Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C 6 H 6 at 9.90 GHz

Debye relaxation times (τ _{j k} ) and dipole moments (μ _{j k} ) of binary (j k) polar mixtures of ethanol (EtOH) and N-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying conductivity of solution at 9.90 GHz for different temperatures, different mole fractions (x _j ) of ethanol and different weight fractions (w _{j k} ) of the mixtures, respectively. The variation of τ _{j k} ?x _j from linear slope of imaginary \((\sigma _{ijk}^{\prime \prime } )\) against real \((\sigma _{ijk}^{\prime })\) part of total conductivity \((\sigma _{ijk}^{\ast })\) curve reveals solute–solute (dimer) or solute–solvent (monomer) molecular associations up to x _j = 0.0?0.3 and thereafter, solute–solvent molecular associations. τ _{j k} s from the ratio of slopes of \(\sigma _{ijk}^{\prime \prime }-w_{jk} \) and \(\sigma _{ijk}^{\prime }-w_{jk} \) curves exhibit solute–solvent molecular association for all x _j s which are consistent with the μ _{j k} ?x _j curves at all temperatures except at 35^°C. This signifies the validity of both the proposed methods in estimating τ and μ. The molecular dynamics of the polar mixture are ascertained from Eyring rate theory. Theoretical dipole moments from bond angles and bond moments (μ _theo) are also calculated to predict associational aspects.     

Relaxation phenomena of polar non-polar liquid mixtures under low and high frequency electric field

Simultaneous calculation of the dipole moment μ_j and the relaxation time τ_j of a certain number of non-spherical rigid aliphatic polar liquid molecules (j) in non-polar solvents (i) under 9.8 GHz electric field is possible from real ε′_ij and imaginary ε″_ij parts of the complex relative permittivity ε*_ij. The low frequency and infinite frequency permittivities ε_0ij and ε_∞ij measured by Purohitet al [1,2] and Srivastava and Srivastava [3] at 25, 35 and 30°C respectively are used to obtain static μ_s. The ratio of the individual slopes of imaginary σ″_ij and real σ′_ij parts of high frequency (hf) complex conductivity σ*_ij with weight fractionsw _jatw _j → 0 and the slopes of σ″_ij— σ′_ij curves for differentw _js [4] are employed to obtain τ_js. The former method is better in comparison to the existing one as it eliminates polar-polar interaction. The hf μ_js in Coulomb metre (C m) when compared with static and reported μs indicate that μ_s s favour the monomer formations which combine to form dimers in the hf electric field. The comparison among μs shows that a part of the molecule is rotating under X-band electric field [5]. The theoretical μ_theos from available bond angles and bond moments of the substituent polar groups attached to the parent molecules differ from the measured μ_js and μs to establish the possible existence of mesomeric, inductive and electromeric effects in polar liquid molecules.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

Studies of linear correlation factor of dielectric polarization and excess dipolar free energies of amides in apolar solvents

The Kirkwood-Frohlich correlation factor (g), Eyring’s parametersG and G^* and the dipolar excess free energies of dilute solutions of formamide, acetamide,N-methyl acetamide,N,N-dimethyl formamide andN,N-dimethyl acetamide in 1,4-dioxan/benzene were obtained from a measurement of their static dielectric permittivities at 308 K. The fluid structure of these amides is discussed. Both in formamide and acetamide a dimeric linear chain with the individual dipoles more or less parallely oriented is preferred. InN-methyl acetamide, the antiparallel orientation of dipoles at lower concentrations turns into a parallel orientation with increase of concentration. In tertiary amides, with increase of concentration, parallel orientation of dipoles with global value ofg tending to unity is observed. The dipolar excess free energy of mixing in a given solvent is of the order primary amide > secondary amide > tertiary amide.     

Relaxation phenomena of binary polar liquid mixture in C6H6 from conductivity of solution measured at 10 GHz electric field

The dielectric relaxation times τ _jk ’s and dipole moments μ _jk ’s of the binary (jk) polar mixtures of N,N-dimethyl formamide (DMF) and pyridine dissolved in benzene (i) are estimated using linear slope of σ _jk ″ − σ _ijk ′ curves as well as ratio of slopes of σ _ijk ″ − w _jk and σ _ijk ″ − w _jk curves at w _jk → 0 for different mole fractions τ _jk ’s of pyridine and experimental temperatures under 9.875 GHz electric field. The measured μ _jk ’s and τ _jk ’s agree well with the reported values validating the proposed methods. The solute-solute (dimer) molecular associations are inferred from the plot of τ _jk − x _j and μ _jk − x _j curves for x _j = 0.0 to 0.5 of pyridine and thereafter solute-solvent (monomer) molecular association occurs. The theoretical μ_theo’s are calculated to predict solute-solute and solute-solvent molecular association. The μ _jk − T curves are drawn to show elongation of bond angles and bond moments with temperatures. The thermodynamic energy parameters are calculated from Eyring’s rate theory equations to know the molecular dynamics as well as to ascertain Debye-Smyth relaxation mechanism of the systems.     

