Initial Constant Value Research Articles

Memory effect of gravitational wave pulses in PP-wave spacetimes

In this paper, we study the gravitational memory effect in pp-wave spacetimes due to the passage of a pulse having the form of a ramp profile through this spacetime. We have analyzed the effect of this pulse on the evolution of nearby geodesics, and have determined analytical solutions of the geodesic equations in the Brinkmann coordinates. We have also examined the changes in the separation between a pair of geodesics and their velocity profiles. The separation (along x or y-direction) increases monotonically from an initial constant value. In contrast, the relative velocity grows from zero and settles to a final non-zero constant value. These resulting changes are retained as memory after the pulse dies out. The nature of this memory is similar to that determined by earlier workers using Gaussian, square, and other pulse profiles, thereby validating the universality of gravitational wave memory.

Mixed-Phase Fe2O3 Derived from Natural Hematite Ores/C3N4 Z-Scheme Photocatalyst for Ofloxacin Removal

Abatement of pharmaceutical pollutants from aquatic systems is crucial but remains a challenge. Semiconductor photocatalysis has emerged as an eco-friendly technique that utilizes renewable solar energy to address environmental issues. Naturally occurring and earth abundant hematite (Fe2O3) ores can be incorporated as a suitable component of a photocatalyst. Herein, Brazilian hematite was partially phase transformed into heterophase (consisting of α/γ-Fe2O3) by a simple single-stage heat treatment procedure. The method of synthesis was simple and economical, requiring neither solvents nor concentrated acids. The existence of α/γ-phases in the produced Fe2O3 (FO) was confirmed by X-ray diffraction analysis. After the phase transformation process, the local structure surrounding the Fe atoms was varied as evidenced from X-ray absorption spectroscopy. Given its low toxicity, narrow bandgap, and chemical stability, FO was further combined with g-C3N4 (CN) to form composites. The optical properties of the synthesized CNFO composites confirmed that the visible light harvesting ability of CN was enhanced after combining with FO. The CN sheets were grown uniformly over the surface of FO as evidenced from scanning electron microscopy. The prepared composites could degrade an aqueous solution of ofloxacin (OFX, 10 ppm) under visible light with remarkable efficacy. The performance of CNFO-5% was 4.8 times higher when compared to pure CN. The initial rate constant value for the photocatalytic degradation of OFX by CNFO-5% was 0.1271 min−1. The catalyst was stable even after five repeated cycles of photodegradation. The photoluminescence spectra and electrochemical measurements confirmed the efficient separation and transfer of the photogenerated charges across their interface. The investigations on different scavengers demonstrated that superoxide anion radicals and holes played a significant role in the degradation of OFX. The mechanism for the charge transfer was proposed to be a Z-scheme heterojunction. These results point to the potential of using inexpensive, abundant, and recyclable natural hematite ores as state-of-the-art photocatalysts for the elimination of pharmaceuticals in wastewater.

Transesterification activity by a zinc(II)-Schiff base complex with theoretical interpretation

The article demonstrates the synthesis, structural characterization and transesterification activity of a mononuclear zinc(II) complex, [Zn(HL)(H2O)]·(H2O) (1) containing a previously reported Schiff base ligand, H3L = N,N′-bis(salicylidene)-1,3-diamino-2-propanol]. X-ray structural analysis of 1 reveals that Zn(II)-Schiff base complex crystallizes in hexagonal crystal system with P61 space group and adopts a distorted tetrapyramidal geometry. Self-assembled molecular units of 1 exhibit a beautiful construction of 3D crystalline architecture through intermolecular hydrogen bond wire. Zinc(II) complex displays an enhancement of fluorescence intensity in comparison to HL in methanol medium. Catalytic behaviour of 1 towards disodium salt of 2,4-dinitrophenylphosphate (PNPP) in aqueous-methanol medium exhibits good transesterification activity with initial rate constant value of 1.73 × 10−4 min−1. Detailed DFT calculations are also employed to cope with the geometrical parameters of 1 as well as to explore the proposed catalytic mechanism of transesterification activity.

