Microspacing In-Air Sublimation

• Microspacing in-air sublimation is a vapor-phase thin-film growth method that exploits a micron-scale gap to confine and control molecular diffusion under near ambient conditions.
• It employs a close source–substrate placement to enable uniform condensation, epitaxial alignment, and precise control over film formation, as demonstrated in PTCDI/hBN systems.
• The technique also extends to soft matter systems like smectic A liquid crystals, where curvature-driven vapor–pressure variations lead to unique morphological transformations.

Microspacing in-air sublimation is a sublimation-based thin-film growth and restructuring regime in which mass transport is confined on micron scales under near-ambient conditions rather than over centimeter-scale source–substrate separations in vacuum. In the PTCDI/hBN system, it denotes microspacing air-gap sublimation (MSAS/MAS): PTCDI is heated so that it sublimates, a target quartz coverslip with exfoliated hBN flakes is placed very close above the source with a fixed air gap of 170 µm, and molecules diffuse through the confined gap and condense on the cooler target to form few-layer crystalline PTCDI films at essentially ambient pressure under a lenient nitrogen atmosphere (LeCoutre et al., 6 Aug 2025). A related in-air sublimation/condensation route in smectic A liquid crystals reshapes layered soft matter through curvature-dependent vapor pressure at a free air–smectic interface, transforming initially negative- and zero-Gaussian-curvature structures into morphologies with pronounced positive Gaussian curvature (Kim et al., 2015).

1. Definition and physical scope

In the PTCDI study, microspacing in-air sublimation is explicitly a physical vapor growth technique with four defining elements: a sublimating organic source, a target substrate positioned very close above the source, a micrometer-scale gap that confines vapor transport, and operation in a nitrogen atmosphere at essentially ambient pressure rather than in vacuum. The small gap sets a short diffusion length for vapor molecules, keeps a quasi-steady, relatively high local vapor density near the substrate, and enables controlled growth of ultrathin, ordered layers with simple bench-top hardware rather than pumps, load-locks, and tightly controlled vacuum pressure profiles (LeCoutre et al., 6 Aug 2025).

The same term is not used in the smectic A study, but the reported mechanism is closely related at the level of in-air sublimation physics. There, sintering within the SmA temperature window is a reshaping process driven by sublimation, condensation, and restructuring at a free air–smectic interface. The operative control parameter is not a source–substrate gap but the local mean curvature of the interface, which modulates the local vapor pressure and hence the balance between sublimation and condensation. This suggests a broader interpretation of microspacing in-air sublimation as a family of near-ambient sublimation processes in which microscale geometry controls mass transport and final morphology (Kim et al., 2015).

A central distinction from conventional physical vapor transport (PVT) or OMBD is the transport regime. Vacuum PVT typically uses centimeter-scale source–substrate spacing and ballistic molecular flow under high or ultra-high vacuum. In the PTCDI implementation, the mean free path is much smaller than the 170 µm spacing, so transport through the confined gap is collisional and diffusive rather than purely ballistic. The smectic implementation, by contrast, operates at a free surface exposed to air at normal atmospheric pressure, where the gas volume is much larger than the film volume and sublimated molecules can diffuse away without significant vapor-pressure buildup (LeCoutre et al., 6 Aug 2025).

2. Experimental embodiments

The PTCDI/hBN implementation uses a vertically stacked geometry. A PTCDI reservoir on a glass coverslip is placed on a copper block mounted on a standard laboratory hotplate, with a PT100 temperature probe embedded in the copper block for accurate and homogeneous temperature control. A quartz coverslip carrying freshly cleaved hBN flakes is positioned above the source, and a standard microscopy cover glass acts as a spacer that fixes the air gap at 170 µm. The stack is covered by a glass beaker and flushed with N$_2$ shortly before sublimation; the beaker is not airtight, so the environment remains near atmospheric pressure with uncontrolled humidity. PTCDI reservoirs were initially prepared by sublimation of PTCDI powder onto a glass slide in the same setup to make the reservoir more homogeneous and avoid the lithographic effect known from prior MAS work. Reported source temperatures include 180 °C, 250 °C, and 270 °C; the AFM monolayer sample used $t_\text{exposure}=2$ min at 180 °C, and a high-coverage polarization sample used 5 min at 270 °C. The interval between exfoliation and sublimation start was kept at 30–60 s to keep hBN clean (LeCoutre et al., 6 Aug 2025).