Dielectric studies of some binary liquid mixtures using microwave cavity techniques

The excess parameter studies in the microwave frequency region (X-band) on complex dielectric permittivity for the binary mixtures are reported. The methods employed are fixed cavity perturbation technique and adjustable plunger cavity technique. Also Gopalakrishna method is used to calculate the relaxation time of the polar solute in a non-polar solvent. The samples under study are acetonitrile, chlorobenzene, dimethyl formamide, carbon tetrachloride and benzene.     

Magnetic and electromagnetic properties of composites of iron oxide and Co-B alloy prepared by chemical reduction

Magnetic and electromagnetic properties were investigated on the composites of iron oxide and Co-B alloy, which were prepared by a modified chemical reduction method. The composites are characterized by scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDXA), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and vibrating sample magnetometry (VSM). The complex electromagnetic parameters (permittivity ε_r=ε_r′+jε_r″ and permeability μ_r=μ_r′+jμ_r″) of paraffin mixed composite samples (paraffin:composites=1:1 in mass ratio) were measured in the frequency range 2-18 GHz by vector network analyzer. The measured real part (ε_r′) and imaginary part (ε_r″) of the relative permittivity show two resonant peaks in the range of 2-18 GHz. The imaginary parts of relative permeability (μ_r″) of all samples exhibited one broad resonant peak over the 2-8 GHz range. The μ_r″ of samples with higher molar ratio of Co to Fe (C and D) shows negative values within 13-18 GHz, which exhibit resonant and antiresonant permeabilities simultaneously. Calculation results indicated that the reflection loss values of the composites and paraffin wax mixtures are less than −10 dB with frequency width of about 6 GHz at the matching thickness.     

Photophysical Studies on the Interaction of Formamide and Alkyl Substituted Amides with Photoinduced Electron Transfer (PET) Based Acridinedione Dyes in Water

Interaction of photoinduced electron transfer (PET) based acridinedione dye (ADR 1) with amides like formamide, acetamide and dimethylformamide (DMF) were investigated by fluorescence spectral techniques. A fluorescence enhancement accompanied with a blue shift in the emission maximum was observed on the addition of amides to ADR 1 dye, which possess C₆H₄(p-OCH₃) in the 9th position of the basic acridinedione ring. The extent of fluorescence enhancement and the blue shift in the emission maximum of ADR 1 dye is of the order of DMF > acetamide > formamide. DMF, which is more hydrophobic and less polar, results in a higher extent of fluorescence enhancement and a larger shift in the emission maximum towards the blue region. On the addition of amides, the ADR 1 dye prefers to orient towards a more hydrophobic phase surrounded by more number of amide molecules. The fluorescence enhancement of ADR 1 dye is attributed to the suppression of PET process occurring through space. The influence of the hydrophobic nature and the polarity of the amides on the excited state properties of acridinedione dyes are elucidated by steady-state and time resolved fluorescence measurements.     

A comparative study of non-polar solvents effect on dielectric relaxation and dipole moment of binary mixtures of mono alkyl ethers of ethylene glycol and of diethylene glycol with ethyl alcohol

Dielectric relaxation and dipole moment of binary mixtures of homologous series of mono alkyl ethers of ethylene glycol and of diethylene glycol, i.e., mono methyl, mono ethyl and mono butyl ethers of ethylene glycol (ROCH₂CH₂OH) and mono methyl, mono ethyl and mono butyl ethers of diethylene glycol (ROCH₂CH₂OCH₂CH₂OH) with ethyl alcohol (C₂H₅OH) of different concentrations were studied in dilute solutions of benzene, dioxane and carbon tetrachloride at 35 °C. Permittivity (ε′) and loss (ε″) at 10.1 GHz, static dielectric constant ε_o at 1 MHz and high frequency limiting dielectric constant ε_∞ = n_D² at optical frequency of these molecules and their binary mixtures at different concentration were measured in dilute solutions of non-polar solvents. The average relaxation time τ_o, relaxation times corresponding to overall molecular reorientation τ₁ and group rotations τ₂ were determined using Higasi's single frequency measurement equations for dilute solutions. The evaluated values of relaxation times and free energy of activation ΔF were used to explore the solvent effect on molecular dynamics of these polar binary systems in non-polar solvents. The excess inverse relaxation time and excess free energy of activation were determined to confirm the existence of hydrogen-bonded heterogeneous cooperative domains of the ethers and alcohol molecules at different concentration their binary mixtures in non-polar solvents. The dipole moment of the binary mixtures was evaluated using Higasi's and Guggenheim's equation for dilute solutions. The evaluated values of dipole moments and computed dipole moment values using a simple mixing equation of the polar molecules binary mixture were used to explore the effect of non-polar solvent environment on heterogeneous molecular interactions between ethers and alcohol molecules. The effect of number of carbon atoms in the molecular structure of these homologous series molecules was also considered for the interpretation of various evaluated dielectric parameters.     

