Complex Relative Dielectric Function Research Articles

AC/DC conductivity and dielectric relaxation behavior of ionic solutions of 1-butyl-3-methylimidazolium chloride in methanol

The complex relative dielectric function, ε*(f) of solutions of 1-butyl-3-methylimidazolium chloride ([BMiM][Cl]) in methanol (MeOH) of varying concentration and temperature have been measured in lower (20 Hz–2 MHz) and microwave (200 MHz–20 GHz) frequency regimes using precision LCR meter and Vector Network Analyzer (VNA) respectively. Complex ac conductivity, σ*(f) of the liquid samples were determined from the measured low frequency ε*(f). DC conductivity, σdc of the samples were also determined. The influence of concentration and temperature variation on the complex permittivity and electrical conductivity of the solutions is discussed. σdc of pure [BMiM][Cl] and pure MeOH is significantly enhanced in diluted to moderately concentrated solution of [BMiM][Cl] in MeOH. Experimental values of σdc at different concentrations were fitted to the empirical Casteel-Amis (CA) equation. Static dielectric constant of ionic solutions was determined from complex permittivity measurements in the microwave frequency range, using which, information about the molecular interaction between [BMiM][Cl] and MeOH was revealed. Viscosity (η), molar conductivities (Λm), infinite dilution conductance (Λ0) and Walden product (W) of the solutions were also determined. Orientational relaxation behavior of the mixture solutions in microwave frequency region is not influenced by variation in concentration of [BMiM][Cl] in MeOH. Different contribution arising in the dielectric spectra are discriminated.

Electrode polarization and ionic conduction relaxation in mixtures of 3-bromoanisole and 1-propanol in the frequency range of 20 Hz to 2 MHz at different temperatures

The complex relative dielectric function ε∗(ω) = ε′ − jε″ of binary mixtures of 3-bromoanisole (3-BA) with 1-propanol (1-PrOH) of varying concentration have been measured using precision LCR meter in the frequency range 20 Hz to 2 MHz at different temperatures (303.15 K, 313.15 K, 323.15 K and 333.15 K). The electric/dielectric properties of the liquid samples are represented in terms of complex relative dielectric function ε⁎(ω), complex electric modulus M⁎(ω), complex electrical conductivity σ⁎(ω) and complex impedance Z⁎(ω). All of these presentations are used to explore various processes contributed in the electrical/dielectric properties of the mixtures of 3-BA and 1-PrOH. Effects of concentration variation of constituents of the binary liquid system and also of temperature on the various relaxation processes are discussed.

Dielectric and electrical properties of coconut water and distilled water in the frequency range 20 Hz to 2 MHz at different temperatures

The complex relative dielectric function e *(ω) = e′ − je″ of coconut water and distilled water in the frequency range 20 Hz to 2 MHz at different temperatures (303 to 333 K) were measured using a precision LCR meter. The electrical/dielectric properties of the liquid samples were represented in terms of complex relative dielectric function e *(ω), complex ac conductivity σ*(ω), and complex impedance Z *(ω). All of these presentations were used to explore various processes contributed in the electrical/dielectric properties of the coconut water and distilled water.

Dielectric and Electrical Properties of Binary Mixtures of Anisole and 1-Heptanol in the Frequency Range 20 Hz to 2 MHz

The complex relative dielectric function ε*(ω) = ε’- jε” of anisole (AN), 1-heptanol (1-HeOH) and their binary mixtures of varying concentration have been measured using Precision LCR meter in the frequency range 20 Hz to 2 MHz at 303 K. The electrical/dielectric properties of the liquid samples are represented in terms of intensive quantities namely, complex relative dielectric function ε*(ω), electrical modulus M*(ω), electrical conductivity σ*(ω) and extensive quantities, i.e. complex admittance Y*(ω) and complex impedance Z*(ω). All of these presentations are used to explore various processes contributed in the electrical/dielectric properties of the mixtures of two polar liquids.

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

The complex Fresnel reflection coefficients r(p) and r(s) of p- and s-polarized light and their ratio ρ=r(p)/r(s) at the pseudo-Brewster angle (PBA) φ(pB) of a dielectric-conductor interface are evaluated for all possible values of the complex relative dielectric function ε=|ε|exp(-jθ)=ε(r)-jε(i), ε(i)>0 that share the same φ(pB). Complex-plane trajectories of r(p), r(s), and ρ at the PBA are presented at discrete values of φ(pB) from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for φ(pB)>70° (high-reflectance metals in the IR) r(p) at the PBA is essentially pure negative imaginary and the reflection phase shift δ(p)=arg(r(p))≈-90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0<φ(pB)<45° and r(p) is pure real negative (δ(p)=π) when θ=tan(-1)(√(cos(2φ(pB)))), and the corresponding locus of ε in the complex plane is obtained. In the limit of ε(i)=0, ε(r)<0 (interface between a dielectric and plasmonic medium) the total reflection phase shifts δ(p), δ(s), Δ=δ(p)-δ(s)=arg(ρ) are also determined as functions of φ(pB).

