2D polymers under the microscope 

July 08, 2022 - The appropriate choice of incident electron energy plays a crucial role in achieving high sample resolution. An international team of researchers from Germany, China and Korea has now analyzed for the first time the optimal accelerating voltage for the quantitative description of the intermediate and short-range order in crystalline and amorphous organic 2D thin films.

The team shows that the appropriate selection of incident electron energy plays a critical role in narrowing the gap between the achievable resolution in the image and the instrumental limit. Using a wide range of tested electron accelerating voltages (300 kV, 200 kV, 120 kV, and 80 kV), the team found that the highest resolution in the HRTEM image is achieved at 120 kV, 1.9 Å. The increased image resolution and improved image contrast at 120 kV enabled the detection of functional groups at the pore interfaces and were also applied to a 2D amorphous organic material.

From organic field-effect transistors (OFETs) to organic solar cells, from gas filtration to catalysis, organic 2D crystals such as 2D polymers and their layer-stacked structures of covalent organic 2D frameworks (COFs) are unleashing their potential in a wide range of novel applications1,2. In the various research areas, structure elucidation is usually the key to a better understanding of structure-function correlations. Therefore, the study of the internal structure of 2D organic crystals down to the atomic scale has been a long-standing goal of materials scientists. For example, one of the intriguing properties of 2D polymers and 2D COFs is the ability to shape the pore interfaces3. Through direct polycondensation or pore surface engineering, selected side groups have been rationally incorporated into the 2D polymer networks to enable functions such as heterogeneous catalysis, proton/metal ion transport, energy storage, and gas adsorption3. In addition, porosity can be fine-tuned by incorporating side groups with different physical sizes without altering the skeletal structure4. However, despite advances in material design, accurate characterization of pore interfaces remains a challenging task. Apart from highly crystalline 2D organic crystals, structural understanding of amorphous 2D organic materials is another major challenge due to the lack of appropriate characterization techniques.

Aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM) allows direct imaging of atomic structures with sub-Ångstrom resolution5,6,7. However, electron irradiation damage often leads to instantaneous decay of the molecular network during the imaging process. Therefore, the achievable imaging resolution for organic crystals is severely limited by the stability of the samples, regardless of the optical performance of the TEMs. The lack of resolution precludes visualization of local structures such as lattice defects and grain boundaries10,11 or sensitive features such as side groups/chains on the framework skeleton3. For amorphous organic 2D materials, the extent of Bragg scattering is much lower due to the lack of long-range order, resulting in a decrease in the signal-to-noise ratio and thus the visibility of the images. For amorphous inorganic 2D materials, this problem can be circumvented by significantly increasing the electron fluence to achieve sufficient image contrast13,15. However, this strategy is not practical for imaging organic amorphous 2D materials due to the severe damage caused by electron irradiation.

In the last decades, several experimental techniques have been developed to obtain high-resolution information from organic crystalline 3D materials. In the most commonly used technique, the low-dose approach, the applied electron fluence is limited below a critical value16. Structural information can then be extracted without significant irradiation damage. In combination with direct electron detectors, a high signal-to-noise ratio can be achieved even at extremely low electron fluence17. Another effective way to achieve better image resolution is to limit the damage process. For example, sample vitrification19 and/or encapsulation21 could impede atomic diffusion after bond cleavage, facilitating bond re-formation and increasing the lifetime of the sample under electron bombardment.

Although high-resolution imaging of inorganic 2D materials could benefit significantly by limiting the electron energy to below 80 keV6,7 the rare TEM studies of organic 2D crystals are still performed with 300 keV electrons8. Therefore, exploration of the lower voltage range remains scarce. The use of high accelerating voltages is based on the fact that radiolysis (i.e., inelastic damage) is predominant in organic materials24. Since the inelastic scattering cross section ?i is proportional to 1/?2 (? = v/c, v: electron velocity, c: speed of light), a higher voltage is beneficial to reduce radiolysis. In conventional bulk samples with large thickness, the secondary electrons lead to a cascade of radiolysis events26. Therefore, suppression of secondary electrons at high voltage was one of the main objectives. An increase in electron energy leads to a decrease in the elastic scattering cross section ?e, which is also proportional to 1/?2. However, the ratio between elastic and inelastic scattering cross section (?e/?i) decreases logarithmically with increasing incident electron energy27. Recently, Russo and co-workers have shown that a 25% increase in ?e/?i can be achieved below 100 kV compared to conventional 300 kV28. Since elastically scattered electrons carry the structural information, an increase in ?e/?i translates into a gain in structural information per unit damage28. Due to the small thickness of 2D organic crystals, the improved efficiency of electron utilization may eventually surpass the deleterious effects of radiolysis damage (especially from secondary electrons). This has inspired us to reconsider the choice of accelerating voltage for imaging thin 2D polymer films.