Dielectric absorption in mixtures of anisole with some primary alcohols at microwave frequency

Dielectric properties of binary mixtures of anisole with methanol (MeOH), 1-propanol (1-PrOH), 1-butanol (1-BuOH) and 1-heptanol (1-HeOH) over an entire concentration range have been studied at a fixed temperature 40°C. The dielectric constant (ε′) and dielectric loss (ε″) of the binary mixtures of polar liquids have been determined at a microwave frequency of 9.1?GHz. The static dielectric permittivity (ε ₀) of the liquid samples was also determined using a precision LCR meter. Determined values of static dielectric permittivity (ε ₀) and dielectric permittivity (ε*) at 9.1?GHz frequency were used to evaluate relaxation time (τ) and high frequency limit dielectric permittivity (ε _∞). Dielectric parameters were interpreted in terms of molecular interaction between the anisole and alcohol molecules.     

Dielectric relaxation of binary polar liquid mixture measured in benzene at 10 GHz frequency

The dielectric relaxation times τ _jk ’s and dipole moments μ _jk ’s of the binary (jk) polar liquid mixture of N,N-dimethyl acetamide (DMA) and acetone (Ac) dissolved in benzene (i) are estimated from the measured real σ′ _ijk and imaginary σ″ _ijk parts of complex high frequency conductivity σ* _ijk of the solution for different weight fractions w _jk ’s of 0.0, 0.3, 0.5, 0.7 and 1.0 mole fractions x _j of Ac and temperatures (25, 30, 35 and 40°C) respectively under 9.88 GHz electric field. τ _jk ’s are obtained from the ratio of slopes of σ″ _ijk -w _jk and σ′ _ijk -w _jk curves at w _jk → 0 as well as linear slope of σ″ _ijk -σ′ _ijk curves of the existing method (Murthy et al, 1989) in order to eliminate polarpolar interaction in the latter case. The calculated τ’s are in excellent agreement with the reported τ’s due to Gopalakrishna’s method. μ _jk ’s are also estimated from slopes β’s of total conductivity σ _ijk -w _jk curves at w _jk → 0 and the values agree well with the reported μ’s from G.K. method. The variation of τ _jk ’s and μ _jk ’s with x _j of Ac reveals that solute-solute molecular association occurs within 0.0–0.3x _j of Ac beyond which solute-solvent molecular association is predicted. The theoretical dipole moments μ _theo’s are calculated from bond angles and bond moments to have exact μ’s only to show the presence of inductive, mesomeric and electromeric effects in the substituent polar groups. The thermodynamic energy parameters are estimated from ln(τ _jk T) against 1/T linear curve from Eyring’s rate theory to know the molecular dynamics of the system and to establish the fact that the mixture obeys the Debye-Smyth relaxation mechanism.      

Moments of a Single Entry of Circular Orthogonal Ensembles and Weingarten Calculus

Consider a symmetric unitary random matrix V = (v _ij )_{1 ≤ i, j ≤ N} from a circular orthogonal ensemble. In this paper, we study moments of a single entry v _ij . For a diagonal entry v _ii , we give the explicit values of the moments, and for an off-diagonal entry v _ij , we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size N. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.     

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.     

Dispersion relation for electromagnetic waves in anisotropic media

Electromagnetic wave propagation in anisotropic dielectric media with two generic matrices εij and μij of permittivity and permeability is studied. In the framework of a metric-free electrodynamics approach, a compact tensorial dispersion relation is derived. The derivation does not require the corresponding matrices to be symmetric, positive definite, nor even invertible. The resulting formula is useful for a theoretical and experimental study of electromagnetic wave propagation in a wide class of linear media.     

