Ambient stability and surface adhesion of 2D polyaramid nanofilms

Abstract

Two-dimensional polyaramids (2DPAs) represent an emerging class of solution-synthesized, molecularly thin polymer sheets that combine the exceptional in-plane mechanical strength and barrier performance of conventional 2D materials with the synthetic versatility of organic polymers. Despite increasing interest in 2D polymers as gas barriers and membrane materials, the long-term stability of nanometer-scale suspended films remains largely unexplored. Here, we report the first longitudinal study of 2D polyaramid (2DPA-1) nanofilm bulges monitored continuously for over 1000 days. Using a microwell bulge test platform integrated with atomic force microscopy and optical interferometry, we show that 2DPA-1 forms highly stable, gas-retaining membranes whose upward deflection persists for years under ambient environmental fluctuations. Using a single-point mechanical model with thermodynamic analysis, we show that initial bulge pressurization proceeds through transient rim seal opening, while the intact seal remains robust during thermal cycling up to 120 °C without measurable gas loss. Together, these results establish a comprehensive mechanistic framework for long-term stability, permeability assessment, and interfacial failure modes in nanofilm bulge systems. This framework enables reliable interpretation of bulge test data and provides design principles for next-generation 2D polymer membranes intended for ultrahigh-barrier, filtration, and separation technologies.

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1 Introduction

Two-dimensional (2D) polymers have attracted interest in recent years as a means of combining the tools of organic chemistry with the in-plane mechanical strength and barrier properties characteristic of conventional, nominally crystalline, 2D materials.^1,2 Accordingly, 2D polyaramids (PA) have emerged as a class of 2D polymers synthesized via irreversible solution-phase polycondensation reactions with outstanding mechanical and chemical stability.^3,4 The intersection of nanoscale physics and macroscale engineering phenomena creates unique challenges in materials characterization, where traditional bulk measurement techniques fail to capture the interfacial effects that dominate nanometer thin film behavior. The microwell bulge for nanofilms is a powerful experimental platform that bridges fundamental materials science with practical engineering assessment, enabling simultaneous measurement of elastic properties,^5–8 inelastic properties,^5,9 and transport phenomena^10–12 through a unified theoretical framework. Moreover, these tests allow for sensitive measurements, such as the ultra-low impermeability of various two-dimensional (2D) materials,^4,10,13,14 which are not possible in the equivalent macroscale experiment. In short, nanofilms are suspended over etched microwells, which allows for the trapping of gas between the film and substrate through pressurization, forming bulges. Herein, we detail an unprecedented longitudinal study of 2D polyaramid nanofilm bulges that have persisted as inflated for more than 1000 days. This prolonged study enables the mechanistic elucidation of factors that influence bulge metrics (e.g., deflection) and, consequently, gas permeability and mechanical measurements. Specifically, we highlight a newly observed confined random walk of the height of pressurized bulges and how temperature and gas-specific interactions influence the interfacial seal of the adhered films. While typically hydroscopic, and sensitive to ambient moisture, polyaramids in this 2D form of stacked platelets appear highly resistant to delamination and film decomposition.

Recent advances in optical interferometry and real-time monitoring capabilities^4,15 have elevated the bulge test to a dynamic platform for understanding the complex interplay between material properties, processing history, and interfacial phenomena that govern nanofilm performance. There are noted fluctuations in the literature of impermeable graphene bulges¹³ which are not attributable to atomic force microscopy (AFM) measurement error and have yet to be explored. The dynamic adhesion of the nanofilm to the substrate, while studied as a mechanical property,¹⁶ has yet to be understood in context of gas transport phenomena. We denote this nanofilm-substrate seal as the rim seal, or the circumferential adhesion of the film along the vertical cylindrical wall of the microwell, thereby sealing gas molecules and forming nanofilm bulges, which we first studied in our previous work.⁴ This is a critical potential failure mode of the gas transport bulge test measurement, as gas may leak through the interface between the nanofilm and substrate. Interfacial leakage confounds permeability measurements through the film itself, which rely on the assumption of molecular transport occurring completely across the film area suspended over the microwell.

