Selective filling of n-hexane in a tight nanopore

Molecular sieving may occur when two molecules compete for a nanopore. In nearly all known examples, the nanopore is larger than the molecule that selectively enters the pore. Here, we experimentally demonstrate the ability of single-wall carbon nanotubes with a van der Waals pore size of 0.42 nm to separate n-hexane from cyclohexane—despite the fact that both molecules have kinetic diameters larger than the rigid nanopore. This unexpected finding challenges our current understanding of nanopore selectivity and how molecules may enter a tight channel. Ab initio molecular dynamics simulations reveal that n-hexane molecules stretch by nearly 11.2% inside the nanotube pore. Although at a relatively low probability (28.5% overall), the stretched state of n-hexane does exist in the bulk solution, allowing the molecule to enter the tight pore even at room temperature. These insights open up opportunities to engineer nanopore selectivity based on the molecular degrees of freedom.


SWCNTs based on hyperspectral imaging
To estimate the number of filled n-hexane molecules, we have to consider the diffraction limit.
The pixel size ( 160 nm) is smaller than the diffraction limit, which stands at  580 nm in our case (calculated form λ 2NA , where λ is the wavelength of the 980 nm emission from (6,5)-SWCNT, and NA = 0.85 is the numerical aperture of the objective used). For this work we used long nanotubes (> 3 μm) to achieve sufficient spatial resolution of PL imaging. It is not possible to completely deconvolute the complexity formed by so many emitting nanotube segments when they are partially filled. However, we may estimate the number of n-hexane molecules in each pixel based on the assumption that strain and PL shift correlation is linear.
In the case of n-hexane filling, the major cause of the photoluminescence (PL) shift is the strain, which is described by Yang's model 1 and other literature reports 2 . The PL shift (ΔE) is observed to be linearly proportional to the strain 3 . Due to the single-file packing, we can consider the system as one dimensional such that the strain is linearly correlated with the number of filled molecules. If this assumption holds, the strain and resulting PL shift is then directly proportional to the number of n-hexane molecules within the nanotube pore.
By considering a linear scaling of the PL peak shift for the empty (0 %) up to the fully filled (100 %) nanotubes, we can obtain the percentage (P) of the nanotube filled with n-hexane from the E11 peak wavelength by the following relation: where E11 is the PL emission peak wavelength in nm, k and b are two constants due to the linear relationship of strain and resulting PL. We then substitute (E11 = 982, P = 0%) and (E11 = 998, P = 100%) into the equation to obtain k (= 0.0625 and b (= 61.375) for this case.When one n-hexane fills inside a nanotube segment, the length of this segment is roughly equal to the length of the stretched n-hexane (1.14 nm, based on the atom center-to-center length of n-hexane, 0.90 nm, plus the van der Waal radii of the two hydrogen atoms, 2 x 0.12 nm = 0.24 nm). Based on these, the numbers of n-hexane can be derived. For example, for pixels that have an E11 peak of 990 nm in Figure 2b, we can calculate the percent filling of the nanotube is 50% n-hexane by plugging in E11 = 990 nm. We can further derive that on average there are  0.43 hexane molecules per nanometer length of (6,5)-SWCNT.
We note that the peak positions (Figure 2a In Figure 4, we show that the n-hexane can be removed from the mixture by (6,5)-SWCNTs.
To estimate the filled pore volume, we assume all the SWCNTs are (6,5)-SWCNTs, though we note the nanotube raw material is synthesized as a mixture of different chiralities, with (6,5)-SWCNTs being the major component. We also considered the SWCNT purity ( 77.1 mass % based on the manufacturer's product specs).
Adsorption of n-hexane should result in the n-hexane molecules packing single-file inside the (6,5)-SWCNTs due to the size limitation. Therefore, we can estimate the percentage of the pore volume filled with n-hexane based on the length of the molecule and that of the SWCNTs. Since only stretched n-hexane can enter (6,5)-SWCNTs, the molecular configuration that fits the nanotube has a length of 1.14 nm. Therefore, we can estimate when 100 % filled, these nanotubes can densely encapsulate at least 2.07 μmol/mL, 3.68 μmol/mL, 7.52 μmol/mL of n-hexane inside 2.51 mg/mL, 4.47 mg/mL, 9.13 mg/mL (6,5)-SWCNTs, respectively. The actual amount of nhexane removed was experimentally determined to be 1.56 μmol/mL, 2.63 μmol/mL, 3.92 μmol/mL, respectively ( Figure 4). From the ratios, we obtained the percentage of the filled space to range from 52% to 82 % for the experiments performed here. These data suggest that the molecules are loosely packed inside the nanotube pore.