Dielectric studies on binary polar mixtures of propanoic acid with esters

It is interesting to see the nature of intermolecular interactions between associative and non-associative polar liquids. Binary polar–polar liquid mixtures of ethyl acetate, ethyl benzoate, ethyl acrylate, ethyl butyrate, n-butyl acetate and benzyl benzoate, each with propanoic acid were subjected to dielectric studies at temperatures 25 °C, 35 °C and 45 °C. Static permittivity (ε_o) and dielectric constant at high frequency (ε_∞) were found through dielectric measurements for different concentrations of each system. The Bruggeman dielectric factor, Kirkwood correlation factor and the excess permittivity were determined. Deviations from the linearity of various models suggest molecular association through hydrogen bonding between the polar–polar constituents of the mixtures. The formation of cyclic and linear α-multimers in the above systems were identified. The results and their temperature dependence were interpreted accordingly.     

Frequency dispersive complex permittivity and permeability of ferromagnetic metallic granular composite at microwave frequencies

We experimentally studied the frequency dependent complex permittivity ε and permeability μ of composite composed of carbonyl iron powder (CIP) and epoxy resin in the frequency range 1-18 GHz. We found that the intrinsic ε and μ of CIP extracted from the measured ε and μ of composites follow the classical Maxwell equations and the Landau-Lifshitz-Gilbert (LLG) equation, respectively. The dependences of ε and μ of composites on the volume fraction of CIP (vf_CIP) were investigated using the two-exponent phenomenological percolation equation (TEPPE). We found that the TEPPE can fit the experimental results very well. Comparing the results of percolation parameters derived by experimental data at different frequencies, we show that the TEPPE is frequency independent for the composites at microwave frequencies. The results also show that the ε and μ spectrums of composites with definite vf_CIP can be correctly calculated by combining the TEPPE with the theoretical models of intrinsic ε and μ.     

Enhanced microwave magnetic and attenuation properties of composites with free-standing spinel ferrite thick films as fillers

Free-standing thick films of spinel ferrite, Ni_0.89−xCu_0.11Zn_xFe₂O₄ with x=0.55 and 0.60, were prepared as fillers to fabricate electromagnetic composites. Compared to those made with conventional spherical fillers, the composites made with thick film fillers showed enhanced static permeability (μ′₀) and maximum imaginary permeability (μ″_max). At the same time, complex permittivity (ε′ and ε″) were almost unchanged. A relative bandwidth W_R of 7–8 was achieved, which is about 75% of the theoretical maximum relative bandwidth. These composites are potential candidates as electromagnetic attenuation materials with ultrabroad absorption bandwidth in L and S bands.     

The electromagnetic energy and momentum of finite charged bodies moving at constant velocity

It is shown that a purely electromagnetic, divergence-free tensorS ^ij , can be defined for any electrically charged body which is held in equilibrium by some cohesive force and moving at some constant velocity. This tensor appears to represent the electromagnetic energy-momentum of the body; the integral (1/c) ∝S ^ij dS _j (dS _j is the differential element of any spacelike hypersurface) iscM ₀ μ ⁱ the electromagnetic four-momentum of the system (M ₀ is the electromagnetic rest mass of the system,U _i is the four-velocity). The divergence-free property ofS ^ij depends only on Maxwell's equation and the condition of uniform motion. It is suggested that whatever the nature of the cohesive forces within such a system the total stress-energy tensor will, in effect, break up into two parts which are separately divergence-free: the purely electromagnetic tensor,S ^ij , and a tensor representing the energy-momentum of the cohesive forces. Just as it makes sense to speak of the electromagnetic mass of a system at rest without regard to the cohesive forces, it makes sense to talk about the electromagnetic momentum of the system, when it is moving at constant velocity, without reference to the cohesive forces.     

Dielectric relaxation study of poly(ethylene glycols) using TDR technique

Temperature dependent dielectric relaxation and thermodynamic properties of polyethylene glycols HO[CH₂CH₂O)_nH with number average molecular weight 200 (n = 4), 300 (n = 7), 400 (n = 9) and 600 (n = 14) g mol^− 1 have been studied using Time Domain Reflectometry (TDR) in the frequency range 10 MHz to 20 GHz. The frequency dependence of the complex dielectric permittivity is analyzed by the Havriliak-Negami expression. The static permittivity ε₀, high frequency limiting static permittivity ε_∞, average relaxation time τ₀ and thermodynamic energy parameters such as free energy, enthalpy of activation and entropy of activation have been determined. The average free energy of activation ΔF_τ for PEG molecules was found to be in the range 4-5 kcal mol^− 1. The values of entropy ΔS_τ for PEG-200, PEG-400 and PEG-600 molecules were found to be positive while entropy ΔS_τ for PEG-300 molecules was found negative, which confirms that the configuration of PEG-300 involved in the dipolar orientation has an activated state, which is more ordered than the normal state compared to PEG-200, PEG-400 and PEG-600 molecules.