Dynamic Response Analysis of Planar Multilink Mechanism considering Wear in Clearances

Clearance wear is one of the factors that affects dynamics for mechanical systems. A numerical methodology suitable for modeling and calculation of wear at multiple revolute clearance pairs in the field of the planar multilink mechanism is proposed. In this paper, the 2‐DOF nine‐bar mechanism considering two revolute clearance joints is regarded as the study object. Normal contact force and friction force models of revolute clearance joints used Lankarani–Nikravesh (L‐N) and LuGre models, respectively. The iterative wear prediction process based upon Archard’s model has been applied to calculate wear characteristics. The wear prediction procedure is integrated with multibody dynamics, wear depths at revolute clearance joints are calculated, and the surface of shaft and bearing is reconstructed twice. The dynamic responses of mechanism considering two nonregular revolute clearances caused by wear are studied in depth. The nonlinear characteristics of the mechanism after wear are studied by the phase diagram and Poincaré map. Influences of different initial constant clearance values and different driving speeds on wear of two revolute joints are also researched. The results show that it is necessary to consider the factor of irregular clearances caused by wear in analysis of dynamics of precision mechanisms. Initial constant clearance values and driving speeds have some influence on wear phenomenon. This research provides a theoretical basis for studying dynamics of the planar multilink mechanism considering wear in multiple clearances.

Lightish but clumpy: scalar dark matter from inflationary fluctuations

It has recently been shown [1] that light vector particles produced from inflationary fluctuations can give rise to the dark matter in the Universe. A similar mechanism has been discussed in [2] for a non-minimally coupled scalar enjoying a Higgs portal interaction. We discuss in detail how such a generation of dark matter works in a minimal setup of a massive scalar non-minimally coupled to gravity. For suitable values of the non-minimal coupling any initial constant value of the field is suppressed during inflation. At the same time, the quantum fluctuations acquired during inflation give rise to a peaked energy density power spectrum. Isocurvature constraints can be avoided since nearly all of the energy is concentrated in fluctuations too small to be observed in the CMB. For masses ≳ eV and sufficiently high inflation scale the energy contained in these fluctuations is sufficient to account for the cold dark matter of the Universe. At small scales ℓtoday∼ 104 km √(m/eV) ∼ 10-4 AU √(m/eV) fluctuations are large and we therefore expect a rather clumpy nature of this form of dark matter.

Estimating apparent maximum muscle stress of trunk extensor muscles in older adults using subject-specific musculoskeletal models.

Maximum muscle stress (MMS) is a critical parameter in musculoskeletal modeling, defining the maximum force that a muscle of given size can produce. However, a wide range of MMS values have been reported in literature, and few studies have estimated MMS in trunk muscles. Due to widespread use of musculoskeletal models in studies of the spine and trunk, there is a need to determine reasonable magnitude and range of trunk MMS. We measured trunk extension strength in 49 participants over 65 years of age, surveyed participants about low back pain, and acquired quantitative computed tomography (QCT) scans of their lumbar spines. Trunk muscle morphology was assessed from QCT scans and used to create a subject-specific musculoskeletal model for each participant. Model-predicted extension strength was computed using a trunk muscle MMS of 100 N/cm2 . The MMS of each subject-specific model was then adjusted until the measured strength matched the model-predicted strength (±20 N). We found that measured trunk extension strength was significantly higher in men. With the initial constant MMS value, the musculoskeletal model generally over-predicted trunk extension strength. By adjusting MMS on a subject-specific basis, we found apparent MMS values ranging from 40 to 130 N/cm2 , with an average of 75.5 N/cm2 for both men and women. Subjects with low back pain had lower apparent MMS than subjects with no back pain. This work incorporates a unique approach to estimate subject-specific trunk MMS values via musculoskeletal modeling and provides a useful insight into MMS variation. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:498-505, 2018.

Poisson Dependency Networks: Gradient Boosted Models for Multivariate Count Data

Although count data are increasingly ubiquitous, surprisingly little work has employed probabilistic graphical models for modeling count data. Indeed the univariate case has been well studied, however, in many situations counts influence each other and should not be considered independently. Standard graphical models such as multinomial or Gaussian ones are also often ill-suited, too, since they disregard either the infinite range over the natural numbers or the potentially asymmetric shape of the distribution of count variables. Existing classes of Poisson graphical models can only model negative conditional dependencies or neglect the prediction of counts or do not scale well. To ease the modeling of multivariate count data, we therefore introduce a novel family of Poisson graphical models, called Poisson Dependency Networks (PDNs). A PDN consists of a set of local conditional Poisson distributions, each representing the probability of a single count variable given the others, that naturally facilitates a simple Gibbs sampling inference. In contrast to existing Poisson graphical models, PDNs are non-parametric and trained using functional gradient ascent, i.e., boosting. The particularly simple form of the Poisson distribution allows us to develop the first multiplicative boosting approach: starting from an initial constant value, alternatively a log-linear Poisson model, or a Poisson regression tree, a PDN is represented as products of regression models grown in a stage-wise optimization. We demonstrate on several real world datasets that PDNs can model positive and negative dependencies and scale well while often outperforming state-of-the-art, in particular when using multiplicative updates.