In general, 2D polymers show promise as novel gas membrane and barrier materials. As a class of materials, they combine the mechanical strength and in-plane energy conduction of conventional 2D materials^7,17–19 with the low densities, synthetic processability, and organic composition of traditional 1D polymers. Recent theoretical²⁰ and experimental³ work has enabled the irreversible, solution-phase polymerization of 2D polyaramids. Using standard spin-coating procedures, 2D polyaramids have already achieved highly oriented, large area free-standing films which exhibit exceptional 2D elastic modulus and yield strength already reaching 12.7 GPa and 0.5 GPa, respectively.³ These ultra-thin, high mechanical strength films have the potential to excel as gas membranes and/or barrier materials.²¹

In this work, we study the behavior of 2DPA-1 nanofilm bulges over 1000 days, and address questions relating to rim seal dynamics, bulge height fluctuations and adhesive stability. We also note the stability of such films to ambient humidity over extended durations. Furthermore, we analyze the impact of different environmental factors on the interfacial rim seal.

2 2D polyaramid system and characterization

2D polymers have promising gas barrier and membrane applications due to their high processability and molecularly controllable pore size and overlap. 2DPA-1, or 2D Polyaramid-1, shown to be molecularly impermeable to N₂ gas,⁴ forms molecularly thin platelets concatenated with amide bonds, which, when spin-coated into nanofilms between 4 and 65 nm in thickness, stack in such a way that any potential voids are inaccessible (Fig. 1A). Using a wet-transfer process,⁴ we have created a variety of samples for the bulge test measurement (Fig. 1B and C). Within this study, we used two types of lithographically etched silicon substrates: the first, Substrate I, has circular wells with depth to width ratios of 5 : 1 (98 : 14 µm) and 7 : 1 (123 : 24 µm) and the second, Substrate II has depth to width ratios of 1 : 8.5 (1.0 : 8.5 µm). These different patterns affect the sensitivity of the bulge height to the net gas leak rate as it is inversely proportional to the well volume. We found that the substrates also had different rim seal adhesions, presumably due to processing conditions.

Fig. 1 (A) Oligomer unit of 2DPA-1 with one pristine nanopore, inset with the side-view of a planar stack of seven 2DPA-1 layers with 0.36 nm interlayer spacing from hydrogen bonded layers after spin coating into a nanofilm. (B) Optical micrographs of substrates covered with 2DPA-1 thin films after spin coating with patterned wells used for this study. Substrate (i) contains wells ranging from 5 to 14 to 24 µm in diameter and 73 to 98 to 123 µm in depth, respectively. Substrate (ii) contains wells that are 8.5 µm in diameter and 1 µm in depth. (C) Side-view schematic of bulge formation with trapped gas (light gray) from a 2DPA-1 film (hatch filled) transferred onto a silicon wafer (blue gray) with pre-patterned, cylindrical wells. A gap between the film and wafer is exaggerated to depict potential gas transfer through the rim seal. Relevant parameters are indicated on the schematic. (D) Snapshots of various bilayer offsets and their interaction energies determined from density functional theory (DFT) calculations. The configurations with the minimum and maximum energies are highlighted. The results show that several staggered arrangements in stacking have similar interaction energy minima, suggesting that the nanofilms are stable with occluded pores, explaining the observed gas impermeability. (E) (i) Different protons within the 2DPA-1 structure, corresponding to the aromatic hydrogen on the main chain (H_A, blue), the hydrogen on the end groups quenched with IPA (H_B, purple), and the methyl hydrogen on the end groups quenched with IPA (H_C, red). (ii and iii) ¹H-NMR spectroscopy of 2DPA-1 powder in TFA-d before (ii) and after (iii) being suspended in 1 : 1 mass ratio of water for 1.5 years. The different colored regions correspond to the same colored protons labelled in (i); acetone is present in (ii) around 2.8 ppm. The results show that prolonged exposure to water does not appear to chemically or physically effect 2DPA-1, consistent with observed, stable bulges exposed to ambient humidity for more than 1000 days, as discussed below.

First, we discuss various characteristics of 2DPA-1 that support the stability and longevity of its impermeability properties. We found with density functional theory (DFT) calculations on bilayer configurations of 2DPA-1 with various interlayer offsets that the most minimum energy, stable configurations have staggered pores. For each offset, we first relaxed the system by performing a geometric optimization in vacuum using DFT. We computed the interlayer interaction energy, E_int, for the final optimized geometry using:

E_int = E_bl − E_ml-1 − E_ml-2 (1)

where E_bl is the energy of the bilayer and E_ml-1 and E_ml-2 are the energies of the two monolayers. Snapshots of the various bilayer configurations considered as well as the corresponding interlayer interaction energies are found in Fig. 1D. We find that staggered pores have the most energetically favorable stacking configurations and that eclipsed stacking (i.e. AA stacking) is the least favored. There are numerous stacking configurations with varied pore-to-pore offsets that possess similarly favorable energies, indicating a tendency to stack in a variety of staggered configurations.

