Identification of molecular cluster evaporation rates, cluster formation enthalpies and entropies by Monte Carlo method

• Published in: Atmospheric chemistry and physics 2020-12, Vol.20 (24), p.15867-15906
• Main Authors: Shcherbacheva, Anna, Balehowsky, Tracey, Kubecka, Jakub, Olenius, Tinja, Helin, Tapio, Haario, Heikki, Laine, Marko, Kurtén, Theo, Vehkamäki, Hanna
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Ammonia; Analysis; Bayesian analysis; Coefficients; Collision dynamics; Collision rates; Data; Enthalpy; Entropy; Entropy of formation; Evaporation; Evaporation rate; Inverse problems; Markov chains; Markov processes; Mathematical analysis; Methods; Molecular clusters; Monte Carlo method; Monte Carlo simulation; Ordinary differential equations; Parameter estimation; Probability theory; Quantum chemistry; Simulation; Statistical methods; Steady state; Sulfuric acid; Sulphuric acid; Temperature; Temperature dependence; Time dependence; Time measurement
• ISSN: 1680-7324; 1680-7316; 1680-7324
• DOI: 10.5194/acp-20-15867-2020

We address the problem of identifying the evaporation rates for neutral molecular clusters from synthetic (computer-simulated) cluster concentrations. We applied Bayesian parameter estimation using a Markov chain Monte Carlo (MCMC) algorithm to determine cluster evaporation/fragmentation rates from synthetic cluster distributions generated by the Atmospheric Cluster Dynamics Code (ACDC) and based on gas kinetic collision rate coefficients and evaporation rates obtained using quantum chemical calculations and detailed balances. The studied system consisted of electrically neutral sulfuric acid and ammonia clusters with up to five of each type of molecules. We then treated the concentrations generated by ACDC as synthetic experimental data. With the assumption that the collision rates are known, we tested two approaches for estimating the evaporation rates from these data. First, we studied a scenario where time-dependent cluster distributions are measured at a single temperature before the system reaches a steady state. In the second scenario, only steady-state cluster distributions are measured but at several temperatures. Additionally, in the latter case, the evaporation rates were represented in terms of cluster formation enthalpies and entropies. This reparameterization reduced the number of unknown parameters, since several evaporation rates depend on the same cluster formation enthalpy and entropy values. We also estimated the evaporation rates using previously published synthetic steady-state cluster concentration data at one temperature and compared our two cases to this setting. Both the time-dependent and the two-temperature steady-state concentration data allowed us to estimate the evaporation rates with less variance than in the steady-state single-temperature case. We show that temperature-dependent steady-state data outperform single-temperature time-dependent data for parameter estimation, even if only two temperatures are used. We can thus conclude that for experimentally determining evaporation rates, cluster distribution measurements at several temperatures are recommended over time-dependent measurements at one temperature.