| Summary: | Effective density (<i>ρ<sub>e</sub></i>) is universally used in atmospheric science as an alternative measure of the density (<i>ρ</i>) of aerosol particles, and its definitions can be expressed in terms of the particle mass (<i>m<sub>p</sub></i>), <i>ρ</i>, mobility diameter (<i>D<sub>m</sub></i>), vacuum aerodynamic diameter (<i>D<sub>va</sub></i>), and dynamic shape factor (<i>χ</i>), as <i>ρ<sub>e</sub><sup>I</sup></i> = 6<i>m<sub>p</sub></i>/(<i>π</i>∙<i>D<sub>m</sub></i><sup>3</sup>), <i>ρ<sub>e</sub><sup>II</sup></i> = <i>ρ</i>/<i>χ</i>, and <i>ρ<sub>e</sub><sup>III</sup></i> = <i>D<sub>va</sub></i>/<i>D<sub>m</sub></i>. However, the theoretical foundation of these three definitions of <i>ρ<sub>e</sub></i> is still poorly understood before their application. Here, we explore the relationship between <i>ρ<sub>e</sub></i> and aerosol size through theoretical calculation. This study finds, for the first time, that <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> inherently decrease with increasing size for aspherical particles with a fixed <i>ρ</i> and <i>χ</i>. We further elucidate that these inherent decreasing tendencies are governed by <i>χ</i>, and the ratio of the Cunningham Slip Correction Factor of the volume-equivalent diameter to that of the mobility diameter (<i>C<sub>c</sub></i>(<i>D<sub>ve</sub></i>)/<i>C<sub>c</sub></i>(<i>D<sub>m</sub></i>)), but not by <i>ρ</i>. Taking the variable <i>χ</i> into consideration, the relationships of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> to particle size become more complicated, which suggests that the values of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> have little indication of the size-resolved physicochemical properties of particles. On the contrary, <i>ρ<sub>e</sub><sup>II</sup></i> is independent on size for fixed <i>χ</i> and <i>ρ</i>, which indicates that the change in <i>ρ<sub>e</sub><sup>II</sup></i> with size can better indicate the change in morphology and the transformation of the chemical compositions of particles. Our new insights into the essence of three <i>ρ<sub>e</sub></i>s provide an accurate and crucial theoretical foundation for their application.
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