In this work, we perform systematic investigations to determine the optimal accelerating voltage for high-resolution imaging of two highly crystalline imine-based 2D polymer thin films (thickness up to 60 nm). The optimization considers the critical fluence and the fraction of elastically scattered electrons under a wide range of electron energies (300 keV, 200 keV, 120 keV, 80 keV). Then, the AC-HRTEM is performed at the optimal accelerating voltage to achieve improved image resolution and contrast for 2D polymers and 2D amorphous organic materials.

Determination of the optimal electron accelerating voltage for 2D polymers

Figure 1a shows the structural models of 2D-PI-BPDA and 2D-PI-DhTPA derived by density functional theory (DFTB) calculations. The selected area electron diffraction (SAED) patterns clearly show the high crystallinity of both samples and the measured lattice parameters of 30 Å (2D-PI-BPDA) and 25 Å (2D-PI-DhTPA). To evaluate the effectiveness of different electron energies, it is necessary to determine the key factors, i.e., the critical fluence and the efficiency of electron utilization during imaging.

As shown in Fig. 1b, after applying a fluence of 4.8 e-/Å2 at 300 kV, 2D-PI-DhTPA retained the high-resolution information up to the diffraction point with index 17 0 0, i.e., 1.4 Å. As the fluence increases, the degradation of the long-range order under electron bombardment leads to the disappearance of the higher-order reflections and thus to a degradation of the achievable image resolution. The critical fluence for a given resolution can be determined when the corresponding reflection intensity is reduced to a threshold (1/e) of its initial value19. And the respective damage cross section is defined as the reciprocal of the critical fluence22.

Because critical fluence analysis involves the evaluation of numerous SAED patterns, we applied machine learning techniques to increase efficiency, accuracy, and reliability. A U-Net23 neural network was trained to automatically identify Bragg reflections in the SAED patterns and generate integrated intensity profiles (Fig. 1c). To increase the reliability of the data, instead of selecting individual Friedel pairs, all reflection intensities within a selected resolution range were integrated and plotted as a function of electron fluence, allowing precise assessment of the critical fluence for the desired resolution range.

Figure 1d shows the critical fluence (?cr) of 2D-PI-BPDA and 2D-PI-DhTPA as a function of accelerating voltage. For clarity, the absolute fluence value below 300 kV was normalized to unity. With decreasing acceleration voltage, the sample was able to withstand lower electron fluence, which can be attributed to increased inelastic scattering and thus increased radiolysis damage24. It seems that a higher accelerating voltage would be beneficial, as reported in the literature24. However, the critical fluence only indicates the total number of applicable electrons, regardless of whether the electron carries structural information or not.

Figure 1e shows the normalized ?el as a function of accelerating voltage. ?el increases with decreasing voltage and reaches an inflection point at 120 kV. According to kinematic theory, the elastic scattering cross section ?e is proportional to 1/?2, suggesting a linear increase in ?el with decreasing voltage8. This linear relationship has been demonstrated experimentally on graphs28. However, the kinematic scattering only applies to very thin samples, where the intensity of the Bragg reflection is negligible compared to that of the direct beam. Due to the finite thickness of 2D polymer thin films (up to 60 nm), the kinematic theory no longer holds, as illustrated by the nonlinear change of ?el in Fig. 1e. In particular, at lower stresses, where the mean free path of elastic scattering is reduced, dynamic scattering leads to intensity exchange between Bragg reflections and the direct beam32. Moreover, increased inelastic events at lower voltages further reduce the amplitude of elastic scattering, resulting in a reduced ?el below 80 kV32.

Figure 1f shows the plots of ? for 2D-PI-BPDA and 2D-PI-DhTPA for different accelerating voltages. It can be clearly seen that 120 kV provides the highest information coefficient for both materials. In other words, at a target resolution, the absolute number of information-carrying electrons is highest at 120 kV, resulting in improved signal-to-noise (S/N) ratio and image contrast. The increase in image contrast has also been demonstrated by image simulations (Fig. 2). As can be seen, a contrast enhancement of 41-113% is expected compared to the conventional 300 kV when the sample thickness is less than 10 nm.

