All-dry free radical polymerization inside nanopores: Ion-milling-enabled coating thickness profiling revealed “necking” phenomena

Unique properties of nanoporous materials, such as unparalleled surface-to-volume ratio and molecular transport under nanoconfinement, afford great advantages to existing and emerging technologies in (bio)sensing,^1–3 membrane filtration,^4–6 antifouling,^7,8 drug delivery,^9,10 and energy storage applications.^2,11 Often the focus is on controlling surface chemistry to promote specific molecular interactions, but nanoconfinement itself also affords a huge potential to exert size-selective control (e.g., control of flux or selective sensing/releasing),^5,6,12 orthogonal to and synergistic with the chemistry-based nanomaterials design. However, the size and shape of nanopores or other nanostructures are challenging to control, presenting a major barrier to deploying nanomaterials in the aforementioned technologies.

One approach to control the size and shape of nanostructures is by shrinking existing pores with nanoscale precision using conformal coating approaches. Previous work has demonstrated the potential of initiated chemical vapor deposition (iCVD) in synthesizing conformal polymer coatings inside high-aspect-ratio nanopores, thus, providing dual control of size and chemistry for the internal porous structures.^13,14 However, coating thickness and its depth profile inside nanopores are exceedingly difficult to characterize, let alone control. Indeed, despite the great promise of polymer-coated nanoporous materials in a wide variety of applications, the thickness of the polymer nanolayers along the longitudinal direction of nanopores has not been successfully characterized thus far, severely limiting the design, synthesis, and deployment of nanoporous materials.

To date, a handful of methods have been developed to infer coating thickness profiles in nanopores. For example, compositional variation of the characteristic elements in the polymer coating can be captured using electron probe microanalysis (e.g., energy-dispersive x-ray) and serve as a proxy for coating conformality.¹⁵ Another approach relies on scanning electron microscopy (SEM) imaging polymer coatings against the surrounding nanopore walls along the longitudinal cross-section of the nanopores.^14,16 Although these approaches confirmed the presence of the polymer coatings throughout the nanopores, they commonly lack sufficient resolution in the longitudinal direction and, instead, often resorted to a few representative indicators such as coating presence at the top and bottom of the nanopores or the average thickness throughout the pores. Furthermore, imaging of the cross section of coated nanopores for coating thickness characterization is extremely challenging and subjective at times because the boundary between the coating layer and the neighboring pore wall is often obscured or invisible (due to the line-of-sight effect of electron microscopy), limiting the reproducibility of such measurements. Furthermore, existing characterization approaches fall short of collecting sufficiently large sample sizes to provide the required statistical power for resolving small changes in coating thickness. These shortcomings associated with the existing characterization methods have hindered the arrival at accurate synthesis–structure–property correlations that could guide the design of nanoporous materials with precisely controlled sizes and shapes.

For this study, anodic aluminum oxide (AAO) membranes were chosen as a nanoporous substrate due to their cylindrical pore structure, narrow distribution of pore sizes, and ease of in-house fabrication with precise control over their dimensions.¹⁷ The formation of nanopores by self-organized anodization of aluminum is a multistage process consisting of

1. pre-treatment, which degreases and electrochemically polishes the aluminum substrate The introduction of pre-treatment step is critical for improving the ordering of nanopores;¹⁸ 

2. anodization, using platinum (Pt) as cathode and aluminum as an anode, with the latter oxidized to form a porous aluminum oxide layer at the surface with ordered hexagonally shaped parallel nanotubes.¹⁹ Pore size, porosity, and depth of the pores can be controlled by adjusting the duration, voltage, and current of anodization, and the concentration of electrolyte solutions;¹⁸ and

3. post-treatment, which is used to widen the pore size to the desired diameter.

The highly ordered array of cylindrical pores obtained using this approach has controlled pore diameters, length, and porosity, thus enabling for the systematic kinetic studies reported here.

To address that critical limitation in nanomaterials design and characterization, we developed a methodology to map the thickness profile of ultrathin polymer coatings (<20 nm) with unmatched nanometer-scale precision in the longitudinal direction of cylindrical nanopores. As proof-of-concept, we explored the depth profiles of ultrathin poly(4-aminostyrene) (PAS) film thickness deposited over nanoporous AAO substrates (D ∼ 100 nm, L ∼ 5 μm, and aspect ratio ∼ 50) under two different iCVD conditions (i.e., low and high monomer concentration). PAS was chosen for its relatively well-understood iCVD kinetics as well as its potential for secondary functionalization afforded by the amine functional groups.^20,21 To guide future materials design, we renewed our previous collision-based model¹⁴ and enabled the prediction of radical-wall collision frequency at a specific depth of the nanopore. In so doing, we were able to explain the observed depth profiles of coating thickness inside nanopores, based on the existing theories of sticking probability and Knudsen diffusion. Using this model, we discussed the role played by free radicals in “sculpting” the pore shape under nanoconfinement.

Chemical reagents used in electrochemical anodization: oxalic acid (anhydrous, 98%) and chromium (VI) oxide were purchased from Alfa Aesar (Haverhill, MA, USA); phosphoric acid (85%) from VWR (Radnor, PA, USA); and sulfuric acid (98%) from Ward's Science (Rochester, NY, USA). Chemical reagents used in iCVD: 4-aminostyrene (AS) and tert-butyl peroxide (TBPO) were both purchased from Sigma-Aldrich (St. Louis, MO, USA). All the chemicals were used as purchased without further purification.

Nanoporous aluminum oxide (AAO) substrates were prepared by two-step anodization (adapted from Masuda and Fukuda)²² of high purity aluminum (Al, 99.998%, Thermo Fisher). Prior to anodization, the Al sheet (0.5 mm thick) was cut into 15 × 40 mm² rectangular coupons, cleaned by sequential sonication in acetone and ethanol, and dried under a stream of nitrogen gas. An annealing step was then performed on a hot plate at 400 °C for 1.5 h to release internal stress. Next, the annealed Al coupons were electrochemically polished in an acid solution, which contained 24.5% (v/v) sulfuric acid and 42.5% (v/v) phosphoric acid, at a constant voltage of 20 V, the temperature of 65–75 °C, and with stirring at 100 rpm. The oxide layer formed on the Al surface was removed in an etching solution comprising 3.6% (w/v) phosphoric acid and 4.5% (w/v) chromic (VI) oxide for 3 h at 65–70 °C with stirring at 70 rpm.

The first anodization was conducted in 0.3M oxalic acid solution for 16.5 h at a constant voltage of 60 V, the temperature of 5 °C, and with stirring at 200 rpm. Afterward, the first porous alumina layer was etched away using the same removal procedure (as described above) and second anodization was carried out in 0.3M oxalic acid for 15 min (at 60 V, 15 °C, 100 rpm), during which pore growth originated from indentation left behind by the nanopores in the first layer, resulting in ordered pore arrays. In order to minimize the variation in pore morphology between different coupons, four Al coupons were anodized simultaneously. Each of the four coupons (anodes) was placed 20 mm away from a Pt rode (cathode) located in the center of the anodization reactor. To obtain the target pore diameter of ∼100 nm, a third step, i.e., pore widening was carried out by submerging the as-anodized substrates in 0.1M phosphoric acid for 110 min at 30 °C with stirring at 60 rpm. Finally, the finished AAO substrates were cleaned by sonication in de-ionized water and acetone for 5 min each and air-dried before future use.

