To summarise, nucleation in the gas phase is a well-established and mature field of study, and as demonstrated, the common theoretical apparatus is working overall relatively well to predict the rates of cluster formation. However, it is important to fine-tune the approach to a specific problem to capture the important physics of the system in the model/theory used.
future perspectives
Based on the research presented in this thesis, at least two new research questions in gas phase cluster formation could be considered next:
1.As mentioned on page 44, the temperatures of critical (and subcriti-cal) clusters compared to the bath temperature are still debated in lit-erature. We believe that the issue could be addressed with large-scale non-equilibrium molecular dynamics simulations by carefully tracing the emerged clusters back in time. The kinetic (and potential) energy distributions of the nucleating clusters as opposed to those clusters that evaporate will help to understand the nature of non-isothermal nucleation
2. In Paper IV, collisions between two interacting neutral molecules were investigated on the molecular level using trajectory simulations in order to calculate the collision rate enhancement over the kinetic theory of gases. The long-range interactions, however, are even more important for ion-ion or ion-dipole collisions. Trajectory simulations can be used to study these systems as well. By studying represen-tative set of different colliding molecules and clusters in this fashion, a simplified theoretical approach could be developed to predict more accurate collision rate coefficients based on simple physicochemical properties of molecules and clusters. Previously similar simulations (and the related parameterisations) have been carried out only using simplified interactions and particles without any structure (Dugan Jr and Magee, 1967; Chesnavich et al., 1980; Su and Chesnavich, 1982;
Maergoiz et al., 1996a,b,c)
Paper I: Effect of conformers on free energies of atmospheric complexes (2016):
L. Partanen, H. Vehkam¨aki, K. Hansen, J. Elm, H. Henschel, T. Kurt´en, R. Halonen and E. Zapadinsky
Objectives and main results: In this article we have shown how to calculate free energies for atmospherically relevant complexes using statistical mechanics methods when multiple conformers and/or isomers are present. We have shown that the thermal (or Boltzmann) averaging-type approaches used in several published works are incorrect and provided numerical evidence that the use of these erroneous formulas can result in errors larger than 1 kcal/mol.
Contribution: The author was responsible of the analysis of the data with L.
Partanen. The author also participated in writing Results and Discussion section.
Paper II: New particle formation from sulfuric acid and amines: Comparison of monomethylamine, dimethylamine, and trimethylamine (2017):
T. Olenius, R. Halonen, T. Kurt´en, H. Henschel, O. Kupiainen-M¨a¨att¨a, I. K.
Ortega, C. N. Jen, H. Vehkam¨aki, and I. Riipinen
Objectives and main results: The potential role of mono-, di-, and trimethy-lamine (MMA, DMA, and TMA, respectively) in atmospheric cluster formation involving sulfuric acid and water was explored by simulations of molecular cluster formation in a range of ambient conditions relevant to the lower tropo-sphere. Quantum chemistry-based cluster fragmentation rate coefficients are applied in a cluster population dynamics model to yield cluster concentrations and formation rates. We found that the studied amines were more capable to stabilise sulfuric acid clusters than ammonia, and the stabilising strength of the bases with respect to each other is DMA≥TMA>MMA>NH3.
Contribution: The author carried out majority of the ACDC simulations and wrote the first draft of the manuscript with T. Olenius.
Paper III: Deviation from equilibrium conditions in molecular dynamic simula-tions of homogeneous nucleation (2018):
R. Halonen, E. Zapadinsky and H. Vehkam¨aki
Objectives and main results: In this article we have compared the results of the standard kinetic scheme with MD simulation results found in the recent literature. The formation free energy for the kinetic scheme has been calculated using a MC approach. The kinetic scheme incorporating the non-isothermal correction factor agrees with MD simulations where carrier gas has been used as a thermostat. In addition, a reasonable agreement is achieved with MD simulations using “artificial” thermostat methods.
Contribution: The author carried out the Monte Carlo simulations and gathered the published molecular dynamics simulation data. The author analysed the simulation data and wrote the paper with contributions from all of the co-authors.
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Paper IV: Rate enhancement in collisions of sulfuric acid molecules due to long-range intermolecular forces (2019):
R. Halonen, E. Zapadinsky, T. Kurt´en, H. Vehkam¨aki, and B. Reischl
Objectives and main results: The statistics of collisions of H2SO4 molecules in a vacuum were studied using molecular dynamics simulations and compared our results against simple theoretical models. We found that the collision rate coefficient is enhanced by a factor of 2.2 at 300 K compared with kinetic gas theory. The enhancement factor is consistent with the discrepancy observed between experimental H2SO4 cluster formation rates and estimated hard-sphere formation rates.
Contribution: The author planned the simulation set-up and performed bench-mark calculations with B. Reischl. The author and E. Zapadinsky provided the theoretical framework. The author analysed and interpret the simulation data, and wrote the paper with B. Reischl.
Paper V: Homogeneous nucleation of carbon dioxide in supersonic nozzles I:
Experiments and Classical Theories (2020):
K. K. Dingilian, R. Halonen, V. Tikkanen, B. Reischl, H. Vehkam¨aki, and B. E.
Wyslouzil
Objectives and main results: In this article we have presented experimental homogeneous nucleation rates for CO2 by expanding CO2-Ar gas mixtures in a supersonic nozzle. The formed CO2 particles were followed using Fourier transform infrared (FTIR) spectroscopy, and the resulting spectra was consistent with the particles being crystalline. The conducted MD simulations, however, revealed that the smallest clusters formed in the nozzle might be liquid-like, and furthermore the simulations suggested an additional term for the free energy expression.
Contribution: The author provided the theoretical model and wrote the corresponding parts of the manuscript. In addition, the author analysed and visualised the molecular dynamics simulation data.
Paper VI: Homogeneous nucleation of carbon dioxide in supersonic nozzles II:
molecular dynamics simulations and properties of nucleating clusters (2021):
R. Halonen, V. Tikkanen, B. Reischl, K. K. Dingilian, B. E. Wyslouzil, and H.
Vehkam¨aki
Objectives and main results: In this article we have carried out large scale MD simulations of the homogeneous nucleation of CO2 in Ar carrier gas in a similar range of temperatures as in Paper V. The formation free energies retrieved from the MD simulations were used to improve CNT by introducing a Tolman-like term into the classical liquid drop model expression. In addition, extensive analyses of the nucleating clusters’ structural and energetic properties were performed to show that despite strong undercooling with respect to the triple point, most clusters are clearly liquid-like during the nucleation stage.
Contribution: The author planned the study and is responsible of analysing and interpreting of the simulation results. The author wrote the paper as one of the two first authors.
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