It should be noted here that the optimal accelerating voltage of 120 kV has been experimentally determined for 2D polymer thin films up to 60 nm thick, which is in good agreement with energy optimization for biological samples of a given thickness28. Reducing the sample thickness would shift the optimal energy to even lower values28. On the other hand, reducing the accelerating voltage leads to more inelastic scattering events, which reduces the elastic scattering amplitude and thus the phase contrast when a finite thickness is considered. When the inelastically scattered electrons undergo another elastic scattering process, the scattered and unscattered parts are coherent and can provide information on the crystal structure32. However, due to chromatic aberration, the inelastically scattered electrons are no longer focused on the Gaussian image plane, resulting in image blurring7,34. The correction of chromatic aberration raises the resolution limit imposed by the temporal coherence attenuation function. At the same time, it improves the image contrast due to the increased S/N ratio by refocusing the coherent inelastic electrons on the Gaussian image plane35. The optimal electron energy for thinner samples and the effects of chromatic aberration correction therefore require further experimental investigation.

AC-HRTEM imaging of 2D-PI-BPDA and 2D-PI-DhTPA under 120 kV

We then performed high-resolution imaging at 120 kV for both polymers. Figures 3a and 4a show the unprocessed AC-HRTEM images of 2D-PI-BPDA and 2D-PI-DhTPA, respectively. The images were acquired with an electron fluence of about 80 e-/Å2, which is close to the specified critical fluence for the resolution range 5-6 nm-1 (1.7-2.0 Å). The FFT patterns (insets) show reflections down to a spatial frequency of 5 nm-1, extending to 1.9 Å. Since a TEM image is a 2D projection of a 3D object, the atomic models are derived using the DFTB method to reveal the structure of the 2D polymer film. As shown in Figures 3b and 4b, the simulated images based on the DFTB models agree well with the experimental images and clearly show the TAPP nodes and BPDA/DhTPA linker molecules. Note that contrast enhancement below 120 kV allows image acquisition with low defocus values (i.e., 40-50 nm), which significantly reduces contrast delocalization36. In other words, the image signal is sharply localized on the molecular scaffold without significant blurring. Together with the resolution of less than 2 Å, the low delocalization allows visualization of even the 4 Å pores on the porphyrin rings37, which is not possible at 300 kV due to the need for higher defocus values for image visibility.

Interestingly, although the agreement between experimental image and simulation is well preserved in most areas of the sample, we occasionally observe an abnormal contrast near the porphyrin nuclei in both 2D polymer materials (Figs. 3c and 4c). For example, in 2D PI-BPDA, we found four bright spots near the porphyrin node arranged along the diagonal of the square lattice (Fig. 3d). Despite our efforts, the bright spots could not be reproduced in the image simulation, regardless of the parameters used (thickness, defocus, aberrations). In other words, the abnormal contrast is not related to image processing and microscope performance, but to additional structural features in the sample that were not previously known. The distance between two diagonal spots was measured to be 17.3 Å, which is approximately the length between the diagonal amino groups of the TAPP molecule39. Because porphyrin and its derivatives can readily assemble into highly ordered aggregates40,41 , we suspected that a small amount of TAPP molecules may have intercalated into the 2D polymer framework (i.e., molecular interstitial defects), resulting in additional image contrast.

Molecular interstitial defects and detection of side groups

To investigate the plausibility of the molecular interstitial sites, we performed quantum mechanical calculations based on self-consistent charge theory (SCC)-DFTB. Additional TAPP molecules were inserted between the TAPP nodes in the 2D polymer scaffold. The DFTB calculations revealed two different types of interstitial TAPPs: either aligned with the 2D polymer network and along the high symmetry axes, i.e., a or a-b, referred to as A-type, or rotated and slightly shifted with respect to the adjacent layers by 31° for 2D-PI-DhTPA and 42° for 2D-PI-BPDA, referred to as R-type (Fig. 3e). Note that exactly eclipsed stacking is energetically unfavorable due to electrostatic repulsion between TAPP molecules42. Moreover, in the synthesis of 2D-PI-BPDA and 2D-PI-DhTPA, the acid constant pKa of the TAPPs in aqueous solution was below the protonation threshold43, indicating the presence of protons on the pyrroline-like rings44 and thus enhanced repulsion between the porphyrin cores. In the formation of face-to-face dimers from di-/tricationic porphyrin, electrostatic repulsion could be minimized by a relative displacement or a rotation between the molecules42. Due to the fourfold symmetry of the 2D polymer lattice, the possible displacement directions of the interstitial TAPPs, e.g., a, -a, b, -b, are nearly isoenergetic. To create a realistic model of the actual crystal for HRTEM simulation, we created a model with a statistical distribution of all equivalent possibilities. A model with 120 layers was created, with 1/3 of the layers replaced by interstitial TAPPs. Each TAPP was randomly assigned one of the equivalent displacements.

