EXISTENCE OF NATURAL FREQUENCIES OF SYSTEMS WITH ARTIFICIAL RESTRAINTS AND THEIR CONVERGENCE IN ASYMPTOTIC MODELLING

A major limitation of the Rayleigh-Ritz method for determining the natural frequencies of a system is the need to choose admissible functions that do not violate the geometric constraints of that system (Courant 1943 Bulletin of the American Mathematical Society49, 1-23). Several researchers have attempted to overcome this problem by asymptotically modelling the rigid constraints with artificial (imaginary) restraints of very large stiffness (Courant 1943Bulletin of the American Mathematical Society49 , 1-23; Warburton and Edney 1984 Journal of Sound and Vibration95, 537-552; Gorman 1989 Journal of Applied Mechanics56, 893-899; Kim et al. 1990 Journal of Sound and Vibration143, 379-394; Yuan and Dickinson 1992 Journal of Sound and Vibration153, 203-216; Yuan and Dickinson 1992 Journal of Sound and Vibration159, 39-55; Cheng and Nicolas 1992 Journal of Sound and Vibration155, 231-247; Yuan and Dickinson 1994Computers and Structures53 , 327-334; Lee and Ng 1994 Applied Acoustics42, 151-163; Amabili and Garziera 1999 Journal of Sound and Vibration224, 519-539; Amabili and Garziera 2000 Journal of Fluids and Structures14, 669-690). While the numerical results thus obtained for the systems considered in the literature were in close agreement with exact values for the natural frequencies corresponding to the first few modes, sample calculations show that the error introduced by the asymptotic modelling increases with mode number and therefore to obtain accurate results for higher modes the magnitude of stiffness should also be increased. In any event, the error due to the asymptotic modelling would remain uncertain, except when the correct frequency values are known. However, the use of artificial restraints with negative stiffness, a new concept which was introduced in a recent publication (Ilanko and Dickinson 1999 Journal of Sound and Vibration219, 370-378) paves the way for estimating the error due to asymptotic modelling. This is possible since in this work, the Rayleigh-Ritz frequencies of the constrained system were found to be bracketed by the frequencies of the asymptotic models with positive and negative restraints. However, the use of artificial restraints with negative stiffness has raised some important questions: would a system with a large negative restraint become unstable, and if so what is the guarantee that the frequencies of the asymptotic model would converge to that of the constrained system? This paper is the result of the author's attempt to answer these questions and gives a proof of existence of natural frequencies for systems with artificial restraints (springs) having positive or negative stiffness coefficients, and their convergence towards constrained systems. Based on Rayleigh's theorem of separation, it has been shown that a vibratory system obtained by the addition of h restraints to an n -degree-of-freedom (d.o.f.) system, where h<n, will have at least (n÷h) natural frequencies and modes and that as the magnitude of the stiffness of the added restraints becomes very large, these (n÷h) natural frequencies will converge to the (n÷h) natural frequencies of a constrained system in which the displacements restrained by the springs are effectively constrained.     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED-CLAMPED AND SIMPLY SUPPORTED-CLAMPED BEAMS

In a previous series of papers (Benamar 1990 Ph.D. Thesis, University of Southampton; Benamaret al. 1991 Journal of Sound and Vibration149, 179-195;164, 399-424 [1-3]) a general model based on Hamilton's principle and spectral analysis has been developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. The results obtained with this model corresponding to the first non-linear mode shape of a clamped-clamped (CC) beam and to the first non-linear mode shape of a CC plate are in good agreement with those obtained in previous experimental studies (Benamaret al. 1991 Journal of Sound and Vibration 149, 179-195;164, 399-424 [2, 3]). More recently, this model has been re-derived (Azar et al. 1999 Journal of Sound and Vibration224, 377-395; submitted [4, 5]) using spectral analysis, Lagrange's equations and the harmonic balance method, and applied to obtain the non-linear steady state forced periodic response of simply supported (SS), CC, and simply supported-clamped (SSC) beams. The practical application of this approach to engineering problems necessitates the use of appropriate software in each case or use of published tables of data, obtained from numerical solution of the non-linear algebraic system, corresponding to each problem. The present work was an attempt to develop a more practical simple “multi-mode theory” based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance. The purpose was to derive simple formulae, which are easy to use, for engineering purposes. In this paper, two models are proposed. The first is concerned with displacement amplitudes of vibrationW_max /H, obtained at the beam centre, up to about 0·7 times the beam thickness and the second may be used for higher amplitudes W_max/H up to about 1·5 times the beam thickness. This new approach has been successfully used in the free vibration case to the first, second and third non-linear modes shapes of CC beams and to the first non-linear mode shape of a CSS beam. It has also been applied to obtain the non-linear steady state periodic forced response of CC and CSS beams, excited harmonically with concentrated and distributed forces.     