Another favorable property of 2DPA-1 is its environmental stability. In contrast to 1D polyaramids which are notoriously hygroscopic,^22–24 we show water to have no notable effect on the chemical or molecular structure of 2DPA-1 after 539 days, or approximately 1.5 years, of exposure (Fig. 1E). We stored a 1 : 1 mass ratio of 2DPA-1 powder in DI water and compared the NMR spectra of the sample before and after the storage. We note that there is a slight increase in the r-value, or ratio of main-chain (H_A) to the end-group proton H_B,²⁵ from 5.15 to 5.45, as well as a decrease in the presence of sharp peaks in the main-chain and end-group proton regions (H_B, H_C, 1–5). These observations are consistent with a slight decrease in the presence of small molecular weight fragments, which could hydrolyze in water. The rate of such hydrolysis is expected to be slow at neutral pH because the amide carbonyl is poorly electrophilic, and water is a weak nucleophile. The amide resonance structure stabilizes the C–N bond, reducing susceptibility to rapid nucleophilic attack.^26,27 Over 18 months, a slow reaction at room temperature may reasonably increase the r value by 6% as observed. A more likely effect of water emersion is water intercalation and disruption of hydrogen bonding. This physical change in 2DPA-1 material assembly may not be immediately observable in ¹H-NMR peaks and corresponding r value, except that the change in hydrogen bonding is known to broaden such features. A stronger influence is the impact on the stability of a suspended nanofilm, as explored later in this work. In powder form, the experiment over 18 months confirms a lack of hygroscopic chemical degradation as expected.

3 Longitudinal stability of 2DPA-1 bulges

We generated a cohort of twenty-five 2DPA-1 bulges suspended over microwells and filled with air, and followed them over the course of more than 1000 days, or 3 years (Fig. 2A). We transferred 2DPA-1 films ranging from 12.8 to 66 nm in thickness onto 8 different wafers with the pattern of Substrate I. These bulges exhibited unexpected stability with all bulges remaining upwardly deflected for the entire study range, invariant to changes in atmospheric temperature, pressure, or continuous exposure to atmospheric humidity. We note that the initial heights of these samples are not equal and that, in general, bulges on the same substrate do not have equal initial heights.⁴ We attribute this stochasticity to variations in the filling behavior. The opening of the rim seal is not currently controllable, leading to bulges that are sometimes adhered to the inside of the well to varying degrees. We also note that the successful suspension of nanofilms was not absolute, and that the yield of suspended films is highly correlated to the 2DPA-1 r-value; 2DPA-1 nanofilms with higher r-values (greater than 4) lead to suspension rates of almost 100%.

Fig. 2 (A) Log–log plots of the height extrema of 10 2DPA-1 bulges suspended over 14 µm diameter wells (i) and 15 2DPA-1 bulges suspended over 24 µm diameter wells (ii) over the course of more than 1000 days. Bulges are filled with captured air from the wet transfer process. (B) Log–log plots of the mean square displacement (MSD) analysis of 2DPA-1 bulges over 14 µm (i) and 24 µm (ii) diameter wells wherein the solid lines are the fit results that have an optimized confinement length, L_c². (C) Other 2D bulges in the literature also show random fluctuations in height. Comparisons of ln(L_c²) for graphene bulges from Sun et al.¹³ (green square: a = 1 µm; blue diamond: a = 0.5 µm) and 2DPA-1 bulges in this work (left pointing triangle: a = 8.5 µm; upwards pointing triangle: a = 24 µm; downwards pointing triangle: a = 14 µm) with logarithm of initial volume, V₀ that describes the volume of the well and bulge system.