All polymerization reactions were conducted in a custom-built iCVD reactor chamber (335 mm diameter and 51 mm height) as described previously with minor adaptation.²¹ Specifically, a separate line consisting of a needle and ball valve were assembled for AS and attached to the iCVD reactor body. This modification was done to prevent potential condensation of the nonvolatile monomer AS.²⁰A summary of the deposition conditions can be found in Table I.

Briefly, AS (monomer) and TBPO (initiator) vapors were metered into the reactor chamber via a needle valve (for AS) and a mass flow controller (for TBPO), respectively. Due to the low vapor pressure of AS (and, thus, low vapor flow rate), inert Ar gas was not included as a patch flow (which would inevitably dilute AS) such that measurable deposition rates can be achieved. Variation in total flow rate was ≤0.07 SCCM (or ∼10% total flow), which had negligible influence on the deposition kinetics according to prior work.²¹ For each deposition, a clean AAO substrate with nominal pore diameter ∼110 nm and thickness ∼5 μm was placed alongside a Si wafer substrate (type: P/Boron ⟨100⟩, Purewafer, San Jose, CA), both affixed to the temperature-controlled reactor stage with Kapton tapes. Stage temperature was set to 54 °C and filament temperature was kept at 240–245 °C for all experiments to keep consistent with those used in previous kinetic studies on iCVD of PAS.²¹ Previously, our group showed that for iCVD deposition of PAS, the transition from a bimolecular termination (BT)-dominated regime (via either recombination or disproportionation), to a primary radical termination (PRT)-dominated regime, took place at $PM/PMsat∼0.16$⁠. Thus, two $PM/PMsat$ values, 0.167 and 0.082, were selected to represent the BT and the PRT regimes, respectively. The progression of deposition was monitored using interferometry (He-Ne laser, 1508P-1, JDSU, Milpitas, CA) on the Si wafer. The exact thickness of the deposited films was determined by a J.A. Woollam AlphaSE spectroscopic ellipsometer (Lincoln, NE) using from 315 to 718 nm at three different incidence angles (65°, 70°, and 75°). A Cauchy-Urbach model was used for data fitting. Fourier Transformed Infrared (FTIR) spectroscopic measurements were performed to characterize the deposited film on the Si wafer.

To evaluate the pore size distribution at specific depth levels of the nanopores, Ar⁺ ion milling (ARC-2036-IM, AJA International Inc., Scituate, MA, USA) was performed on both the pristine AAO substrates and those coated with PAS thin films. To this end, AAO substrates were first placed on a rotary sample holder and stabilized with steel clips. A collimated Ar⁺ beam (from a 22 cm diameter Kaufman RF-ICP gridded ion source) was used to provide uniform etching of samples over a large surface area up to 6-in. diameter. The sample holder was maintained at 20 °C by circulating water, which served as the heat sink. The heat generated during ion milling was effectively conducted away via a copper mesh placed between the sample holder and the heat sink. Note that a typical etch rate for polymers with a carbon backbone (∼55 nm min⁻¹) more than doubles that for anodized alumina (∼20 nm min⁻¹) (data not shown). That difference in etch rate, along with the line-of-sight effect of Ar⁺ beam, could lead to the artifact that the PAS polymer coating recedes further into the pore in relation to the surrounding pore wall at any given time during IM (Fig. S1 in the supplementary material).⁴⁸ Although this artifact should not affect the coating thickness profile per se since the amount of offset, $doffset$⁠, is expected to be constant throughout the IM process, it does bias the absolute z position. Furthermore, ion milling is known to potentially cause physical and chemical damages to polymers. To mitigate those effects, we chose a low acceleration voltage of 600 V with a grazing Ar⁺ beam incident angle, i.e., $φ=10°$⁠.²³ The acceleration voltage was chosen based on the extensive experimental evidence that direct damage of polymers by the ion beam is minimal at acceleration voltages below 1 kV.^23–27 For example, x-ray adsorption near-edge structure spectroscopy demonstrated that ion milling of polyacrylamide at acceleration voltages below 1 kV did not change the chemical composition and molecular structure of the polymer.²³ Although heat generated by the ion beam could cause thermal degradation, the acceleration voltage of 1 kV was shown to lead to temperature elevation that is less than 0.1 °C.²³ Given the pore diameter D = 110 nm and $φ=10°$⁠, we can estimate the upper bound for $doffset$ to be $D⋅tanφ=110nm⋅tan(10°)=19.4nm$⁠, which is less than 0.4% of the total pore length of 5 μm. Therefore, even in the extremely unlikely event that the low acceleration voltage we chose somehow led to degradation and redeposition of the polymer, the effect of that degradation-redeposition process on coating thickness is limited to a small region of the treated polymer and, thus, unlikely the cause for the necking phenomena. A smaller $φ$ could further reduce $doffset$ at the cost of IM rate. Thus, a balance between accuracy and rate should be considered for individual applications.

To determine the etching rate on AAO under the above conditions, a standard curve correlating the removed thickness of the porous oxide layer (⁠$z$⁠) and etch time (⁠$t$⁠) was constructed at t of 0, 0.5, 1.0, and 2.0 h. field emission scanning electron microscopy (FESEM) (Zeiss Gemini 500, 3 keV, Jena, Germany) cross-sectional images of the porous oxide layer of the AAOs were taken at the end of each etching time point to determine the amount of AAO removed.

Average coating thickness at a specific IM depth level was obtained by comparing the average pore sizes of the pristine and the PAS-coated AAO substrates. To this end, at least three top-view SEM images from representative areas (5.0 × 3.4 μm²) of each sample were acquired for image analysis using ImageJ (version 1.53c, NIH, USA),²⁸ amounting to ∼2000 or more individual nanopores analyzed for each sample. Those SEM images then underwent image analysis using a custom-designed ImageJ macro, which performs automatic thresholding (i.e., converting an 8-bit grey-scale image into a binary image), pore recognition, and pore size analysis (see Fig. S2 in the supplementary material,⁴⁸ for examples). At each specific depth z (i.e., z = 0, 0.1, 0.25, 0.5, 1.0, and 2.2 μm), the average diameters of the pristine and the PAS-coated nanopores, denoted $D0¯(z)$ and $Dpoly¯(z)$⁠, respectively, were calculated assuming circular pore shapes. The average thickness, $Th¯(z)$⁠, was derived using the following equation:

$Th¯(z)$ was later used for plotting the coating thickness profiles (Fig. 3) and deriving depth-specific deposition rates inside nanopores (Fig. 4).

