Lett., 78:4506–4509.

Rytk¨onen, A., Valkealahti, S., and Manninen, M. (1997). Melting and evaporation of argon clusters. J. Chem. Phys., 106:1888–1892.

Saltz, D. (1994). Using the noninteracting cluster theory to predict the properties of real vapor. J. Chem. Phys., 101:6038–6051.

Sanz, E., Vega, C., Espinosa, J., Caballero-Bernal, R., Abascal, J., and Valeriani, C. (2013).

Homogeneous ice nucleation at moderate supercooling from molecular simulation.J. Am.

Chem. Soc., 135(40):15008–15017.

Schmelzer, J. W., Boltachev, G. S., and Abyzov, A. S. (2013). Temperature of critical clusters in nucleation theory: Generalized Gibbs’ approach. J. Chem. Phys., 139(3):034702.

Smoluchowski, M. v. (1916). Drei Vortrage ¨uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Z. Phys., 17:557–585.

Stolzenburg, D., Simon, M., Ranjithkumar, A., K¨urten, A., Lehtipalo, K., Gordon, H., Ehrhart, S., Finkenzeller, H., Pichelstorfer, L., Nieminen, T., et al. (2020). Enhanced growth rate of atmospheric particles from sulfuric acid. Atm. Chem. Phys., 20(12):7359–7372.

Su, T. and Chesnavich, W. J. (1982). Parametrization of the ion–polar molecule collision rate constant by trajectory calculations. J. Chem. Phys., 76(10):5183–5185.

Ter Horst, J., Bedeaux, D., and Kjelstrup, S. (2011). The role of temperature in nucleation processes. J. Chem. Phys., 134(5):054703.

Tolman, R. C. (1949). The effect of droplet size on surface tension.J. Chem. Phys., 17:333–

337.

Toxvaerd, S. (2016). Nucleation and droplet growth from supersaturated vapor at tempera-tures below the triple point temperature. J. Chem. Phys., 144(16):164502.

Van Sang, L., Van Hoang, V., and Thuy Hang, N. (2013). Molecular dynamics simulation of melting of fcc Lennard-Jones nanoparticles. Eur. Phys. J. D, 67(3):64.

Vehkam¨aki, H. (2006). Classical nucleation theory in multicomponent systems. Springer.

Vehkam¨aki, H. and Ford, I. J. (2000). Critical cluster size and droplet nucleation rate from growth and decay simulations of Lennard-Jones clusters.J. Chem. Phys., 112:4193–4202.

Viisanen, Y., Strey, R., and Reiss, H. (1993). Homogeneous nucleation rates for water. J.

Chem. Phys., 99:4680–4692.

Vinˇs, V., Hykl, J., Hrub`y, J., Blahut, A., Celn`y, D., ˇCensk`y, M., and Prokopov´a, O. (2020).

Possible anomaly in the surface tension of supercooled water: New experiments at extreme supercooling down to -31.4C. J. Phys. Chem. Lett., 11(11):4443–4447.

Wales, D., Doye, J., Dullweber, A., Hodges, M., Naumkin, F., Calvo, F., Hern´ andez-Rojas, J., and Middleton, T. (2020). The Cambridge Cluster Database. http://www-wales.ch.cam.ac.uk/CCD.html.

Wattis, J. A. (2006). An introduction to mathematical models of coagulation–fragmentation processes: a discrete deterministic mean-field approach.Physica D, 222(1-2):1–20.

Weakliem, C. L. and Reiss, H. (1994). The factor 1/S in the classical theory of nucleation.

J. Phys. Chem., 98:6408–6412.

Wedekind, J., Reguera, D., and Strey, R. (2007a). Influence of thermostats and carrier gas on simulations of nucleation.J. Chem. Phys., 127(6):064501.

Wedekind, J., Strey, R., and Reguera, D. (2007b). New method to analyze simulations of activated processes.J. Chem. Phys., 126:134103.

olk, J. and Strey, R. (2001). Homogeneous nucleation of H2O and D2O in comparison:

The isotope effect.J. Phys. Chem. B, 105:11683–11701.

Wyslouzil, B. E. and Seinfeld, J. H. (1992). Nonisothermal homogeneous nucleation. J.

Chem. Phys., 97:2661–2670.

Wyslouzil, B. E., Wilemski, G., Strey, R., Seifert, S., and Winans, R. E. (2007). Small angle X-ray scattering measurements probe water nanodroplet evolution under highly non-equilibrium conditions. Phys. Chem. Chem. Phys., 9(39):5353–5358.

Xie, H.-B., Li, C., He, N., Wang, C., Zhang, S., and Chen, J. (2014). Atmospheric chemical reactions of monoethanolamine initiated by OH radical: mechanistic and kinetic study.

Env. Sci. Tech., 48(3):1700–1706.

Yasuoka, K. and Matsumoto, M. (1998). Molecular dynamics of homogeneous nucleation in the vapor phase. I. Lennard-Jones fluid. J. Chem. Phys., 109:8451–8462.