We find that the AFM-measured deflections of the bulges show that bulges can increase or decrease between measurements on the order of tens of nanometers, and we show that this can be modelled by the confined diffusion of gas molecules within the bulges (Fig. 2B and C). Such fluctuations on the order of days are observable in other published data sets¹³ but, to our knowledge, studied here for the first time. We begin with an expression for the mean squared displacement (MSD):

where X is the position vector of a molecule, N is the total number of molecules within the system, τ is an arbitrary time, and i is an integer. The MSD has different relationships with t dependent on the type of diffusion: linear indications Brownian motion, quadratic indicates Brownian motion with drift, and sublinear indicates confined diffusion. For confined diffusion,²⁸where L_c is a characteristic size of the region of confinement, a is a scaling parameter, b and c depend on the shape of the region, and σ is a constant ‘diffusion’ coefficient, characterizing the daily random walk of the bulge height, bounded by the size constraint. For our 25 2DPA-1 bulges measured over 3 years, we calculated the MSD over time (Fig. 2B) and fit a scaling relationship, which was found to be an exponential plateau for all 25 bulges. We then extracted L_c from each of these fits and compared them to the corresponding bulge volume (Fig. 2C), assuming the bulge approximates a circular paraboloid (Fig. S1). We also analyzed and included 10 graphene bulges with diameters of 0.5 and 1.0 µm from the literature¹³ measured over 800 hours, or over 30 days, using mechanical properties from literature.^13,16 We find that the L_c corresponds to the bulge volume with R² = 0.95 and that this correlation holds when analyzing the different bulge materials and bulge diameters. This physical correlation is appropriate; the range of motion of the bulge should be determined by its initial volume, bounding the 1D random walk of the bulge height. We also find correlations between L_c and the initial bulge height, initial bulge surface area, and initial pressure difference across the bulge (Fig. S2); however, these correlations have lower correlation coefficients.

There are subtle fluctuations in atmospheric temperature and pressure as well as environmental vibrations that the bulges may be subject to as they are stored and then transferred to the AFM, and these conditions may have a delayed impact on the bulges though latent adhesion mechanics. We rule out that fluctuations in temperature directly cause appreciable thermal expansions in the substrate, leading to these variations, by using known coefficients of thermal expansion for silicon and estimating sub-angstrom changes in the well diameters (eqn S3). Instead, we note that the temperature/pressure fluctuations would result in some change in the observed gas volume within the wells and thus the bulge height, and while the bulges correlate in their height fluctuations, there is a lack of correlation with ambient conditions (Fig. S3), supporting the idea of mechanical or latent delay in effect. The bulge system is pushed upward by the encapsulating gas pressure but restrained by both the in-plane tension of the nanofilm and the van der Waals adhesion of the nanofilm to the wall. The dynamics of upward shock and downward restoration need not be matched. Such a mismatch would convert perturbative shocks from changes in temperature and vibration to fluctuations about an equilibrium height and allow the observations of the 1D random walk.

We also find that there are subtle fluctuations in the bulge diameters (±1 µm) but similarly rule out the effect of these fluctuations on the bulge heights (Fig. S4). These fluctuations can be attributed to measurement error and have no correlation between bulges on the same substrate or bulges measured on the same day.

We note that there exists a verification technique to show that these longitudinal bulges in fact retain gas and are not permeating throughout the study; this entails puncturing the bulges, such as with an AFM tip in contact mode, and observing its deflation. We have multiple examples of punctured bulges returning to their initial, un-inflated states (Fig. S5); however, we do note that the type of puncture and amount of interaction between the AFM tip and bulge can affect the deflation dynamic (Fig. S5). Given the destructive nature of this technique, we have sampled only a few but not all of the samples, showing that they can be punctured in this way.

4 Environmental impact on bulge stability

4.1 Pressurization-induced rim seal opening model

The persistence of a bulge, while attributable to the impermeability of the nanofilm, is also strongly coupled with the strength of the interfacial rim seal of each observed microwell – understanding the nature of the rim seal is crucial to repeatedly forming extremely stable bulges.

To understand further the behavior of the interfacial rim seal, we sought to model the gas-filling procedure of 2DPA-1 bulges with N₂. Bulge samples can controllably be made to have negative deflections by transferring 2DPA-1 films onto the substrates at elevated temperatures (50 °C), and then made to have positive deflections by pressurizing the sample at 150 kPa with N₂. Our analysis with an optical interferometry technique verifies that the bulge heights steadily increase throughout the filling.^4,15 Given 2DPA-1's ultra-low permeability to N₂, we propose that N₂ enters the bulge through the interfacial rim seal.

