Titania (TiO2) nanomaterials have found profound applications in our daily lives, ranging from catalysis to paints, energy storage, sensors, drug delivery, etc. 1,2 The more oxygen rich family of titanates, with layered titanates (LTs) being of particular interest, have shown a similar range of applications. [3][4][5] LTs, akin the materials discussed herein, require an interlayer cation to balance the additional negative charge provided by the additional oxygen in the backbone. 6,7 Titanium oxide nanoparticles and nanosheets have been extensively investigated, while one-dimensional (1D) titania received less attention. 6,[8][9][10] The reported 1D morphologies of titania and LTs include nanotubes 11 , nanorods 12 , and nanoribbons 13 , and they can be synthesized by various methods primarily requiring hydrothermal environments, various additives, or extensive post-processing. 11,12,14,15 Most recently, a simple, one-pot solution-based method was developed to synthesize subnm, 1D LT filaments as shown schematically in Scheme 1A. 16,17 These nanofilaments are hereafter labelled 1D lepidocrocite or, 1DL. Their synthesis relies on the dissolution of Ti-containing precursors in a high pH environment. For example, concentrated (25% w/w in water) tetramethylammonium hydroxide (TMAOH) is used to supply both the high pH and large cation as a templating agent 17 . Alkali bases, under the same conditions, do not result in a similar product 18 .
Note, that in the literature, there are many reports of 1D titania or LTs. [10][11][12]19,20 What sets this work apart is that 1DLs are the first to see a major increase in band gap energy, as a result of quantum confinement along two dimensions. 21 Many of the promising applications of 1DLs, such as adsorptive [22][23][24][25] and photocatalytic 22,26 properties, are associated with their high specific surface areas and the ultra-thin primary filament structure. Theoretically, one gram of 1DL spans 600 million kilometers and covers ≈ 500 m 2 .
Based on the processing method, both porous mesoscale particles 24 or an extremely stable colloidal suspension can be obtained 27 . Much of the work on 1DLs, including the results presented herein, focus on the 1DL colloidal suspension. During early work, the cross-section of a 1DL nanofilament building block was assumed as 0.5 x 0.7 nm 17 . The 0.5 nm dimension is unimpeachable since it is based on X-ray diffraction (XRD) patterns and high-resolution transmission electron microscope, HRTEM, micrographs 17,27,28 . The 0.7 nm dimension, however, has been more speculative and simply based on the shape isotropy of the 1DLs in HRTEM images.
Upon drying, lateral aggregation of 1DL occurs, and the 1DLs merge and form 2D layered structures based on XRD, with the layer normal being identified as the [0k0] direction. Scheme 1A,B shows schematic representations of 1DL and 2D structures viewed from different crystallographic axes. It follows that a major goal of this work is retaining the 1D nature of the primary structure in the solid-state is scientifically intriguing and could be technologically of high impact. Polymers, including natural and synthetic macromolecules, have been routinely used to modify nanoparticle surfaces for dispersion and assembly purposes. 29,30 For example, polymers can be chemically grafted onto nanoparticle surfaces to form polymer brushes. 29,31,32 They can also wrap onto 1D nanotube or nanowire surfaces via physical interaction. 29,31,33 We hypothesize that a polymer coating on the 1DL nanofilament in aqueous solution could sterically prevent the interfilament merging (Scheme 1C).
In this work, bPEI was chosen to form the polymer coating on 1DL nanofilaments because it is a water soluble polymer and the branched architecture increases the primary amine content, enabling strong and efficient interaction with the titania nanoparticle surfaces. 34 The main variable used was the polymer to 1DL weight ratio. Our results show that ordered bPEI-1DL hybrids can be readily formed using solution blending. The bPEI molecules effectively interact with the 1DL surfaces, arresting their transition to a 2D layered structure. More interestingly, upon drying, these bPEI-coated 1DLs self-assemble into hybrid columnar hexagonal (Col hex ) liquid crystalline (LCs) phases, with an average primary 1DL diameter filament of ~ 0.6 nm. The inter-filament distance can be readily tuned by varying the bPEI to 1DL ratio. The structural evolution from 1D to 2D, or lack thereof, was systematically investigated.