Synthesis of 2,3-dimorpholino-6-aminoquinoxaline derivatives and application to a new intramolecular fluorescent probe

Two fluorescent monomers having a quinoxaline skeleton, N-(2,3-dimorpholinoquinoxalin-6-yl)acrylamide (QxA) and N-(1-(2,3-dimorpholinoquinoxalin-6-ylamino)prop-2-yl)methacrylamide (QxAlaMA), were synthesized. Thermo-responsive copolymers of N-isopropylacrylamide (NIPAM) and a small amount of a fluorescent monomer were synthesized and their fluorescence properties investigated. The fluorescent monomers showed intense solvatochromism in their fluorescence. The wavelength at the maximum fluorescence intensity of the QxAlaMA-labeled PNIPAM dramatically blue-shifted and the fluorescence intensity of the QxA-labeled PNIPAM significantly increased around the transition temperature. It was found that these fluorescent dyes can sense and report the thermo-responsive behavior of the PNIPAM in water. Both QxAlaMA and QxA were demonstrated to be applicable to new intramolecular fluorescent probes.     

Cubic helimagnets in magnetic field and at pressure

Cubic helimagnets with B20 structure display several unusual properties such as anisotropy of the spin-wave spectrum al small momenta q, rotation of the helix vector k in magnetic field and quantum phase transition at pressure. We demonstrate that first two phenomena are a result of umklapp processes mixing excitations with momenta q, q+k and q−k. At very low magnetic field perpendicular to k the helical structure remains stable due to spin-wave gap Δ. Its square is sum of two parts. The first one is a result of the magnon interaction and the second negative part stems from magneto-elastic interaction. It is suggested that competition between these parts leads to the quantum phase transition observed in MnSi and FeGe. For MnSi from rough estimations at ambient pressure was shown that both parts are comparable with the experimentally observed gap. The magneto-elastic interaction is also responsible for 2k modulation of the lattice and contributes to the magnetic anisotropy. Experimental observation by X-ray and neutron scattering of this lattice modulation allows to determine the strength of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.     

Photophysical characteristics of 4,4′-bis(N-carbazolyl)tolan derivatives and their application in organic light emitting diodes

4,4′-bis(N-carbazolyl)tolan (BCT) and 4,4′-bis[N-(3,6-di-t-butyl)carbazolyl]tolan (BCT-t-Bu) were synthesized as π-expanded analogs of 4,4′-bis(N-carbazolyl)biphenyl. Their photophysical characteristics both in solution and films were thoroughly investigated. Interestingly, the phosphorescence spectrum of BCT was significantly medium-dependent, and the emission maximum was red-shifted by 131 nm from 489 nm in solution at 77 K to 620 nm in a deposited film at 5 K, suggesting the presence of strong intermolecular interactions in the film. BCT and BCT-t-Bu were found to be useful as host materials for fluorescence-based organic light emitting diodes (OLEDs). However, their low triplet energy levels in films negated their potential to act as hosts in phosphorescence-based OLEDs.     

Organic radical molecular solids based on [(TCNQ)n] (n=1 or 2): Syntheses, crystal structures, magnetic properties and DFT analyses

Four molecular solids consisting of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical and benzylpyridinium or benzylquinolinium derivatives with molar ratios of 1:1 (1-3) and 2:1 (4) have been prepared and characterized. In the crystals of 1 and 3, TCNQ⁻ monoanions and the corresponding cations form segregated stacks, which are regular in 1 but irregular in 3. Instead of segregated stacks, TCNQ⁻ monoanions in 2 form isolated π-dimers. In the crystals of 4, two crystallographic independent TCNQ species possess almost equal fractional negative charge (ca. −0.5). Two types of TCNQ species form a tetrad, these tetrads make a TCNQ stack with the pattern …BAAB…BAAB… along the crystallographic a-b direction. The magnetisms for 1-4 can be simply explained by the formation of singlet spin state. A broken symmetry approach in a density functional theory framework at the ub3lyp/6-31 g level was used to calculate the magnetic exchange constants in 1-4. The results qualitatively demonstrate the observed magnetic properties.     