The determination of confidence intervals [see Figs. 2(c), 2(e), and 4(c)] and the two-tailed student t-test [α = 0.05, see Fig. 4(c)] was carried out by implementing a self-written code using statistical software R-studio (version 1.2.1335).¹⁴ R-studio was also used for developing and running the renewed collision-based model (see Sec. III for details).

In our earlier work,¹⁴ we discovered that the average effective concentration of free radicals (⁠$[R⋅]eff$⁠) inside nanopores can exceed that of the bulk headspace due to the more frequent radicals-surface collision per unit area [Fig. 1(a)] than in the case of a flat surface [Fig. 1(b)]. The relative areal collision frequency (inside pores as opposed to on a flat surface), $β$⁠, was introduced to capture the overall effect of this amplification of $[R⋅]eff$ on the average deposition rate along the entire pore length, $DRpore$⁠. Here, in order to explain the variation of $DRpore$ along the z-direction inside nanopores, i.e., $DRpore(z)$⁠, we derived $β(z)$ to capture the local amplification of $[R⋅]eff$ as a function of distance z along the pores. The introduction of $β(z)$ is important because it allows us to approximate the local $[R⋅]eff$⁠, which we think played a key role in forming the non-conventional depth profile of coating thickness. The reason why theoretical derivation of $[R⋅]eff$ is necessary is that direct experimental measurement of such local free radical concentrations, if ever possible, would be extremely difficult to perform in an iCVD chamber^29,30—let alone conducting such measurements inside nanopores.

To derive, $β(z)$⁠, we start with the formulas derived previously for calculating the averaged effect, $β$⁠.¹⁴ Below, we first derive the case for through pores that are open at both ends and then adapt it to account for pores with only one open end [Fig. 1(a)], as is the case for AAO substrates used in this work.

First, the same assumptions as those previously described¹⁴ are also applicable here.

1. Nanopores are cylindrical with smooth walls.

2. Radical-surface collisions are purely elastic with specular reflection.

3. The model assumes that radicals become non-reactive with the same probability per collision inside or outside the pores.

4. Radical sticking probability remains constant while traveling inside nanopores.

5. Only free radicals entering the nanopores in the radial directions were considered, which could lead to an underestimation of the collision frequency. Nevertheless, radicals entering via off-radial trajectories could be analyzed using the same theories elucidated below.

6. The effect of the nanoconfinement on the vapor-phase primary radical recombination was negligible.^31–33 

In our earlier study¹⁴ which unveiled the phenomenon that the concentration of free radicals is amplified inside a nanopore, we derived the average number of collisions that radical experiences, $Npore$⁠, before reacting away (or sticking) or exiting the pore can be expressed as the following:

where L is the pore length, D the pore diameter, $θ$ the radical incident angle, $Γ$ the sticking probability, n the number of radical-surface collisions before sticking, and $Nmax$ the maximum number of collisions a radical can have before exiting the pore without reacting,

Following the same derivation method, we can derive $Npore(z)$ as the number of free radical-surface collisions that occur within the depth range of [0, $z$] inside a pore (⁠$z≤L$⁠),

where $Nmax(z)$ represents the maximum number of collisions the radical experiences within the depth range of [0, $z$] inside a pore (⁠$z≤L$⁠),

Next, the effect of nanoconfinement on deposition kinetics within the depth range [0, $z$] was extracted by averaging the number of collisions at all incident angles,

Thus, the amplification of the areal collision frequency between depth z and $z+dz$⁠, contributed by the forward radical flux [i.e., moving down the pore, brown trajectories, Fig. 1(c)], can be derived using Eq. (6) below:

where $ρ$ is the number density of surface-impinging radicals per area (on a flat surface) and $Sflat$ is the surface area of a flat surface. The subscript “F” in $β(z)F$ stands for “forward.”

For pores that are open on both ends, the total $β(z)$ is contributed solely by the forward flux and hence $β(z)=β(z)F$⁠, whereas for pores that have one closed end the contribution from the backward flux—i.e., those radicals that reached the bottom and then returned [see lighter trajectories, Fig. 1(c)]—should also be accounted for when computing $β(z)$⁠. In that case, $β(z)=β(z)F+β(z)B$ (subscript “B” stands for “backward”). Since the radicals that returned to depth z have effectively traveled the full distance of the pore, L, forward and then the distance of $L−z$ backward, we can see that $β(z)B$ is equivalent to $β(2L−z)F$ and, therefore, can be computed using the following:

Finally, in the case of pores with a closed bottom, $β(z)$ can be computed as the sum of $β(z)F$ and $β(z)B$ as the following:

The numerically computed values of $β(z)$ were later used for calculating the local $[R⋅]eff$ at specific z inside a nanopore (see Sec. IV E).

Stepwise ion milling of the AAO substrates with a grazing Ar⁺ incident angle of $φ=10°$ [Fig. 2(a)], followed by FESEM imaging at each depth level [Fig. 2(b)], provided a robust way to generate depth profiles of the pore diameter for both the iCVD-coated and the pristine AAO nanopores. Coating thickness profiles can then be derived by calculating the decrease in pore diameter due to coating at each specific depth level (see Experimental Details). One strength of this IM-based approach is that it enables us to acquire high-quality micrographs containing a large sample size of PAS-coated AAO pores (∼2000 total from three randomly selected non-overlapping views on any sample) via FESEM at the predetermined depth z (Fig. S2 in the supplementary material).⁴⁸ That large sample size is essential to acquiring accurate and precise mean pore diameter before and after iCVD coating, from which the mean coating thickness at a specific z location can then be derived following Eq. (1). Nevertheless, it should be noted that IM is an invasive approach. Thus, additional samples dedicated for IM characterization should be prepared alongside the actual samples throughout the steps of anodization and iCVD deposition. Both anodization and iCVD processes are well-suited for handling a large number of samples in one batch with small sample-to-sample variations,^34,35 which is essential to improving the reproducibility of the characterization results.

Ar⁺ milling rate on a given material increases with the kinetic energy of the Ar⁺ beam, $EAr+$⁠, and the incident angle, φ. The substrate was placed on a stage that is cooled by a circulating chiller, which served as a heat sink to prevent excessive heating of the AAO substrate caused by Ar⁺ bombardment during ion milling. During the milling process, the sample stage was spun at a fixed rate to minimize uneven etching caused by the line-of-sight effect. The thickness removed, z, which was used to infer the depth into the pores (or distance along the pores), can then be controlled with etching time, t, under an ion milling rate that was fixed at 1.21 μm h⁻¹ (or 20.1 nm min⁻¹) throughout our experiments. The side views of AAO in Fig. 2(c) demonstrate the gradual decrease in AAO thickness after 0, 0.5, 1, and 2 h of ion milling. At each time point, top-view images were taken for analyzing pore diameter by ImageJ. The average pore diameter at each depth level was calculated using ∼5000 pores [by pooling results obtained from two AAO coupons with 100-nm pore size, Fig. 2(d)]. The purpose of pooling was to reduce the influence of the small between-substrate variation in pore diameter at various z. To convert $t$to a specific z depth level of the AAO substrate, we established a standard curve between z and t [Fig. 2(c)], by plotting the thickness of the porous layer against t. The R² value of 0.992 indicated high linearity, which ensured precise control over the removed thickness and hence allowed accessing the pore size distribution at precise z. The slope of the calibration curve suggested an ion milling rate of 1.21 μm h⁻¹ (or 20.1 nm min⁻¹), as mentioned above, with CI95% = [16.9, 23.5] nm min⁻¹. The average pore diameters extracted from the top-view images [Fig. 2(b)] were then correlated with the calculated depth values to produce the depth profile that captures variations in the diameter of the nanopores in the longitudinal direction [Fig. 2(d)].

