Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.     

Photophysical characteristics of three novel benzanthrone derivatives: Experimental and theoretical estimation of dipole moments

The effect of solvents on absorption and fluorescence spectra and dipole moments of novel benzanthrone derivatives such as 3-N-(N′,N′-Dimethylformamidino) benzanthrone (1), 3-N-(N′,N′-Diethylacetamidino) benzanthrone (2) and 3-morpholinobenzanthrone (3) have been studied in various solvents. The fluorescence lifetime of the dyes (1-3) in chloroform were also recorded. Bathochromic shift observed in the absorption and fluorescence spectra of these molecules with increasing solvent polarity indicates that the transitions involved are π→π^?. Using the theory of solvatochromism, the difference in the excited-state (μ_e) and the ground-state (μ_e) dipole moments was estimated from Lippert-Mataga, Bakhshiev, Kawski-Chamma-Viallet, and McRae equations by using the variation of Stokes shift with the solvent’s relative permittivity and refractive index. AM1 and PM6 semiempirical molecular calculations using MOPAC and ab-initio calculations at B3LYP/6-31 G^? level of theory using Gaussian 03 software were carried out to estimate the ground-state dipole moments and some other physicochemical properties. Further, the change in dipole moment value (Δμ) was also calculated by using the variation of Stokes shift with the molecular-microscopic empirical solvent polarity parameter (E_T^N). The excited-state dipole moments observed are larger than their ground-state counterparts, indicating a substantial redistribution of the π-electron densities in a more polar excited state for all the systems investigated.     

Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin

The dipole moments of vibronic transitions P _0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the ³ B _1u (π π*) → S ₀ electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P _0R )² over R on the constant of spin-orbit coupling ?_A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?_A) to the value of P _0R ⁱ for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P _0R ⁱ and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.     

An investigation of theL 2-L 3 Coster-Kronig transition probability for 63≦Z≦96

Nuclear spin polarization in the 4f ¹⁴6s ^{2 1} S ₀ ground state of¹⁷⁵Lu⁺(I=7/2) ions is achieved by optical pumping with the resonance line (¹ S ₀-¹ P ₁,λ=261.5 nm). Nuclear magnetic resonance of the free ions in He buffer gas yields for the magnetic dipole momentμ(¹⁷⁵Lu)=2.2240(11)μ _n (with diamagnetic correction). This value can be used for a more accurate determination of the magnetic dipole moments of other Lu isotopes from knownA factor ratios. A comparison with nuclear induction measurements in solids results in the chemical shiftsδ(LuB₁₂)=?23(5)·10^?4 andδ(LuSb)= ?31(5)·10^?4.     

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.     

Photosensitized luminescence of thermostable polynuclear Eu(III) complexes

Tetranuclear europium(III) complexes, [Eu₄(μ-O)(L₁)₁₀] (L₁=2-hydroxy-4-octyloxybenzophenone,1) and [Eu₄(μ-O)(L₂)₁₀] (L₂=2-hydroxy-4-dodecyloxybenzophenone,2) were synthesized by the reaction of lanthanide nitrates with L₁ or L₂ in the presence of triethylamine in methanol. The photosensitized emission bands of the both Eu(III) complexes in THF-d₈ were observed around 579, 590, 615, 653, and 699 nm by the excitation of the ligands at 380 nm, whereas the emission from the mononuclear complex 3 containing ethanol molecules was almost quenched. The emission efficiencies were determined to be 3.1±0.1% for 1 and 3.9±0.1% for 2, respectively. The differential scanning calorimetry (DSC) measurements demonstrated that the decomposition points of 1 and 2 were 309 °C and 320 °C, respectively, indicating high thermostability of these complexes compared to the mononuclear Eu(III) complex 3 (250 °C). New strategy for designing stable rare earth compounds giving strong emission would be emphasized by introducing polynuclear complexes. Polynuclear complexes should open a wide range of molecular design for photosensitized luminescence and thermal stability.     

Magnetic phase diagrams of the CrB- and FeB-type HoSi compounds

The temperature magnetic phase diagrams of the dimorphic HoSi compound were studied by neutron diffraction. The sample comprises 35.5% CrB- (Cmcm) and 64.5% FeB-type (Pnma) of structure. Both phases order antiferromagnetically below T_N=25 K and undergo first-order magnetic transitions at T_ic=16.5 K. Their T-phase diagrams comprise a low temperature (LT) 2.7 K−T_ic and a high temperature (HT) range T_ic−T_N with distinct wave vectors.The LT magnetic ordering of the CrB-type HoSi with the wave vector q₁=(1/2, 0, 1/2) corresponds to a uniaxial magnetic structure, with the Ho moments along the shortest axis c. At 2.7 K the ordered moment value is 8.6(2) μ_B/Ho atom. The HT ordering, described by the wave vector q₂=(q_2x, 0, q_2z) with a T-variable length, corresponds to an amplitude modulated structure.The magnetic ordering of the FeB-type HoSi requires two symmetry independent vectors q₃=(0, q_3y, q_3z) for the LT- and q₄=(q_4x, q_4y, 0) for the HT range. Both vectors correspond to sine wave modulated structures with the Ho magnetic moments confined along the shortest axis b. The q₃ vector has an almost invariable length vs. T close to ≈(0, 9/17, 1/11). At 2.7 K the amplitude of the wave is 10.9(1) μ_B/Ho atom. At T_icq₃ jumps to the wave vector q₄=(q_4x, q_4y, 0) with a T-variable length. At 17 K q₄=(0.092(1), 0.538(3), 0). Around T_ic there is a narrow coexistence range of the q₃ and q₄ competing phases. Various models are discussed and compared with the isomorphic RSi (R=rare earth) compounds counterparts of HoSi, a comparison that has led us to briefly review the magnetic structures available in the literature for this interesting class of compounds.     