Reinvestigation of crystal growth of thiosemicarbazide potassium chloride and thiosemicarbazide lithium chloride

Reinvestigation of the growth of thiosemicarbazide potassium chloride crystal (1) (Chandrasekaran et al. [1]) and thiosemicarbazide lithium chloride crystal (2) (Maadeswaran et al. [2]), unambiguously confirms that compounds 1 and 2 are pure thiosemicarbazide and do not contain any alkali metal or chloride ions. In this paper we demonstrate the use of classical halide test, flame test, as well as infrared (IR) spectra for correct product characterization.     

Luminescence and crystal-field fitting of two optical isomeric complexes of europium

FT-IR and Raman vibrational spectra and electronic emission spectra have been recorded for enantiomers of europium complexes with DBM: dibenzoylmethanate 1,2, and TTFA: 2-thenoyltrifluoroacetonate 3,4, employing the chiral ligands L_SS(+)- and L_RR(-)-4,5-pinene bipyridine. Contrary to the previously published X-ray data, where geometrical differences were stated to occur for particular enantiomers, the vibrational (and the emission) spectra of the individual optical isomers of a complex are not distinguishable. Using excitation into the Eu³⁺⁵D₂ multiplet term, the emission intensity is weak from ⁵D₁, whereas a complex structure is observed for the ⁵D₀→⁷F_J transitions. Features in the vibronic sidebands exhibit similar derived vibrational energies to those observed in the Raman spectra. Fittings of 25 4f⁶ crystal-field energy levels of 2 and 4 have been attempted with some approximations concerning the local Eu³⁺ environments. The ⁵D₀ emission lifetimes are monoexponential and are 0.5 (1,2) and 0.9 ms (3,4) at room temperature.     

GEOMETRICALLY NON-LINEAR FREE VIBRATION OF FULLY CLAMPED SYMMETRICALLY LAMINATED RECTANGULAR COMPOSITE PLATES

The geometrically non-linear free vibration of thin composite laminated plates is investigated by using a theoretical model based on Hamilton's principle and spectral analysis previously applied to obtain the non-linear mode shapes and resonance frequencies of thin straight structures, such as beams, plates and shells (Benamar et al. 1991Journal of Sound and Vibration149 , 179-195; 1993, 164, 295-316; 1990 Proceedings of the Fourth International Conference on Recent Advances in Structural Dynamics, Southampton; Moussaoui et al. 2000 Journal of Sound and Vibration232, 917-943 [1-4]). The von Kármán non-linear strain-displacement relationships have been employed. In the formulation, the transverse displacement W of the plate mid-plane has been taken into account and the in-plane displacements U and V have been neglected in the non-linear strain energy expressions. This assumption, quite often made in the literature has been adopted in reference [2] and (El Kadiri et al. 1999 Journal of Sound and Vibration228, 333-358 [5]), in the isotropic case and has been mentioned here because the results obtained have been found to be in very good agreement with those based on the hierarchical finite element method (HFEM). In a previous study, it was assumed, based on the analogy with the isotropic case, that the fundamental carbon fibre reinforced plastic (CFRP) plate non-linear mode shape could be well estimated, by using nine plate functions, obtained as products of clamped-clamped beam functions in the x and y directions, symmetric in both the length U001and width directions [3]. In the present work, a convergence study has been performed and has shown that, although such an assumption may yield a good estimate for the non-linear resonance frequency, 18 plate functions should be taken into account instead of nine in the first non-linear mode shape and associated bending stress patterns calculations. This allows the anisotropy induced by the fibre orientations to be taken into account. Results are given for the fundamental mode of fully clamped CFRP rectangular plates, for various plate aspect ratios and vibration amplitudes. The non-linear mode shows a higher bending stress near the clamps at large deflection, compared with that predicted by linear theory. Some experimental measurements are presented which are in good qualitative agreement with the theory.     