The hybrids were prepared by mixing a 1DL-water suspension and an aqueous PEI solution at precalculated mass ratios. The resulting mixtures were then poured into petri dishes, and solid films were formed as the solvent evaporated. The bPEI to 1DL mass ratio, m, was varied from 0 to 19, and m = 0 indicates neat 1DL. Henceforth, the composite samples are denoted as mbPEI-1DL. Fig. 1A presents typical, low 2 angles, XRD patterns of a neat 1DL along with 0.1bPEI-1DL and 0.2bPEI-1DL. The XRD pattern has characteristic diffraction peaks at 2θ of 7.69°, 15.44°, and 23.22°, following a ratio of 1:2:3 (black arrows in Fig. 1A). This suggests that the packing of the neat 1DL is 2D with an inter-layer distance of 1.15 nm. The XRD patterns of 0.1bPEI-1DL and pristine 1DL are similar, showing multiple diffraction peaks with 2θ ratios of 1:2:3, confirming the 2D structure in 0.1bPEI-1DL as well. Note that the main diffraction peak of 0.1bPEI-1DL slightly downshifts from 7.71° (d-spacing of 1.146 nm) to 7.65° (d-spacing of 1.16 nm) and becomes asymmetric with stronger intensity developed on the peak's low angle shoulder. This shoulder is stronger in the 0.2bPEI-1DL XRD pattern (bottom pattern in The XRD pattern of the 0.5bPEI-1DL sample (Fig. 1B), is significantly different from Fig.
1A. Here a series of diffraction peaks are observed at the 2θ angles of 5.61°, 9.71°, 11.22°, and their relative ratios are ~ 1:√3:2. Relatively weak scattering at ~ 14.84°, and 16.83 can also be seen, and their relative ratios to the primary peak are ~ 1: √7 :3. This pattern represents a characteristic 2D hexagonal packing, and the diffraction peaks can be assigned as ( 01), ( 11), ( 20), ( 21) and (30), respectively. The structure can, therefore, be identified as a hexagonal columnar (Col hex ) LC phase, where polymer-coated 1DLs pack into a 2D hexagonal lattice. Such Col hex phases are often observed in small molar mass discotic LCs and polymer LCs. [35][36][37][38][39] In the present case, the polymer molecules wrap the 1DLs, and self-assemble into a hexagonal packing. Based on the (10) d-spacing of 1.44 nm (from 2θ = 5.61°), the 2D hexagonal unit cell dimension a hex can be calculated as 1.66 nm. Inset in Fig. 1B is a schematic of the Col hex phase viewed along the hexagonal axis. Here the inter-filament space is occupied by bPEI (not shown for clarity). Since the 1DLs are coated with bPEI, it is reasonable to assume that they are axially symmetric, i.e., the in-plane orientation of the 1DL in the hexagonal lattice is random, as indicated in the scheme. Note that individual 1DLs are 1D crystals of TiO6 octahedra, as shown in Scheme 1A. 24 Therefore, the 0.5bPEI-1DL structure is hierarchical, comprising an inter-filament Col hex packing at the 1-2 nm length (inset in Fig. 1B) scale and an intra-filament 1D crystalline structure with a period of 0.38 nm, which is a lattice parameter of the 1DLs. 28 Since the original 1DL samples contained residual TMAOH, thermogravimetric analysis (TGA) was conducted to estimate the solid content (Fig. S1). The TMAOH content in pristine 1DL is ~ 9.7 wt.%, and the TMAOH is assumed to be retained in the final hybrid film since the solution blending/evaporation method was utilized to prepare the sample. The organic-toinorganic phase ratio in the 0.5bPEI-1DL therefore can be estimated to be (0.5+0.097)/(1-0.097) = 0.66. Assuming the bPEI and 1DL densities are 1.03 g/ml and 3.96 g/ml, respectively, the volume ratio can be estimated to be ϕ = vorg/vin = 2.54. The 1DL density was estimated based on the DFT-obtained 1DL structure and is similar to the density of anatase 28 Assuming a round crosssection of 1DLs, the 1DL filament diameter, d1DL, and the bPEI layer thickness between the 1DL, dPEI, can be calculated based on
and 𝑑 𝑃𝐸𝐼 = 𝑎 ℎ𝑒𝑥 -𝑑 1𝐷𝐿 (eq. 2).