Dielectric and Electrical Properties of Binary Mixtures of Anisole and Some Primary Alcohols in the Frequency Range 20 Hz to 2 MHz

The complex relative dielectric function ε*(ω) = ε-jε of binary mixture of anisole (AN) with methanol (MeOH) ,1-propanol (1-PrOH), 1-butanol (1-BuOH), 1-heptanol (1-HeOH) of varying concentration have been measured using Precision LCR meter in the frequency range 20 Hz to 2 MHz at 303 K. The electrical/dielectric properties of the liquid samples are represented in terms of intensive quantities namely, complex relative dielectric function ε*(ω), electrical modulus M*(ω), and extensive quantities, i.e. complex admittance Y*(ω) and complex impedance Z*(ω). All of these presentations are used to explore various processes contributed in the electrical/dielectric properties of the mixtures of polar-polar liquids.

Difference between the second-Brewster and pseudo-Brewster angles when polarized light is reflected at a dielectric–conductor interface

For a given pseudo-Brewster angle phi(pB) of minimum reflectance |r(p)| of p-polarized light at a dielectric-conductor interface, the second-Brewster angle phi(2B) of minimum reflectance ratio |rho|=|r(p)|/|r(s)| of the p and s polarizations is determined for all possible values of the complex relative dielectric function epsilon that lead to the same phi(pB). The difference phi(2B)-phi(pB) is considered as a function of phi(pB) and theta=arg(epsilon). For any given phi(pB), the difference phi(2B)-phi(pB)=0 at theta=0(epsilon(r)>0,epsilon(i)=0) increases monotonically as a function of theta and reaches maximum value {phi(2B)-phi(pB)}(max) in the limit as theta-->180 degrees (epsilon(r)<0,epsilon(i)=0). This maximum difference {phi(2B)-phi(pB)}(max) has an upper limit of 15.701 degrees when phi(pB)=28.195 degrees.

Plurality of principal angles for a given pseudo-Brewster angle when polarized light is reflected at a dielectric-conductor interface

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for a given phi (pB) is determined, and the maximum difference(phi -phi(pB))(max) is obtained as a function of phi(pB). The maximum difference (phi -phi(pB))(max) approaches 45 degrees and 0 in the limit as phi(pB)-->phi 0 and 90 degrees , respectively. For phi(pB)<22.666 degrees , multiple principal angles phi (i), i=1,2,3, appear for each epsilon in a subdomain of fractional optical constants. This leads to an elaborate pattern of multiple solution branches for the difference phi (i)-phi(pB), i=1,2,3, as is illustrated by several examples.

Characterization of solvent effect on low-frequency dielectric dispersion and relaxation behaviour of ethylene glycol oligomers

The complex relative dielectric function ɛ⁎( ω) = ɛ′ − jɛ″, electric modulus M⁎( ω) = M′ + jM″, alternating current electrical conductivity, and loss tangent tan δ = ɛ″ / ɛ′ spectra of binary mixture of ethylene glycol oligomers (EGOs) namely, ethylene glycol (EG), diethylene glycol (DEG) and poly(ethylene glycol)s (PEGs) of average molecular weight 200, 300, 400 and 600 g mol − 1 with water (W), ethyl alcohol (EA) and 1,4-dioxane (Dx) in the frequency range 20 Hz to 1 MHz were investigated at 298 K. In the lower-frequency range, the EGOs + W, EGOs + EA and EGOs + Dx mixtures show the direct current conductivity behaviour, and their values can be monitored by concentration variation of the mixture constituents, specially in case of EGOs + W and EGOs + Dx mixtures. The frequency value corresponding to tan δ peak, separates the contribution of the bulk and the electrode polarization phenomena, which is used to evaluate the electrode polarization relaxation time. The M″( f) peak frequency value is considered to evaluate the ionic conduction relaxation time. In these binary mixtures, as compared to rigid chain EG and DEG molecules, the flexible chain EGOs of higher molecular weight have significantly different dielectric response.

Characterization of ionic conduction and electrode polarization relaxation processes in ethylene glycol oligomers

The complex relative dielectric function, dielectric loss tangent, electric modulus, alternating current electrical conductivity and impedance spectra of ethylene glycol oligomers (EGOs) i.e., ethylene glycol, diethylene glycol and poly(ethylene glycol)s of average molecular weight 200, 300, 400 and 600 g mol-1 have been investigated in the frequency range 20 Hz to 1 MHz at 25 °C. These EGOs show the low frequency dielectric/electrical dispersion due to electrode polarization and ionic conduction effects. The ‘master curves representation’ of the real and imaginary parts of the intensive dielectric/electrical functions were used to evaluate the relaxation times corresponding to these effects processes. The comparative dielectric study of EGOs confirms that the values of low frequency relaxation times and direct current electrical conductivity are influenced by the chain flexibility and its random coiling.

