Monolayer particles of two-dimensional (2D) materials represent a scientifically and technologically interesting class of anisotropic particles with colloidal-scale lateral sizes but sub-nanometer thicknesses. This atomic-scale thickness leads to interesting phenomena that can be exploited in next-generation thin-film technologies, and fluid–fluid interfaces provide a potentially scalable platform to confine, assemble, and deposit functional thin films of 2D materials. However, directly observing how these materials interact and assemble into a given film morphology is experimentally challenging because of their sub-nanometer thicknesses. Here, we demonstrate the ability to directly observe graphene, molybdenum disulfide (MoS2), and hexagonal boron nitride (h-BN) particles at fluid–fluid interfaces using interference reflection microscopy (IRM). Monolayer MoS2 and graphene particles demonstrated >10% optical contrast at an air–water interface, which allowed us to quantitatively analyze in situ images of self-assembled MoS2 particles and to map trajectories of interacting graphene particles. Additionally, the Brownian motion of a graphene particle was tracked and analyzed in the context of passive microrheology theory for 2D particle probes. Our results demonstrate how IRM can be used to obtain quantitative spatiotemporal information regarding the self-assembly and dynamics of 2D materials at fluid–fluid interfaces. It will have a significant impact on our ability to investigate systems of atomically thin particles at fluid–fluid interfaces, an area that has fundamental scientific importance and materials science applications but has suffered from a lack of direct, in situ observation techniques.

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We examine the dynamics and morphology of graphitic films at an air-water interface in a Langmuir trough by varying interfacial surface coverage, by observing in situ interfacial structure, and by characterizing interfacial structure of depositions on mica substrates. In situ interfacial structure is visualized with Brewster angle microscopy and depositions of the interface are characterized with atomic force microscopy and field-emission scanning electron microscopy. Compression/expansion curves exhibit a monotonically decreasing surface pressure between consecutive compressions, but demonstrate a "rebound" of hysteretic behavior when the interface is allowed to relax between consecutive compressions. This dynamic results from a competition between consolidation of the interface via agglomeration of particles or the stacking of graphene sheets, and a thermally-driven relaxation where nanometer-thick particles are able to overcome capillary interactions. These results are especially relevant to applications where functional films with controlled conductivity and transparency may be produced via liquid-phase deposition methods. V C 2018 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2018 Figure 3. Different microscopy methods used to characterize interfaces at different length scales. From left to right, BAM image at 11 mN/m, AFM image at 3 mN/m, FESEM image at 13 mN/m. [Color figure can be viewed at wileyonlinelibrary.com] AFM images taken from an interface deposited at 3 mN/m after a 15 h relaxation time. Mono-and few-layer graphene sheets are present between large islands of graphitic material. (b) AFM image (left) that reveals few-and mono-layer graphene sheets present at the interface at a surface pressure of 20 mN/m. A corresponding height trace (right) follows the red path indicated in image on the left.Figure 5. Compression curves for graphene interfaces. The upper left plot shows pre-relaxation and post-relaxation compression curves for a 2.5 h relaxation period, and the upper right plot shows the pre-relaxation and postrelaxation compression curves for a 15 h relaxation period. Pre-relaxation curves are plotted with red dashes, post-relaxation curves are plotted with blue dots. The bottom two plots contain the same data, but the postrelaxation curves have been shifted along both axes. The shift factors were obtained "by eye" to overlap the first compressions of the pre-relaxation and post-relaxation curve sets. The inset FESEM images (scale bars: 10 μm) were obtained fromdepositions at low Π (indicated by the black boxes). The images reveal that aggregates are present at all times and are surrounded to different degrees by micron and sub-micron particles. [Color figure can be viewed at wileyonlinelibrary.com] Figure 7. BAM images taken during each of the three compression cycles for both the pre-relaxation and postrelaxation interfaces.White areas indicate graphitic material. All images were taken with the barriers in a fully open state and show the evolution of the interface between cons...

Two-dimensional (2D) materials such as graphene prefer to interact in a face-to-face manner when colloidally suspended but are forced to interact in an edge-to-edge manner when trapped at a fluid−fluid interface. However, molecular dynamics (MD) simulations suggest these platelet-like particles can spontaneously stack and adopt the preferred face-to-face orientation after lateral edge-to-edge assembly, while experiments tend to contradict these findings. Thus, conditions under which these stacking events occur are unknown. Herein, MD simulations are employed to elucidate the physical origin of the free-energy barrier inhibiting instantaneous particle stacking: the surface energy penalty associated with deforming a fluid−fluid interface. Simulations suggest stacking kinetics are governed by a Boltzmann-like relation between the time to stack and the particle−particle contact edge length, and thus, the interfacial area deformed. A thermodynamic model is also shown to predict the change in excess interfacial free-energy as particles transition from the laterally aggregated to vertically stacked state at a fluid interface. Finally, experimental evidence is presented that corroborates these results. These results suggest that the existence of nanometer-scale edge defects is expected to influence the stacking behavior of 2D particles at fluid interfaces, which has broad, practical implications spanning from emulsion stability to the integrity of Langmuir film morphology.

Advances in synthesis of model 3D colloidal particles with exotic shapes and physical properties have enabled discovery of new 3D colloidal phases not observed in atomic systems, and simulations and quasi-2D studies suggest 2D colloidal systems have an even richer phase behavior. However, a model 2D (one-atomthick) colloidal system has yet to be experimentally realized because of limitations in solution-phase exfoliation of 2D materials and other 2D particle fabrication technologies. Herein, we use a photolithography-based methodology to fabricate size-and shapecontrolled monolayer graphene particles, and then transfer the particles to an air−water interface to study their dynamics and selfassembly in real-time using interference reflection microscopy. Results suggest the graphene particles behave as "hard" 2D colloidal particles, with entropy influencing the self-assembled structures. Additional evidence suggests the stability of the self-assembled structures manifests from the edge-to-edge van der Waals force between 2D particles. We also show graphene discs with diameters up to 50 μm exhibit significant Brownian motion under optical microscopy due to their low mass. This work establishes a facile methodology for creating model experimental systems of colloidal 2D materials, which will have a significant impact on our understanding of fundamental 2D physics. Finally, our results advance our understanding of how physical particle properties affect the interparticle interactions between monolayer 2D materials at fluid−fluid interfaces. This information can be used to guide the development of scalable synthesis techniques (e.g., solution-phase processing) to produce bulk suspensions of 2D materials with desired physical particle properties that can be used as building blocks for creating thin films with desired structures and properties via interfacial film assembly.