In the 0.5bPEI-1DL sample, 𝑎 ℎ𝑒𝑥 = 1.66 nm, we obtain a d1DL of 0.64 nm and dPEI of 1.02 nm (see inset Fig. 1B and Table 1). The d1DL of 0. 64 nm is consistent with the 0.5x0.7 nm 2 crosssectional dimension based on DFT calculations.
At this juncture it is instructive to summarize our DFT calculations. Since the 1DL structure is that of lepidocrocite, they must be comprised of edge-sharing TiO6 octahedra. It follows that their width in the c-direction has to be multiples of these octahedra, which begs the question: Is the width comprised of 2 or 3 TiO6 octahedra? The DFT calculations yield values of 0.6 and 0.9 for 2 and 3 TiO6 structures, respectively. Based on the totality of the results shown herein, there is little doubt that the answer is 2. This is a crucial result that cannot be emphasized enough since it unambiguously sets a lower limit on the number of TiO6 octahedra along the c-direction to be 2.
The 1DLs cross-sections are thus comprised of 2x2 TiO6 octahedra ≈ 0.6x0.6 nm 2 in cross-section.
Furthermore, since we assume the 1DLs to be axially symmetric in the lattice and Col hex is centrosymmetric (P6mm space group), we can estimate the electron density map using the XRD pattern shown in Fig. 1B, without detailed phase information (see SI for detailed procedure). 40,41 The hexagonal symmetry of the 1DLs can be reconstructed, as shown in Fig. 1C. The high electron density region, attributed to 1DL, is approximated 0.6 nm in diameter (see Fig. S2), which is consistent with the density estimation results presented in Table 1. A top view of a DFT-obtained 1DL cross-section is shown as a small inset in center of Fig. 1C. Given the several simplifying assumptions made to generate Fig. 1C, the match has to be considered excellent.
These observations confirm our conjecture that bPEI molecules coat individual 1DLs and arrest the 1D-2D transition previously observed. In Fig. 1D, we show the reconstructed electron density map of neat 1DL based on the strongest layer scattering peaks. The layer thickness is 0.53 nm, which is consistent with the TiO2 distance along the b axis. The organic layer thickness therefore is 0.62 nm. One layer of DFT-obtained 2D lepidocrocite structure is included in Fig. 1D to demonstrate the consistent TiO2 layer thickness obtained from the electron density reconstruction and the simulation. Table 1 summarizes the characteristic Col hex dimension, d10, as a function of m. Also listed are the 1DL dimensions, d1DL, obtained from d10 (column 9 in Table 1). As noted above the primary filament thickness or 'diameter' is ~ 0.6 nm. To further support this result in real space, atomic force microscopy (AFM) was utilized. Neat 1DL and 0.5bPEI-1DL solutions were spun cast onto glass slides for AFM imaging. The fast spin coating process was utilized to avoid the 1D-2D transition during sample preparation. As shown in Figure 1E,F, the thinnest filament height of 1DL and 0.5bPEI-1DL is 0.8 and 1.5 nm, respectively. The 0.8 nm thickness, rather than 0.6 nm, is most probably due to the coating of TMAOH on the 1DL surfaces, and the increased size to 1.5 nm in 0.5bPEI-1DL is attributed to the bPEI coating. These results are, again, consistent with the Col hex structural dimensions determined from the XRD results as shown in Table 1, further confirming that the polymer wrapping did significantly alter the 1DL self-assembly pathways.