The PTCDI materials choice is structurally specific. PTCDI is a planar perylene derivative with a large aromatic $\pi$-conjugated core and two imide groups capable of double hydrogen bonding with neighboring PTCDI molecules, making it a natural test system for supramolecular ordering, excitonic coupling, and fluorescence. hBN provides an atomically flat, chemically inert, wide-bandgap dielectric substrate with low visible absorption and three equivalent armchair directions, which promotes epitaxial alignment of adsorbed perylene derivatives (LeCoutre et al., 6 Aug 2025).

The smectic A implementation uses Y002, a semifluorinated SmA liquid crystal, drop-cast in its isotropic phase onto a PEI-coated silicon wafer and then cooled into SmA, where it spreads into a flat film of thickness $h \approx 10\text{–}20~\mu\mathrm{m}$. Sintering is performed within the SmA temperature window, 130–190 °C, under ambient air and normal atmospheric pressure. The initial state is a hexagonal array of toroidal focal conic domains (TFCDs) produced by antagonistic boundary conditions: planar anchoring at the PEI-coated substrate and homeotropic anchoring at the free surface. Time scales span seconds to minutes near 190 °C and tens to hundreds of hours near 130 °C, with sintering times reported from 5 to $10^6$ s (Kim et al., 2015).

3. Mass transport, condensation, and surface kinetics

For PTCDI on hBN, the growth sequence comprises sublimation of the lower PTCDI reservoir, diffusion through the 170 µm air or N$_2$ gap, adsorption on the cooler hBN target, surface diffusion, nucleation, and lateral growth. The paper identifies temperature and exposure time as the practical growth controls: increasing temperature or exposure time increases PTCDI coverage and thickness, and therefore fluorescence brightness. At 250 °C, the spread of fluorescence intensity across different flakes on the same chip becomes larger, tentatively ascribed to inhomogeneity in the dye reservoir. For long exposure times, fluorescence tends to concentrate at flake edges, interpreted as a sign of increased molecule mobility and trapping at edge sites. The general diffusive expectation stated for the confined gap is $$J \propto D_\text{gas}(c_\text{source}-c_\text{substrate})/L$$, where $L \approx 170~\mu\mathrm{m}$, so reducing the gap increases flux for a given sublimation rate and reduces sensitivity to large-scale convection and turbulence (LeCoutre et al., 6 Aug 2025).

The PTCDI study further argues that surface growth is likely diffusion-limited at the surface rather than interface-limited condensation, because MD yields a 2D diffusion constant for a single PTCDI molecule on hBN of

$$D \approx (8.6 \pm 0.1)\times 10^{-9}\ \mathrm{m}^2/\mathrm{s}.$$

The mechanistic picture is therefore one of mobile adsorbates on hBN that aggregate through strong intermolecular hydrogen bonding into extended islands, with edge trapping and local heating influencing the final morphology (LeCoutre et al., 6 Aug 2025).

In the smectic A system, the mass transport law is curvature-dependent. The local saturated vapor pressure above a curved free surface is written as

$$p = p_0 \exp\!\left(\frac{2 H \gamma_\perp v_1}{k_B T}\right) \approx p_0\left(1+\frac{2H\gamma_\perp v_1}{k_B T}\right),$$

where $t_\text{exposure}=2$0 is the mean curvature, $t_\text{exposure}=2$1 is the saturated vapor pressure over a flat surface, $t_\text{exposure}=2$2 is the surface tension for a homeotropic interface, $t_\text{exposure}=2$3 is the molecular volume, and $t_\text{exposure}=2$4 is the absolute temperature. The corresponding evaporation flux is curvature-sensitive, so regions with positive $t_\text{exposure}=2$5 exhibit enhanced sublimation, regions with negative $t_\text{exposure}=2$6 exhibit net condensation, and flat regions with $t_\text{exposure}=2$7 are comparatively inert. In the TFCD geometry, the mean curvature changes sign across each domain: the outer ring near the periphery has $t_\text{exposure}=2$8, the inner region near the axis has $t_\text{exposure}=2$9, and the interstitial flat areas have $\pi$0. This establishes a microscopically resolved pattern of ablation and redeposition at the free surface (Kim et al., 2015).

