Infinite Columns Research Articles

Solid phase microextraction device coupled with miniature mass spectrometry and mathematical model of its ion chronogram

Modern solid phase microextraction (SPME) device linked with mass spectrometry (SPME-MS) has evolved from producing ion chronogram as flat noisy signal to as unimodal-like signal. We designed a SPME device, which is closer in morphology to LC column, linked it with a miniature mass spectrometer (SPME-Mini MS), and proposed a mathematical model that elution of compound from the SPME device is equivalent to overlay of elution of the compound from the infinite LC columns with the lengths between 0 and the length of the device and it can generate an ion chronogram as right-skew unimodal signal. Rhodamine B as analyte was used for experimental verification and its unimodal signal was used to fit the parameters of a computer simulation program based on the model. The experimental results and simulations empirically cross-confirmed that SPME-Mini MS can generate ion chronogram as clean right-skew unimodal signal. Furthermore, the SPME-Mini MS system was used for quantitative analysis of psychotropic drugs (i.e. risperidone and aripiprazole) in artificial urine. The results preliminarily demonstrated that the system can utilize area under unimodal signal for quantitative analysis and has potential to be applied for on-site, fast and accurate quantification of drugs and other compounds.

Experimental and Numerical Study of Floating Stone Columns Using Unit Cell Model Test

Stone columns serve as a remedial measure to alleviate settlements and expedite the consolidation process, particularly in soft soils where excessive settlement and slow consolidation are the common problems. This paper presents the experimental and numerical investigation into the effects of area replacement ratio and stone column length on the consolidation settlement of floating stone columns using finite element software i.e. PLAXIS 3D. The model setup adopted unit cell concept resembling an infinite column grid pattern with uniform load. The study examined two distinct area replacement ratios (15% and 33%) and five varying lengths of stone columns (80 mm, 160 mm, 240 mm, 320 mm, and 400 mm). The findings indicated that as column length and area replacement ratio increase, settlement decreases, together with the improvement in consolidation rate. Generally, the numerical results agreed with the experimental results albeit slightly faster rate of consolidation obtained.

Isolated bubble ascent in a non-Newtonian media inside an infinite bubble column: a CFD study

Isolated bubble ascent in a non-Newtonian media inside an infinite bubble column: a CFD study

Four Slip-Stacked Arrangements, Three Types of Photophysics: Crystal Structure and Solid-State Fluorescence of 3,6-Diaryl Substituted Furo[3,4-c]furanone Polymorphs and Regioisomers.

Six symmetrical 3,6-diaryl (aryl=phenyl, 2-, 3- and 4-tolyl, 2,4- and 3,5-xylyl) substituted furo[3,4-c]furanones (DFF) were synthesized. The computational analysis, based on density functional theory, found eight possible centrosymmetrical slipped π-stack arrangements, formed according to electron repulsion minimization principle, as for previously reported for π-isoelectronic diketopyrrolopyrroles (DPP). One of these slipped stack arrangements was found to form infinite columns in the crystals of a new polymorph of parent phenyl derivative (with centre-to-centre distance CC=6.975 Å), other three types of stacks were found for 3-tolyl (CC=6.153 Å), 4-tolyl (CC=3.849 Å) and 2,4-xylyl (CC=4.856 Å) derivatives by single crystal X-ray diffractometry. All six derivatives show intense solution fluorescence in blue/green region, with a maximum driven entirely by a number and position of methyl substituents on phenyl rings. On the other hand, the solid-state fluorescence from yellow over orange to red is observed only for four derivatives and its presence/absence, spectral position and vibronic structure is driven exclusively by the slips in π-stacks (with interplanar distance always less than 3.5 Å) of almost planar DFF molecules, resulting in J-type emission, H-type excimer-like emission and H-type quenching.

Charge invertible nanowires [Ni5Bi5.6]x (x = 1+, 0, 1−): Infinite columns [Ni5Bi5.6]− in a novel quasi-one-dimensional compound KNi5Bi5.6

A novel quasi-one-dimensional (Q1D) compound KNi5Bi5.6 has been synthesized and its crystal structure has been determined by X-ray crystallography. The structure contains double-walled anionic nanowires [Ni5Bi5.6]− separated by potassium cations. KNi5Bi5.6 forms a new series of compounds together with previously reported Bi5.6Ni5I and Bi28Ni25 featuring [Ni5Bi5.6]x (x = 1+, 0, 1−) nanowires for which the charge can be cationic, neutral or anionic without appreciably affecting the structure and composition. This unique characteristic provides a new platform to investigate charge invertible Q1D transition metal systems. Resistivity measurement of KNi5Bi5.6 reveals a metallic type of conductivity. Magnetic susceptibility obeys a modified Curie-Weiss behavior with a small average effective magnetic moment of Ni and shows a weak magnetic anisotropy.

