Vertical stacking of monolayers via van der Waals (vdW) interaction opens promising routes toward engineering physical properties of two-dimensional (2D) materials and designing atomically thin devices. However, due to the lack of mechanistic understanding, challenges remain in the controlled fabrication of these structures via scalable methods such as chemical vapor deposition (CVD) onto substrates. In this paper, we develop a general multiscale model to describe the size evolution of 2D layers and predict the necessary growth conditions for vertical (initial + subsequent layers) versus in-plane lateral (monolayer) growth. An analytic thermodynamic criterion is established for subsequent layer growth that depends on the sizes of both layers, the vdW interaction energies, and the edge energy of 2D layers. Considering the time-dependent growth process, we find that temperature and adatom flux from vapor are the primary criteria affecting the self-assembled growth. The proposed model clearly demonstrates the distinct roles of thermodynamic and kinetic mechanisms governing the final structure. Our model agrees with experimental observations of various monolayer and bilayer transition metal dichalcogenides grown by CVD and provides a predictive framework to guide the fabrication of vertically stacked 2D materials.

We use density functional theory calculations to study a group of 2D materials known as MXenes toward the electrochemical nitrogen reduction reaction (NRR) to ammonia. So far, all computational studies have only considered the NRR chemistry on unfunctionalized (bare) MXenes. In this study, we investigate a total of 65 bare and functionalized MXenes. We establish free energy diagrams for the NRR on the basal planes of 55 different M 2 XT x MXenes (M = Ti, V, Zr, Nb, Mo, Ta, W; X = C, N) to span a large variety of possible chemistries. Energy trends with respect to the metal as well as nonmetal constituent of the MXenes are established for both bare and functionalized MXenes. We determine the limiting potentials and find that either the formation of NH 3 from *NH 2 or the formation of *N 2 H is the potential limiting reaction step for bare and functionalized MXenes, respectively. We find several Mo-, W-, and V-based MXenes (Mo 2 C, Mo 2 N, W 2 N, W 2 NH 2 , and V 2 N) to have suitable theoretical overpotentials for the NRR. Importantly, calculated Pourbaix stability diagrams combined with selectivity analysis, however, reveal that all bare MXenes are not stable under relevant NRR operating conditions. The only functionalized MXene with the three minimum required properties (i) having a low theoretical overpotential, (ii) being stable under NRR conditions, and (iii) having selectivity toward NRR rather than the parasitic HER is W 2 CH 2 , which is a H-terminated MXene. Finally, on the basis of our findings, we explore other routes for improving the NRR chemistry by studying 10 additional MXenes with the chemical formula M 3 X 2 T x and MXenes with other functional groups (T x = S, F, Cl). This opens up a larger variety and tunability of MXenes to be considered for the NRR.

We investigate the glass transition behavior in polymer thin films using a model equation-of-state approach, which involves molecular parameters whose values are determined from fits to bulk information only (pressure− volume−temperature and surface tension data). Following an earlier proof-ofconcept application to freestanding polystyrene (PS) films, here we both extend the study to poly(methyl methacrylate) (PMMA) films and generalize the model so that it is applicable for either freestanding or supported films. In the case of the freestanding PMMA film, model predictions for the T g suppression (relative to bulk) as a function of film thickness are in very good agreement with the corresponding experimental data, reflecting the fact that freestanding PMMA films are evidently less perturbed by the presence of free surfaces than those made of PS. We then turn to the case of PMMA films supported on a silica substrate by accounting for possible polymer−substrate interactions, such that when these are switched off the same model maps smoothly back to the case of a PMMA freestanding film. We then probe the origin of the interaction required such that the model can capture the experimentally observed T g enhancement for supported PMMA films while also accounting for the relative lack of impact on the T g behavior of supported PS films relative to their freestanding counterparts. Finally, we make connections between related experimental and simulation studies and our own results for the differences between supported PMMA and PS films. INTRODUCTIONThe study of the effect of confinement on glassy polymeric systems has continued to draw strong research interest over the past two decades. 1−5 Polymer thin films have been a particularly popular system to study. Beyond important material and engineering applications, they show a diverse range of behavior, depending both on the polymer's characteristic properties and on the nature of the confinement. Films of interest include both freestanding films (two free surfaces) and films supported on a substrate. These supported films have one free surface and one surface in contact with a substrate (e.g. silica, gold, a substrate coating, a polymeric underlayer, or other). The effect that confinement has on a film's glass transition temperature (T g ) has been of particularly strong interest and much remains to be understood. Although many experimental investigations have shown that there can be a strong and varied change in the film T g relative to the corresponding bulk value, other investigations have shown little or no change in T g , and adding to this is evidence that such effects can depend on cooling rate. 6−9 In general, experimental results show that for freestanding films (e.g., refs 10−12), as the film gets thinner (e.g., less than 100 nm) the film T g is suppressed (lowered) compared to the corresponding bulk T g value. For supported films, the behavior can be quite diverse. In these cases, the film T g can either be enhanced or suppressed relative to the bulk, dependi...

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have been the subject of sustained research interest due to their extraordinary electronic and optical properties. They also exhibit a wide range of structural phases because of the different orientations that the atoms can have within a single layer, or due to the ways that different layers can stack. Here we report a unique study involving direct visualization of structural transformations in atomically thin layers under highly non-equilibrium thermodynamic conditions. We probe these transformations at the atomic scale using real-time, aberration-corrected scanning transmission electron microscopy and observe strong dependence of the resulting structures and phases on both heating rate and temperature. A fast heating rate (25 °C/sec) yields highly ordered crystalline hexagonal islands of sizes of less than 20 nm which are composed of a mixture of 2H and 3R phases. However, a slow heating rate (25 °C/min) yields nanocrystalline and sub-stoichiometric amorphous regions. These differences are explained by different rates of sulfur evaporation and redeposition. The use of non-equilibrium heating rates to achieve highly crystalline and quantum-confined features from 2D atomic layers present a new route to synthesize atomically thin, laterally confined nanostructures and opens new avenues for investigating fundamental electronic phenomena in confined dimensions.

Bilayer two-dimensional (2D) van der Waals (vdW) materials are attracting increasing attention due to their predicted high quality electronic and optical properties. Here we demonstrate dense, selective growth of WSe2 bilayer flakes by chemical vapor deposition with the use of a 1:10 molar mixture of sodium cholate and sodium chloride as the growth promoter to control the local diffusion of W-containing species. A large fraction of the bilayer WSe2 flakes showed a 0 (AB) and 60 o (AA') twist between the two layers, while moiré 15 and 30 o -twist angles were also observed. Well-defined monolayer-bilayer junctions were formed in the as-grown bilayer WSe2 flakes, and these interfaces exhibited p-n diode rectification and an ambipolar transport characteristic. This work provides an efficient method for the layer-controlled growth of 2D materials, in particular, 2D transition metal dichalcogenides and promotes their applications in next-generation electronic and optoelectronic devices.