Analysis of Time-Varying, Stochastic Gas Transport through Graphene Membranes

Molecular transport measurements through isolated nanopores can greatly inform our understanding of how such systems can select for molecular size and shape. In this work, we present a detailed analysis of experimental gas permeation data through single layer graphene membranes under batch depletion conditions parametric in starting pressure for He, H₂, Ne, and CO₂ between 100 and 670 kPa. We show mathematically that the observed intersections of the membrane deflection curves parametric in starting pressure are indicative of a time dependent membrane permeance (pressure normalized molecular flow). Analyzing these time dependent permeance data for He, Ne, H₂, and CO₂ shows remarkably that the latter three gases exhibit discretized permeance values that are temporally repeated. Such quantized fluctuations (called “gating” for liquid phase nanopore and ion channel systems) are a hallmark of isolated nanopores, since small, but rapid changes in the transport pathway necessarily influence a single detectable flux. We analyze the fluctuations using a Hidden Markov model to fit to discrete states and estimate the activation barrier for switching at 1.0 eV. This barrier is and the relative fluxes are consistent with a chemical bond rearrangement of an 8–10 atom vacancy pore. Furthermore, we use the relations between the states given by the Markov network for few pores to determine that three pores, each exhibiting two state switching, are responsible for the observed fluctuations; and we compare simulated control data sets with and without the Markov network for comparison and to establish confidence in our evaluation of the limited experimental data set

Graphene Blisters with Switchable Shapes Controlled by Pressure and Adhesion

We created graphene blisters that cover and seal an annular cylinder-shaped microcavity in a SiO₂ substrate filled with a gas. By controlling the pressure difference between the gas inside and outside of the microcavity, we switch the graphene membrane between multiple stable equilibrium configurations. We carried out experiments starting from the situation where the pressure of the gas inside and outside of the microcavity is set equal to a prescribed charging pressure, <i>p</i>₀ and the graphene membrane covers the cavity like an annular drum, adhered to the central post and the surrounding substrate due to van der Waals forces. We decrease the outside pressure to a value, <i>p</i>_e which causes it to bulge into an annular blister. We systematically increase the charging pressure by repeating this procedure causing the annular blister to continue to bulge until a critical charging pressure <i>p</i>_cⁱ is reached. At this point the graphene membrane delaminates from the post in an unstable manner, resulting in a switch of graphene membrane shape from an annular to a spherical blister. Continued increase of the charging pressure results in the spherical blister growing with its height increasing, but maintaining a constant radius until a second critical charging pressure <i>p</i>_c^o is reached at which point the blister begins to delaminate from the periphery of the cavity in a stable manner. Here, we report a series of experiments as well as a mechanics and thermodynamic model that demonstrate how the interplay among system parameters (geometry, graphene stiffness (number of layers), pressure, and adhesion energy) results in the ability to controllably switch graphene blisters among different shapes. Arrays of these blisters can be envisioned to create pressure-switchable surface properties where the difference between patterns of annular versus spherical blisters will impact functionalities such as wettability, friction, adhesion, and surface wave characteristics

Adhesion, Stiffness, and Instability in Atomically Thin MoS₂ Bubbles

We measured the work of separation of single and few-layer MoS₂ membranes from a SiO_<i>x</i> substrate using a mechanical blister test and found a value of 220 ± 35 mJ/m². Our measurements were also used to determine the 2D Young’s modulus (<i>E</i>_2D) of a single MoS₂ layer to be 160 ± 40 N/m. We then studied the delamination mechanics of pressurized MoS₂ bubbles, demonstrating both stable and unstable transitions between the bubbles’ laminated and delaminated states as the bubbles were inflated. When they were deflated, we observed edge pinning and a snap-in transition that are not accounted for by the previously reported models. We attribute this result to adhesion hysteresis and use our results to estimate the work of adhesion of our membranes to be 42 ± 20 mJ/m²

Ultrathin Oxide Films by Atomic Layer Deposition on Graphene

In this paper, a method is presented to create and characterize mechanically robust, free-standing, ultrathin, oxide films with controlled, nanometer-scale thickness using atomic layer deposition (ALD) on graphene. Aluminum oxide films were deposited onto suspended graphene membranes using ALD. Subsequent etching of the graphene left pure aluminum oxide films only a few atoms in thickness. A pressurized blister test was used to determine that these ultrathin films have a Young’s modulus of 154 ± 13 GPa. This Young’s modulus is comparable to much thicker alumina ALD films. This behavior indicates that these ultrathin two-dimensional films have excellent mechanical integrity. The films are also impermeable to standard gases suggesting they are pinhole-free. These continuous ultrathin films are expected to enable new applications in fields such as thin film coatings, membranes, and flexible electronics

Observation of Pull-In Instability in Graphene Membranes under Interfacial Forces

We present a unique experimental configuration that allows us to determine the interfacial forces on nearly parallel plates made from the thinnest possible mechanical structures, single and few layer graphene membranes. Our approach consists of using a pressure difference across a graphene membrane to bring the membrane to within ∼10–20 nm above a circular post covered with SiO_<i>x</i> or Au until a critical point is reached whereby the membrane snaps into adhesive contact with the post. Continuous measurements of the deforming membrane with an AFM coupled with a theoretical model allow us to deduce the magnitude of the interfacial forces between graphene and SiO_<i>x</i> and graphene and Au. The nature of the interfacial forces at ∼10–20 nm separation is consistent with an inverse fourth power distance dependence, implying that the interfacial forces are dominated by van der Waals interactions. Furthermore, the strength of the interactions is found to increase linearly with the number of graphene layers. The experimental approach can be used to measure the strength of the interfacial forces for other atomically thin two-dimensional materials and help guide the development of nanomechanical devices such as switches, resonators, and sensors