Supplementary Note 3: Raman spectroscopy
We conducted Raman spectroscopy to further investigate the effect of SWCNT strain. The D peak of SWCNTs, which originate from the structural disorder, are commonly located at ≈ 1355 cm -1 , while G peaks are at ≈ 1585 cm -1 and represent the ordered graphitic structure. Supplementary   Figure1a shows the G and D peaks of the Raman spectra from the end-opened and end-capped nanotubes. After the end opening process, the D/G ratio slightly increases from 0.021 to 0.032.
This low increase of disorder suggests the amount of nanotube oxidation during the opening process was small. Furthermore, such oxidative defects are known to quench the SWCNT photoluminescence (PL). 5 However, we observed bright PL from the nanotubes (

Supplementary Note 4: Grid size used in simulation
To have more confidence on the inferences we might have made from the 1x1x4 grid, we performed additional simulations to compare the energies obtained from using a finer grid. We find that the energies obtained from the 4x4x1, 2x2x2 and 4x4x4 grid differ from the values obtained from the 1x1x4 by around 0.005 eV (Supplementary Table 4 √3l C-C π √n 2 +m 2 +mn based on wrapping a graphene sheet with a C-C bond distance lC-C of 1.44 Å.

Supplementary Figure 1. Raman spectra of n-hexane-filled (6,5)-SWCNTs in comparison with H 2 O-filled and end-capped controls. a,
Raman spectra for end-opened SWCNTs (black curve) and end-capped SWCNTs (red curve). b, Raman spectra of (6,5)-enriched SWCNTs that are filled with n-hexane (black curve) and H2O (red curve). c, RBMs of the n-hexane-filled and H2O-filled (6,5)-SWCNTs. Note that all the spectra are normalized to the G or RBM peak intensity. Note: Raman spectra were collected under 532 nm laser excitation. For each nanotube, the PL peak position is plotted as a false color image along with the intensity image. Scale bars represent 500 nm. Note that the peak position is from spectral fitting of each data set with a Gaussian function.

Supplementary Figure 4. Ensemble PL spectra of end-capped and end-opened SWCNTs that
were incubated with n-hexane or cyclohexane. a, PL spectra and b, schematic of end-opened (green) and end-capped (6,5)-SWCNTs (red) that were incubated with n-hexane. c, PL spectra and d, schematic of end-capped (6,5)-SWCNTs that were incubated with n-hexane (light red) and cyclohexane (dark red). e, PL spectra and f, schematic of end-capped (8,4)-SWCNTs that were incubated in n-hexane (light red) and cyclohexane (dark red). Note that the spectra are normalized at the peak intensity and offset for clarity.
Supplementary Figure 6. Response of nanotube photoluminescence to filling molecules. Excitation-emission PL maps of SWCNTs that are incubated with a, cyclohexane and b, n-hexane. Note that the black dots mark the PL peak position of water-filled SWCNTs. The PL intensity beyond 1060 nm is plotted at 1.5× scale to make the minority nanotube species visible. c, Peak position of the E11 PL for SWCNTs incubated with cyclohexane (red) or n-hexane (black), and those filled with water (blue) or empty (green). The arrows indicate the direction of the spectral shift between water and alkane-filled species.