Second player’s cannot-lose strategy for Cylinder-Infinite-Connect-Four with circumference 11

Cylinder-Infinite-Connect-Four is Connect-Four played on a cylindrical square grid board with infinite row heights and columns that cycle about its width. In previous work, the first player’s cannot-lose strategies were discovered for all circumferences, and the second player’s cannot-lose strategies were discovered for all circumferences except for 6 and 11. In this paper, we show the second player’s cannot-lose strategy for circumference 11.

Catalysis enabled synthesis, structures, and reactivities of fluorinated S8-corona[n]arenes (n = 8-12).

Previously inaccessible large S8-corona[n]arene macrocycles (n = 8-12) with alternating aryl and 1,4-C6F4 subunits are easily prepared on up to gram scales, without the need for chromatography (up to 45% yield, 10 different examples) through new high acceleration SNAr substitution protocols (catalytic NR4F in pyridine, R = H, Me, Bu). Macrocycle size and functionality are tunable by precursor and catalyst selection. Equivalent simple NR4F catalysis allows facile late-stage SNAr difunctionalisation of the ring C6F4 units with thiols (8 derivatives, typically 95+% yields) providing two-step access to highly functionalised fluoromacrocycle libraries. Macrocycle host binding supports fluoroaryl catalytic activation through contact ion pair binding of NR4F and solvent inclusion. In the solid-state, solvent inclusion also intimately controls macrocycle conformation and fluorine-fluorine interactions leading to spontaneous self-assembly into infinite columns with honeycomb-like lattices.

Synthesis, crystal structure and Hirshfeld surface analysis of the binuclear Cu(II) complex with 4-nitrobenzoic acid and triethanolamine

In this paper, the synthesis and structure of the binuclear copper complex [Cu 2 (PNBA) 2 (TEA) 2 ]∙2H 2 O (where PNBA – para -nitrobenzoic acid, TEA – triethanolamine) was discussed. The structure was determined by the single-crystal X-ray diffraction method. The complex molecule lies on the inversion center. Cu (II) ions coordinate two PNBA and two TEA molecules by mono- and tetradentate fashions, respectively. Two water molecules are located in outer coordination sphere associating complex molecules into infinite columns. Hirschfeld surface analysis indicates that the most significant contacts are H•••O/O•••H (36.5%) and H•••H (43.7%) interactions.

Architectural diversity in the solid-state behaviour of crown ether and [2.2.2]-cryptand complexes of K+TCNQ˙− salts

Ionophore complexes of K(TCNQ˙−)(TCNQ0)n adopt a variety of stacking motifs such as wave-like infinite TCNQ columns separated by K+-cryptates (left) and K+-π-dimerised cation complexes separated by infinite slipped TCNQ stacks (right).

FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX

AbstractFor an infinite Toeplitz matrix T with nonnegative real entries we find the conditions under which the equation $\boldsymbol {x}=T\boldsymbol {x}$ , where $\boldsymbol {x}$ is an infinite vector column, has a nontrivial bounded positive solution. The problem studied in this paper is associated with the asymptotic behaviour of convolution-type recurrence relations and can be applied to problems arising in the theory of stochastic processes and other areas.

Crystal structure and photoreactivity of a halogen-bonded cocrystal based upon 1,2-diiodoperchlorobenzene and 1,2-bis(pyridin-4-yl)ethylene.

The formation of a photoreactive cocrystal based upon 1,2-diiodoperchlorobenzene (1,2-C6I2Cl4) and trans-1,2-bis(pyridin-4-yl)ethylene (BPE) has been achieved. The resulting cocrystal, 2(1,2-C6I2Cl4)·(BPE) or C6Cl4I2·0.5C12H10N2, comprises planar sheets of the components held together by the combination of I...N halogen bonds and halogen-halogen contacts. Notably, the 1,2-C6I2Cl4 molecules π-stack in a homogeneous and face-to-face orientation that results in an infinite column of the halogen-bond donor. As a consequence of this stacking arrangement and I...N halogen bonds, molecules of BPE also stack in this type of pattern. In particular, neighbouring ethylene groups in BPE are found to be parallel and within the accepted distance for a photoreaction. Upon exposure to ultraviolet light, the cocrystal undergoes a solid-state [2 + 2] cycloaddition reaction that produces rctt-tetrakis(pyridin-4-yl)cyclobutane (TPCB) with an overall yield of 89%. A solvent-free approach utilizing dry vortex grinding of the components also resulted in a photoreactive material with a similar yield.

Boron-Nitrogen Double Tweezers Comprising Arylboronic Esters and Diamines: Self-Assembly in Solution and Adaptability as Hosts for Aromatic Guests in the Solid State.