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Universality in fast quantum quenches

We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general $d$-dimensional conformal field theory deformed by a relevant operator of dimension $\Delta$ with a time-dependent coupling. The quench consists of changing the coupling from an initial constant value $\lambda_1$ by an amount of the order of $\delta \lambda$ to some other final value $\lambda_2$, over a time scale $\delta t$. In the fast quench limit where $\delta t$ is smaller than all other length scales in the problem, $ \delta t \ll \lambda_1^{1/(\Delta-d)}, \lambda_2^{1/(\Delta-d)}, \delta \lambda^{1/(\Delta-d)}$, the energy (density) injected into the system scales as $\delta{\cal E} \sim (\delta \lambda)^2 (\delta t)^{d-2\Delta}$. Similarly, the change in the expectation value of the quenched operator at times earlier than the endpoint of the quench scales as $<{\cal O}_\Delta> \sim \delta \lambda (\delta t)^{d-2\Delta}$, with further logarithmic enhancements in certain cases. While these results were first found in holographic studies, we recently demonstrated that precisely the same scaling appears in fast mass quenches of free scalar and free fermionic field theories. As we describe in detail, the universal scaling refers to renormalized quantities, in which the UV divergent pieces are consistently renormalized away by subtracting counterterms derived with an adiabatic expansion. We argue that this scaling law is a property of the conformal field theory at the UV fixed point, valid for arbitrary relevant deformations and insensitive to the details of the quench protocol. Our results highlight the difference between smooth fast quenches and instantaneous quenches where the Hamiltonian abruptly changes at some time.

Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The Composite Riemann Problem and its numerical solution

In a two-phase free-surface flow, the transition from a mobile-bed condition to a fixed-bed one (and vice versa) occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly. This leads to the possibility of conceiving a new type of Riemann Problem (RP), which we have called Composite Riemann Problem (CRP), where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity. In this paper, we present a strategy for solving a CRP by reducing it to a standard RP of a single, composite system of equations. This can be obtained by combining the two original systems by means of a suitable weighting function, namely the erodibility variable, and the introduction of an appropriate differential equation for this quantity. In this way, the CRP problem can be analyzed theoretically with standard methods, and the features of the solutions can be clearly identified. In particular, a stationary contact wave is able to correctly describe the sharp transition between mobile- and fixed-bed conditions. A finite volume scheme based on the Multiple Averages Generalized Roe approach (Rosatti and Begnudelli (2013) [22]) was used to numerically solve the fixed–mobile CRP. Several test cases demonstrate the effectiveness, exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model.

Single and mixed adsorption of Cd(II) and Cr(VI) onto citrate-coated magnetite nanoparticles

In the present work, we compared single and mixed adsorption of Cd(II) and Cr(VI) onto co-precipitation synthesized citrate-coated magnetite nanoparticles (NPs). Single kinetic studies revealed Cr(VI) to be better adsorbed than Cd(II). Otherwise, Cd(II) adsorption ratio was improved with Cr(VI) in the binary mixture. Single and mixed adsorption data followed in good agreement the pseudo-second-order kinetic model, with higher initial adsorption rate and rate constant values for Cr(VI). Equilibrium data from single Cd(II) and Cr(VI) adsorption only fitted concordantly the Freundlich isotherm model. The sorption capacity of magnetite NPs as function of initial metal concentrations was found to be 3 mg/g for Cd(II) and 4.65 mg/g for Cr(VI).

Pure creep, maturity and MP-creep in concrete in terms of an exo-process

Pure asymptotic creep of concrete is described as a manifestation of relaxation under low constant stress, where creep-induced damage is absent. An analytical solution for pure creep is obtained as a time-operator and is shown as an exo-function. The potential of stress loss in pure creep is found to be essentially higher than in relaxation due to steady re-elevation of the relaxed stress to the initial constant value. The duration of pure creep is described and found to be prolonged versus relaxation. Elastic maturity (the increase of the elastic modulus with time) and strength maturity (increase in concrete strength with time) are also exo-processes, described by a common time-operator. For structural concrete, they differ in the exponent – for elastic maturity, the exponent is 4·2–4·8 and for strength maturity its value is 3·8–4·2, depending on the type and content of cement. The influence of temperature up to 70°C is incorporated in the exo-operator of maturity. MP-creep – a combination of plain creep and increasing maturity – is described by equations, based on material parameters determined from tests. It is shown that elastic strain decreases under MP-creep.

