Temperature Dependence in Efflorescence Relative Humidity of (NH₄)₂SO₄ and NaCl Particles: A Theoretical Study Using Classical Nucleation Theory

Understanding the phase state of aerosol particles is important for both atmospheric chemistry and physics. Phase transitions of aerosol particles are induced by changes in the temperature (T) and relative humidity (RH). In the case of atmospherically important inorganic chemical species such as (NH4)2SO4 and NaCl, phase transitions occur as deliquescence and efflorescence. The temperature dependence of deliquescence is well described by the Clausius–Clapeyron equation. However, the temperature dependence of the efflorescence RH (ERH) of inorganic salts has not been theoretically well described. We employed the classical nucleation theory (CNT) for modeling the ERH of (NH4)2SO4 and NaCl particles. The model outputs were compared to literature data. The literature data included a recent ERH measurement for size-selected particles using the low-temperature hygroscopicity tandem differential analyzer (low-T HTDMA). In the case of (NH4)2SO4, the temperature dependence of water solubility and interfacial energy between the nuclei and aqueous phase (γaq_nu) needed to be considered to reproduce the experimental ERH values. That is, γaq_nu needed to be represented by the following equation: γaq_nu (T) = γaq_nu (298.15 K)(T/298.15 K)n (where n is an empirically determined parameter). The value of n for (NH4)2SO4 was identified as 0.6. In the case of NaCl, the CNT estimation and low-T HTDMA result agreed well when n = 0.7, while the temperature dependence of ERH in the literature was highly variable. Further studies employing laboratory experiments and numerical simulations are required to facilitate a molecular-level understanding of the temperature dependence of ERH.