Shaping the aggregates of discotic particles with directional pair interactions

TL;DR

This work investigates how directional pair interactions control discotic particle aggregation using the coarse-grained Oblate-Gay-Berne-Kihara (OGBK) model. By comparing three interaction schemes (K, E, F) through Monte Carlo and Brownian Dynamics simulations, it shows that topology ranges from globular clusters (K) to flat multilayer aggregates (E) to columnar bundles (F), with aggregation onset $T_c^*$ and percolation governed by density $\rho^*$ and temperature. The study provides cluster-size distributions, internal ordering insights, and kinetic analyses that reveal a non-monotonic temperature dependence of aggregation and density-driven percolation, illustrating how directionality can tailor suprastructural materials. These findings offer design principles for discotic materials with targeted electronic, optical, and sensing properties by tuning directional interactions.

Abstract

Aggregation processes in systems of planar macromolecules and colloids drive a broad range of phenomena in natural systems and soft materials. Depending on chemical architecture, intermolecular interactions in these systems may favor different relative pair orientations, such as stacking face-face or percolating edge-edge arrangements. In this work, we employ a versatile coarse-grained interaction model for disk-like particles to provide a general framework to rationalize the thermotropic formation of aggregates and predict the topology of the resulting suprastructures. Monte Carlo and Brownian Dynamics simulations show that, with an appropriate tuning of the interactions, discotics spontaneously nucleate into clusters with globular, planar or stacked geometries, leading to materials with specific internal order and associated physicochemical properties.

Figures (7)

• Figure 1: a) Illustration of the OGBK model for two interacting platelets MAR11MOR21. The interaction energy depends on the relative position of the particles (${\bf r}_{ij}$), director vectors that define the orientation of the particles (${\bf \hat{u}}_i$ and ${\bf \hat{u}}_j$), and on the minimum distance between the particle cores ($d_m$) CUE08. Four pair configurations are considered as reference to describe the model: stacking "face-face" (ff), T-shaped "face-edge" (fe), parallel "edge-edge" (eep), crossed "edge-edge" (eec). b--d): Potential energy curves for two platelets in each of the four reference configurations, interacting with the OGBK parametrization employed in this work: b) model K (uniform interactions), c) model E (eep favored) and d) model F (ff stacking preferred).
• Figure 2: Classification of the BD simulated states of the K, E and F fluids into aggregation regimes. The solid line represents the onset of aggregation (the highest temperature at which stable clusters are formed). Symbols are used to represent states with no aggregates ($\blacksquare$), states that coalescence into large clusters ($\blacklozenge$), into multiple small clusters ($\bullet$), or into a percolated mesoporous structure ($\blacktriangle$). Snapshots and radial functions for the states with $\rho^*$=0.2 and T$^*$/$T_c^*$=0.8 are provided to illustrate the internal structure of the clusters and the overall fluid. See Figs. \ref{['fig-clustersK']}--\ref{['fig-clustersF']} for a more complete set of configurations.
• Figure 3: Fraction of particles belonging to an aggregate of size $i$, $F(i)$, as defined in Section \ref{['sec-MC']}. Results for models K, E, and F are shown in the top, middle, and bottom rows, respectively. For each model, the results are shown for densities $\rho^* =0.01$ and $0.2$ (left and right columns, respectively) and temperatures $T/T_c = 0.8, 0.5$, and $0.1$ (red, green and blue bars, respectively). Note the different range of sizes (x-axis) employed in the representations of the two densities.
• Figure 4: Examples of snapshots of stable configurations after long simulations, obtained for model K in relevant states. Columns from left to right $\rho^* = 0.01, 0.1, 0.2, 0.3$ and $0.5$. Rows from top to bottom $T^*/T_c^* = 0.95, 0.80, 0.50$ and $0.10$. The color of the particles indicates their orientation.
• Figure 5: Examples of snapshots of stable configurations after long simulations, obtained for model E in relevant states. Columns from left to right $\rho^* = 0.01, 0.1, 0.2, 0.3$ and $0.5$. Rows from top to bottom $T^*/T_c^* = 0.95, 0.80, 0.50$ and $0.10$. The color of the particles indicates their orientation.