The thermodynamic stability of 1 : 1 and 2 : 1 boron-nitrogen (B←N) adducts formed between aromatic boronic esters with mono- and diamines was studied in solution by NMR and UV-vis spectroscopy with association energies (ΔG°) ranging from -11 to -28 kJ mol-1 . The effect of different substituents in the boronic ester, the nature of the diamine linker, and the effect of the solvent was explored. Stable 2 : 1 B←N adducts with diamines such as 1,3-diaminopropane were produced in solutions of hydrogen-bonding acceptor solvents (acetonitrile and ethyl acetate), which can be isolated in the solid state as crystalline solvates, whereas the use of noncoordinating solvents such as 1,2-dichloroethane afforded mainly 1 : 1 B←N adducts. In suitable combinations, aromatic bis-pyridyl diamines produced stable 2 : 1 B←N adducts that were isolated either as solvent-free solids, solvates, or cocrystals. In these crystalline forms, double-tweezer hosts were observed with an exceptional syn/anti conformational guest-adaptability driven by simultaneous donor-acceptor and C-H⋅⋅⋅π interactions in the tweezer cavities, resembling preorganized covalent tweezer hosts. Interestingly, cocrystals with electron-rich guests such as tetrathiafulvalene and pyrene showed non-centrosymmetric crystal lattices with infinite π-stacked donor-acceptor columns.

Formation of Pores and π-Stacked Columns in Benzothienobenzothiophene-based Linear Coordination Polymers

Porous coordination polymer (PCP) with 2,7-bis(4-pyridyl)-[1]benzothieno[3,2-b][1]benzothiophene (BTBT-4py) ligands was synthesized. The PCP provides both pores and infinite π-stacked columns via t...

From Fe32+δGe35-xPx to Fe32+δGe35-x-yPxAsy: Fine geometry optimization in new intergrowth structures

A new compound with a two-dimensional intergrowth structure, Fe32+δGe35-xPx (x = 1.7–4.4, δ = 0.6–0.75), and the solid solution on its base, Fe32+δGe35-x-yPxAsy (δ < 0.2, x = 0–4.4, y = 0–2), were obtained by the two-stage synthesis from elements. The crystal structure of Fe32+δGe35-xPx can be described as an alternation of infinite columns of two intermetallic structure types: MgFe6Ge6 and Co2Al5. The characteristic feature of Fe32+δGe35-xPx is that P partially replaces Ge in one of the 6k sites in the MgFe6Ge6-type column and does not form the X2 dumbbells consisting of As atoms that are present in Fe32+δGe33As2. In the Fe32+δGe35-x-yPxAsy solid solution, P and As atoms occupy the same sites as in the initial Fe32+δGe35-xPx and Fe32+δGe33As2 compounds, respectively. The magnetic behavior of Fe32+δGe35-xPx is similar to that of Fe32+δGe33As2, and the antiferromagnetic transition is observed at TN ∼130 K.

The Structure of Cis-2,2′-Azopyridine in the Solid State

Descriptions of azoheteroaromatic compounds in their cis-isomeric form in the solid state are almost non-existent. Cis-2,2′-azopyridine is a known compound which structure differentiates from the trans-isomer based on spectroscopic evidence (UV–Vis absorption, 1H, and 13C NMR spectroscopy) and with studies regarding its stability, thermal reversion to the trans-isomer, and dipole moment in solution. However, the structure of this compound in the solid state has been unresolved. Herein, we present the crystal structure of cis-2,2′-azopyridine that forms red prismatic crystals in the monoclinic space group C2/c. The unit cell parameters are: a = 23.485 (4), b = 5.9241 (12), c = 21.656 (4) A, and V = 2717.1 (9) A3 with 12 molecules per unit cell. Molecules are arranged as two helical conformers (P and M) with C–N=N–C torsion angles and aromatic ring planes’ angles comparable to those reported for cis-azobenzene. The rare structural determination of an azoheteroaromatic cis-isomer of 2-azopyridine that was synthesized, isolated and crystallized is presented. X-ray structure analysis reveals that the molecule forms dimeric complexes containing both M- and P-helical conformers as well as infinite stacked columns in the solid state through a combination of C–H⋯N hydrogen bonds, C–H⋯π interactions and lone pair⋯π contacts.

Synthesis, and Crystal and Electronic Structures, of the Titanium-Rich Bismuthides AE3Ti8Bi10 ( AE = Sr, Ba, Eu).

Three isotypic compounds with the chemical formula AE3Ti8Bi10 ( AE = Sr, Ba, Eu) have been obtained via both high-temperature solid state and flux growth reactions. Their crystal structure, representing a new type (space group P63/ mmc, Pearson symbol hP42), features an open framework composed of interlinked TiBi5 square pyramids and TiBi6 octahedra. The Ti-Bi substructure is penetrated by infinite columns of face-sharing AE6 polyhedra centered by Bi atoms. First-principle calculations and physical property measurements indicate metallic behavior and absence of localized magnetic moments on the Ti atoms. Analysis of the chemical bonding reveals strong Ti-Bi and Ti-Ti bonds. The latter demonstrate classic two-center, as well as multicenter, interactions.

