Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Electrical conductivity in a non-covalent two-dimensional porous organic material with high crystallinity

Electroactive macrocycle building blocks are a promising route to new types of functional two-dimensional porous organic frameworks. Our strategy uses conjugated macrocycles that organize into two dimensional porous sheets via non-covalent van der Waals interactions, to make ultrathin films that are just one molecule thick. In bulk, these two-dimensional (2D) sheets stack into a three-dimensional van der Waals crystal, where relatively weak alkyl–alkyl interactions constitute the interface between these sheets. With the liquid-phase exfoliation, we are able to obtain films as thin as two molecular layers. Further using a combination of liquid-phase and mechanical exfoliation, we are able to create non-covalent sheets over a large area (>100 μm²). The ultrathin porous films maintain the single crystal packing from the macrocyclic structure and are electrically conductive. We demonstrate that this new type of 2D non-covalent porous organic framework can be used as the active layer in a field effect transistor device with graphene source and drain contacts along with hexagonal boron nitride as the gate dielectric interface.

Ultrathin porous films held together by non-covalent van der Waals interactions was obtained by a top-down approach, which is then utilized as channel material in a two-dimensional planar field-effect transistor device through easy stamp transfer.

We describe a new type of two-dimensional (2D), molecularly-thin porous organic framework that is formed from macrocyclic building blocks that assemble, through non-covalent interactions, into a porous two-dimensional plane. Covalent organic frameworks (COFs) are promising in applications due to their ability to host other functional molecules in the voids.^1–7 Many porous frameworks have been demonstrated to be useful in energy storage,⁸ catalysis,^9–11 separation,^12,13 optoelectronics^4,14 and sensing.^15,16 In order to construct nanodevices with porous channels, ultrathin films of porous frameworks has been prepared with bottom-up^4,17–20 and top-down^1,21 approaches. The top-down approaches to these materials are enabled by strong covalent bonds in the two-dimensional plane and weak van der Waals interactions between them, similar to what is seen in two-dimensional materials such as graphene and TMDs.^22–27 For porous ultrathin films, the electrical conductance has not been extensively investigated.^2,7,20,28,29Here, we explore making molecularly thin layers in which conjugated macrocycles are used as building blocks and non-covalent van der Waals interactions are the adhesive that assembles these molecules into rigid, porous layers. By adjusting the relative strengths of the interactions that direct the assembly within the plane and those holding the two-dimensional layers with respect to each other, we can exfoliate these non-covalent porous frameworks using the same means employed for traditional two-dimensional van der Waals materials.³⁰ Using liquid-phase and mechanical exfoliation, we create porous films that are as thin as two-layers of molecules. These new results are exciting and useful because previously we were not able to obtain such high-ordered thin porous film directly from its bulk crystal and were limited to investigating the electronic properties of this hollow organic capsules in spin-coated films. These ultrathin porous films are ordered over large areas and maintain the single crystal packing from the macrocyclic building blocks. To demonstrate the utility of this new type of ultrathin material, we fabricated 2D field effect transistor (FET) devices in which graphene is the source/drain contacts, hexagonal boron nitride is the gate dielectric interface, and the exfoliated molecular sheet is the active layer. These ultrathin self-assembled materials are efficacious at transporting electrons and will find utility in gas sensing and applications similar to traditional two-dimensional materials. Fig. 1 displays the molecular building block (1). Characterization is contained in the ESI^† and a previous report.³¹1 has several important molecular features in its solid-state assembly. It is a rigid and shape persistent macrocycle that has an interior and an exterior (Fig. 1a), and in bulk, has a pore of ∼11.4 Å in diameter and a surface area of 20 m² g⁻¹ from BET measurements.³¹ When it assembles in the crystalline state, it forms two-dimensional porous sheets with two types of cavities (Fig. 1b), one molecule thick, that are held together by relatively strong π–π contacts and Br–PDI interaction between the bromine atoms on the thiophenes and adjacent PDI molecules (Fig. 1c), which plays a crucial role in the self-assembly of the films. The close proximity of the molecules in the 2D plane together with the conjugation within the macrocycle facilitate charge transport of electrons in the 2D plane. These electrically conductive porous sheets then stack into a three-dimensional crystal in which adjacent sheets are separated from one another by the alkane sidechains of the perylene diimide (Fig. 1d). It is in this alkane gallery that we see an opportunity for exfoliation to yield ultrathin 2D sheets.Open in a separate windowFig. 1Structure and packing of molecule 1. (a) Chemical structure, side view and top view of molecular structure of 1. C, N, O, S, Br are colored in grey, blue, red, yellow and green, respectively. The vertical distance of one macrocycle is about 1.5 nm. (b) Face-on view and edge-on view of one layer of 1. The internal cavity of 1 and the cavity formed by the packing of 1 are labeled as i and i′, respectively. (c) Interactions binding two adjacent macrocycles from neighboring brominated thiophene rings. (d) View of packing of 1 along the c axis through the interaction of alkane sidechains. Exfoliation takes place at the alkyl–alkyl interface. One layer of 1 is about 2 nm in thickness.We isolated crystals of this material that were grown from solution and then tested whether they can be exfoliated. Fig. 2a displays a representative micrograph of one of the crystals. The crystal has a pseudo-hexagonal packing of the molecular building blocks in the two-dimensional plane, and this symmetry is mirrored in the hexagonally-shaped crystals. The simplest method for exfoliation is mechanical exfoliation, which is most commonly performed using scotch-tape.