Ice nucleation is an important process to form ice particles in clouds. Gaps still exist in understanding how the mixing state alters the INP efficiency. The study quantifies the impact of INP mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. The authors first derive analytical expressions of the frozen fraction of internally and externally mixed INP populations. Results from a multi-species immersion freezing scheme into the particle-resolved model with a Binned Tau-Leaping algorithm to speed up the simulation confirm the theoretical prediction that internally mixed INPs yield higher frozen fractions than externally mixed INPs under otherwise identical conditions. The model framework (PartMC+ABIFM) can be a useful tool to study ice nucleation under complex mixing state conditions. In general, I think the paper is well written and I have some minor comments listed below.

1. Overall, I find results from this study interesting. However, I am concerned about a key assumption—that the volume ratio of the species equals their surface area ratio. This assumption is unlikely to be held under realistic atmospheric conditions (e.g., I am thinking about aging or coating). My main concern is the representativeness of this assumption for real atmospheric INPs and how it affects the applicability of findings in this study to other research. I think it is worth including a discussion of this assumption, along with its potential limitations.
2. Line 20: I suggest adding “extreme” before “external mixture” and “internal mixture” when first mentioning them in the paper, because there are many situations of “external” and “internal” mixture. “Each particle consists of a single chemical species” and “all particles share the same composition” are extreme conditions.
3. Line 140: From the measurement point of view, people usually measure INP efficiency (INP spectrum) without knowing the chemical composition or mixing state of aerosols. Theorem 1 is not surprising from this point of view because internal mixture basically increases the number concentration of efficient INPs compared with external mixture. Therefore, I think it is equivalent to say the mixing state can change the INP spectrum. I wonder whether the authors can have one figure to show the change of INP spectrum by changing the mixing state.
4. Line 186: Provide parameterization equation of Jhet and values of parameters of Fe2O3 and other species (e.g., those used in Figure 3) in the appendix, instead of just referring to Knopf and Alpert (2013).
5. Figure 3. Mention the simulation condition in the caption, e.g., a constant temperature of -33 C and a duration of 10 minutes.
6. Figure 7 caption. Specify “2, 5, and 9 minutes” in the caption, insteady of saying "at specific times".
7. Line 388, “the \chi index” is not defined before. Consider changing it to “the mixing state”.