Appearance of a Debye process at the conductivity relaxation frequency of a viscous liquid

The existence of a Debye-type ultraslow process in dielectric spectra of bulk polyalcohols and similar materials has been reported repeatedly in the recent literature. Its loss peak is observed at frequencies that are decades below those of the primary structural relaxation, in a range where the loss signal is usually dominated by dc-conductivity or even electrode polarization. We show that this peak originates from an incomplete filling of the capacitor volume, e.g., as a result of gas bubbles, a situation that gives rise to a Debye process at the conductivity relaxation frequency of the material, where the values of storage and loss components of permittivity are identical. The result implies that these peaks are not endemic to the liquid and can lead to various misinterpretations of the dielectric relaxation spectra. Techniques avoiding the occurrence of such artifacts are discussed.     

Frequency dependence of the shear moduli of spectrin studied using a multiple lumped resonator viscoelastometer

The frequency dependence (119-7860 Hz) of the storage and loss shear moduli, G' and G', of human erythrocyte spectrin dimer crude solutions at 22.5 degrees C has been measured using a Birnboim-Schrag multiple lumped resonator viscoelastometer. The measurements were carried out on solutions of ionic strength 1 mM containing 1.1-3.7 mg ml-1 spectrin. This corresponds to the terminal zone for G' and G'. Analysis of the data using the standard theory of hybrid relaxation spectra yields a relaxation time of 22.5 +/- 1 microseconds. The pure spectrin dimer relaxation time is estimated to be 16 +/- 3 microseconds. This result suggests that at an ionic strength of 1 mM, the spectrin dimers are extended and that the main relaxation process is simple end-over-end rotation.     

Localization and coherent dynamics of excitons in the two-dimensional optical spectrum of molecular J-aggregates

Two-dimensional optical spectra of J-aggregates at low temperature provide a large amount of information about the nature and dynamics of exciton states that is hidden in conventional broad band pump-probe spectra. By using numerical simulations, we study the two-dimensional absorption spectrum and find that it is dominated by a V-shaped negative peak and a blueshifted elliptic positive peak. We demonstrate a simple method to derive the energy dependence of the exciton localization size from the distance between these two features in the zero waiting time experiment. When the waiting time is turned on, the V peak is filled with an extra positive peak resulting from population relaxation. From the time evolution of this peak, energy dependent relaxation rates can be obtained. The oscillations of coherent contributions to the two-dimensional spectrum are not damped by inhomogeneous mechanisms and can be seen clearly.     

Measurement of the dielectric relaxation property of water-ion loose complex in aqueous solutions of salt at low concentrations

Electrolytes and their dissociated ions are thought to form positive or negative hydration layers around them. In this study, we have developed a method to determine the volume and the dielectric relaxation property (relaxation frequency f c, dispersion intensity delta) of the water hydrating ions in salt solutions. The method consists of four steps: (1) By use of a high-resolution microwave dielectric spectroscopy technique, the dielectric spectra of sample salt solution and bulk water are measured in pair. (2) The dielectric spectrum of solutes (ions) with water layers for a given volume fraction varphi is then calculated from each pair of dielectric spectra of a sample salt solution and reference water according to the Hanai mixture theory. (3) Each spectrum of solutes with water layers at a given varphi is decomposed into a few Debye relaxation functions and the bulk water component. (4) The volume fraction varphi is operationally decreased from 0.5, and steps (2) and (3) are repeated at each varphi until the bulk water component vanished. Then the volume fraction of the hydrated solutes (ions) in solution is determined. The method was applied to NaF and NaCl solutions. As a result the different spectral intensity was nearly proportional to the salt concentration below 0.2 M in the frequency range of 3-26 GHz. The hydration number N h and the dielectric relaxation property of the hydration layer for each salt solution was successfully determined as ( f c1, delta 1, N h)= (18.7, 44.9, 27.9) for NaCl and ( f c1, delta 1, f c2, delta 2, N h) = (26.0, 6.70, 5.64, 19.2) for NaF.     

