Crystal Nucleation Kinetics and Mechanism: Influence of Interaction Potential

TL;DR

The paper investigates how modifying the repulsive and attractive components of a Lennard-Jones–like potential affects crystal nucleation kinetics and mechanisms. By comparing a standard 12-6 LJ potential with a softer 7-6 variant at the same driving force using RETIS, CNT with seeding, and LeaPP analysis, the authors show that nucleation rates are similar while the pathways and resulting polymorphs differ: the 12-6 system predominantly forms FCC nuclei, whereas the 7-6 system exhibits competing BCC-dominated and FCC-HCP-dominated pathways leading to polymorphism. The study reveals that polymorph selection can be controlled through interaction potentials without altering overall nucleation rates, and demonstrates the utility of LeaPP for dissecting nucleation pathways and post-critical growth. These insights advance understanding of how tunable interactions influence self-assembly and polymorph design in colloidal and molecular systems, with implications for material design and crystallization control.

Abstract

Modulating liquid-to-solid transitions and the resulting crystalline structure for tailored properties is much desired. Colloidal systems are exemplary to this end, but the fundamental knowledge gaps in relating the influence of intermolecular interactions to crystallization behavior continue to hinder progress. In this study, we address this knowledge gap by studying nucleation and growth in systems with modified Lennard-Jones potential. Specifically, we study the commonly used 12-6 potential and a softer 7-6 potential. The thermodynamic state point for the study is chosen such that both systems are investigated at the same level of supercooling and pressure. Under these conditions, we find that the nucleation rate for both systems is comparable. Interestingly, the nucleation pathways and resulting crystal structures are different. In the 12-6 system, nucleation and growth occur predominantly through the FCC structure. Softening the potential alters the critical nucleus composition and introduces two distinct nucleation pathways. One pathway predominantly leads to the nucleus with a body-centered cubic (BCC) structure, while the other favors the face-centered cubic (FCC) arrangement. Our study illustrates that polymorph selection can be achieved through modifications to intermolecular interactions without impacting nucleation kinetics. The results have significant implications in designing approaches for polymorph selection and modulating self-assembly mechanisms.

Figures (11)

• Figure 1: (A) The potentials studied, (B) the negative of their derivatives, (C) liquid RDF ($g_{liq}(r)$) at $p=5$, $T=0.78T_{\text{m}}$, and (D) FCC crystal RDF ($g_{FCC}(r)$) at $p=5$, $T=0.78T_{\text{m}}$.
• Figure 2: Crossing probability histogram, $P(\lambda|\lambda_0)$, constructed from WHAM. The vertical lines represent each interface ensemble, $\lambda_i$. The red line follows the probability of reaching some interface value ($\lambda$) given that it starts from the first interface. The physical interpretation of this plot is: (A) for the 7--6 system, the probability of reaching a crystal size of 720 particles, starting from a crystal size of 45, is $~1 \times 10^{-11}$. (B) For the 12--6 system, the probability of reaching a crystal size of 600 particles, starting from a crystal size of 45, is $~2 \times 10^{-10}$.
• Figure 3: $p_B$ projection of configurations from (A) 7--6 and (B) 12--6 system onto n$_\text{tf}$ (x-axis) and Q$_\text{6,tf}^\text{cl}$ (y-axis). The plot is colored by the committor value from 0 to 1. Projection of the average fraction of cloud particles (f$_\text{cloud}$) along n$_\text{tf}$ and Q$_\text{6,tf}^\text{cl}$ for the (C) 7--6 and (D) 12--6 system. The red triangle and star on panel D signify the configurations where n$_\text{tf} = 300$ and Q$_\text{6,tf}^\text{cl}\approx 0.20$ (star)/Q$_\text{6,tf}^\text{cl}\approx 0.30$ (triangle). The color map reflects the values of f$_\text{cloud}$, which increases from 0 to 1. Details of this OP calculation are described in SI Section S5.
• Figure 4: $p_B$ projection of configurations from the 12--6 system onto n$_\text{ld}$ (x-axis) and f$_\text{cloud}$ (y-axis). The plot is colored by the committor value from 0 to 1.
• Figure 5: The distribution of critical nucleus composition for (A) 7-6 and (B) 12-6 system. We define critical nucleus configurations as those with $0.45 \leq p_B \leq 0.55$. The x-axis describes the fraction of each composition as shown by the colors: blue -- BCC, cyan -- HCP, purple -- FCC. The y-axis accounts for the weighted contributions of each configuration (and the curves are shifted for visual clarity). Each configuration weight is calculated from the reweighted path ensemble weight of each trajectory.