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.     

Syntheses, structures and photophysical properties of heteronuclear Zn-Ln coordination complexes

Four heteronuclear Zn-Ln coordination complexes, [Nd₂Zn₂(p-toluylate)₁₀(phen)₂] (1), [Ln₂Zn₂(p-toluylate)₁₀(phen)₂]·2(HAc)_1/2 (Ln=Tb 2, Ho 3) and [PrZn₂(p-toluylate)₅(Ac)₂(phen)₂] (4) (phen=1, 10-phenanthroline), are synthesized by the hydrothermal method and their structures are measured by single-crystal X-ray diffraction. The IR and UV-vis-NIR absorption spectra and the emission spectra in the visible and near-infrared (NIR) regions of the four complexes are determined at room temperature. In the NIR region (or in the visible region), the complexes show the characteristic emission bands of Ln³⁺ ions, which may be attributed to sensitization from the ligands (the ligand directly-coordinated to Ln³⁺ ions and d-block) to Ln³⁺ ions after forming the Zn-Ln complexes. It is reported for the first time in this paper that the Zn-Pr complex 4 can exhibit the broad emission band in the NIR region. In addition, the shift, split or broadness of the ff emission bands in the NIR region of complexes 1, 3 and 4 are discussed.     

Relativistic comparison theorems for the Klein-Gordon equation with scalar and vector potentials in d-dimensions

Relativistic comparison theorems are established for discrete eigenvalues of Klein-Gordon equation with vector and scalar potentials in d-dimensions. Theorem 1: If V(λ) and S(λ) depend on a parameter λ, ∂S/∂λ?0, S?0, ∂V/∂λ?0, V?0, E>0, then it follows that ∂En/∂λ?0. Theorem 2: If S₂?S₁?0, 0?V₂?V₁, E>0, then the corresponding eigenvalues are ordered as En(2)?En(1). Theorem 3: If 0?V₂?V₁, S₂?|S₁|, En(1)>0, En(2)>0, then En(2)?En(1). Some illustrative examples are given.     

Syntheses, structures, fluorescence and thermal properties of three lanthanide coordination polymers built by N-benzoyl-N′-(4-benzoxy)thiourea

Three novel lanthanide 1-D chain coordination polymers, namely {[Tb(μ₂-L)₂(η²-NO₃)(CH₃OH)(H₂O)]·0.5CH₃OH·0.5H₂O}_n (1), {[Dy(μ₂-L)₂(η²-NO₃)(CH₃OH)(H₂O)]·H₂O}_n (2) and {[Ce(μ₂-L)₂(η²-NO₃)(H₂O)₃]·H₂O}_n (3) (HL=N-benzoyl-N′-(4-benzoxy)thiourea), have been prepared and characterized by IR spectroscopy, elemental analysis and single-crystal X-ray diffraction. The luminescence properties and themostabilities of polymers 1-3 have been determined as well.     

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.     

Sonochemical syntheses and characterization of nano-sized lead(II) coordination polymer with ligand 1H-1,2,4-triazole-3-carboxylate

Nanoparticles of a two-dimensional coordination polymer, {[Pb(L)(μ_1,1-NCS)(H₂O)]}_n (1), (L⁻ = 1H-1,2,4-triazole-3-carboxylate), have been synthesized by a sonochemical process and characterized by scanning electron microscopy, X-ray powder diffraction, IR spectroscopy and elemental analyses. The thermal stability of compound 1 both its bulk and nano-size has been studied by thermal gravimetric (TG) and differential thermal (DTA) analyses and compared each other. Concentration of initial reagents effects and the role of power ultrasound irradiation on size and morphology of nano-structured compound 1, have been studied. Calcination of the single crystals and nano-sized compound 1 at 400 °C under air atmosphere yields mixture of PbS and Pb₂(SO₄)O nanoparticles. Results show that the size and morphology of the PbS and Pb₂(SO₄)O nanoparticles are dependent upon the particles size of compound 1. A decrease in the particles size of compound 1 leads to a decrease in the particles size of the PbS and Pb₂(SO₄)O.     