As the Col hex was formed by the bPEI wrapping around the 1DLs, we further hypothesized that the structure dimension can be tuned by controlling m. To this end, a series of samples, with m up to 19, were prepared. Figure 2A shows the XRD results for 0.5, 0.8, 0.9, 1.2 and 1.5bPEI-1DL samples. Similar multi-diffraction peaks can be seen in all these samples, with the main peaks gradually downshifting with increases in bPEI content. Detailed analysis confirms that all the patterns follow a ~ 1:√3:2: √7:3 ratio, suggesting that they are Col hex structures. The d-spacings of these diffraction peaks are listed in Table 1, along with their indices following the Col hex structure. As m increases from 0.5 to 1.5, d( 10) increases from 1.437 nm to 2.48 nm, and the unit cell dimension, 𝑎 ℎ𝑒𝑥 , increases from 1.66 nm to 2.86 nm (Fig. 2B). Using Eqs. 1 and 2, d1DL and dPEI for all the samples can be estimated. The d1DL values are approximately 0.64, 0.72, 0.83, 0.80, and 0.83 nm, while dPEI is 1.02, 1.40, 1.71, 1.89, and 2.17 nm, respectively (Table 1). The 1DL filament size increases slightly -from 0.6 nm to 0.83 nm -while the inter-1DL distance doubles as m increases from 0.5 to 1.5. Fig. S3 shows the reconstructed electron density map of the 1.5bPEI-1DL sample. Not surprisingly, the structure is similar to that shown in Fig. 1C.
Based on the full width of half maximum (FWHM) of the (10) diffraction peaks, the crystallite correlation size, ξ, can be estimated using Scherrer equation, viz. 𝜉 = (𝐾𝜆)/(𝛽 cos 𝜃), where K is the shape factor, 𝜆 is the X-ray wavelength, and 𝛽 is the FWHM. The (10) correlation lengths, ξ (10), are listed in Table 1, along with the correlation units n = ξ(10) /d (10). In all Col hex structures, the ξ(10) value gradually increases from 2.6 nm to 5.0 nm as m increases from 0.5 to 1.5.
However, the correlation units n maintains approximately 2, indicating the relatively poor ordering.
To compare, in the 0.1bPEI-1DL samples where the 2D structure was observed, ξ was estimated to be 8.02 nm, and n ~ 6.9, indicating that the 2D structure maintains a longer-range order.
The structural evolution with increased bPEI contents was followed using SEM imaging, shown in Figs. 2C-J. The apparent stacking of 2D sheets is seen in neat 1DL (Fig. 2C,D) and are consistent with previous reports. 24 The sheets are parallel to the film surface, and there are thin fibrils at the edge of the tips (arrows in Fig. 2C,D), suggesting sheet formation is likely related to the aggregation of filaments. Similar 2D sheets are clear in 0.1bPEI-1DL (Figs. 2E,F) samples, but absent in the 0.5bPEI-1DL (Fig. 2G,H) and 0.8bPEI-1DL (Fig. 2I,J) samples. In the 0.5bPEI-1DL sample, a layer of coating appears on the film surface, and in 0.8bPEI-1DL, the image seems formed by 1D materials coated with polymers, and the film is less dense. The SEM observations, therefore, further confirm the arrest of 2D structure formation in 0.5bPEI-1DL and 0.8bPEI-1DL.