With that robust z control attainable via IM, we first characterized the pore size of the pristine AAO substrates (i.e., before iCVD coating). An average pore size of 110.4 nm was obtained with the standard deviation of 14.5 nm for pores captured at varying depths [at z = 0, 0.1, 0.25, 0.5, 1.0, and 2.2 μm, Fig. 2(d) and Fig. S3 in the supplementary material].⁴⁸ To evaluate the overall variation in the z-direction (of the pore size), the probability density distributions of pores at all z values from the two AAO substrates were compared (Fig. S4 in the supplementary material).⁴⁸ The probability density distributions overlapped at all depths, confirming the uniformity of pore size along the z-direction. Indeed, the standard deviation for the average pore diameters at all depths was only ∼2.2 nm, which was 2.0% of the average pore diameter (110.4 nm). Taken together, these results confirmed that it is reasonable to treat a typical pristine AAO nanopore as a cylindrical pore with a closed-end at the bottom side and straight pore walls. With this baseline pore size distribution along z, we were able to capture the depth profiles of iCVD coating thickness along the walls of nanopores for the two $PM/PMsat$ conditions with nanoscale precision, as detailed below.

Recently, we reported that the deposition kinetics under nanoconfinement, such as that imposed by the nanopores, can be quite different than the kinetics previously studied in micro-confined space (e.g., microtrenches) or on flat surfaces (e.g., Si wafer).¹⁴ We attributed the difference to the altered areal collision frequency of primary radicals with pore walls under the nanoconfinement, which in turn increased the $[R⋅]eff$ inside nanopores. One of the key questions that remained to be answered was whether one could leverage that variation in polymerization kinetics in the z-direction to control the size and shape of nanopores. Conventionally, a monotonous decrease in coating thickness with increasing longitudinal distance down the pores has been assumed based on the reaction-diffusion theory under the Knudsen regime,¹⁵ whereas here we hypothesize that the maximum coating thickness should be achieved at some distances below the top surface due to the amplification of free radicals under nanoconfinement, thus enabling potential control of the pore size and shape in the longitudinal direction. To achieve that control, it is critical to unraveling the thickness profile in the longitudinal direction of a nanopore and the local $[R⋅]eff$ at specific pore depths, as detailed below.

Progression of iCVD film growth (on all substrates in the same batch of deposition) was inferred from the film thickness on a flat Si wafer monitored in real-time using interferometry. The reason why the seemingly high target thickness of ∼ 135 nm on Si wafer (i.e., 129.3 and 149.5 nm, Table I) was chosen for our depositions is that, in general, deposition rates on flat substrates are faster than those inside nanopores due to diffusion constraints imposed by the nanoconfinement. Based on the target deposition conditions used here (i.e., $PM/PMsat<0.2$⁠, $PI/PIsat∼0.003$⁠, $[I]bulk∼5.55mmolm−3$⁠) and prior knowledge of the relationship between $DRpore$ and $DRflat$⁠,¹⁴ we estimated $DRpore$ to be ∼1/30 of $DRflat$ in our experiments. This means that a coating thickness of ∼ 135 nm on the Si wafer would be needed to produce an average coating thickness of ∼ 4.5 nm along the nanopore walls, which borders the resolution of SEM imaging used in this study (4.9 nm/pixel, see discussion in the supplementary material).⁴⁸ Thinner coatings would potentially be more challenging to discern under SEM.

Two deposition conditions were used to represent low $PM/PMsat$ conditions, i.e., 0.082, which corresponds to the quadratic growth regime and predominantly PRT mechanism [Fig. 3(a)], and high $PM/PMsat$ conditions, i.e., 0.167, which corresponds to linear growth regime and predominantly bimolecular termination mechanism [Fig. 3(c)].²¹ FTIR spectra confirmed that PAS polymer films were successfully synthesized via iCVD under both conditions. A representative FTIR spectrum of the PAS thin films deposited on Si wafer is shown in Fig. S5 in the supplementary material⁴⁸ which is in good agreement with that reported elsewhere. Briefly,^20,21 the polymerization of AS into PAS through radical vinyl polymerization is verified by the absence of peaks corresponding to¸CH and ¸CH₂ bending at ∼900 cm⁻¹ along with the emergence of the sp³ C—H stretching peaks below ∼3000 cm⁻¹ in the PAS spectrum. Also, it is worth noting that, in comparison with AS, the peaks corresponding to the pendent primary amine groups are well preserved in PAS, evidenced by the N—H bending peak at ∼1516 cm⁻¹, the N—H out-of-plane “wagging” peak at ∼825 cm⁻¹, and the peak corresponding to the C—N stretching at ∼1271 cm⁻¹.

To evaluate the thickness profile of the PAS thin coatings as a function of distance (z) down the cylindrical nanopores, we sequentially milled away the predetermined thickness of the PAS-coated AAO nanopores according to the standard curve to obtain samples at z = 0, 100, 250, 500, 1000, and 2200 nm [Fig. 2(c)]. This was done under the assumption that milling of AAO was the rate-determining step and, thus, PAS coating had a negligible effect on the overall IM rate. This is a reasonable assumption because the etch rate of AAO under IM is about half of that of polymer coatings as discussed earlier.

Remarkably, the majority of the pores coated under the $PM/PMsat=0.082$ condition were clogged about 250 nm into the pores [Fig. 3(a), “z = 0.25 μm”], even though those pores look completely open at the top under FESEM [Fig. 3(a), “Top”], contrary to the monotonous decrease in thickness to be expected from previously reported diffusion-reaction theory.¹⁵ Also, by comparing images of “Top” and “z = 0.25 μm” in Fig. 3(a), we notice that when such inverted-cone-shaped voids are present, the SEM images taken at the top surface (which indicate an average pore diameter of 77.9 nm) could miss out on the clogged pores 250 nm down below [compare Fig. 3(a)]. This finding brings into question the validity of simply using top SEM images to estimate the critical pore diameter of nanopores coated via iCVD, which can have important implications for inferring the exclusion size of a nanoporous membrane accurately. As indicated in the FESEM images acquired at “z = 0.25 μm” and “z = 0.5 μm” [Fig. 3(a)], the clogged pores were found to have a distinctively lighter shade compared with open pores, suggesting polymer filling of some of the pores. (In SEM, lighter shade, in general, indicates more electrons collected by the detector, which is often a result of the incident electrons interacting with materials with larger nuclear size, higher molecular density, or lower electron conductivity.³⁶) Furthermore, the majority of pore-clogging occurred within a narrow depth range between z = 0.10 μm and z = 0.5 μm. Such localized pore-clogging was not observed for the sample coated under $PM/PMsat=0.167$⁠.