Low frequency dielectric relaxation processes and ionic conductivity of montmorillonite clay nanoparticles colloidal suspension in poly(vinyl pyrrolidone)−ethylene glycol blends

The dielectric dispersion behaviour of montmorillonite (MMT) clay nanoparticles colloidal suspension in poly(vinyl pyrrolidone)-ethylene glycol (PVP-EG) blends were investigated over the frequency range 20 Hz to 1 MHz at 30°C. The 0, 1, 2, 3, 5 and 10 wt% MMT clay concentration of the weight of total solute (MMT+PVP) were prepared in PVP-EG blends using EG as solvent. The complex relative dielectric function, alternating current (ac) electrical conductiv- ity, electric modulus and impedance spectra of these materials show the relaxation processes corresponding to the micro- Brownian motion of PVP chain, ion conduction and electrode polarization phenomena. The real part of ac conductivity spectra of these materials obeys Jonscher power law σ'(ω )= σdc + Aω n in upper frequency end of the measurement, whereas dispersion in lower frequency end confirms the presence of electrode polarization effect. It was observed that the increase of clay concentration in the PVP-EG blends significantly increases the ac conductivity values, and simultaneously reduces the ionic conductivity relaxation time and electric double layer relaxation time, which suggests that PVP segmen- tal dynamics and ionic motion are strongly coupled. The intercalation of EG structures in clay galleries and exfoliation of clay sheets by adsorption of PVP-EG structures on clay surfaces are discussed by considering the hydrogen bonding inter- actions between the hydroxyl group (-OH) of EG molecules, carbonyl group (C=O) of PVP monomer units, and the hydroxylated aluminate surfaces of the MMT clay particles. Results suggest that the colloidal suspension of MMT clay nano particles in the PVP-EG blends provide a convenient way to obtain an electrolyte solution with tailored electrical con- duction properties.

Solvent effects on the dielectric dispersion of poly(vinyl pyrrolidone)-poly(ethylene glycol) blends

The complex relative dielectric function \( \varepsilon *{\left( \omega \right)} = \varepsilon \prime - j\varepsilon \prime \prime \), loss tangent \( \tan \delta = {\varepsilon \prime \prime } \mathord{\left/ {\vphantom {{\varepsilon \prime \prime } {\varepsilon \prime }}} \right. \kern-\nulldelimiterspace} {\varepsilon \prime } \), complex electric modulus \( M*{\left( \omega \right)} = M\prime + jM\prime \prime \) and alternating current electrical conductivity dispersion behaviour of liquid poly(vinyl pyrrolidone)-poly(ethylene glycol) (PVP–PEG) blends in water, ethyl alcohol and 1,4–dioxane solvent over the entire volume mixture concentration range has been investigated in the frequency range of 20 Hz to 1 MHz at 25 °C. The PVP–PEG blends show the dielectric dispersion corresponding to the micro-Brownian motion of the PVP chain in the upper frequency region, whereas in the lower frequency region, dielectric dispersion is due to ionic conduction and electrode polarization phenomena. Results show that the conductivity values of these blends in water and dioxane can be monitored with the change in the solvent concentration, whereas it has a small variation with ethyl alcohol concentration. The comparative dielectric dispersion shape study confirms that the chain dynamics of polymers blend is influenced by heterogeneous interactions and solvent polar strength.

Principal angles and principal azimuths of in-line symmetric three-reflection mirror system: application to circular polarization of vacuum ultraviolet radiation

Contours of constant principal angle Φ and constant principal azimuth Ψ for an in-line, symmetric, three-reflection mirror system are presented. The three mirrors are assumed to be uncoated substrates of the same homogeneous isotropic material with complex relative dielectric function e. By assigning values to Φ from 45 to 85 deg in 5-deg steps, the constraint on complex e is determined numerically and represented graphically. The special case of Φ = 45 deg, which applies to a right-angle parallel-mirror beam displacer, enables an analytical solution. These results have important applications for the production of circular polarization over the entire spectrum, and especially in the VUV, where transmission-type devices are not possible. The performance of the three-mirror system as a VUV quarter-wave retarder/circular polarizer using different metals is also considered.

Contours of constant principal angle and constant principal azimuth in the complex ∊ plane

For light reflection at a planar interface between two homogeneous isotropic media with complex relative dielectric function ∊, we show that the constant-principal-angle contours are a family of semicircles, whereas the constant-principal-azimuth contours are a family of (segments of) hyperbolas in the complex ∊ plane. We also find the exact envelope curve of both families and hence determine the domain of the ∊ plane of multiple (three) principal angles that is bougded by the envelope curve and the real axis. A unique and peculiar interface with ∊ =(5-j2)/27 is shown to have three coincident principal angles of 30° and an associated curve of relative phase shift (Δ) versus angle of incidence that exhibits a distinct shoulder at the principal angle.

Reflection of an electromagnetic plane wave with 0 or π phase shift at the surface of an absorbing medium

An electromagnetic plane wave incident obliquely from a transparent medium onto the surface of an absorbing medium can be reflected with 0 or π phase shift if (i) the wave is p (TM) polarized, and (ii) the complex relative dielectric function ∊ is such that 0⩽|∊|2/2Re(∊)⩽1. Furthermore, the locus of ∊ such that the reflection coefficient for the p polarization is real at the same angle of incidence, is a circle, and that of ∊1/2 (the complex relative refractive index) is Bernoulli’s lemniscate.