Dynamic light scattering in liquid and supercooled diphenylmethane

We use a dynamic light scattering technique to measure both polarized (VV) and depolarized (VH) spectra of liquid diphenylmethane (DPM) between 288 and 362 K, covering both normal and supercooled liquid ranges. Our results allow extracting information on structural relaxation processes, rotational motions, rotation-translation couplings, and molecular reorientation phenomena in liquid DPM. The VV spectra are modeled according to the microscopic theory of Wang, which assumes that a structural relaxation process dominates the spectrum. We find that the relaxation time of the structural relaxation in DPM follows an Arrhenius behavior. The Rayleigh dip was observed in the VH spectra, which are described using the Andersen-Pecora theory. Our results are discussed in terms of the rotation-translation coupling parameter, which we find independent of temperature over the experimental range. The collective reorientation time also follows an Arrhenius behavior with temperature. Finally, we calculate the hydrodynamic volumes for the reorientation process from geometric molecular models in two hydrodynamic limits: slip and stick boundary conditions. Our results suggest that the DMP molecule reorientates in quasi-slipping conditions in the bulk liquid.     

Hydration of poly(ethylene oxide)s in aqueous solution as studied by dielectric relaxation measurements

The hydration state of poly(ethylene oxide)s (PEOs) in aqueous solutions was investigated using dielectric relaxation measurements at 25 degrees C over a frequency range up to 20 GHz, which is the relaxation frequency of water molecules in a bulk state. The dielectric relaxation spectra obtained indicated decomposition into two major and one minor relaxation modes with relaxation times of 8.3, 22, and 250 ps, respectively. The two major modes were attributed to rotational relaxation of water molecules belonging to the bulk state and water molecules hydrogen bonded to ethylene oxide (EO) monomer units. The number of hydration water molecules per EO unit depended on the molar mass of PEO (M) and reached a constant value of 3.7 at M > 1500, which agrees with the value obtained by other experiments.     

On the low frequency loss peak in the dielectric spectrum of glycerol

We measured dielectric spectra of glycerol at pressures exceeding 1 GPa in order to examine the slow Debye-like peak. This peak is not a relaxation process, but its frequency is consistent with an origin in dielectric discontinuities due to impurities. These heterogeneities have a non-negligible bulk modulus and are identified as volatile, relatively non-polar liquid contaminants. Although this slow peak is often found in the dielectric spectra of polyalcohols, it is not an intrinsic feature thereof, unlike the ostensibly similar relaxation peak in monoalcohols.     

Small-angle X-ray scattering in sodium dodecyl sulfate solutions and micelle clustering

The small-angle X-ray scattering (SAXS) in micellar sodium dodecyl sulfate solutions has been studied in the range of overall concentrations c from 8 mM (CMC₁) to 300 mM and the absolute values of scattering vector q from 0.07 to 3.0 nm^–1. The total intensity of isotropic scattering has been revealed to increase with solution concentration. At c > 27 mM, the SAXS spectra have been found to exhibit an interference peak, which testifies a correlation in the arrangement of micelles in the bulk solution. This peak corresponds to the magnitude of q close to 1.55 nm^–1. Using the position of this maximum, average distance r₀ between the centers of micelles has been determined, which is equal to 4.1 nm and remains almost unchanged upon an increase in the overall concentration of sodium dodecyl sulfate. The observed regularities have been explained in terms of the DLVO theory taking into account the electrostatic and molecular intermicellar interaction.     

Near-edge x-ray absorption and natural circular dichroism spectra of L-alanine: a theoretical study based on the complex polarization propagator approach

The complex polarization propagator method [J. Chem. Phys. 123, 194103 (2005)] has been employed in conjunction with density functional theory and gauge-including atomic orbitals in order to determine the near-edge x-ray absorption and natural circular dichroism spectra of L-alanine in its neutral and zwitterionic forms. Results are presented for the K-edges of carbon, nitrogen, and oxygen. In contrast to traditional methods, the proposed approach enables a direct determination of the spectra at an arbitrary frequency instead of focusing on the rotatory strengths for individual electronic transitions. The propagator includes a complete set of nonredundant electron-transfer operators and allows for full core-hole relaxation. The theoretical spectrum at the nitrogen K-edge of the zwitterion compares well with the experimental spectrum.     