Hereon, we refer to this pore-clogging in the unexpected depth profile as “necking,” for the resemblance of the resulting pore shape to a neck. For $PM/PMsat=0.167$⁠, again, necking was not as pronounced [Fig. 3(d)], the coating thickness profile in general agreed with what one would expect from the diffusion–reaction model, except for the lack of thickness decline within the initial 100-nm-section of the pore.

Taken together, the necking in coating thickness (most prominent under $PM/PMsat=0.082$⁠) suggests that the fastest deposition rate along the z-direction occurred around 250 nm down the cylindrical nanopores, rather than at the very top of the pore, like previously assumed. Furthermore, this non-conventional variation of thin-film deposition kinetics is less obvious under the higher $PM/PMsat=0.167$⁠. The deposition kinetics will be discussed in detail in Sec. IV C.

Precise and accurate determination of how the kinetics of free radical polymerization vary in the z-direction inside nanopores was not possible before. Our approach joins the robust control in the longitudinal direction afforded by IM, with the high x–y resolution of 4.9 nm/pixel and large sampling capacity afforded by high-resolution SEM, and consequently provides a new capability to study polymerization kinetics under nanoconfinement in a three-dimensional space.

To investigate the deposition kinetics at a specific depth (z) inside nanopores, the depth profiles shown in Fig. 3 were analyzed in the form of two deposition rates, $DRpore(z)$ and $DRnorm(z)$[defined as the ratio of $DRpore(z)$ to $DRflat$]. Specifically, for each $PM/PMsat$ condition, $DRpore(z)$ was obtained through dividing the coating thickness at specified z by the respective deposition time. Note that for $PM/PMsat=0.082$⁠, where substantial pore closure was observed, the effective deposition time for the pore section below where the closure occurred (i.e., z ≥ 0.5 μm) should be shorter than the recorded total deposition time. Nevertheless, we used the total deposition time for calculating $DRpore(z)$ at all depths, which may result in an underestimation of deposition rates for locations with z ≥ 0.5 μm. That is not the case for $PM/PMsat=0.167$ since no pore closure was detected. It is noteworthy that the $DRpore(z)$ results presented here are time-averaged deposition rates. The instant $DRpore(z)$ may decrease as the growing polymer coating shrinks the effective pore diameters over time, mainly due to reduced diffusion of monomers into the pores.

It has been well established that on a flat surface (e.g., Si wafer), the rate of deposition (or polymerization) should increase with increasing $PM/PMsat$⁠.^37,38 In our prior work, we also demonstrated that this trend holds well for the average deposition rate inside nanopores, i.e., higher $PM/PMsat$ results in faster z-averaged $DRpore$ (obtained via a “weight method”).¹⁴ Nonetheless, when evaluating depth-specific $DRpore(z)$⁠, we noticed that this relationship was more complex. The higher $PM/PMsat$ [i.e., 0.167, solid lines, Fig. 4(a)] indeed resulted in faster $DRpore(z)$ within the top 250-nm-section of the nanopores (i.e., z < 250 nm), agreeing with previous observations that deposition rate increases with increasing $PM/PMsat$⁠. Nonetheless, reversal of this relationship seemed to have occurred further down the pore—i.e., for z > 250 nm, $DRpore(z)$ of “$PM/PMsat=0.082$” appears to be greater than that of “$PM/PMsat=0.167$⁠.” One possible explanation for this apparent reversal could be the following: for “$PM/PMsat=0.167$” and z < 250 nm, faster polymerization occurred due to the higher local $PM/PMsat$⁠, which in turn led to faster depletion of monomers vapor locally. This allowed less monomers to proceed to deeper regions of the pore, resulting in lower effective local $PM/PMsat$—and hence lower $DRpore(z)$—deeper down the pore than in the case of “$PM/PMsat=0.082$⁠.” $DRnorm(z)$ emphasizes on the deposition kinetics inside nanopores relative to that on a flat surface [Fig. 4(b)], which has been used to highlight the effect of nanoconfinement on the polymerization kinetics because it is normalized by the rate of deposition on a flat surface.¹⁴ While $PM/PMsat=0.167$ led to a much-reduced rate of deposition under the nanoconfinement, with $DRnorm(z)$ ranging from 0.01 to 0.24, performing iCVD at $PM/PMsat=0.082$ bridged that gap, with the maximum $DRnorm(z)$ being 0.37, over one-third of the deposition rate on a flat surface. Taken together, depth profiling of deposition kinetics revealed that a lower $PM/PMsat$ could in fact lead to a greater rate of deposition deeper down the pores, both in terms of the absolute as well as the relative rates. We hypothesized that this effect was caused by the intricate interactions between (i) $Γ$ of primary radical species on the pore walls upon collision (which has been shown to increase with $PM/PMsat$³⁹) and (ii) amplification/attenuation of effective free radical concentrations under nanoconfinement (denoted $[R⋅]eff$⁠) and its variation in the longitudinal direction. Next, we will derive $Γ$ inside the nanopores (based on the coating thickness profiles shown above), then derive the variation of $[R⋅]eff$ using the theoretical framework discussed earlier, and eventually provide mechanistic insight into the origin of necking and the essential conditions for its occurrence.

The sticking probability of primary radicals (⁠$Γ$⁠)—defined as the probability for a free radical to chemisorb on a substrate (i.e., sticking) per collision—is an important parameter that affects the conformality of polymer coating on 3D structures. Sticking probability inside nanoconfined space, such as nanopores, is poorly understood compared to that in microtrenches,^39,40 mainly due to the lack of a robust approach to assess polymer coating thickness inside nanopores.

Typically, the Knudsen regime is in effect when performing iCVD under nanoconfinement, as indicated by Knudsen number (⁠$Kn$⁠, defined as the ratio of the mean free path to the length scale of the confinement) that is common in the hundreds in this case. As previously shown,^41,42 under the Knudsen regime, $Γ$ inside a cylindrical nanopore can be regressed using the following equation:

where S is the “step coverage,” here defined as the ratio of coating thickness at given depth z to the thickness at the top of the pore [Fig. 5(a)]. We plotted $ln⁡(S)$ against $(z/r)2$ according to Eq. (10) to extract $Γ$⁠. Interestingly, unlike the overall linearity often observed from such plots made in the case of microtrenches, we observed two distinct regimes under both $PM/PMsat$ conditions in the case of nanopores [Fig. 5(b)].