Figure 3e illustrates the statistical models showing possible molecular configurations of interstitial TAPPs in 2D PI-BPDA. As shown by the image simulation, the interstitial sites lead to additional contrast near the porphyrin nuclei (Fig. 3e). To our delight, the bright spots were well reproduced with the R-type configuration, indicating the presence of rotated TAPPs intercalated into the 2D PI-BPDA framework. It is worth noting that we did not observe any A-type interstitials in the experimental images, which could be due to their higher relative energy compared to the R-type. In contrast to 2D-PI-BPDA, A-type interstitial defects were detected in 2D-PI-DhTPA, leading to a crescent-shaped contrast near the porphyrin nodes (Fig. 4c, f). The energetic preference of the A-type in 2D-PI-DhTPA was also confirmed by theoretical calculations.

Comparing the structure of 2D-PI-DhTPA and 2D-PI-BPDA, the main difference is in the linker molecules. DhTPA contains two hydroxyl groups, while BPDA has no side chains. By plotting the integrated line profiles across the center of the linker molecules, we measured the FWHM of the linker intensities in both 2D polymers (Fig. 4e). Interestingly, 2D-PI-DhTPA and 2D-PI-BPDA showed a significant difference in linker width (Fig. 4e). A statistical analysis averaging 100 linker sites revealed that the FWHM of DhTPA is approximately 70% (0.9 Å) wider than that of BPDA, which may be related to the presence of hydroxyl groups. We believe that these results open an interesting possibility for direct visualization and discrimination of functional groups at the molecular skeleton, especially when longer and more complicated side chains are present, such as carboxylic acids and phenyl groups. Direct observation of functional groups at the pore interface is highly desirable to study structure-property correlation, such as host-guest interactions. However, there are still many challenges. For example, although surface shaping of pores in 2D powdered COFs3 is well established, exfoliation of organic crystals down to a few nanometers or a few tens of nanometers while maintaining the original long-range order is not a trivial task46. Moreover, functionalization (by direct polymerization or subsequent synthetic modification) of 2D polymer thin films synthesized at the interface is still in its infancy and needs to be explored.

Visualization and quantification of short-range ordering in 2D amorphous organic materials

Since 120 kV provides a higher information coefficient, we hypothesize that our experimental setup could also be useful for visualizing short-range orders in 2D organic materials due to the increased image contrast. To demonstrate this, we applied 120 kV imaging to an amorphous polyimine thin film (a-PI, Fig. 5c), which is an amorphous analog of the viologen-immobilized 2D polymer synthesized by Schiff base polycondensation at the air-water interface33. The SAED pattern shows diffuse 100- and 200-rings (Fig. 5b), indicating the lack of long-range order and thus low scattering ability. The TEM image at low magnification (Fig. 5e) shows that the a-PI film consists of a highly disordered network, indicating its amorphous nature. To gain a better insight into the local structure of a-V2DP, AC-HRTEM imaging was performed at sub-cell unit resolution (Fig. 5c). The molecular network could be resolved with the bright spots corresponding to the nodal positions. It was found that a-PI consisted of a mixture of expected hexagons and defective pentagons and heptagons. To quantitatively analyze the short-range order in a-PI, we developed a neural network based on the U-net architecture to automatically determine the node positions (see Methods). Based on this, the length and angle between nodes, nearest neighbor distribution, and mapping in real space (Fig. 5d) and percentage of polygons (Fig. 5f) can be statistically extracted. The combination of high image contrast and machine learning has allowed us to build a quantitative structural profile of the a-PI, which may pave the way to understanding structural signatures between different organic a-2D materials in the future.

Resource: Liang, B., Zhang, Y., Leist, C., Ou, Z., Položij, M., Wang, Z., Mucke, D., Dong, R., Zheng, Z., Heine, T., Feng, X., Kaiser, U. & Qi, H. (2022). Optimal acceleration voltage for near-atomic resolution imaging of layer-stacked 2D polymer thin films. Nature communications, 13(1), 1-9.