We use a single point model, wherein the bulge is approximated as a cone with maximum deflection δ, in combination with the ideal gas law to validate the basic assumptions of these observations and our hypothesis. The conical bulge total volume is approximated as:

where V_C is defined as V_C = πr²d as the volume of the well cylinder with diameter d. We begin with a force balance on the conical bulge, normal to the top of the bulge.where P_int is the pressure internal to the bulge, P_ext is the pressure external to the bulge, and F_spring is the tension force within the bulge modelled as a Hookean spring. The internal pressure is defined by the ideal gas law as follows:

We use a modified spring constant, γ = k/A, and thus have the following pressure term for the bulge tension:

where x is the extensional slant length of a cone, , and x₀ is the extensional slant length of a cone at r = 0. During the initial transfer of the 2DPA-1 film onto the substrate at 50 °C, we assume that the film is unstressed and flat and that P_int = P_ext = 1 atm, which thus gives us an initial condition to calculate γ, hence referred to as γ₁. We also assume an initial molar amount of internal gas, n_0,1. We now can apply our model to our experimentally monitored system wherein we used Substrate II (Fig. 3A).

Fig. 3 Single-point conical bulge model depiction of the nitrogen pressurization process for 2DPA-1 bulges, where sequentially the external pressure and temperature are modulated to induce bulge filling. The bulge is assumed to encapsulate an ideal gas. The single point model shows agreement with experimental observations: (i) initial condition with air at 50 °C trapped in a well during transfer with δ = 0, and initially unstressed (x₀ = r) with a 1 Pa m⁻¹ estimated spring constant. (ii) Cooling to 25 °C produces negative deflection consistent with experimental observation. (iii) Update of the spring constant to match the −380 nm experimental deflection. (iv) Pressurize to 2.48 atm using pure N₂. The single-point model predicts that the film should compress and adhere to the bottom of the well when the pressure reaches 1.8 atm. (v) Instead, the height increases to −200 nm, consistent with rim seal opening and an increase of N₂ molecules in the bulge. (vi) Once external pressurization falls to P_ext = 1 atm, the height rises to 1100 nm, reflecting the increased gas volume in the bulge from the filling process. The model does overpredict the resulting height increase, however outward deflection necessarily involves the adhesion at the surface around the well, increasing the effective spring constant. (vii) Update to the spring constant to reflect the final corrected bulge deflection of 225 nm. (B) Comparison of the one-point cone model results with experimental deflection data during nitrogen pressurization. Reproduced with permission from Ritt, Quien, Wei et al.⁴ (C) Schematic of the helium experiment, wherein bulges prefilled with N₂ (red circles) are subjected to helium gas (blue circles) of negligible pressure. If permeable, the bulges should increase in height (top), whereas if impermeable the bulges should not change in height (bottom). (D) Results of the full pressurization experiment with nitrogen, then helium, on 8 studied bulges (35 nm thick, r = 9.18). (i, ii) Change in height, determined interferometrically, during the He flow (gray box) for a 7 min flow (i) and 15 min flow (ii). (iii) Change in height, determined interferometrically and with AFM, over entire measurement time with He flow in gray. Bulges were observed to remain invariant on exposure to He. At long times, all bulges neither increased or remained invariant, but flattened after He exposure (1150 min) presumably from rim seal leaking. The results suggest He impermeability through 2DPA-1 in addition to the other gases tested.

Fig. 3A-i depicts the initial condition with air at 50 °C trapped in a well with δ = 0, and an initially unstressed membrane such that x₀ = r. An initial guess for γ (γ₁) from scaling is made as approximately 1 Pa m⁻¹. Upon cooling to 25 °C, we observe that the bulge becomes negatively deflected (Fig. 3A-ii); this is reflected in the calculations when using γ₁, though the magnitudes are not equal (−380 nm experimentally, −709.6 nm theoretically). To rectify this, we thus calculate γ such that it results in them being equal, γ₂ (resulting deflection in Fig. 3A-iii). Then, we pressurize the system to 2.48 atm using pure N₂. If the system is pressurized without any rim seal opening, using γ₂, we find that the film would touch the bottom of the well at around 1.8 atm, which would result in the film becoming irreversibly adhered via van der Waals forces (Fig. 3A-iv). This counterfactual supports the observation that, instead, upon pressurization, the rim seal opens, allowing an inflow of N₂. Experimentally, we find that the bulge height reaches −200 nm during this pressurization and, when P_ext is reduced to 1 atm, the height rises to 225 nm. We calculate n₀ such that it would result in the height of −200 nm in the given conditions (Fig. 3A-v), n_0,2, and then compute that, upon pressure reduction to 1 atm, the height rises to 1110 nm (Fig. 3A-vi). This accurately predicts the bulge's positive deflection, though it does overestimate the observation, and we can correct this by computing a new γ from experimental data, γ₃, which leads us to finally model the experimentally measured bulge height (Fig. 3A-vii)

The one-point model is thus able to describe several bulge observations corresponding to before, during and after pressurization (Fig. 3B), with corresponding states from Fig. 3A assigned to the pressurization process. Overall, the model shows that the bulge behavior is consistent with the ideal gas law and a pressurized rim opening.

