Improved identification of evaporation rates and thermodynamic data by Monte-Carlo method
Authors: Shcherbacheva Anna , Helin Tapio , Haario Heikki , Vehkamäki Hanna 
Published: March 2020

&lt;p&gt;Atmospheric new particle formation and successive cluster growth to aerosol particles is an important field of research, in particular due to climate change phenomena and air quality monitoring. Recent developments in the instrumentation have enabled quantification of ionic clusters formed in the gas phase at the first steps of particle formation under atmospherically relevant mixing ratios. However, electrically neutral clusters are prevalent in atmospheric conditions, and thus must be charged prior to detection by mass spectrometer. The charging process can lead to cluster fragmentation and thus alter the measured cluster composition.&lt;/p&gt;&lt;p&gt;Even when the cluster composition can be measured directly, this does not quantify individual cluster-level properties, such as cluster collision and evaporation rates. Collision rates contain relatively small uncertainties in comparison to evaporation rates, which are computed using detailed balance assumption together with the free energies of cluster formation, which can in turn be obtained from Quantum chemistry (QC) methods. As evaporation rates depend exponentially on the free energies, even difference by several kcal/mol between different QC methods results in orders of magnitude differences in evaporation rates.&lt;/p&gt;&lt;p&gt;On the other hand, in spite of the error margins associated with the evaporation rates, simulations of cluster populations, which incorporate collision and evaporation rates as free parameters (such as Becker-D&amp;#246;ring models), have demonstrated good qualitative agreement with experimental data. The Becker-D&amp;#246;ring equations are a system of Ordinary Differential equations (ODE) which account for cluster birth and death processes, as well as external sinks and sources. In mathematical terms, prediction of cluster concentrations using kinetic simulations with given cluster collision and evaporation rates is called a forward problem.&lt;/p&gt;&lt;p&gt;In the present study, we focus on the so-called inverse problem of how to derive the evaporation rates and thermodynamic data (enthalpy change and entropy change due to addition or removal of molecule) from available measurements, rather than on the forward problem. We do this by Delayed Rejection Adaptive Monte Carlo (DRAM) method for the system containing sulfuric acid and ammonia with the maximal size of the pentamer. Initially, we tested the method on the synthetic data created from Atmospheric Cluster Dynamic Code (ACDC) simulations. By so doing, we identify the combination of fitted parameters and concentration measurements, which leads to the best identification of the evaporation rates. Additionally, we demonstrated that the temperature-dependent data yield better estimates of the evaporation rates as compared to the time-dependent data measured before the system has reached the steady state.&lt;/p&gt;&lt;p&gt;Next, we apply the technique to improve the identification of the evaporation rates from CLOUD chamber data, which contain cluster concentrations and new particle formation rates measured at different temperatures and a wide range of atmospherically relevant sulfuric acid and ammonia concentrations. As a result, we were able to obtain the probability density functions (PDFs) that show small standard variations for thermodynamic data. By using the values from the PDFs as parameters in the ACDC model, we achieve a fair agreement with the measured NPFs and cluster concentrations for a wide range of temperatures.&lt;/p&gt;