Sorption kinetics of diuron on volcanic ash derived soils

Diuron sorption kinetic was studied in Andisols, Inceptisol and Ultisols soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Two types of kinetic models were used to fit the experimental dates: those that allow to establish principal kinetic parameters and modeling of sorption process (pseudo-first-order, pseudo-second-order), and some ones frequently used to describe solute transport mechanisms of organic compounds on different sorbents intended for remediation purposes (Elovich equation, intraparticle diffusion, Boyd, and two-site nonequilibrium models). The best fit was obtained with the pseudo-second-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the behavior of Diuron in each soil, in Andisols were observed the highest values for both parameters. The application of the models to describe solute transport mechanisms allowed establishing that in all soils the mass transfer controls the sorption kinetic across the boundary layer and intraparticle diffusion into macropores and micropores. The slowest sorption rate was observed on Ultisols, behavior which must be taken into account when the leaching potential of Diuron is considered.

A Simple Method for the Consecutive Determination of Protonation Constants through Evaluation of Formation Curves

A simple method is presented for the consecutive determination of protonation constants of polyprotic acids based on their formation curves. The procedure is based on generally known equations that describe dissociation equilibria. It has been demonstrated through simulation that the values obtained through the proposed method are sufficiently consistent with the actual values. In contrast with the universally known and applied Bjerrum's method, no differences in the accuracy of determination of subsequent protonation constant values are observed. The proposed method requires the value of one of the protonation constants (e.g., of the first one, K1) of the polyprotic acid. An iterative method is proposed for finding the value, starting from approximate values determined from the environment of point n = 0.5(n-average degree of protonation). Apart from high accuracy, the proposed method also has didactic advantages because it illustrates the problem of multiple acid equilibria in a visual (almost graphic) manner. The proposed method may also provide initial constant values for numerical methods of nonlinear approximation of the formation curve.

Modeling the sorption kinetic of metsulfuron-methyl on Andisols and Ultisols volcanic ash-derived soils: Kinetics parameters and solute transport mechanisms

Metsulfuron-methyl sorption kinetic was studied in Andisol and Ultisol soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Different kinetic models were applied to the experimental results. The pseudo-second-order model fitted sorption kinetics data better than the pseudo-first-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the different behavior of metsulfuron-methyl in both kinds of soils, both parameters being the highest for Andisol. The application of Elovich equation, intraparticle diffusion model and a two-site nonequilibrium model (TSNE) allowed to conclude that: (i) the high organic matter content is the governing factor for Andisols where mass transfer across the boundary layer, and in a lesser degree, intraparticle diffusion were the two processes controlling sorption kinetic and (ii) the mineral composition was more relevant in Ultisols where rate was controlled almost exclusively by intraparticle diffusion into macropores and micropores. The slower sorption rate on Ultisols, the mechanism involved and the lower sorption capacity of this kind of soils must be taken into account to assess leaching behavior of this herbicide.

Drying of a partially saturated rock matrix by fracture ventilation: Experiments and modeling in a single fracture‐matrix system

We present an efficient approach for modeling drying resulting from airflow through fractures embedded within a rock matrix by coupling a nonlinear diffusion equation for moisture transport in the matrix with a depth‐averaged quasi steady state advection‐dispersion equation for the vapor transport in the fracture. Coupling between the moisture transport equation in the fracture and matrix is achieved by applying Kelvin's equation at the fracture‐matrix interface. The proposed modeling approach was then validated based on a single fracture‐matrix drying experiment involving airflow through a fracture sandwiched between two matrix blocks. The moisture diffusivity for the rock matrix was first estimated in a one‐dimensional matrix drying experiment using a mass balance method. Numerical simulations based on our coupled modeling approach captured the important characteristics of the drying behavior in the single fracture‐matrix experiment. Additional numerical simulations are presented to clarify the factors controlling drying behavior. The important features of drying in a single fracture‐matrix system are as follows: (1) The total evaporation rate exhibits an initial constant value at early time, followed by a 1/t decrease with time. (2) At early time a “drying toe” forms near the fracture entrance and propagates along the fracture length as the fracture‐matrix interface becomes progressively drier. During this period, the moisture content distributions in the rock matrix are two‐dimensional, with gradients both parallel and perpendicular to the fracture. (3) At late time, after the drying toe reaches the end of the fracture, a “drying front” forms and propagates away from the fracture‐matrix interface, leading to a largely one‐dimensional (perpendicular to the fracture) variation of moisture content in the rock matrix. The experimental measurements could not fully resolve the early time two‐dimensional moisture content variations due to the coarse resolution, precluding a rigorous comparison with simulated behavior. However, the later‐time one‐dimensional moisture content variation observed in the experimental data was reasonably reproduced in the numerical simulations.