4.2 Gas-specific effects

Gases including N₂, SF₆, Ar, and CH₄ have been shown to form 2DPA-1 bulges persisting for multiple days while gases including O₂, CO₂, He, and H₂ did not.⁴ To elucidate the rim seal's potential contribution to permeance, we observed a system of N₂ filled bulges (24+ hours) exposed to He (35 nm thick, r = 9.18, Substrate II).

We found that persistent 2DPA-1 bulges filled with N₂ consistently deflated after exposure to He (Fig. 3C and D), supporting the hypothesis that He molecules can alter the rim seal and affect the bulge test measurement. We began with 8 microwells, all initially downward deflected due to the annealing of the sample and pressurized them with 150 kPa of N₂ for 6 hours. The resulting samples were positively deflected and maintained this deflection for at least 24 hours, which is empirical evidence that they had an intact rim seal. Then, within an environmental chamber, we applied a gentle flow of He at near-atmospheric pressure, manually confirmed at the chamber outlet, across the bulges for 7 or 15 minutes (Fig. 3D-i, ii). In a system with an intact rim seal, we anticipate that the He either permeates inside the well, increasing the heights, or does not permeate, leaving the heights unaffected (Fig. 3C). Using an algorithm based in interferometry that converts optical micrographs to height data,^4,15 we were able to convert the optical images of the bulges within this environmental chamber into height information and validate that all 8 bulges maintained their upward deflection during the He flow. However, after the He flow, the heights appear to slowly increase, and then, over the course of 24 hours, all 8 bulges were measured with an AFM to be downward deflected (Fig. 3D-ii). Given that these bulges initially retained their rim seal during the N₂ pressurization and He flow, as evidenced by insignificant deflection changes, it is possible that the interaction of He with the film and substrate caused the rim seal to open, leading to this eventual bulge deflation. In all cases tested, the resulting downward deflected state was within 50 nm of the initial state of these bulges, supporting that all the gas, including the nitrogen, had left the bulges. However, future work will attempt to elucidate this curious behavior.

4.3 Temperature effects

To better understand the longitudinal stability of 2DPA-1 bulges, we studied the effects of temperature on its permeability and the ability to maintain the rim seal at elevated temperatures. This also elucidates the potential impact of physisorbed water molecules on the observed film impermeability. Using the Substrate II design, we measured the deflections within a temperature-controlled AFM of four 2DPA-1 bulges (35 nm thick, r = 9.67). We first increased the temperature from 35 to 80 to 120 °C, then modulated it between 80 and 120 °C.

We find that all 4 bulges exhibit the same behavior: initially decaying upon the first temperature increase, then oscillating between heights as the temperature is modulated (Fig. 4A). None of the bulges completely deflated, which is what would be expected if physisorbed water contributed to the observed impermeability. We hypothesize that the initial decay is due to a temporary and reversible opening of the rim seal, likely owing to the influence of heating on the adhesion between the film and substrate. Supporting this is the observation of an irreversible expansion in the observed AFM diameter (Fig. 4B). However, after this, the bulges are observed to follow the ideal gas law for the encapsulated gas, consistent with stable capture of the gas. When subsequently oscillating the temperature between 80 °C and 120 °C for 2.5 cycles, for example, the bulge deflections similarly oscillated on the order of 10 nm consistent with the ideal gas law.

Fig. 4 (A) AFM height extrema of each bulge (35 nm thick, r = 9.67) throughout the experiment (blue circles) with the temperature profile inset (red-yellow gradient). (B) Corresponding change in bulge diameter (blue asterisk) throughout the experiments corresponding to the systems in (A). The initial height declines observed in (A) appear to correspond to a change in film adhesion and expansion of the diameter. Once stabilized, the diameter appears to remain invariant throughout the temperature cycling. Temperature profile is inset along the bottom (red-yellow gradient). (C) Comparison of the calculated height of an impermeable bulge at 120 °C (light blue dashed line), using the ideal gas law applied to the gas within the 80 °C (dark blue dashed line), with the experimental data points at 80 °C (dark blue circles) and 120 °C (light blue circles). Temperature profile is inset along the bottom (red-yellow gradient). The results show that the temperature cycling produced the effect expected for a stable, encapsulated gas subject to the ideal gas law.