For $PM/PMsat=0.082$⁠, within the first 250 nm from the top of the pore, the step coverage increased with greater z, curiously enough, above unity, due to the aforementioned necking phenomenon. A negative $Γ$ would result when equation Eq. (10) is applied to compute the sticking probability of that region, implying that a fundamentally different mechanism (rather than the simple initiation-limited free radical polymerization) is at play. This is novel for iCVD because this can only occur if enhanced primary radical termination somehow led to decreased deposition rate—a phenomenon rarely observed on flat surfaces or in microtrench systems (further discussion see Sec. IV F). Nevertheless, for depths greater than 250 nm, strong linearity (R² = 0.99) between $ln⁡(S)$ and $(z/r)2$ was observed, giving rise to a $Γ$ value of 7.0 × 10⁻³ with CI95% = (5.3 × 10⁻³, 8.7 × 10⁻³).

For $PM/PMsat=0.167$⁠, two linear regimes with different sticking probabilities were observed, with the transition occurring at around z = 250 nm. The first regime (z = 0–500 nm) corresponds to the top-500-nm-section of the pore, where $Γ$ regressed by applying Eq. (10) turned out to be 4.4 × 10⁻² (CI95% = [3.2 × 10⁻², 5.6 × 10⁻²]). (To ensure the rigor of the regression, we included the last four points—rather than three—of the coating thickness profile when regressing for $Γ$ in the second regime. Thus, the thickness data at z = 250 and 500 nm were included in both regressions.) $Γ$ from the first regime is significantly higher than $Γ$ = 9.4 × 10⁻³ (CI95% = [0, 2.0 × 10⁻²]) obtained from the second regime (z = 250–2200 nm). $Γ$ from the second regime is comparable with $Γ$ ∼3.0 × 10⁻³ for iCVD of PAS over microtrenches (with a width of ∼1 μm and aspect ratio of 8.7) at a much higher $PM/PMsat$ of ∼0.5.²⁰ 

While a clear transition in $Γ$ occurred at the location of necking under $PM/PMsat=0.082$ [around z = 250 nm, see navy blue points, Fig. 5(b)], no such transition was observed under $PM/PMsat=0.167$ [see dark blue points, Fig. 5(b)], probably because necking (if present at all ∼z = 100 nm) was greatly suppressed under the high $PM/PMsat$⁠. Nonetheless, under $PM/PMsat=0.167$⁠, we observed a noticeable “kink” between z = 250 nm and z = 500 nm [indicated by the dashed red and the dashed dark blue regression lines in Fig. 5(b)], whereas this transition was absent among the points corresponding to the low $PM/PMsat$ [navy blue, Fig. 5(b)]. Also, note that $Γ$ for the low and high $PM/PMsat$ conditions were similar (p > 0.05) for all depths greater than 250 nm [Fig. 5(c)], likely a result of the monomer-diffusion-limited condition deep down a nanopore; a $Γ$ of nearly an order of magnitude greater than those was observed under high $PM/PMsat$ (0.167) and near the pore entrance (for z < 500 nm), likely due to the faster monomer diffusion under these conditions and, thus, the higher surface density of monomers.

Based on the observations above, we postulate that the mechanism that underpins the transition of $Γ$ inside a nanopore might be dependent on both $PM/PMsat$ and the effective free radical concentration. Specifically, under $PM/PMsat$ corresponding to a-monolayer-or-greater coverage of a flat surface by monomers (e.g., $PM/PMsat=0.167$⁠), a transition in $Γ$ (with increasing depth into the pore) might have occurred due to the switch from monolayer coverage to less than monolayer coverage; whereas under lower $PM/PMsat$ (e.g., 0.082) where the entire pore is populated with less than a monolayer of monomers throughout, the importance of such monomer surface density (⁠$[M]surf$⁠)-induced transition in $Γ$ could give way to a free radical-induced transition (see discussion later), which dwindles under the high-$[M]surf$ condition. It is important to note that despite the apparent variations in sticking coefficients along the nanopore, it does not invalidate the assumption of a constant sticking coefficient made in the collision-based model. As demonstrated previously,¹⁴ the resulting variation in the collision frequency (due to the difference in sticking probability) was merely 0.02 (with effective relative collision frequency ranging from 0.62 to 0.64), which does not cause significant deviations of the model predictions.

Next, we use the estimates of $Γ$ in nanopores and the theory introduced earlier to investigate the variation of effective free radical concentration $[R⋅]eff$ along z.

As introduced earlier, the incident primary free radicals (⁠$R⋅$⁠) may bounce between the nanopore walls many times before they react away, owing to the high Knudsen number in nanopores under the experimental conditions (⁠$Kn∼372≫10$⁠, see the supplementary material⁴⁸ for details) and the relatively low $Γ$ of $R⋅$ when interacting with pore walls with low coverage of monomers and other reactive derivatives [e.g., when depth is greater than 250 nm, Fig. 5(c)]. Our previous work introduced the parameter $β$ to capture the areal collision frequency in a nanopore relative to that on a flat surface,¹⁴ which was expressed as an average over the entire pore (i.e., averaged over the longitudinal direction and all radical incident angles). Depending on the pore geometry (e.g., diameter, length, and shape) and $Γ$ of $R⋅$ on the pore wall, $β$ can be (i) above unity—meaning that the presence of nanopore amplified the areal collision frequency relative to the bulk case, thus boosting the effective concentration of free radicals, i.e., $[R⋅]eff$⁠, inside nanopores or (ii) below unity—meaning an overall attenuation of $[R⋅]eff$ under nanoconfinement.

To investigate the potential relationship between the observed necking phenomenon and depth-specific local $[R⋅]eff$⁠, we derived a local $β$ for any given depth z inside a nanopore, denoted $β(z)$⁠. We started by mapping the entire $β(z)$ space with regard to a wide range of $Γ$ that could be encountered during iCVD, i.e., 10⁻¹–10⁻⁷, by applying Eq. (9) derived in the “Theory” section, which resulted in Fig. 6. From there, some general trends regarding the behavior of β(z) can be observed: (i) $β(z)$ increases as $Γ$ decreases from 10⁻¹ to 10⁻⁷, consistent with a previous observation that $Γ$ constitutes greater $β$- or z-averaged $β(z)$ and (ii) with a specific $Γ$ value, $β(z)$ falls sharply as z increases, especially near the top of the pores, and gradually tapers off beyond z ∼ 1000 nm. Log transformation of the horizontal axis seems to linearize the curves, suggesting $β(z)∝logz$ (Fig. S6 in the supplementary material).⁴⁸ Although the theoretical implication of this relationship is still unclear, this relationship does provide a facile way to populate the β(z)–z space without intensive numerical computation.

Next, we discuss the variation of β(z) with regard to both z and the experimentally derived $Γ$ under the two $PM/PMsat$ conditions.