Preparation and magnetic properties of Mn12 clusters with 4-cyanobenzenecarboxylate ligand, [Mn12O12(O2CC6H4-p-CN)16(H2O)4] and its tetraphenylphosphonium salts

The new Mn₁₂ magnetic clusters with 4-cyanobenzenecarboxylate ligand, [Mn₁₂O₁₂(O₂CC₆H₄-p-CN)₁₆(H₂O)₄] (1) and its singly (2) and doubly (3) reduced analogs as their tetraphenylphosphonium salts, have been synthesized and characterized by elemental analyses, Raman, ESI-MS spectra and magnetic measurements with a SQUID magnetometer. Unlike the known Mn₁₂ oxocarboxylate clusters, which are very soluble in CH₃CN or CH₂Cl₂, the complex 1 is not dissolved in organic solvents providing an indication for strong intermolecular interactions which lead to strong dipole–dipole interactions between clusters and affect the magnetic behavior. The one-electron and two-electron reduced clusters (2, 3) contain the bulk counterion and dissolve in CH₃CN. They show magnetic properties characteristic for anion Mn₁₂ single-molecule magnets.     

The thermal conductivity of polar gases in a magnetic field

Measurements are reported of the change in the thermal conductivity coefficients ?λ^∥ and ?λ^⊥ of polar gases under the influence of a magnetic field at room temperature. Investigated are the linear molecules HCl, DCl, HCN, OCS and CO₂ and the symmetric top molecules CH₃F, CD₃F, CH₃CN, CHF₃, NH₃ and ND₃. The results on the nonequilibrium polarizations WJ and W?JJ obtained from these experiment are expressed in terms of effective cross sections. With the present results the amount of data now available on certain effective cross sections has grown to an extent that justifies a systematic overview. Correlations are presented between the effective cross sections and various molecular properties such as the electric dipole moment and the moments of inertia.     

Synthesis, X-ray structure and magnetic properties of the quinone cobalt complexes [Co(3,5-DTBSQ)(bpy)2]x2 (x=BF4, ClO4)

Double oxidation of [Co^III(3,5-DTBCat)(3,5-DTBSQ)(bpy)] (1,ls-Co(III)) by AgBF₄ and of [Co^II(3,5-DTBSQ)₂(bpy)] (1,hs-Co(II)) by a mixture of HClO₄/H₂O₂ yielded [Co^III(3,5-DTBSQ) (bpy)₂]X₂, where X⁻=BF₄⁻ (4) and ClO₄⁻ (5), respectively. The mechanism for the double-oxidation process that leads to a loss of one of the quinone ligands and in some cases to a redistribution of the electronic charge is discussed here.     

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.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

χ measurement and optical limiting studies of urea picrate

The molecular charge complex urea picrate (UP) was synthesized and its third order nonlinear optical properties have been investigated using a single beam Z-scan technique with nanosecond laser pulses at 532 nm. Open aperture data of the compound indicates two photon absorption at this wavelength. The nonlinear refractive index n₂, nonlinear absorption coefficient β, magnitude of effective third order susceptibility χ⁽³⁾, the second order hyperpolarizability γ_h and the coupling factor ρ have been estimated. The experimentally determined values of β, n₂, Re χ⁽³⁾ and Im χ⁽³⁾, γ_h and ρ of the compound UP are 2.146 cm/GW, −1.258×10⁻¹¹ esu, −1.347×10⁻¹³ esu, 0.377×10⁻¹³ esu, 0.69×10⁻³² esu and 0.28, respectively. The compound exhibits good optical limiting at 532 nm with the limiting threshold of 80 μJ/pulse. Our studies suggest that compound UP is a potential candidate for optical device applications such as optical limiters.     

Syntheses of two new hybrid metal-organic polymers using flexible aliphatic dicarboxylates and pyrazine: Crystal structures and magnetic studies

The reaction of metal ions, flexible aliphatic dicarboxylates and pyrazine in aqueous solution afford two new metal-organic coordination polymers, {[Cu₂(μ₂-η²-O₂C(CH₂)₂CO₂-η²-μ₂)₂(H₂O)₂]·2H₂O}_n (1) and [Eu₂(μ₂-η²-O₂CCH₂CO₂-η¹-μ₁)₂(μ₂-η²-O₂CCH₂CO₂-η²-μ₂)(H₂O)₆]_n (2). Polymer 1 contains the paddle-wheel cage dicopper(II) units, forming a one-dimensional (1D) double-stranded chain structure along the a-axis, in which the copper(II) atoms are bridged by the carboxylate groups of four succinates. The intradimer Cu-Cu distance is 2.613(2) Å; the interdimer Cu?Cu distance is 6.473 Å. To our knowledge, compound 1 represents the first example of a double-stranded chain structure containing dinuclear paddle-wheel type cage. In the three-dimensional (3D) compound 2, each central Eu(III) ion have a distorted monocapped square antiprism coordination geometry. The structure is built up from two types of polymeric chains with [EuO₆(H₂O)₃]_n units as tethers, resulting in microporous framework. The magnetic behavior of 1 shows that the occurrence of a strong antiferromagnetic coupling between the copper(II) ions through the short bridges via the carboxyl groups can be obtained; the best fittings to the experimental magnetic susceptibilities gave −2J=314 cm⁻¹.