Aspect ratio dependence of the enhanced fluorescence intensity of gold nanorods: experimental and simulation study

Experimental observations and theoretical treatments are carried out for the band shape and relative intensity of the emission from gold nanorods of various aspect ratios in the range between 2.25 (1.5 theory) and 6.0 (9 theory). The calculation of the fluorescence spectra requires knowledge of the nanorod size distribution, the enhancement factors, and the shape of the unenhanced fluorescence spectrum. The size distribution is determined from the fit of the observed absorption spectrum for each value of aspect ratio studied to the theoretical model of Gans. The theory by Boyd and Shen is used for calculating the enhancement of the fluorescence spectrum of the previously observed weak emission of bulk gold, which originates from the interband transition. This is carried out for nanorods of different aspect ratios. To compare theory to the observed nanorod fluorescence spectra, which suffer from self-absorption, the calculated nanorod fluorescence spectra are corrected for this effect using the observed absorption spectra. The comparison between the observed and the calculated fluorescence band shapes is found to be good. The calculated changes in the relative intensities upon changing the aspect ratios are found to be much greater than that observed. This is due to the fact that for the observed emission of all the nanorods studied nonradiative processes dominate the relaxation mechanism of the excited state, a fact that was not included in the theoretical treatments.     

Vibrational dynamics of some anions in aqueous solutions from isotropic Raman scattering

From the I_VV and I_VH Raman spectra of a totally symmetric vibration, isotropic scattering profiles have been obtained for several anions in dilute aqueous solutions at various temperatures. The Raman spectrometer was connected to an A/D converter and a small computer, which allowed multiple scanning, data accumulation, and numerical processing of these profiles with good precision over a frequency range of about 20 times their full width at half peak height.The theoretical analysis of the isotropic Raman profiles was accomplished by assuming vibrational phase relaxation based on a MARKOV-GAUSS mechanism. Fitting procedures to the experimental data permitted the determination of the vibrational frequency distribution and its modulation time. Temperature effects are discussed in relation to the distribution and motional characteristics of the immediate environment of water molecules of the anions.     

Temperature dependent dielectric relaxation spectroscopy of amyl acetate-xylene solutions – An approach to molecular and co-operative dynamics

Dielectric relaxation parameters of AMA-Xylene solutions have been investigated thoroughly to discern the associativeness as well as heterogeneous behavior among the hetero molecules in the solutions such that dielectric constant (ε_o) and relaxation time (τ) of solutions has been determined. Complex permittivity spectra (CPS) for Amyl Acetate (AMA)-Xylene solutions were measured in 10 MHz–50 GHz frequency range using Time domain reflectometry (TDR) technique. It is exciting to explore the cooperative nature and association between AMA-Xylene. With co-operative domains (CDs), dynamics in AMA-AMA and AMA-Xylene molecules have been explicated while Kirkwood validates CDs with diverse exchanges through bonding. The experimental values of ε_o are compared with theoretical values obtained from the molecular parameters suggested by the Luzar. Thermodynamic parameters for AMA-Xylene show positive values of Enthalpy and Entropy for all concentrations, indicating that the system is endothermic and less ordered. Gibbs free energy decreases with increase in volume fraction of amyl acetate (V_AMA).     

Distributions of conduction electrons as manifested in MAS NMR of gallium nitride

A strategy is demonstrated for identifying unambiguously and characterizing quantitatively the effects of distributions of conduction electron concentrations arising from intentional or unintentional dopants in semiconductors by magic-angle spinning (MAS) NMR. The 71Ga MAS NMR spectra of a number of chemically synthesized GaN samples with no intentional doping show inhomogeneously broadened absorptions to high frequency of the main peak. These broad signals are shown, from spin-lattice relaxation time measurements as a function of shift position in a single sample, to be due to Knight shifts arising from degenerate conduction electrons. For a GaN sample with Ge as an intentional dopant at the 0.13% (wt) level, the spectrum is dramatically broadened and shifted to high frequency by up to several hundred parts per million. Analysis of the inhomogeneously broadened line shape yields a quantitative probability density function for electron carrier concentration in the bulk sample that reflects significant compositional heterogeneity due to a variety of possible sources.     

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.     