For $PM/PMsat=0.082$⁠, the collision-based model predicted that at depth z = 10 nm, β(z) should be between 1.05 (lower bound, corresponding to Γ = 1.0 × 10⁻²) and 1.66 (upper bound, corresponding to Γ = 1.0 × 10⁻³)—or (1.05, 1.66) for short—suggesting that up to 66% increase in $[R⋅]eff$ under nanoconfinement relative to that in bulk may be present at the very top section of the pore, potentially leading to slower polymer growth due to the dominance of primary radical termination.^14,21,30 Note that at z = 10 nm, even the lower bound of β(z) was estimated to be greater than unity, indicating an amplified $[R⋅]eff$ (i.e., $[R⋅]eff>[R⋅]bulk$⁠) at the entrance of the pores compared with that on a flat surface. As the depth increased further, β(z) precipitated sharply, especially for the first 100-nm-section of the pore; recall that this region matches where the unexpected deviation from the monotonous decrease in deposition rate took place (Fig. 4). Next, β(z) fell into the range of (0.56, 1.16), which encompassed β(z) = 1.0 (and hence $[R⋅]eff=[R⋅]bulk$⁠), for z = 250 nm—where fastest $DRpore$ (and “necking”) was observed, likely a result of rapid chain initiation and slow termination;²¹ it became (0.28, 0.86) for z = 2200 nm—the deepest z sampled via IM, and finally (0.21, 0.79) for z = 5000 nm—representing the situation at the bottom of a pore, where the lower rate of chain initiation and, thus, slow rate of deposition occurred. The rate of change in β(z) appears much greater from z = 10 to 200 nm than in the deeper regions; in fact, β(z) appears to reach a plateau beyond z = 1000 nm under all Γ. Interestingly, according to the model, under the Γ estimated for the tert-butoxy—AS system, i.e., 10⁻³–10⁻² [highlighted in yellow in Figs. 6(a) and 4(b)], β(z) plateaued below unity, suggesting an attenuated $[R⋅]eff$ compared with that on a flat surface, which may contribute to the observed low rate of polymerization. Also noteworthy is that all the β(z) values discussed in this section have considered the contributions from both the forward and the backward flux of free radicals (see Fig. 1).

For $PM/PMsat=0.167$⁠, contrary to the abovementioned transition of $[R⋅]eff$ from amplification to attenuation down the pore, $[R⋅]eff$ was predicted to stay attenuated [i.e., β(z) < 1] throughout the entire pore. The root cause of this contrast lies in the first 500 nm [or the first regime identified in Fig. 5(b)], where under the high $PM/PMsat$ condition, the elevated Γ value of 4.4 × 10⁻² [Fig. 5(c)] evidently lowers its corresponding β(z) to that of a higher “Γ bracket” of (10⁻², 10⁻¹). Specifically, at z = 10 nm, β(z) under the high $PM/PMsat$ was found to be between 0.66 (lower bound, corresponding to $Γ=1.0×10-1$⁠) and 1.05 (upper bound, corresponding to $Γ=1.0×10-2$⁠); β(z) decreases further over the rest of the 500-nm range. Interestingly, as a free radical ventured into the second regime for sticking probability (i.e., z > 250 nm), its $Γ$ reduced to 9.4 × 10⁻³ [CI95% = [0, 2.0 × 10⁻²], Fig. 5(c)], which in a sense countered the dwindling of β(z) further down the pore and consequently maintained its β(z) at about the same level of attenuation as that of the first regime.

This renewed collision-based model also provides fresh insights into the relative contribution to radical-wall collision by the forward and the backward radical flux [see Eq. (9)]. Under the current estimation for Γ [i.e., (10⁻³, 10⁻²)], the model predicted that up to ∼22% of β(z) for z < 100 nm might be contributed by radical-wall collisions resulted from the backward radical flux. Although the forward radical flux is still the main contributor to the radical-wall collisions near the entrance (i.e., at least ∼78%), the backward flux nonetheless played an important yet underexplored role, which only becomes more prominent with lower Γ (e.g., the contribution by backward flux may increase to ∼41% at Γ = 10⁻⁷). Clearly, more research is needed to understand the interplay between confinement geometry, free radical flux, and the iCVD kinetics inside nanopores.

The discussion on β(z) above provides the basis for one possible mechanism for the necking phenomenon, which will be the focus of Sec. IV F.

The nanoconfinement-induced amplification of $[R⋅]eff$ could explain the observed necking phenomenon. Due to the amplification of $[R⋅]eff$⁠, within 200 nm of the nanopores, it is much more likely for $[R⋅]$ to be excessively high such that the local termination mechanism becomes dominated by PRT. The deposition rate of iCVD is generally thought to be of zeroth-order with regard to $[R⋅]$ when the initiator (or primary free radical) species can be considered in excess in relation to monomers and growing polymer chains.³⁰ Nevertheless, there has been experimental evidence suggesting that excessively high initiators could lead to reduced deposition rates of both non-crosslinking monomers (e.g., glycidyl methacrylate)⁴³ and crosslinking monomers (e.g., trivinyltrimethylcyclotrisiloxane and hexavinyldisiloxane).⁴⁴ Although the exact mechanism remains unclear, previous work has attributed the diminished deposition rate (DR) to the formation of low molecular weight chains that were initiated and rapidly terminated followed by desorption due to their high volatility or the higher recombination rate of primary radicals⁴⁴—both of which would become more probable at elevated $[R⋅]$⁠. However, this hypothesis has not been validated experimentally due to the challenge of depositing PAS in sufficient quantities for molecular weight determination (e.g., using gel permeation chromatography). Our future work will place a strong emphasis on the characterization of the molecular weight of iCVD PAS, which will likely require novel techniques and/or sample preparation protocols that are beyond the scope of the current report.²¹ 

Based on these initial observations of $[R⋅]$-induced DR reduction, we postulate that due to the nanoconfinement, the high β(z) within the first 200-nm-section of the nanopores could have resulted in elevated $[R⋅]eff$⁠, which in turn led to reduced $DRpore(z)$ at the entrance and thereby contributing to the necking phenomenon [Fig. 7(a)]. The reason why the necking phenomenon was largely absent in the case of higher $PM/PMsat$ (∼0.167) is possibly a combination of the increased sticking probability $Γ$—hence lower $[R⋅]eff$ [due to lower β(z), see Fig. 6]—and longer kinetic chain lengths, hence lower volatility for the surface oligomer species. The latter can be attributed to the increased likelihood for (i) a nascent growing chain to react with a surface-adsorbed monomer (rather than being terminated right away by another primary radical) or (ii) bimolecular chain termination due to the higher surface density of such nascent growing chains [Fig. 7(b)].