^32,33 We place the single crystals onto clean scotch-tape and repeat the mechanical exfoliation process for a few repetitions, and then we transfer the exfoliated crystals onto a clean silicon wafer. Fig. 2b displays an atomic force microscopy (AFM) micrograph of the typical non-covalent porous 2D sheet of 1 we obtained from this method. The porous sheets are flat and smooth and a few micrometers in diameter with a thickness of ∼8 nm; this thickness corresponds to a stack of five molecular layers of 1. This result demonstrates that non-covalent interactions are strong enough to hold molecules together to form ultrathin porous materials. Just as with traditional two-dimensional materials, the non-covalent porous organic 2D sheets of 1 are flexible as evidenced by the wrinkles and folds in the micrograph in Fig. 2b and S2.^†Open in a separate windowFig. 2Mechanical exfoliation of 1. (a) Optical microscopy and scanning electron microscope (SEM) (inset) images of a single crystal of macrocycle 1. (b) AFM and optical microscope (inset) images of the ultrathin non-covalent porous sheet of 1 on a silicon wafer obtained from mechanical exfoliation.We were unable to obtain porous films as thin as a single layer and also large-area samples using mechanical exfoliation, and thus we next explored if liquid-phase exfoliation^34,35 could produce them. Because the halogen bonds that hold the sheets together should be most robust in solvents with a low-dielectric constant that lack heteroatoms, and because the groups holding the sheets together are the alkane sidechains, we chose saturated hydrocarbons (hexane or heptane) as the solvents for exfoliation. Fig. 3a shows the process we follow for the liquid-phase exfoliation. We suspend single crystals of 1 in heptane and sonicate the mixture for five minutes. We drop cast the supernatant solution on silicon wafer and examine them with AFM. Remarkably, we are able to obtain non-covalent porous organic frameworks as thin as only two molecular layers (Fig. 3b).³⁶ Nevertheless, the lateral size of the porous 2D sheets of 1 we could obtain using this method are quite small, making it difficult to fabricate devices from them.Open in a separate windowFig. 3Liquid-phase exfoliation and combination of liquid-phase and mechanical exfoliation. (a) Schematic showing the liquid-phase exfoliation process. (b) AFM image of the ultrathin sheet of 1 on a silicon wafer obtained from liquid-phase exfoliation method. The sheets in this micrograph are two molecular layers (left) and three molecular layers (right) in thickness. (c) AFM image of the ultrathin sheet of 1 on a silicon wafer obtained from combination of liquid-phase and mechanical exfoliation, inset: optical microscope image of the ultrathin sheet 1. (d) AFM image showing the height change across the ultrathin sheet of 1 on silicon wafer obtained with combination methods, inset: optical microscope image of the ultrathin sheet of 1.To get large-area films characteristic of the mechanical exfoliation and thin films characteristic of the liquid-phase exfoliation, we combined the two methods. We first immerse the crystal of 1 in heptane for a few minutes to let the solvent seep into the gallery between the sheets and weaken the interlayer interactions. Then, we use mechanical exfoliation to isolate the ultrathin films. With this method, we obtained sheets of 1 with a lateral size of over ten micrometers, as shown in Fig. 3c. By carefully examining the exfoliated non-covalent porous 2D sheets of 1, we were also able to observe the height change across the sheet (Fig. 3d) with integer values of the layer thickness after the exfoliation steps. As marked red in Fig. 3d, we could identify a single layer of 1 with a height difference between these two surfaces of about 1.5 nm, corresponding to monolayer of molecule 1.We conducted transmission electron microscopy (TEM) studies to characterize the crystallinity of the as-prepared non-covalent porous 2D sheets of 1. As shown in Fig. 4a (inset), the 2D sheets exhibit a layered structure after liquid-phase exfoliation. The selected area electron diffraction (SAED) in the area (marked by the red circle) reveals a hexagonal diffraction pattern, with the bright reflections corresponding to the (2 1(−) 0) plane, with a spacing of 11.3 Å. This diffraction pattern confirms that the non-covalent, porous 2D sheets of 1 retain the single crystal packing and are stable to the liquid-phase processing.Open in a separate windowFig. 4TEM characterization and device fabrication. (a) SEAD pattern and TEM image (inset) of the non-covalent porous ultrathin sheet 1 obtained by liquid-phase exfoliation. (b) Schematic showing the structure of the hBN/Graphene/1 device based on the non-covalent porous ultrathin sheet 1 with graphene as electrodes and hBN as the dielectric layer. (c) Optical microscope image showing the as-fabricated hBN/Graphene/1 device. (d) Transfer curve of the hBN/Graphene/1 device.We next sought to determine the ability of these non-covalent porous ultrathin layers to transport charge. Because these films are van der Waals materials, we sought to make devices with van der Waals interfaces. [The ESI^† contains the current/voltage curves for 1 in a more traditional organic FET with Au contacts and trichloro(octadecyl)silane coated SiO₂ as the gate dielectric.] The source-drain contacts were fabricated from graphene and the dielectric interface was hexagonal boron nitride (hBN). A schematic of the device is shown in Fig. 4b. To create this device, we first exfoliate graphene and hBN onto a silicon substrate. We then follow a published procedure³⁷ to first pick up hBN and then graphene to make the hBN/graphene stack. We transfer this hBN/graphene stack onto another clean silicon substrate. Then the graphene was cut using electron beam lithography and an oxygen plasma to open a 300 nm gap between graphene electrodes (see Fig. S4^† for the AFM details of graphene electrodes). In order to transfer the non-covalent porous ultrathin sheets of 1 onto the graphene electrodes, we exploit the combined liquid/mechanical exfoliation method above to obtained 2D sheet of 1 with polydimethylsiloxane (PDMS) polymer as the substrate, which was then used for the stamp transferring. In this manner, we were able to transfer the ultrathin sheets (∼20 nm) onto the graphene electrodes. Fig. 4c displays the optical microscope image of the device, and Fig. 4d displays the FET transfer curves revealing that the material is an efficacious, n-type transistor. Several features of the device are noteworthy. The electron mobility in the linear regime was estimated to be 1.6 × 10⁻⁴ cm² V⁻¹ s⁻¹ from the transfer curve. As expected, it is somewhat lower than the electron mobility estimated from the saturation regime of the traditional OFET shown in Fig. S3.^†38 Despite the small size and the nanoscale thickness, the material exhibits over 3 orders of magnitude difference in current between the off and on state of the device. The threshold voltage is about 39 V, implying that the device turns on at relatively high voltage. We surmise that the contact, through the alkane sidechains is an impediment to more efficient charge transport.     