4. Structural and spectroscopic manifestations

The PTCDI films are characterized structurally by tapping-mode AFM and optically by fluorescence microscopy and polarization-resolved PL. For samples grown at 180 °C for 2 min with 170 µm spacing, AFM height images show contiguous islands with well-defined edges on hBN, AFM phase images show distinct contrast relative to the substrate, and line profiles yield a step height of approximately 0.5 nm. This height is slightly larger than the $\pi$1 nm literature value for a face-on PTCDI monolayer, but smaller than expected for a face-on bilayer or edge-on monolayer; the discrepancy is attributed to AFM tip–sample interaction differences between PTCDI and hBN. These islands are therefore interpreted as single PTCDI monolayer islands arranged in a face-on configuration. In larger domains grown at 270 °C for 5 min, correlative AFM and confocal PL show flat, uniform-height islands with the same $\pi$2 nm step and lateral sizes up to $\pi$3 µm; occasional holes of $\pi$4 nm depth with distinct AFM phase are tentatively assigned to contamination (LeCoutre et al., 6 Aug 2025).

The optical signatures are consistent with long-range molecular order. Widefield fluorescence images show modest brightness at 180 °C and substantially stronger fluorescence at 250 °C, consistent with increased thickness. Local PL spectra from the 270 °C, 5 min sample show a narrow $\pi$5 line at $\pi$6 nm with FWHM $\pi$7 nm, a weaker broader $\pi$8 vibronic peak at $\pi$9 nm, and in one position a slightly blue-shifted $h \approx 10\text{–}20~\mu\mathrm{m}$0 peak at 611 nm. Under linearly polarized 532 nm excitation with parallel detection, different PTCDI domains display near 100% contrast between bright and dark states as the polarization axis is rotated from $h \approx 10\text{–}20~\mu\mathrm{m}$1 to $h \approx 10\text{–}20~\mu\mathrm{m}$2 in $h \approx 10\text{–}20~\mu\mathrm{m}$3 steps. The intensity follows cos$h \approx 10\text{–}20~\mu\mathrm{m}$4-like dipole patterns, and angular maps extracted via a 2D Fourier transform show emission dipole axes separated by multiples of $h \approx 10\text{–}20~\mu\mathrm{m}$5. These observations confirm in-plane molecular alignment and epitaxial locking to one of the three equivalent armchair directions of hBN (LeCoutre et al., 6 Aug 2025).

In the smectic A system, the principal structural outcome is curvature reprogramming. Initially equilibrium films consist of TFCD interiors with negative Gaussian curvature and flat interstitial regions with zero Gaussian curvature. Sintering transforms these into a sequence of morphologies that includes spherical caps, conical pyramids, concentric rings, Udumbara flowers, and domes. Spherical caps and domes exhibit positive Gaussian curvature; hemi-toroidal rings have cross-sectional widths in the 100 nm–1 µm range; TFCD base radii are approximately 5–6 µm; and high-temperature sintering near 190 °C can remove about 90% of the original film volume while leaving dome-like caps over TFCD bases. The reported morphology map identifies eight types of structures as a function of temperature and time, with lower temperatures and longer times favoring intermediate states such as caps, pyramids, Udumbara flowers, and rings, and higher temperatures favoring more rapid progression toward domes (Kim et al., 2015).

5. Atomistic and continuum modeling

The PTCDI paper uses DFT and classical MD to infer the microscopic building blocks of the adsorbed monolayer. Candidate monolayer structures taken from earlier PTCDI and PTCDI-derivative studies include canted and wavelike motifs as well as other hydrogen-bonded arrangements. Formation-energy calculations in vacuum identify the canted structure as the lowest-energy monolayer and the wavelike structure as the next most stable; the energetic preference is attributed to denser packing and more favorable hydrogen bonding in the canted motif. This makes the canted arrangement the most likely building block for PTCDI monolayers on hBN (LeCoutre et al., 6 Aug 2025).