The molecular vibration-rotation kinetic-energy operator for general internal coordinates

The molecular kinetic-energy operator for general internal coordinates is formulated in terms of simple generalisations of the matrices A, B, α, and β of Crawford. A new matrix γ of the gradients of the translational and rotational constraints facilitates the calculation of the β matrix. It is shown that the kinetic pseudo-potential U is most conveniently calculated as an atomic sum, and results are given for valence coordinates in various types of molecules.     

A Theoretical Study of MgNC and MgCN in the X?Σ Electronic State

The MgNC radical was the first Mg-containing species to be observed in interstellar space. This fact has stimulated considerable spectroscopic interest in this molecule, and in its isomer MgCN, but nevertheless the only rotationally resolved spectroscopic data presently available for X?²Σ⁺ MgNC comprise the rotational spectrum (K. Kawaguchi et al., 1993, Astrophys. J.406, L39-L42; K. Ishii et al., 1993, Astrophys. J.410, L43-L44; M. A. Anderson and L. M. Ziurys, 1994, Chem. Phys. Lett.231, 164-170; E. Kagi et al., 1996, J. Chem. Phys.104, 1263-1267; E. Kagi and K. Kawaguchi, J. Mol. Spectrosc. 2000, 199, 309-310) together with a few vibronic bands, all originating in the vibronic ground state and belonging to the òΠ←X?²Σ⁺ electronic transition (R. R. Wright and T. A. Miller, 1999, J. Mol. Spectrosc.194, 219-228). For MgCN, only the rotational spectrum in the vibrational ground state is known (M. A. Anderson, T. C. Steimle, and L. M. Ziurys, 1994, Astrophys. J.429, L41-L44). We report here potential energy surfaces calculated by the Averaged Coupled-Pair Functional (ACPF) method with TZ3P+f (Mg), TZ2P+f(N,C) basis sets including core-valence correlation due to the Mg 2s and 2p electrons. The ab initio results are used for determining the standard spectroscopic constants of X?²Σ⁺ MgNC and MgCN. Also, we report variational calculations of the rotation-vibration energies, and variational simulations of the lowest rotation-vibration bands, carried out with the MORBID program system (P. Jensen, 1988, J. Mol. Spectrosc.128, 478-501). We hope that our theoretical results will encourage and facilitate further characterization of X?²Σ⁺ MgNC and MgCN by high-resolution spectroscopy.     

Correlation between adsorption and thermal properties of lanthanide(III) dinicotinates

Structural and thermal properties of the two isostructural lanthanide metal-organic frameworks: [Er₂(pdc)₃(dmf)₂]·dmf (1) and [Tm₂(pdc)₃(dmf)₂]·dmf (2) where pdc = C₅H₃N(COO)₂²⁻ and dmf = N,N′-dimethylformamide, have been investigated. They are characterized by the BET surface area of 302 and 101 m²/g for 1 and 2, respectively. This paper deals with the influence of activation conditions on sorption properties of the investigated complexes. Thermal investigations of as-made and activated complexes point to their entirely different thermal decompositions.     

Photophysical properties of a series of high luminescent europium complexes with fluorinated ligands

A series of high luminescent europium complexes have been synthesized, such as Eu(TFNB)₃phen (1), Eu(PFNP)₃phen (2), Eu(HFNH)₃phen (3) and Eu(PFND)₃phen (4), which have β-diketone ligands containing fluorinated alkyl chains with different lengths and conjugated naphthyl groups, i.e., 4,4,4-trifluoro-1-(2-naphthyl)butane-1,3-dione (TFNB); 4,4,5,5,5-pentafluoro-1-(2-naphthyl)pentane-1,3-dione (PFNP); 4,4,5,5,6,6,6-heptafluoro-1-(2-naphthyl)hexane-1,3-dione (HFNH) and 4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-pentadecafluoro-1-(2-naphthyl)decane-1,3-dione (PFND). And 10-phenanthroline (phen) is coordinated as the neutral second ligand in 1-4. The crystal structures of 1 and 2 have been studied, which are typical and similar to that of 3. The results of TGA-DTA suggest that these Eu complexes have good thermal stabilities. By means of absorption and (time resolved) emission spectroscopy including determination of luminescence quantum yields, energy transfer dynamics and so on, the following results have been obtained: first, these Eu complexes show characteristic pure red color photoluminescence emission with high quantum efficiencies from the central Eu³⁺ ions through the excitation of the ligands; secondly, photophysical properties of 1, 2, 3 and 4, especially the lifetimes of excited states ⁵D₀ of Eu³⁺ ions and quantum efficiencies are influenced by the different lengths of fluorinated alkyl chains, though the singlets (S₁) and triplets (T₁) of the fluorinated ligands are almost the same.     