Isotope ratio monitoring of small molecules and macromolecules by liquid chromatography coupled to isotope ratio mass spectrometry

In the field of isotope ratio mass spectrometry, the introduction of an interface allowing the connection of liquid chromatography (LC) and isotope ratio mass spectrometry (IRMS) has opened a range of new perspectives. The LC interface is based on a chemical oxidation, producing CO2 from organic molecules. While first results were obtained from the analysis of low molecular weight compounds, the application of compound-specific isotope analysis by irm-LC/MS to other molecules, in particular biomolecules, is presented here. The influence of the LC flow rate on the CO2 signal and on the observed delta13C values is demonstrated. The limits of quantification for angiotensin III and for leucine were 100 and 38 pmol, respectively, with a standard deviation of the delta13C values better than 0.4 per thousand. Also, accuracy and precision of delta13C values for elemental analyser-IRMS and flow injection analysis-IRMS (FIA-LC/MS) were compared. For compounds with molecular weights ranging from 131 to 66,390 Da, precision was better than 0.3 per thousand, and accuracy varied from 0.1 to 0.7 per thousand. In a second part of the work, a two-dimensional (2D)-LC method for the separation of 15 underivatised amino acids is demonstrated; the precision of delta13C values for several amino acids by irm-LC/MS was better than 0.3 per thousand at natural abundance. For labelled mixtures, the coefficient of variation was between 1% at 0.07 atom % excess (APE) for threonine and alanine, and around 10% at 0.03 APE for valine and phenylalanine. The application of irm-LC/MS to the determination of the isotopic enrichment of 13C-threonine in an extract of rat colon mucosa demonstrated a precision of 0.5 per thousand, or 0.001 atom %.     