As previously mentioned, the diameters of all 4 bulges increase during the first temperature ramp, correlating to the observed bulge deflation (Fig. 4B). 3 of the bulges exhibit the diameter increase at the first temperature increase (Fig. 4B-i, ii, iv) while the fourth does so at an approximately 15 minute delay (Fig. 4B-iii). The rim seal thus appears to have some stochasticity to its behavior. Then, the diameters either decrease or stay approximately constant, with variations that could be attributed to measurement error. This corresponds to the hypothesis that the rim seal closes after the initial temperature increases. We can characterize the adhesion energy between the film and the substrate based on the initial diameter increase, assuming that this delamination is driven by pressure increases:²⁹

where Γ is the adhesion energy, p₀ is the internal pressure of the bulge, V₀ is the initial volume of microwell, V_B is the volume of the nanofilm bulge as a function of the bulge radius a, p_ext is the external (atmospheric) pressure, and C is a constant based on Poisson's ratio. Because this analysis does not consider temperature effects on the van der Waals forces between the film and substrate, we consider this quantitative analysis as a lower bound estimation of the surface adhesion energy. We find the adhesion energies to be 0.019, 0.014, 0.022, and 0.017 J m⁻². We previously reported an adhesion energy, calculated for a flat 2DPA-1 thin film, of 0.29 J m⁻², which is an overestimation of a bulged 2DPA-1 thin film's adhesion energy.³⁰ We therefore conclude that the true value of the surface energy can be bounded by the values we provide here and the values calculated for a flat film.

At the elevated temperatures of 80 and 120 °C, we propose that the bulges maintain their impermeability, the rim seal is still intact, and the gas within the well is expanding its volume in agreement with the ideal gas law. To quantify this, we begin with using the ideal gas law to relate the bulge state at 80 °C to 120 °C, assuming no permeation:

Then, we insert an expression for the well volume, assuming that the bulge approximates a circular paraboloid (V = πr²L + πr²δ/2), and insert Hencky's solution³¹ as the expression for pressure, as this model accounts for material properties such as the elastic modulus. This yields:where A and B are constants within Hencky's solution dependent on material properties. Thus, for a given T₁, T₂, and δ₁, one can calculate δ₂.

Using the average experimental height at 80 °C for each of the bulges, we calculated what the corresponding height should be at 120 °C (Fig. 4C). We calculated this using the mean of experimentally reported elastic moduli for 2DPA-1.³ We also investigated the effect of the ideal gas assumption by comparing it to the van der Waals equation of state, finding negligible differences in the resulting bulge heights (Fig. S6). We find that the percent error between the theoretical and experimental bulge heights at 120 °C range from 0.2% to 13.6%; per bulge, the average percent error is 4.1% (Fig. 4C-i), 7.4% (Fig. 4C-ii), 6.7% (Fig. 4C-iii), and 3.7% (Fig. 4C-iv). Hence, our results do not indicate any discernible gas loss while oscillating between 80 and 120 °C and supports the notion that physisorbed water cannot be the mechanistic explanation for the film's measured impermeability. In conjunction with the 1000 day data set, the impermeability properties of 2DPA-1 are unaffected by modulations in atmospheric humidity.

5 Conclusions

In this study, we present the first comprehensive framework for understanding long-term stability mechanisms in nanoscale thin film bulge test systems through an unprecedented 1000 day monitoring of 2DPA-1 microwells. The molecular-level packing architecture of 2DPA-1, validated through computational modeling, provides the fundamental basis for sustained impermeability across multiple environmental conditions. Our confined diffusion model successfully explains daily height fluctuations as intrinsic gas molecule dynamics rather than measurement artifacts, with characteristic length scales directly correlating to bulge geometry (R² > 0.96 for volume correlation). We demonstrate temperature-independent rim seal integrity up to 120 °C through thermodynamic validation, while revealing critical gas-specific failure mechanisms that establish clear operational boundaries.

This mechanistic framework enables expansion of bulge test methodology to emerging nanomaterials systems where long-term reliability is paramount. The findings discussed here will guide the design of next-generation membrane materials and provide insight for assessing new material systems under realistic operating conditions.