Single-molecule adsorption calculations resolve three adsorption sites on hBN: N-centered, B-centered, and hollow. The energetically preferred configuration is N-centered and aligned along one of the armchair directions of hBN. Relative to that state, the B-centered and hollow configurations are less favorable by 0.23 eV and 0.29 eV, respectively. The equilibrium PTCDI–hBN distances are 0.340 nm for N-centered adsorption, 0.342 nm for B-centered adsorption, and 0.346 nm for hollow adsorption. Lateral corrugation barriers at the N-centered equilibrium height range from $h \approx 10\text{–}20~\mu\mathrm{m}$6 to $h \approx 10\text{–}20~\mu\mathrm{m}$7 eV, and relax to $h \approx 10\text{–}20~\mu\mathrm{m}$8 and $h \approx 10\text{–}20~\mu\mathrm{m}$9 eV when the molecule–surface distance is allowed to relax at the saddle points. Classical MD, performed with GAFF for intramolecular PTCDI interactions and a custom interlayer potential parameterized to reproduce the DFT energies, deposits PTCDI molecules randomly 3 nm above hBN at a surface coverage of $10^6$0 and anneals the system at 600 K for 40 ns. After 40 ns, the molecules form well-ordered aggregated layers with canted packing and lattice parameters $10^6$1 nm, $10^6$2 nm, and $10^6$3, while the molecular long axes align with specific hBN directions in agreement with the threefold polarization pattern (LeCoutre et al., 6 Aug 2025).

The smectic A study uses differential geometry and elasticity to model sublimation-driven reshaping. Gaussian and mean curvatures are written in the standard form,

$10^6$4

For the curved SmA interface above a TFCD, one principal radius is approximated as $10^6$5, while the second depends on geometry through $10^6$6, producing a sign-changing mean-curvature field across the domain. The elastic free-energy density is written as

$10^6$7

and the competition between elastic cost and interfacial anchoring is quantified for a hemispherical dome of radius $10^6$8. Using $10^6$9, $_2$0, and $_2$1, the study estimates $_2$2 and $_2$3, concluding that surface anchoring dominates and can stabilize positively curved structures that are otherwise rare in equilibrium SmA textures (Kim et al., 2015).

6. Comparative position, limitations, and research uses

Relative to vacuum PVT or OMBD, the PTCDI implementation is radically simplified: it requires no vacuum system, no pumps, no sealed chamber, no load-locks, and no pump-down or venting cycles. The hardware is a hotplate, a copper block, glass coverslips, and a beaker, and the absence of bulky vacuum hardware leaves room for in-situ control or diagnostics around the setup. At the same time, the resulting films show monolayer steps in AFM, strong polarization anisotropy, narrow PL lines, and domain sizes reported as large domains and up to tens of microns in the general discussion, with optical properties described as comparable to those of vacuum-grown films. Compared with solution deposition, MAS is solvent-free and avoids solubility and drying-dynamics constraints (LeCoutre et al., 6 Aug 2025).

Its limitations are also explicit. Thickness control is coarse and depends on temperature, exposure time, and reservoir homogeneity; some flakes show outlying densities, especially at higher temperature; uniformity over large areas is not complete; edge clustering indicates sensitivity to local features such as edges and grain boundaries; and the beaker environment does not tightly control humidity or residual oxygen. Fine control over the exact number of layers is not detailed, and the PTCDI work characterizes the present approach as “coarse + post-selection” for obtaining minimal coverage and isolated monolayer islands. In the smectic A case, the Kelvin-based model is near-equilibrium whereas the experiments are strongly time-dependent, fine control over ring spacing and dome shape is not fully predictive, and many morphologies such as Udumbara flowers are transient under prolonged sintering (LeCoutre et al., 6 Aug 2025).

The application space follows directly from these material capabilities. For PTCDI on hBN, the reported targets include collective emission in molecular layers, J-aggregates, superradiance, collective excitonic states, electroluminescence in hBN-based tunnel barriers and van der Waals heterostructures, and quantum-technology platforms involving single-photon emitters and optically readable spin qubits. The paper further suggests transferability to other organic semiconductors and 2D substrates for OFETs, 2D heterostructures with TMDCs or graphene, and integrated photonic or optoelectronic devices requiring ultrathin, ordered molecular crystals. For smectic A, the curvature-programmed sublimation route points toward templates for self-assembly, optical elements such as domes and rings, microfluidic interfaces, adhesion and friction control, and hierarchical scaffolds. A plausible implication is that microspacing in-air sublimation is valuable not only as a low-complexity deposition technique, but also as a general route for geometry-mediated control of layered organic and soft-matter systems under near-ambient conditions (Kim et al., 2015).