The morphological features of these hybrid Col hex solids were further studied using polarized light microscopy (PLM). Figure 3A shows, from left to right, respectively, typical PLM images of samples 0.1PEI-1DL, 0.5bPEI-1DL, 1.5bPEI-1DL and 5bPEI-1DL. Images for the complete sample set can be found in Fig. S4. Referring to Fig. 3A, the 0.1PEI-1DL sample (leftmost) shows strong birefringence from both the 1DL crystals and the 2D structure. Note that in the LC terminology, the 2D structure can be viewed as a smectic phase. The LC texture does not change significantly in 0.5bPEI-1DL when the materials enter the Col hex phase region, while it becomes significantly weaker in the 1.5PEI-1DL samples, which is attributed to the high polymer content (87.1 vol.%). When the bPEI content is further increased in 5bPEI-1DL (95.6 vol.%), birefringence completely disappears, suggesting an isotropic phase. The formation of the latter is confirmed by XRD patterns, shown in Fig. 3B, for the 5bPEI-1DL and 19bPEI-1DL samples. The diffraction pattern shows a broad hump at 2θ angles of ~ 5°. The broad 2θ range of the scattering hump and the lack of high-order diffraction peaks suggest that the 1DLs in these two samples are disordered, consistent with the PLM observation (Fig. S4). This is not surprising since the volume fraction of 1DLs in these composites, 4.4 vol.% and 1.2 vol.%, respectively, are quite low.
Figure 3C summarizes the structural evolution of the mbPEI-1DLs hybrid samples. First, when m is 0.1 and 0.2 (Fig. 1A), a 2D structure is seen, and the layer spacing remains relatively constant. Secondly, when m is 0.5 -1.5, a Col hex structure is formed, and the hexagonal dimension gradually increases with m. Note that since the material is formed by coating inorganic 1DLs with polymers, it can be characterized as hybrid inorganic/organic solid with a Col hex LC symmetry.
Solid "liquid crystals" have been conventionally discussed in biomolecules such as DNA and rigid polymers. 42 The bPEI-1DL hybrid present a new hybrid LC solid with a Col hex structure. Finally, increasing m to 5 and 19 leads to an isotropic phase where no clear 1DLs order is observed.
We have successfully utilized bPEI to coat ultra-thin 1D sub-nm filaments to arrest the spontaneous 1D-2D transition. As the bPEI to 1DL mass ratio increases from 0.1 to 19, the bPEI-1DL hybrids go from a 2D structure to a Col hex LC, before entering an isotropic phase. The Col hex lattice dimension can be tuned by the mass ratio, varying from 1. 66 nm in 0.5bPEI-1DL to 3.00 nm in 1.5 bPEI-1DL. While the lattice parameter doubled from 0.5bPEI-1DL to1.5 bPEI-1DL, the average 1DL diameter increased moderately from 0.64 nm to 0.83 nm, and the (10) correlation units remained at ~2. The isotropic phase was observed when the bPEI to 1DL mass ratio exceeded 5. The polymer wrapping approach confirms the true 1D nature of the 1DLs, and these hierarchically ordered bPEI-1DL hybrids could find applications such as energy storage, water remediation, C capture, and catalysis, among others. Lastly, when our DFT calculations are compared to the results obtained herein, we can, for the first time, confidently conclude that the minimum cross-section of the 1DLs is comprised of 2x2 edge-sharing TiO6 octahedra.
Branched polyethyleneimine (bPEI, Mw = 25 kDa) was purchased from Sigma Aldrich. 1DLs were synthesized using a recently developed one-pot solution-based method detailed in the supporting information.
bPEI-1DL nanocomposite samples were prepared by mixing bPEI and 1DLs in deionized, DI, water at precalculated mass ratios. The 1DL suspension was bath-sonicated for 1 min and then further diluted to a concentration of 2 g/L (1DL to water) before being sonicated again for 1 min. calculated from the neat 1DL XRD pattern in (A). (E, F) AFM height images of neat 1DLs and 0.5bPEI-1DLs. Height profiles suggest the thicknesses of the filaments is ~ 0.8 nm and 1.8 nm, respectively.