A universal and accurate LPMI method for calculating mismatch in heterogeneous ice nucleation

The interfacial correlation factor f(m,x), where m refers to the interaction among ice, water and the substrate and x refers to the ratio of the critical nucleation size to the surface topography characteristic size of the substrate, plays a crucial role in the classical theory of heterogeneous ice nucleation as it significantly impacts the energy of nucleation. Generally, a smaller value of f(m,x) indicates a higher propensity for ice nucleation. The degree of structural compatibility between ice and the substrate greatly influences f(m,x), particularly on specific substrates. Several approaches have been proposed to calculate the lattice matching based on this idea, which allows whether a surface is favorable for nucleation to be determined. However, none of these methods adequately correlates the mismatch index with ice growth phenomena. In this paper, we embarked on a new attempt to calculate the mismatch index by combining the lattice parameter and Miller index (LPMI). Droplet freezing experiments have been carried out on α-Al₂O₃ and silicon surfaces with different Miller indices to verify the rationality of the LPMI method. Furthermore, we validated the LPMI method extensively against other works and further demonstrated its readiness, accuracy and universality for freezing problems. The results consistently show that δ_d = 2|d_i - d_s|/(d_i + d_s) with interplanar spacing more accurately predicts heterogeneous ice nucleation rates across a wide range of substrates than δ₁ = (a_i - a_s)/a_i with the lattice parameter of ice and the substrate and is more generally applicable than δ_2D = (d_i - d_i)/d_i with the distances between two adjacent and congener atoms on the same plane. We believe that the proposed approach will aid in the selection of substrates for promoting or inhibiting heterogeneous nucleation on a specific substrate.