6 Methods

6.1 Sample preparation

We transferred 2DPA-1 thin films onto the wafers using polystyrene (PS) as a sacrificial support layer. Silicon/silicon oxide (Si/SiO₂) wafers were sequentially sonicated in acetone, then isopropanol for 5 minutes each, and dried with nitrogen gas. Then, 10 wt% PS dissolved in anisole was spin-coated onto the cleaned Si/SiO₂ substrates at 2000 rpm for 60 seconds. The PS-coated substrates were immediately transferred to a 110 °C hotplate to anneal for 15 minutes under a glass cover to prevent contamination during solvent removal. Subsequently, 2DPA-1 solutions in trifluoroacetic acid (TFA) were spin-coated using identical parameters (2000 rpm, 60 seconds) onto the PS layer. Film thickness was controlled by varying the 2DPA-1 concentration in TFA. Following deposition, samples underwent brief thermal treatment at 50 °C for 5 minutes to eliminate residual TFA, with non-uniform film edges trimmed to ensure thickness uniformity.

Then, we transferred the PS-supported 2DPA-1 films onto the etched substrates via wet-transfer. Using a razor blade, we excised sections of the films and floated them on DI water such that the 2DPA-1 layer faced upward. Etched substrates were brought into contact with the 2DPA-1 surface, oriented so that the 2DPA-1 contacted the substrates, and carefully lifted from the water. Film-covered substrates were dried overnight at ambient conditions, with substrates requiring downward-deflected films annealed at 50 °C during the drying process.

Following transfer, PS was dissolved away with sequential solvent treatments: initial exposure to 20 mL of 25% v/v chloroform in hexane for 4 hours, followed by 20 mL of 30% v/v chloroform in hexane for an additional 4 hours. Substrates were gently rinsed with hexane and air-dried to remove residual solvents. Completed 2DPA-1-coated substrates were stored under ambient laboratory conditions.

Bulge samples were prepared by initially creating downward-deflected membranes through controlled evacuation, followed by nitrogen pressurization at 150 kPa for 5 hours to create upward-deflected bulges. The pressurization chamber was maintained at room temperature with humidity control during sample preparation.

6.2 ¹H-NMR characterization

We first prepared samples by suspending 2DPA-1 powders in deuterated trifluoroacetic acid at a concentration of 10 mg mL⁻¹. We sonicated the solution in a BRANSON Ultrasonic Cleaner for 15 min before adding into a WILMAD NMR tube (5 mm diam., economy). All the ¹H NMR measurements were performed at room temperature on an Avance III HD 500 NMR Bruker spectrometer.

6.3 Atomic force microscopy

To measure the deflections of bulge test samples, we used a Cypher S in tapping mode with an AC240 tip. We use a setpoint of 800 mV, scan rate of 1.5 Hz, a scan area of 20 µm, and a resolution of 256 × 256 points and lines. Each bulge on the substrates is 8.5 µm in diameter. For the temperature-controlled measurements, we used the heating stage attachment on a Cypher ES and the same parameters as above. For the puncture experiments, we used a Cypher S in contact mode.

Author contributions

M. S. S., M. Q., and C. L. R. conceived and supervised the study. M. Q., C. L. R., S. S. G., and Z. W. performed polyaramid synthesis and prepared thin film devices for gas permeability measurements. M. Q., C. L. R., and Z. W. performed characterization of the material. M. Q., C. L. R., and S. S. G. measured bulge deflections with AFM and developed the interferometric protocol for tracking bulge deflection optically. M. T. D. and N. R. A simulated material properties. M. S. S., M. Q., and S. S. G. performed the modeling and bulge height prediction theory. M. Q., S. S. G, and M. S. S. wrote the manuscript. All authors contributed to the discussion of the results and revision of the manuscript.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d6fd00034g.

Acknowledgements

This work was supported as part of the Center for Enhanced Nanofluidic Transport (CENT), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0019112. This work was carried out in part through the use of MIT.nano's facilities. S. S. G. is supported by the National Science Foundation Graduate Research Fellowship Program under grant no. 2141064. The authors acknowledge the use of the parallel computing resource Lonestar6 provided by the Texas Advanced Computing Center (TACC) at The University of Texas at Austin. The authors also acknowledge work that was carried out in part under auspices of the Institute for Soldier Nanotechnologies (ISN).

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