On the ability of the gas/particle partitioning constant Kp to consider the effects of mean MW and the presence of high MW compounds

The advantages of the original form of the predictive expression for the gas/particle partition constant Kp (m3 μg−1) are considered. The expression Kp,i for compound i   contains pL,io, ζiζi and MW¯. These are the pure-compound liquid vapor pressure, the mole-fraction-scale activity coefficient in the absorbing particulate matter (PM) phase, and the mean molecular weight (g mol−1) of the absorbing phase. Algorithms are available for predicting ζiζi values in mixtures of organic compounds and water as they are affected by energetic and entropic effects; Flory–Huggins Theory provides a convenient way to examine the entropic effects of the presence of high MW compounds on the ζiζi values of lower MW compounds. In the exposition of their volatility basis set (VBS) approach for modeling organic aerosol condensation, Donahue et al. (2006, Environ. Sci. Technol., 40, 2635–2643, Supplementary Material) argued that the need to consider MW¯ values can be avoided by switching from the mole fraction scale to a mass fraction scale and accompanying Ci∗ values that incorporate mass-fraction-scale activity coefficient values ζi′. In practice however, the VBS approach usually ignores both activity and MW¯ corrections by setting ζi′=1. (An equation for ζi′ is developed here in the event that modeling with ζi′≠1 becomes of interest.) Regardless of the advantages of the prediction equation for Kp,i, there will undoubtedly be circumstances when MW¯ and ζiζi values become inaccessible, as for aged organic particulate matter in which a large mass fraction of the absorbing PM of is of indeterminable molecular nature. In such cases, “prediction” of Kp,i values may only be possible by means of empirical correlation of log Kp,i vs. logpL,io for the PM type of interest.

Research highlights
► Thermodynamic derivation of traditional gas/particle partitioning constant Kp is reviewed.
► Varying thermodynamics of absorbing phase most easily considered in Kp approach.
► This includes the effects of varying mean molecular weight and activity coefficients.