Trilocal structures. III. Expansion in tree functions

An alternative set of expansion functions is described. The first 48 in the set are listed explicitly, and 16 generalized formulas are given, from which the entire rest-system set of functions can be constructed. Explicit and generalized matrix elements for the rest Hamiltonian are given. An auxiliary condition is introduced, leading to explicit formulas and generalized formulas for the expansion coefficients,C _j, accompanying the expansion functions, _j.     

Application of Combinatorial Procedures in the Search for Serine-Protease-Like Activity with Focus on the Acyl Transfer Step

Recursive deconvolution of a 729-membered peptide library has identified three active sequences, in which both Ser and His are present in one of the two tripeptidic chains generated on a steroidal scaffold (see structural formula), for the cleavage of an activated p-nitrophenyl ester. This combinatorial approach aims at searching for serine-protease-like activity.     

Quantitative analysis of triacylglycerol regioisomers in fats and oils using reversed-phase high-performance liquid chromatography and atmospheric pressure chemical ionization mass spectrometry

Positional distribution of fatty acyl chains of triacylglycerols (TGs) in vegetable oils and fats (palm oil, cocoa butter) and animal fats (beef, pork and chicken fats) was examined by reversed-phase high-performance liquid chromatography (RP-HPLC) coupled to atmospheric pressure chemical ionization using a quadrupole mass spectrometer. Quantification of regioisomers was achieved for TGs containing two different fatty acyl chains (palmitic (P), stearic (S), oleic (O), and/or linoleic (L)). For seven pairs of 'AAB/ABA'-type TGs, namely PPS/PSP, PPO/POP, SSO/SOS, POO/OPO, SOO/OSO, PPL/PLP and LLS/LSL, calibration curves were established on the basis of the difference in relative abundances of the fragment ions produced by preferred losses of the fatty acid from the 1/3-position compared to the 2-position. In practice the positional isomers AAB and ABA yield mass spectra showing a significant difference in relative abundance ratios of the ions AA(+) to AB(+). Statistical analysis of the validation data obtained from analysis of TG standards and spiked oils showed that, under repeatability conditions, least-squares regression can be used to establish calibration curves for all pairs. The regression models show linear behavior that allow the determination of the proportion of each regioisomer in an AAB/ABA pair, within a working range from 10 to 1000 microg/mL and a 95% confidence interval of +/-3% for three replicates.     

Shock-absorbing and failure mechanisms of WS2 and MoS2 nanoparticles with fullerene-like structures under shock wave pressure

The excellent shock-absorbing performance of WS2 and MoS2 nanoparticles with inorganic fullerene-like structures (IFs) under very high shock wave pressures of 25 GPa is described. The combined techniques of X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, thermal analysis, and transmission electron microscopy have been used to evaluate the diverse, intriguing features of shock recovered IFs, of interest for their tribological applications, thereby allowing improved understanding of their antishock behavior and structure-property relationships. Two possible failure mechanisms are proposed and discussed. The supershock-absorbing ability of the IF-WS2 enables them to survive pressures up to 25 GPa accompanied with concurrent temperatures of up to 1000 degrees C without any significant structural degradation or phase change making them probably the strongest cage molecules now known.     

Electron Delocalization in Perylene Diimide Helicenes

We report two new helicenes derived from the double fusion of an acene with two perylene diimide (PDI) subunits. These PDI‐helicene homologs exhibit very different structural and electronic properties, despite differing by only a single ring in the link between the PDI units. The shorter inter‐PDI link brings the two PDI subunits closer together, and this results in the collision of their respective π‐electron clouds. This collision facilitates intramolecular through‐space electronic delocalization when the PDI‐helicene is reduced.