An optimization problem related to the modeling of atmospheric inorganic aerosols

A mathematical model for the computation of chemical equilibrium of atmospheric inorganic aerosols is proposed. The equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual method solving the Karush–Kuhn–Tucker conditions is detailed. An active set/Newton method permits the computation of the minimum and track solid salts at the equilibrium. To cite this article: N.R. Amundson et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Laser-Induced Acoustic Desorption/Atmospheric Pressure Chemical Ionization Mass Spectrometry

Laser-induced acoustic desorption (LIAD) was successfully coupled to a conventional atmospheric pressure chemical ionization (APCI) source in a commercial linear quadrupole ion trap mass spectrometer (LQIT). Model compounds representing a wide variety of different types, including basic nitrogen and oxygen compounds, aromatic and aliphatic compounds, as well as unsaturated and saturated hydrocarbons, were tested separately and as a mixture. These model compounds were successfully evaporated into the gas phase by using LIAD and then ionized by using APCI with different reagents. From the four APCI reagent systems tested, neat carbon disulfide provided the best results. The mixture of methanol and water produced primarily protonated molecules, as expected. However, only the most basic compounds yielded ions under these conditions. In sharp contrast, using APCI with either neat benzene or neat carbon disulfide as the reagent resulted in the ionization of all the analytes studied to predominantly yield stable molecular ions. Benzene yielded a larger fraction of protonated molecules than carbon disulfide, which is a disadvantage. A similar but minor amount of fragmentation was observed for these two reagents. When the experiment was performed without a liquid reagent (nitrogen gas was the reagent), more fragmentation was observed. Analysis of a known mixture as well as a petroleum cut was also carried out. In summary, the new experiment presented here allows the evaporation of thermally labile compounds, both polar and nonpolar, without dissociation or aggregation, and their ionization to predominantly form stable molecular ions.     

An optimization problem related to the modeling of atmospheric organic aerosols

A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is proposed. The equilibrium is given by the minimum of the Gibbs free energy and is characterized using the notion of phase simplex of its convex hull. A primal-dual interior-point method solving the Karush–Kuhn–Tucker conditions is detailed. Numerical results show the efficiency of our algorithm. To cite this article: N.R. Amundson et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols

A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is presented. The phase equilibrium is given by the global minimum of the Gibbs free energy for a system that involves water and organic components. This minimization problem is equivalent to the determination of the convex hull of the corresponding molar Gibbs free energy function. A geometrical notion of phase simplex related to the convex hull is introduced to characterize mathematically the phases at equilibrium. A primal-dual interior-point algorithm for the efficient solution of the phase equilibrium problem is presented. A novel initialization of the algorithm, based on the properties of the phase simplex, is proposed to ensure the convergence to a global minimum of the Gibbs free energy. For a finite termination of the interior-point method, an active phase identification procedure is incorporated. Numerical results show the robustness and efficiency of the approach for the prediction of liquid-liquid equilibrium in multicomponent mixtures.Communicated by R. GlowinskiThis work was supported by US Environmental Protection Grant X-83234201. The second author was partially supported by Swiss National Science Foundation Grant PBEL2-103152.     

Primal-Dual Active-Set Algorithm for Chemical Equilibrium Problems Related to the Modeling of Atmospheric Inorganic Aerosols

A general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols is proposed. The thermodynamic equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase, and solid salts. A primal-dual algorithm solving the Karush-Kuhn-Tucker conditions is detailed. An active set/Newton method permits to compute the minimum of the energy and tracks the presence or not of solid salts at the equilibrium. Numerical results show the efficiency of our algorithm for the prediction of multiphase multireaction chemical equilibria.Communicated by R. GlowinskiThis work has been partially supported by the United States Environmental Protection Agency through Cooperative Agreement X-83234201 to the University of Houston. The second author was supported by the Swiss National Science Foundation, Grant PBEL2-103152.