The relaxation spectra of polymer networks with different types of topology,ordering, heterogeneity

Many characteristic features of the relaxation spectra of the different types of polymer networks (meshlike and tree-like) manifesting in experimental behaviour are determined by manifold types of local and long-range irregularities or inclusions existing even in the simplest network structures. These irregularities in the local topology, in the fluctuations of the local orientational order existing due to stretching of the chains in the bulk elastomers (even in the non-ordered elastomers), also due to possible LC-ordering, the distribution of chain lengths between junctions and possible existence of cross-link agglomerations and domains at random cross-linking and the influence of the position of the chain element relative to junctions lead to variety of relaxation spectra, frequency and time-dependencies. The long-range hydrodynamic effects in bulk network can also lead to drastic variation of relaxation spectra. The inclusion of elongated rigid particles in polymer gels and network leads to the appearance of new branches of relaxation spectra changing and overlapping the relaxation spectra of the primary network system.     

Measurements of relaxation time of a polyethylene melt

A device for measuring the elasticity of polymer melts has been designed by one of us (B. Maxwell). The device was used to obtain the relaxation modulus in shear of a linear polyethylene melt. From these data a discrete relaxation spectrum was derived. The range of the obtained spectrum was confirmed to correspond to the terminal zone of the “entanglement plateau” of the spectrum. The limiting dynamic viscosity (as frequency approaches zero) was obtained by integrating the relaxation modulus with respect to time. The viscosity and its activation energy were found to agree closely with the flow viscosity and the flow activation energy, respectively, involved in capillary flow.     

A theoretical study on surfactant adsorption kinetics: effect of bubble shape on dynamic surface tension

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.     

Vibrational spectroscopy investigation using ab initio and density functional theory on p-anisaldehyde

The FTIR and FT Raman spectra of p-anisaldehyde has been recorded in the regions 4,000-400 and 3,500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of p-anisaldehyde were obtained by ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) basis set. A complete vibrational assignment aided by the theoretical harmonic frequency analysis has been proposed. The harmonic vibrational frequencies calculated have been compared with experimental FTIR and FT Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

Ultrasonic absorption spectroscopy between 5 and 3100 MHz on some aqueous polyelectrolyte solutions

The ultrasonic absorption coefficient has been measured as a function of frequency between 5 MHz and 3.1 GHz for aqueous solutions of polyacrylic acid and of its sodium, potassium, and tetraethylammonium salts. Unlike an aqueous solution of propionic acid, all polymer solutions clearly exhibit excess absorption. Within the frequency range under consideration the excess absorption spectra can be analytically represented by two Debye-type relaxation terms. At 25°C the corresponding relaxation times adopt values between 3 and 12.4 ns, and between 0.12 and 0.22ns, respectively. The former process is discussed in accordance with previous models. The relaxation of the polyacrylic acid solutions is assumed to be related to the formation of hydrogen bonds of the polymeric molecules and that of the polyacrylate solutions may be due to interactions of counterions with chain segments. The latter process, the existence of which has been first proven in this study, is likely to reflect rotational motions of carboxyl groups.     

Theoretical study on the sound absorption of electrolytic solutions. II. Assignments of relaxations

The theory on the ultrasonic absorption spectrum of electrolytic solutions recently proposed by us is applied to the model system that resembles to the aqueous solution of MgSO4. The charges on ions are reduced to +/-1.5e in order to obtain the equilibrium structure by the integral equation theory. The theory reproduces the existence of two relaxations around 100 kHz and 1 GHz. The physical origin of the relaxation is analyzed based on the theoretical expression. The slower relaxation is shown to originate in the formation of contact ion pair, in harmony with the conventional assignment. The amplitude of this relaxation agrees with the experimental one fairly well. The absorption cross section is a weakly increasing function of the concentration of the salt in theory, whereas it depends little on the concentration in experiment, which is ascribed to the weaker association of the pair in the theory. The deviation from the Debye relaxation is found for the faster process, and the concentration dependence is small. The analysis shows that this relaxation stems from the coupling between the pressure and the long-range concentration fluctuation, and the concentration independence and the non-Debye relaxation are explained based on the theoretical analysis. In particular, the theory demonstrates that this process has the t(-3/2) tail in the time domain, which is confirmed by numerical calculation. The deviation of the theoretical relaxation amplitude from the experimental one is elucidated in terms of the theoretical expression of the coefficient.