Fundamental scaling laws for the direct-write chemical vapor deposition of nanoscale features: modeling mass transport around a translating nanonozzle.

The nanometer placement of nanomaterials, such as nanoribbons and nanotubes, at a specific pitch and orientation on a surface, remains an unsolved fundamental problem in nanotechnology. In this work, we introduce and analyze the concept of a direct-write chemical vapor deposition (CVD) system that enables the in-place synthesis of such structures with control over orientation and characteristic features. A nanometer scale pore or conduit, called the nanonozzle, delivers precursor gases for CVD locally on a substrate, with spatial translation of either the nozzle or the substrate to enable a novel direct write (DW) tool. We analyze the nozzle under conditions where it delivers reactants to a substrate while translating at a constant velocity over the surface at a fixed reaction temperature. We formulate and solve a multi-phase three-dimensional reaction and diffusion model of the direct-write operation, and evaluate specific analytically-solvable limits to determine the allowable operating conditions, including pore dimensions, reactant flow rates, and nozzle translation speed. A Buckingham Π analysis identifies six dimensionless quantities crucial for the design and operation of the direct-write synthesis process. Importantly, we derive and validate what we call the ribbon extension inequality that brackets the allowable nozzle velocity relative to the CVD growth rate - a key constraint to enabling direct-write operation. Lastly, we include a practical analysis using attainable values towards the experimental design of such a system, building the nozzle around a commercially available near-field scanning optical microscopy (NSOM) tip as a feasible example.

Mechanism and Prediction of Gas Permeation through Sub-Nanometer Graphene Pores: Comparison of Theory and Simulation.

Due to its atomic thickness, porous graphene with sub-nanometer pore sizes constitutes a promising candidate for gas separation membranes that exhibit ultrahigh permeances. While graphene pores can greatly facilitate gas mixture separation, there is currently no validated analytical framework with which one can predict gas permeation through a given graphene pore. In this work, we simulate the permeation of adsorptive gases, such as CO2 and CH4, through sub-nanometer graphene pores using molecular dynamics simulations. We show that gas permeation can typically be decoupled into two steps: (1) adsorption of gas molecules to the pore mouth and (2) translocation of gas molecules from the pore mouth on one side of the graphene membrane to the pore mouth on the other side. We find that the translocation rate coefficient can be expressed using an Arrhenius-type equation, where the energy barrier and the pre-exponential factor can be theoretically predicted using the transition state theory for classical barrier crossing events. We propose a relation between the pre-exponential factor and the entropy penalty of a gas molecule crossing the pore. Furthermore, on the basis of the theory, we propose an efficient algorithm to calculate CO2 and CH4 permeances per pore for sub-nanometer graphene pores of any shape. For the CO2/CH4 mixture, the graphene nanopores exhibit a trade-off between the CO2 permeance and the CO2/CH4 separation factor. This upper bound on a Robeson plot of selectivity versus permeance for a given pore density is predicted and described by the theory. Pores with CO2/CH4 separation factors higher than 102 have CO2 permeances per pore lower than 10-22 mol s-1 Pa-1, and pores with separation factors of ∼10 have CO2 permeances per pore between 10-22 and 10-21 mol s-1 Pa-1. Finally, we show that a pore density of 1014 m-2 is required for a porous graphene membrane to exceed the permeance-selectivity upper bound of polymeric materials. Moreover, we show that a higher pore density can potentially further boost the permeation performance of a porous graphene membrane above all existing membranes. Our findings provide insights into the potential and the limitations of porous graphene membranes for gas separation and provide an efficient methodology for screening nanopore configurations and sizes for the efficient separation of desired gas mixtures.

Observation of extreme phase transition temperatures of water confined inside isolated carbon nanotubes.

Fluid phase transitions inside single, isolated carbon nanotubes are predicted to deviate substantially from classical thermodynamics. This behaviour enables the study of ice nanotubes and the exploration of their potential applications. Here we report measurements of the phase boundaries of water confined within six isolated carbon nanotubes of different diameters (1.05, 1.06, 1.15, 1.24, 1.44 and 1.52 nm) using Raman spectroscopy. The results reveal an exquisite sensitivity to diameter and substantially larger temperature elevations of the freezing transition (by as much as 100 °C) than have been theoretically predicted. Dynamic water filling and reversible freezing transitions were marked by 2-5 cm-1 shifts in the radial breathing mode frequency, revealing reversible melting bracketed to 105-151 °C and 87-117 °C for 1.05 and 1.06 nm single-walled carbon nanotubes, respectively. Near-ambient phase changes were observed for 1.44 and 1.52 nm nanotubes, bracketed between 15-49 °C and 3-30 °C, respectively, whereas the depression of the freezing point was observed for the 1.15 nm nanotube between -35 and 10 °C. We also find that the interior aqueous phase reversibly decreases the axial thermal conductivity of the nanotube by as much as 500%, allowing digital control of the heat flux.

