Review and comparative analysis of the theories on partitioning between the gas and aerosol particulate phases in the atmosphere

Abstract

An analysis has been carried out of the different approaches used to describe partitioning between the gas and aerosol particulate phases. The equation of Junge (Fate of Pollutants in the Air and Water Environments, edited by I.H. Suffet, Part I, pp. 7–26, Wiley, New York, 1977) has been shown to be based on a linear Langmuir isotherm, and as such has been shown to be equivalent to the equation of Yamasaki et al. (Environ. Sci. Technol. 16, 189–194, 1982). Prior to this work, Bidleman and Foreman (The Chemistry of Aquatic Pollutants, edited by R.A. Hites and S.J. Eisenreich, ACS Advances in Chemistry Series, 1987) developed a parameterization describing an equivalence between these two equations that is applicable when the enthalpy of desorption (Q₁) from the paniculate matter surface is similar to the enthalpy of vaporization (Q_v) of the pure liquid compound. That parameterization is valid when ¦Q₁- Q_v¦ is significantly less than 1 kcal mole⁻¹. A fundamental consideration of the process of gas/solid partitioning is used in this work to develop predictive equations for the value of the equilibrium constant $\text{K}{}_{\mathrm{Y}}\text{=}\text{c}{}_{\mathrm{<mtext>g</mtext>}}\text{(TSP}{}_{\mathrm{Y}}\text{)}\text{c}{}_{\mathrm{<mtext>p</mtext>}}$ where c_g and c_p are the gas phase and paniculate phase-associated concentrations (ng m⁻³), respectively, and TSP_Y is the concentration of suspended paniculate matter (ng m⁻³). In particular, it is derived that for a given compound, log $\text{K}{}_{\mathrm{<mtext>Y</mtext>}}\text{=}\text{−Q}{}_1\text{(2.303 RT)}\text{+}\text{log}\text{[}\text{2.53 × 10}{}^5\text{(M}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/A}{}_{\mathrm{<mtext>tsp</mtext>}}\text{t}{}_{\mathrm{O}}\text{]}$ where R = gas constant, T = temperature, M = mol. wt, A_tsp = specific surface area for the paniculate matter and t₀ is a characteristic molecular vibration time. In terms of the vapor pressure p_o (torr) of a compound or series of compounds, $\text{K}{}_{\mathrm{Y}}\text{=}\text{1.6 × 10}{}^4\text{p}{}_{\mathrm{o}}\text{N}{}_{\mathrm{s}}\text{A}{}_{\mathrm{tsp}}\text{Texp}\text{[}\text{(Q}{}_1\text{- Q}{}_{\mathrm{v}}\text{)}\text{RT}\text{]}$ where N_s is the number of moles of sorption sites per cm² of particulate matter surface area. When sorption to the surface is liquid-like (i.e. $\text{¦Q}{}_1\text{- Q}{}_{\mathrm{v}}\text{¦∼-0}$), then $\text{K}{}_{\mathrm{y}}\text{= 1.6 ×}\text{10}{}^4\text{p}{}_{\mathrm{o}}\text{N}{}_{\mathrm{s}}\text{A}{}_{\mathrm{tsp}}\text{T}$