According to the collision-based ballistic model for primary free radicals, the amplification of $[R⋅]eff$ is largely contributed by free radicals that entered the nanopores with a very small incident angle $θ$⁠. This is consistent with our earlier finding that under the same $Γ$⁠, $R⋅$ with smaller $θ$ gave rise to greater total collisions (⁠$α$⁠) and areal collision frequency amplification factor (⁠$β$⁠).¹⁴ However, the effect of these free radicals does not propagate very far along the pore wall because of the elevated likelihood of reacting away as they bounce back-and-forth between the walls (solid trajectories in Fig. 7). On the contrary, those that enter with larger incident angles may have a less pronounced yet more extended influence on $[R⋅]eff$ (dashed-line trajectories in Fig. 7), therefore exerting uniform influence on deposition kinetics over the entire span of the pore length. It should be noted, however, that the shift in $θ$ of the free radical population with regard to z is confounded with the change in monomer surface density, the role of which on $Γ$ has been wellestablished.^39,45 It is also plausible that the dominance of radical-wall collisions by the small-$θ$ free radicals, which is largely confined to z < 250 nm, could be an underexplored factor that may explain the distinct regimes observed near pore entrance, i.e., the much higher $Γ$ under $PM/PMsat=0.167$ and at the entrance of the nanopores, and the growth inhibition observed under $PM/PMsat=0.082$⁠. This is because the asymmetric AS molecules are likely to have a preferred orientation when adsorbed on the pore wall, thus presenting the vinyl bonds also at a non-random fashion, which may make the rate constant of initiation and termination dependent on $θ$⁠, and hence z.

We think this necking phenomenon is not unique to the monomer AS; necking has also been observed for iCVD of poly(2-hydroxyethyl methacrylate) in through-pore AAO membranes (nanopores diameter of ∼200 nm, length ∼55 μm, see Fig. S7 in the supplementary material).⁴⁸ One future direction is to examine how the chemical nature of the monomers influences the occurrence of necking. For instance, can we take advantage of this initiator-mediated growth inhibition to confine the thin film growth to specific regions of a nanopore, akin to “sculpting” the polymer coating? As for potential applications in membranes, can the hourglass-shaped pores⁴⁶ resulted from necking serve as mechanically gated channels for separation of nanoparticles, e.g., achieving different size-exclusion thresholds under different transmembrane pressure? Compared with membranes with the selective layer exposed on the surface, this new shape can better protect the active region with more mechanically robust support (e.g., AAO), thus achieving a longer lifespan. Future research should explore both the fundamental and the applied aspects of the necking phenomena.

We demonstrated the feasibility of precise depth profiling of ultrathin polymeric coatings along nanopore walls by using IM and high-resolution FESEM. A non-conventional coating profile termed “necking,” where the fastest deposition rate occurred not at the top of the nanopore (as would be generally predicted by a diffusion–reaction model) but at ∼250 nm down the pore, was uncovered using this novel profiling approach. This necking phenomenon was reversed to the conventional coating profile when $PM/PMsat$⁠, and, hence, the density of the surface-adsorbed monomer was higher near the top surface.

Furthermore, we renewed our collision-based statistical model to enable accounting for the variation in $[R⋅]eff$ as a function of distance along the pore length and the sticking probability. The event of radical recombination in the vapor-phase or other gas-phase reaction events were not considered in the model because of their low probability, which has been demonstrated in previous studies,^31,32 showing that reaction kinetics and activation energy can be fully accounted for by considering only surface reactions. Although vapor-phase reactions that involve monomers are insignificant compared to those on the surface, radical recombination in the vapor phase could occur and its effect on the rate of polymerization has not been well understood because of the extremely high reactivity of free radicals. A widely adopted treatment in iCVD and plasma-enhanced CVD is to neglect the vapor-phase free radical recombination, justified by the low-pressure condition typically used in these processes that favors surface reaction.^33,47 The model suggested a 66% increase of $[R⋅]eff$ at the top 100-nm-section of the nanopores (compared to that of the bulk), coinciding with where diminished local $DRpore$ was observed. This local amplification of $[R⋅]eff$ may have promoted primary radical termination, leading to stunted growth of polymer chains and even potentially volatile R-M₁-R species that contribute to reduced local $DRpore$⁠. Although the exact mechanism by which higher $[R⋅]eff$ at the top section of nanopores reduces $DRpore$ remains speculative and warrants further research, the evidence presented here seems to suggest two necessary conditions for the initiator-mediated growth inhibition to occur: (i) less than monomer layer coverage by active monomer species and (ii) excessively high $[R⋅]eff$⁠, achieved through large β(z) and/or high $[R⋅]$ in the bulk.

These results have shed new light on the different kinetic regimes of iCVD under nanoconfinement, especially the potential presence of drastic spatial variation in a connected nanoconfined space. A better understanding of these phenomena will not only improve our ability to produce conformal coatings over high-aspect-ratio nanoscale features but also enable advanced coating profile engineering, for instance, placing check valves in nanopores.

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 2144171 to R.Y. and through Award No. USDA NIFA 2021-67034-35040 to Y.C. The authors also want to acknowledge the Samuel C. Fleming Family Graduate Fellowship for the support granted to A.K. Finally, the authors want to acknowledge Cornell NanoScale Facility (Grant No. NNCI-2025233) and Cornell Center for Materials Research (Grant No. DMR-1719875) for providing the facilities required for conducting this research. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.

The authors have no conflicts to disclose.

Y.C. and A.K. contributed equally to this work.

The data that support the findings of this study are available within the article and its supplementary material.

 Dr. Yifan Cheng received his joint B.Sc. degree in Food Science from Shanghai Jiao Tong University (China) and Cornell University (USA) with distinctions. He then remained at Cornell to pursue a Ph.D. with Professor Carmen I. Moraru, investigating bacterial attachment to material surfaces with precisely controlled nanotopography, with a focus on developing predictive models for elucidating bacteria-surface interactions. He is currently a U.S. Department of Agriculture (USDA) National Institute of Food and Agriculture (NIFA) postdoctoral research fellow working with Professor Rong Yang on vapor deposition of functional polymer thin films within nanoconfined structures, which have important applications in advanced membrane separations and enzymatic membrane reactors for food- and bio-processing.

 Alexandra Khlyustova received her bachelor's degree in Chemical Engineering from the University of Minnesota, Twin Cities in 2018. Currently, she is a Ph.D. student in the research group of Assistant Professor Rong Yang at Cornell University. Her research has been centered on studying the polymerization reaction kinetics under nanoconfinement, the development of environmentally friendly antifouling coatings, bacteria-surface interactions, and enzyme immobilization.

 Dr. Rong Yang is an assistant professor in the Smith School of Chemical and Biomolecular Engineering at Cornell University. She received her B.S. in Chemical Engineering in 2009 from the Tsinghua University in Beijing, M.S. Chemical Engineering Practice (MSCEP) from Massachusetts Institute of Technology (MIT) in 2012, and Ph.D. in Chemical Engineering from MIT in 2014. From 2014 to 2016, she was a postdoctoral fellow at Boston Children’s Hospital and Harvard Medical School, where she later became an assistant professor before joining Cornell in July 2019. Her research lies at the intersection of chemical engineering, material science, and biomedical engineering, with a focus on the molecular design of functional polymers and nanomaterials, with applications in water purification, agriculture, and infectious disease treatment. Her work has been recognized by the National Science Foundation (NSF) CAREER Award, the National Institutes of Health (NIH) Pathway to Independence Award, the Innovators Under 35 China Award by the MIT Technology Review, the Child Health Research Award from the Hood Foundation, the Outstanding Research Award by the International Society for Otitis Media, and the Mr. & Mrs. Richard F. Tucker Teaching Award at Cornell University, among others.