Nature of electric and magnetic dipoles gleaned from the Poynting theorem and the Lorentz force law of classical electrodynamics

Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, ρ_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S = μ_o^− 1E × B and S = E × H. Here E is the electric field, H is the magnetic field, B is the magnetic induction, and μ_o is the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is intimately tied to the nature of magnetic dipoles and the way in which these dipoles exchange energy with the electromagnetic field. In addition, the manifest nature of both electric and magnetic dipoles in their interactions with the electromagnetic field has consequences for the Lorentz law of force. If the conventional identification of magnetic dipoles with Amperian current loops is extended beyond Maxwell's macroscopic equations to the domain where energy, force, torque, momentum, and angular momentum are active participants, it will be shown that “hidden energy” and “hidden momentum” become inescapable consequences of such identification with Amperian current loops. Hidden energy and hidden momentum can be avoided, however, if we adopt S = E × H as the true Poynting vector, and also accept a generalized version of the Lorentz force law. We conclude that the identification of magnetic dipoles with Amperian current loops, while certainly acceptable within the confines of Maxwell's macroscopic equations, is inadequate and leads to complications when considering energy, force, torque, momentum, and angular momentum in electromagnetic systems that involve the interaction of fields and matter.     

Structure and thermal behaviors of organic crystals based on substituted 1,3,4-thiadiazoles

The crystalline structure of some compounds containing the 1,3,4-thiadiazole moiety, (1) 5-ethyl-2-amino-1,3,4- thiadiazole (EATZ), (2) 5-benzylsulfany-2-amino-1,3,4-thiadiazole (BSATZ) and (3) 2,5-bis-benzylsulfanyl-1,3,4-thiadiazole (BBSTZ) were determined. Both EATZ and BBSTZ show orthorhombic structures with space group Pbca and BSATZ a monoclinic system with space group C2/c. The lattice parameters: a=0.72280 (14), b=1.0811 (2), c=1.6210 (3) nm for 1, a=2.5282 (5), b=0.59083 (12), c=1.5390 (3) nm for 2 and a=0.87530 (18), b=1.0365 (2), c=3.6098 (7) nm for 3. To compare the intra- and intermolecular interactions in thiadiazole containing organic crystals, thermal analysis studies on each crystal is performed using DSC and TG in N₂ atmosphere to describe the thermal behaviors. Based on the results, the changing regularity of melting point and decomposition temperature of these compounds is educed     

Effect of C and SiC additions into in situ or mechanically alloyed MgB2 deformed in Ti sheath

Effect of 3.4 wt.% C and 5 wt.% SiC doping into the standard in situ (IN) process and mechanically alloyed (MA) MgB₂ was studied. Powders of IN and MA process were carried out in air and in argon filled glove box, respectively. Wire samples were prepared by two-axial rolling deformation of IN and MA powders inside the Ti tube. Titanium as sheath material allows to use higher sintering temperatures, we used 700 °C and 800 °C for 30 min in Argon. Critical current densities (J_c) were measured at variable temperatures 4.2 K, 10 K, 15 K and 20 K in the external magnetic fields ranging to 15 T. Critical temperatures, upper critical fields and irreversibility fields of IN and MA with SiC and C additions are compared and discussed. The highest transport properties were observed for wires with MA SiC doped MgB₂ in the whole scale of temperatures 4.2–20 K. Upper critical field was rapidly enhanced in the case of carbon doped MA samples at 4.2 K. MA samples have shown decreased J_c values for higher temperatures (15 K, 20 K), in some case even worse than for the not doped reference IN sample. Carbon substitution and grain connectivity of analyzed samples are compared and discussed. Presented results show that for 20 K applications some new ways (additions) have to be found for increasing the J_c substantially.     

