Visualizing defect dynamics by assembling the colloidal graphene lattice

Two-dimensional (2D) materials, particularly graphene, have garnered significant scientific interest due to their exceptional optical, mechanical, and electronic properties. Graphene's honeycomb structure, formed by a monolayer of carbon atoms in a sp²-like bonded lattice, gives rise to a photonic and phononic band gap, promising applications in various fields. The creation of large, defect-free single-crystalline graphene, whether atomic or colloidal, poses a significant challenge, limiting its potential applications. Defects in graphene are critical to its properties, influencing factors such as band-gap tuning in electronic devices. While defects are inevitably introduced during growth or intentionally added to tailor material properties, a complete understanding of their formation and dynamics remains elusive. The complexity arises from the possibility of various structural arrangements for the trivalent atoms or particles, leading to multiple pathways for defect rearrangement. While electron microscopy has advanced our ability to visualize graphene defects, the kinetics and healing mechanisms are still poorly understood. Colloidal systems, consisting of micro-scale particles, offer advantages in studying these phenomena due to their ease of observation via optical microscopy, allowing real-time visualization of defect formation and dynamics with single-particle resolution—a challenge for atomic systems. The synthesis of anisotropic particles, particularly patchy particles with specific valency and bond angles, has enabled the construction of more intricate structures, opening possibilities for investigating complex 2D materials.

Extensive research has focused on the properties and applications of 2D materials like graphene (Akinwande et al., 2017; Li et al., 2019; Kang et al., 2020). The influence of defects on graphene's properties has been widely studied (Liu et al., 2015; Banhart et al., 2011; Yang et al., 2018), highlighting the importance of understanding defect formation mechanisms. Colloidal systems have been used as models to study crystallization and defect dynamics (Pusey & van Megen, 1986; Herlach et al., 2010; Gabrys et al., 2019), providing insights into atomic systems. Studies of colloidal crystal growth and defect formation have been conducted using various techniques (de Villeneuve et al., 2005; Weitz et al., 2006; Wang et al., 2015; Schall et al., 2004; Pertsinidis & Ling, 2005; Semwogerere et al., 2007; Lu & Weitz, 2013; Liu et al., 2020). The synthesis of anisotropic patchy particles (Sacanna et al., 2010; Kim et al., 2012; Kraft et al., 2009; Gong et al., 2017) has expanded the possibilities for creating complex colloidal structures (Wang et al., 2012; Swinkels et al., 2021; Stuij et al., 2021; Chen et al., 2011; Liu et al., 2020; Noya et al., 2019; Rao et al., 2020; He et al., 2020). Studies on the assembly of specific structures like colloidal diamond have highlighted the challenges of controlling kinetic pathways (Neophytou et al., 2021).

The researchers fabricated patchy particles from polystyrene (PS) and 3-(trimethoxysilyl)propyl methacrylate (TPM) spheres using colloidal fusion. These tetrahedrally coordinated particles, with a PS core and fluorescently labeled TPM patches, had a diameter of 2.0 µm and a patch diameter of approximately 0.2 µm. The particles were suspended in a binary solvent mixture of lutidine and water near its critical point, creating tunable attractive critical Casimir interactions between the patches. The strength of these interactions was controlled by adjusting the temperature offset (ΔT) from the solvent's critical point. A 1 millimolar solution of MgSO₄ was added to screen electrostatic repulsion and enhance lutidine adsorption on the hydrophobic patches. The suspension was injected into a hydrophobically treated glass capillary, causing the particles to adsorb to the surface via one patch. The remaining three patches acted as effectively trivalent bonding sites. Near-equilibrium assembly was achieved by slowly approaching the critical temperature in steps, allowing sufficient time for equilibration at each step. Confocal microscopy was employed to track particle positions and fluorescent patches, enabling determination of bond angles and the identification of defects. The configurational energy of the lattice was calculated from bond saturation and bond angle distortions, allowing the study of energy evolution during defect rearrangement and healing. Bright field and confocal microscopy images were used to observe crystal growth, defect formation, and healing processes with high temporal and spatial resolution. Image analysis using particle tracking software provided the data for quantitative analysis. The bending potential was determined from angle fluctuations of three bonded particles.

The study revealed the formation of large honeycomb lattice flakes characteristic of graphene. However, defects, including grain boundaries and vacancies, were also observed. Grain boundaries consisted of alternating pentagons and heptagons, geometrically compatible with the honeycomb lattice and energetically favorable due to reduced angular mismatch compared to pentagon-hexagon combinations. The energy cost associated with bond bending near grain boundaries was found to be localized, diminishing rapidly away from the interface. Vacancies, ranging from divacancies to larger polyvacancies, were observed; these showed differing effects on the surrounding lattice. Crucially, the research demonstrated that pentagonal defects are kinetically favored in the early stages of growth, acting as nucleation sites for grain boundaries. Energy analysis revealed that pentagon formation is kinetically favored over hexagon formation, even though hexagons are energetically more favorable. The study followed the evolution of defects over time, observing reconfigurations of grain boundaries and vacancies. Highly dynamic regions showed energy minimization through reconfigurations, while static regions exhibited little change. The interplay between dangling bond saturation and lattice distortions was identified as a driving force for these reconfigurations. The increasing number of hexagons during reconfiguration reflects the system's approach to the energetically more favorable honeycomb lattice.

The findings directly address the research question concerning the origin and dynamics of defects in graphene-like structures. The demonstration that pentagonal motifs are kinetically favored in the initial stages of assembly provides a crucial mechanistic insight into the prevalence of grain boundaries in the final structure. This kinetic preference, despite the thermodynamic preference for hexagons, explains the significant presence of defects even under near-equilibrium conditions. The observation of defect reconfigurations and energy minimization processes highlights the dynamic nature of the system and the driving forces behind defect evolution. These results are consistent with previous observations of defects in atomic graphene, though the direct visualization of the initial assembly stages in this colloidal model provides unique insights. The study's findings are relevant to the broader field of materials science, contributing to our understanding of 2D material self-assembly and defect formation mechanisms. The direct observation of defect dynamics opens up new possibilities for controlling the assembly process and tailoring the properties of 2D materials.

This research provides a novel understanding of defect dynamics in graphene-like structures through direct visualization of the assembly process using colloidal analogs. The kinetic preference for pentagonal motifs in early growth stages was shown to be a critical factor in the formation of defects, particularly grain boundaries. The observed reconfiguration of defects towards lower-energy states highlights the interplay of dangling-bond saturation and lattice distortions. This work contributes significantly to the understanding of 2D material assembly and paves the way for developing strategies to control defect formation and enhance the quality of 2D materials. Future research could focus on exploring different patchy particle designs and interaction potentials to control the kinetic pathways and minimize defect formation. Investigating the effects of different substrate interactions and exploring the use of this colloidal model to study other 2D materials are also promising avenues for future work.

The colloidal system, while providing a valuable model, is not identical to atomic graphene. Differences in bonding potential and interactions may lead to discrepancies in specific defect behavior. The time scale of defect reconfiguration in the colloidal system is much longer than in atomic graphene, primarily due to the lower attempt frequency in the colloidal case. While the study demonstrates near-equilibrium conditions, the range of interaction strengths explored might not encompass the complete spectrum of conditions experienced during atomic graphene growth. The size and shape of the colloidal patchy particles might influence the observed defect patterns.