How valid is Taylor dispersion formula in slugs?

How valid is Taylor dispersion formula in slugs?

C6 H14 N]PbBr3 : An ABX3 -Type Semiconducting Perovskite Hybrid with Above-Room-Temperature Phase Transition.

Organic-inorganic hybrid perovskites, with the formula ABX3 (A=organic cation, B=metal cation, and X=halide; for example, CH3 NH3 PbI3 ), have diverse and intriguing physical properties, such as semiconduction, phase transitions, and optical properties. Herein, a new ABX3 -type semiconducting perovskite-like hybrid, (hexamethyleneimine)PbBr3 (1), consisting of one-dimensional inorganic frameworks and cyclic organic cations, is reported. Notably, the inorganic moiety of 1 adopts a perovskite-like architecture and forms infinite columns composed of face-sharing PbBr6 octahedra. Strikingly, the organic cation exhibits a highly flexible molecular configuration, which triggers an above-room-temperature phase transition, at Tc =338.8 K; this is confirmed by differential scanning calorimetry (DSC), specific heat capacity (Cp ), and dielectric measurements. Further structural analysis reveals that the phase transition originates from the molecular configurational distortion of the organic cations coupled with small-angle reorientation of the PbBr6 octahedra inside the inorganic components. Moreover, temperature-dependent conductivity and UV/Vis absorption measurements reveal that 1 also displays semiconducting behavior below Tc . It is believed that this work will pave a potential way to design multifeatured perovskite hybrids by utilizing cyclic organic amines.

Syntheses of four new asymmetric Schiff bases and their Cu(II) complexes: Theoretical calculations to rationalize the packing of molecules in the crystals

Abstract Four new asymmetric Schiff bases, N-α-methylsalicylidene-N′-2-hydroxynapthylidene-1,3-propanediamine (H2L1), N-α-methylsalicylidene-N΄-5-bromosalicylidene-1,3-propanediamine (H2L2), N-α-methylsalicylidene-N΄-3-methoxysalicylidene-1,3-propanediamine (H2L3) and N-(3-methoxysalicylidene)-N΄-(2-hydroxynapthylidene)-1,3-propanediamine (H2L4) and their Cu(II) complexes [CuL1] (1), [CuL2] (2), [CuL3] (3) and [CuL4] (4) have been synthesized. All the complexes (1–4) have been structurally characterized by single crystal XRD. The Cu-atom is four coordinated square planar in complexes 1–3 but in 4 a water molecule coordinates to one of its axial positions making it penta-coordinated with square pyramidal geometry. The mononuclear complex molecules of 1 and 2 form infinite 1D columns that are arranged parallel forming 2D sheets where as in 3 they form self-assembled dimers that are inter-connected by weak van der Waals interactions and in 4 the molecules are packed in the form of infinite 1D ladders. The structure of a recently reported complex with a similar asymmetric ligand (H2L5) N-α-methylsalicylidene-N′-salicylidene-1,3-propanediamine where the phenoxido oxygen coordinates mutually to the axial position of another molecule to form a dimer is compared to the present complexes. The packing of the molecules in all the crystals are rationalized by theoretical molecular electrostatic potential surface (MEPS) calculations. DFT calculations show the significant role of CH·π (chelate ring) and π⋯π (chelate ring) interactions governing the crystal packing in all the complexes. Both the interactions are evaluated energetically by means of high level DFT calculations (M06-2X/def2-TZVP) and characterized using Bader's theory. Energetic differences between the monomeric and dimeric complexes in 1 and 5 have also been evaluated.

Hysteresis and Horizontal Redistribution in Porous Media

It is well known that multiphase flow in porous media exhibits hysteretic behaviour. This is caused by different fluid–fluid behaviour if the flux reverses. For example, for flow of water in unsaturated soils the process of imbibition and drainage behaves differently. In this paper we study a new model for hysteresis that extends the current playtype hysteresis model in which the scanning curves between drainage and imbibition are vertical. In our approach the scanning curves are non-vertical and can be constructed to approximate experimentally observed scanning curves. Furthermore our approach does not require any book-keeping when the flux reverses at some point in space. Specifically, we consider the problem of horizontal redistribution to illustrate the strength of the new model. We show that all cases of redistribution can be handled, including the unconventional flow cases. For an infinite column, our analysis involves a self-similar transformation of the equations. We also present a numerical approach (L-scheme) for the partial differential equations in a finite domain to recover all redistribution cases of the infinite column provided time is not too large.