Reversible photomagnetism in a cobalt layered compound coupled with photochromic diarylethene

Photomagnetism is one of the most attractive topics in recent research on molecular solids. In order to produce a photo-controllable magnet, we have synthesized a novel organic-inorganic hybrid system coupled with a photochromic diarylethene anion, 2,2′-dimethyl-3,3′-(perfluorocyclopentene-1,2-diyl)bis(benzo[b]thiophene-6-sulfonate) (1a) and cobalt LDHs (layered double hydroxides). Based on the elemental analysis, the title compound, which was synthesized by the anion exchange reaction between Co₂(OH)₃(CH₃COO)·H₂O (2) and 1a, has the chemical composition, Co₄(OH)₇(1a)_0.5·3H₂O (3). Powder X-ray diffraction analysis revealed the interlayer distance of c=27.8 Å. The magnetic susceptibility measurements elucidated the ferromagnetic intra- and inter-layer interactions and the Curie temperature of T_c=9 K. By UV irradiation of 313 nm, 3 shows the photo-isomerization of diarylethene anion from the open form to the closed one in solid state, which leads to the decreases in the coercive field and the remnant magnetization. Furthermore, the photo-excited state is returned to the initial state (open form) almost reversibly by visible irradiation of 550 nm.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Supramolecular selectivity of [60]-fullerene among equivalently photoactive porphyrins

The photophysical investigation of different para-substituted tetraphenylporphyrins (TP), viz., meso-tetra(4′-hydroxyphenyl)-21H-23H-porphyrin(1),meso-tetrakis(4′-hex-5-enyloxyphenyl)-21H-23H-porphyrin(2), meso-tetrakis(4′-oct-7-enyloxyphenyl)-21H-23H-porphyrin(3) and meso-tetrakis(4′-undecyloxyphenyl)-21H-23H-porphyrin (4) revealed that except for quantum yield (φ) the para-substitution has little effect on any other photophysical properties like lifetime, excitation, emission wavelength, etc. The host-guest type interactions of these tetraarylporphyrins (TP 1-4), with [60]-fullerene (F) have been studied with ¹H NMR and fluorescence spectrometric techniques in carbon tetrachloride medium. Fluorescence studies revealed that the Q band of the TPs was sufficiently quenched upon addition of F. All the fullerene/porphyrin systems were found to produce stable complexes with 1:1 stoichiometry. Binding constants (K) of all the fullerene/porphyrin complexes have been determined by fluorescence quenching method. The association constant values for 1/F have been determined from plots of the Stern-Volmer equation (103.713×10⁴) and the Benesi-Hildebrand equation (110.440×10⁴). It has been observed that the insertion of long chain oxo-alkenyl/alkyl group in the para position of TPs in 2, 3 and 4 diminished the K values for F by two, four and even ten times with respect to that of 1. The observed trend in variation of the binding constants was supported by a gradual variation in the shift of ¹H NMR signal when measurements were carried out in CDCl₃.     

Synthesis,structures and near-infrared luminescence properties of Ho and Yb coordination complexes

Four Ln³⁺ coordination complexes with the formulas [Ln(p-toluylate)₂(Ac)(H₂O)]_n (Ln=Ho 1, Yb 2) and {[Ln₂(OOCCH₂CH₂COO)₃(H₂O)₄]·6H₂O}_n (Ln=Ho 3, Yb 4) were synthesized hydrothermally. Their structures were determined by single-crystal X-ray diffraction. Complexes 1 and 2 are isomorphic and form infinite 2D network structures comprising p-toluylate and acetate (Ac^–) moieties. Complexes 3 and 4 are also isomorphic and possess infinite 2D structures in which succinate acts as bridging ligands that are connected to a 3D hydrogen bonding network by O–H…O hydrogen bonds. Solid-state IR and UV-Vis-NIR spectra, excitation and emission spectra were determined for the four complexes at room temperature. Complexes 1 and 2 exhibit characteristic NIR emission bands of Ln³⁺ ions but these are shifted and split relative to the theoretical positions. This is also evident for their UV-Vis-NIR spectra. The influence of ligands on enhancing the NIR luminescence of Ln³⁺ ions in complexes is discussed.