Coordination Behaviour of Novel Macrobicyclic Tricompartmental Ligands: Synthesis, Magnetic, Electrochemical and Kinetic Studies of Unsymmetrical Mono- and Binuclear Copper(II) Complexes

Several mono- and binuclear copper(II) complexes of general formula [CuL](ClO4) and [Cu2L(ClO4)](ClO4) have been synthesized from macrobicyclic ligands having different compartments originating from their corresponding precursor compound (PC: 3,4:9,10-dibenzo-1,12[N,N′-bis{(3-formyl-2-hydroxy-5-methyl)benzyl}diaza]-5,8-dioxacyclohexadecane). Electrochemical studies show that one quasi-reversible reduction wave (E pc=-0.75 to -0.83 V) for the mononuclear complexes and two quasi-reversible one-electron transfer reduction waves (=-0.78 to -0.86 V, =-1.01 to -1.28 V) for the binuclear complexes are obtained in the cathodic region. Room temperature magnetic moment studies indicate the presence of antiferromagnetic coupling in the binuclear complexes (μ eff=1.44–1.56 BM), which is confirmed by the broad ESR spectra with g=2.10–2.11, whereas the mononuclear complexes show hyperfine splitting in the ESR spectra and have magnetic moment values close to the spin-only value (μ eff=1.69–1.72 BM). Variable temperature magnetic susceptibility study of the complex finds that the observed -2J values for the binuclear complexes [Cu2L1(ClO4)](ClO4) and [Cu2L4(ClO4)]-(ClO4) are 216 cm-1 and 236 cm-1, respectively. The observed initial rate constant values for catechol oxidation using the complexes as catalysts range from 6.57×10-3 to 4.93×10-2 min-1 and the values are found to be higher for the binuclear complexes than the corresponding mononuclear complexes. It is proposed that a distortion of the copper ion geometry arises as the macrocyclic ring size increases. This is supported by spectral, electrochemical and catalytic studies.

Compartmental unsymmetrical lateral macrobicyclic ligands with an aromatic backbone providing a phenoxo bridge: synthetic, spectral, magnetic, electrochemical and kinetic features of mono and binuclear copper(II) complexes

From macrobicyclic ligands having different compartments originated from their corresponding precursor compounds (PC-1: 3,4:9,10-dibenzo-1,12[ N, N ′-bis{(3-formyl-2-hydroxy-5-methyl)benzyl}diaza]-5,8-dioxacyclotetradecane and PC-2: 3,4:9,10-dibenzo-1,12[ N, N ′-bis{(3-formyl-2-hydroxy-5-methyl)benzyl}diaza]-5,8-dioxacyclopentadecane) several mono and binuclear copper(II) complexes denoted as [CuL](ClO) 4 and [Cu 2L(ClO 4)](ClO 4) have been synthesized. Electrochemical studies vindicate that one quasireversible reduction wave ( E pc=−0.80 to −0.88 V) for the mononuclear complexes and two quasireversible one electron transfer reduction waves ( E pc 1=−0.84 to −0.94 V, E pc 2=−1.25 to −1.40 V) for the binuclear complexes are obtained in the cathodic region. The probe of room temperature magnetic moment studies depicts the presence of an antiferromagnetic interaction in the binuclear complexes ( μ eff of 1.35–1.42 B.M.), which is also observed from the broad ESR spectra with a g value of 2.10 or 2.11. Whereas, hyperfine splitting in ESR spectra is observed for mononuclear complexes and the magnetic moment value is found to be close to the spin only value ( μ eff of 1.69–1.71 B.M.). A variable temperature magnetic susceptibility study of the complex was carried out and the calculated −2 J values for the binuclear complexes [Cu 2L 1a(ClO 4)](ClO 4) and [Cu 2L 1b(ClO 4)](ClO 4) are 240 and 219 cm −1, respectively. The initial rate constant values of catechol oxidation using the complexes as catalysts have been found to span a domain ranging from 5.06 × 10 −3 to 2.56 × 10 −2 min −1 and the values are found to be higher for binuclear complexes than the corresponding mononuclear complexes. Spectral, electrochemical and catalytic studies support the distortion of the copper ion geometry that arises as the macrocyclic ring size increases.