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.

Observation and analysis of the Coulter effect through carbon nanotube and graphene nanopores.

Carbon nanotubes (CNTs) and graphene are the rolled and flat analogues of graphitic carbon, respectively, with hexagonal crystalline lattices, and show exceptional molecular transport properties. The empirical study of a single isolated nanopore requires, as evidence, the observation of stochastic, telegraphic noise from a blocking molecule commensurate in size with the pore. This standard is used ubiquitously in patch clamp studies of single, isolated biological ion channels and a wide range of inorganic, synthetic nanopores. In this work, we show that observation and study of stochastic fluctuations for carbon nanopores, both CNTs and graphene-based, enable precision characterization of pore properties that is otherwise unattainable. In the case of voltage clamp measurements of long (0.5-1 mm) CNTs between 0.9 and 2.2 nm in diameter, Coulter blocking of cationic species reveals the complex structuring of the fluid phase for confined water in this diameter range. In the case of graphene, we have pioneered the study and the analysis of stochastic fluctuations in gas transport from a pressurized, graphene-covered micro-well compartment that reveal switching between different values of the membrane permeance attributed to chemical rearrangements of individual graphene pores. This analysis remains the only way to study such single isolated graphene nanopores under these realistic transport conditions of pore rearrangements, in keeping with the thesis of this work. In summary, observation and analysis of Coulter blocking or stochastic fluctuations of permeating flux is an invaluable tool to understand graphene and graphitic nanopores including CNTs.

Understanding and Analyzing Freezing-Point Transitions of Confined Fluids within Nanopores.

Understanding phase transitions of fluids confined within nanopores is important for a wide variety of technological applications. It is well known that fluids confined in nanopores typically demonstrate freezing-point depressions, ΔTf, described by the Gibbs-Thomson (GT) equation. Herein, we highlight and correct several thermodynamic inconsistencies in the conventional use of the GT equation, including the fact that the enthalpy of melting, ΔHm, and the solid-liquid surface energy, γ(SL), are functions of pore diameter, complicating their prediction. We propose a theoretical analysis that employs the Turnbull coefficient, originally derived from metal nucleation theory, and show its consistency as a more reliable quantity for the prediction of ΔTf. This analysis provides a straightforward method to estimate ΔTf of nanoconfined organic fluids. As an example, we apply this technique to ibuprofen, an active pharmaceutical ingredient (API), and show that this theory fits well to the experimental ΔTf of nanoconfined ibuprofen.

Molecular valves for controlling gas phase transport made from discrete ångström-sized pores in graphene.

An ability to precisely regulate the quantity and location of molecular flux is of value in applications such as nanoscale three-dimensional printing, catalysis and sensor design. Barrier materials containing pores with molecular dimensions have previously been used to manipulate molecular compositions in the gas phase, but have so far been unable to offer controlled gas transport through individual pores. Here, we show that gas flux through discrete ångström-sized pores in monolayer graphene can be detected and then controlled using nanometre-sized gold clusters, which are formed on the surface of the graphene and can migrate and partially block a pore. In samples without gold clusters, we observe stochastic switching of the magnitude of the gas permeance, which we attribute to molecular rearrangements of the pore. Our molecular valves could be used, for example, to develop unique approaches to molecular synthesis that are based on the controllable switching of a molecular gas flux, reminiscent of ion channels in biological cell membranes and solid-state nanopores.

Mechanisms of gas permeation through single layer graphene membranes.

Graphene has enormous potential as a unique molecular barrier material with atomic layer thickness, enabling new types of membranes for separation and manipulation. However, the conventional analysis of diffusive transport through a membrane fails in the case of single layer graphene (SLG) and other 2D atomically thin membranes. In this work, analytical expressions are derived for gas permeation through such atomically thin membranes in various limits of gas diffusion, surface adsorption, or pore translocation as the rate-limiting step. Gas permeation can proceed via direct gas-phase interaction with the pore, or interaction via the adsorbed phase on the membrane exterior surface. A series of van der Waals force fields allows for the estimation of the energy barriers present for various types of graphene nanopores. These analytical models will assist in the understanding of molecular dynamics and experimental studies of such membranes.