Synthesis of mono and binuclear copper(II) complexes using new macrobicyclic tricompartmental unsymmetrical ligands: magnetic, electrochemical and catalytic studies

A series of new mono and binuclear copper(II) complexes [CuL 1a–eH 2](ClO 4) 2 and [Cu 2L 1a–e(ClO 4)](ClO 4), where L is a macrobicyclic tricompartmental ligand obtained from the condensation of the precursor compound (PC) 3,4:10,11-dibenzo-1,13[ N, N ′-bis{(3-formyl-2-hydroxy-5-methyl) benzyl}diaza]-5,9-dioxocyclohexadecane with various diamines have been synthesized. In this system, there are three compartments: the first compartment (N 2O 2) comprises two ether oxygens and two tertiary nitrogens, the second compartment (N 2O 2) contains two tertiary nitrogens and two phenolic oxygens and the third compartment (N 2O 2) is composed of two phenolic oxygens and two imine nitrogens. In mononuclear complexes the geometry of copper(II) ion present in the phenolic oxygen and imine nitrogen compartment is distorted square planar and in binuclear complexes the geometry of Cu(II) ion present in imine nitrogen and phenolic oxygen compartment is distorted square planar and the another Cu(II) ion present in phenolic oxygen and tertiary nitrogen compartment is square pyramidal. The synthesized complexes were characterized by spectroscopic (IR, UV–Vis and ESR) techniques. Electrochemical studies of the complexes reveal that all the mononuclear copper(II) complexes show a single quasireversible one-electron transfer reduction wave ( E pc=−0.76 to −0.84 V) and the binuclear complexes show two quasireversible one-electron transfer reduction waves ( E 1 pc=−0.86 to −1.01 V, E 2 pc=−1.11 to −1.43 V) in the cathodic region. The ESR spectra of the mononuclear complexes show four lines with nuclear hyperfine splittings with the observed g ∥ values in the range 2.20–2.28, g ⊥=2.01–2.06 and A ∥=125–273. The binuclear complexes show a broad ESR spectra with g=2.10–2.11. The room temperature magnetic moment values for the mononuclear complexes are in the range [ μ eff =(1.70 to 1.72) BM] and for the binuclear complexes the range is [ μ eff =(1.46 to 1.59) BM]. Variable temperature magnetic susceptibility study of the binuclear complex [Cu 2L 1d(ClO 4)](ClO 4) shows that the observed −2 J value is 225 cm −1. The calculated initial rate constant values for oxidation reaction of catechol to o-quinone ranges from 8.52 × 10 −3 to 3.08 × 10 −2 min −1. The catalytic activity of binuclear copper(II) complexes (1.65 × 10 −2 to 3.08 × 10 −2 min −1) is higher than the mononuclear copper(II) complexes (8.52 × 10 −3–9.67 × 10 −3 min −1).

Lateral macrobicyclic tricompartmental ligands: synthetic, spectral, magnetic, electrochemical and kinetic aspects of binuclear copper(II) complexes

New macrobicyclic tricompartmental ligands and their binuclear copper(II) complexes of type [Cu 2L](ClO 4) 2 have been synthesized from the precursor compound 3,4:10,11-dibenzo-1,13[ N,N′-bis(3-formyl-2-hydroxy-5-methyl)benzyl}diaza]-5,9-dioxacycloheptadecane with diamines (like ethylene, propylene and butylene) by template method. These complexes have been characterized by IR, UV–Vis spectral studies. Electrochemical studies of binuclear complexes evidence two quasireversible one electrontransfer reduction waves ( E 1 pc=−0.75 to −0.86 V, E 2 pc=−0.99 to −1.29 V). Room temperature magnetic moment studies convey the presence of antiferromagnetic coupling in binuclear complexes ( μ eff, 1.52 to 1.59 B.M.) which is also observed from the broad ESR spectra with g=2.11. A variable temperature magnetic susceptibility study of the complex evidences the observed −2 J value is 236 cm −1. The calculated initial rate constant values of catalytic reaction of oxidation of catechol to o-quinone ranges from 0.97×10 −2 to 2.30×10 −2 min −1. It is proposed that a distortion of the copper ion geometry arises as the macrocyclic ring size increases. This is supported by spectral, electrochemical and catalytic studies.