Dielectric relaxation pattern of dilute colloidal suspensions

An immediate method of analysis of the relaxation characteristics of a colloidal suspension, like of any dielectric, is based on the so-called Cole-Cole representation (imaginary part versus real part) of its complex dielectric constant in a wide frequency range. In this work, we show theoretical plots calculated according to the models developed by DeLacey and White (J Chem Soc Faraday Trans 2 77:2007–2039), and by Rosen et al. (J Chem Phys 98: 4183–4194; this model uses the dynamic Stern layer theory). Both theoretical approaches to the dielectric relaxation pattern of a colloidal suspension are compared to each other, and to experimental data obtained on polystyrene suspensions. Although no significant differences are found between the theoretical predictions of the relaxation patterns (except for the values of the dielectric constant; the DSL model yields higher polarizabilities of the suspensions), none of the models can exactly reproduce the frequency dependence of the dielectric constant of a colloidal system. We propose a modification of DeLacey and White's model to include the possibility that the ionic drag coefficients depend on the ion position in the double layer. The final results show that the general trends of the frequency dependence of the quantities involved are not modified, irregardless of the changes in ionic drag coefficients.     

Numerical and approximate studies on the theoretical dielectric relaxation of colloidal suspensions in the time domain

In this work we show numerical calculations on the dielectric behavior of colloidal suspensions in the time domain. The theory elaborated by DeLacey and White ((1981) J Chem Soc Faraday Trans 2 77:2007–2039) for dilute suspensions in the frequency domain, will be the basis for the present study. The different contributions, and their relative importance, to the transient current density generated in the suspensions after the application of a step electric field, are calculated from the dielectric response function associated to the DeLacey and White's model. In particular, we analyze the conduction and absorption current densities in the transient states upon changing the concentration of the supporting electrolyte in the suspension. With the aim of characterizing the response of the suspension for short times, an approximation to the distribution function of relaxation times that best fits the dielectric model, is calculated. Finally, an exhaustive analysis of the behavior of the dielectric response function is carried out, together with a comparison with other models in the time domain.     

Dielectric properties of aqueous zwitterionic liposome suspensions

The dielectric spectra of aqueous suspensions of unilamellar liposomial vesicles built up by zwitterionic phospholipids (dipalmitoylphosphatidyl-choline, DPPC) were measured over the frequency range extending from 1 kHz to 10 MHz, where the interfacial polarization effects, due to the highly heterogeneous properties of the system, prevail. The dielectric parameters, i.e., the permittivity epsilon'(omega) and the electrical conductivity sigma(omega), have been analyzed in terms of dielectric models based on the effective medium approximation theory, considering the contribution associated with the bulk ion diffusion on both sides of the aqueous interfaces. The zwitterionic character of the lipidic bilayer has been modeled by introducing an "apparent" surface charge density at both the inner and outer aqueous interface, which causes a tangential ion diffusion similar to the one occurring in charged colloidal particle suspensions. A good agreement with the experimental results has been found for all the liposomes investigated, with size ranging from 100 to 1000 nm in diameter, and the most relevant parameters have briefly discussed in the light of the effective medium approximation theory.     

Dielectric relaxation behavior of colloidal suspensions of palladium nanoparticle chains dispersed in PVP/EG solution

Dielectric measurements were carried out on colloidal suspensions of palladium nanoparticle chains dispersed in poly(vinyl pyrrolidone)/ethylene glycol (PVP/EG) solution with different particle volume fractions, and dielectric relaxation with relaxation time distribution and small relaxation amplitude was observed in the frequency range from 10(5) to 10(7) Hz. By means of the method based on logarithmic derivative of the dielectric constant and a numerical Kramers-Kronig transform method, two dielectric relaxations were confirmed and dielectric parameters were determined from the dielectric spectra. The dielectric parameters showed a strong dependence on the volume fraction of palladium nanoparticle chain. Through analyzing limiting conductivity at low frequency, the authors found the conductance percolation phenomenon of the suspensions, and the threshold volume fraction is about 0.18. It was concluded from analyzing the dielectric parameters that the high frequency dielectric relaxation results from interfacial polarization and the low frequency dielectric relaxation is a consequence of counterion polarization. They also found that the dispersion state of the palladium nanoparticle chain in PVP/EG solution is dependent on the particle volume fraction, and this may shed some light on a better application of this kind of materials.     

On the nature of the high-frequency relaxation in a molecular glass former: a joint study of glycerol by field cycling NMR, dielectric spectroscopy, and light scattering

Fast field cycling (1)H NMR relaxometry is applied to determine the dispersion of spin-lattice relaxation time T(1)(omega) of the glass former glycerol in broad temperature (75-360 K) and frequency (10 kHz-30 MHz) ranges. The relaxation data are analyzed in terms of a susceptibility chi(")(omega) proportional, variantomegaT(1)(omega), related to the second rank (l=2) molecular orientational correlation function. Broadband dielectric spectroscopic results suggest the validity of frequency temperature superposition above the glass transition temperature T(g). This allows to combine NMR data of different temperatures into a single master curve chi(")(omegatau(alpha)) that extends over 15 decades in reduced frequency omegatau(alpha), where tau(alpha) is the structural alpha-relaxation time. This master curve is compared with the corresponding ones from dielectric spectroscopy (l=1) and depolarized light scattering (l=2). At omegatau(alpha)<1, NMR susceptibility is significantly different from both the dielectric and light scattering results. At omegatau(alpha)>1, there rather appears a difference between the susceptibilities of rank l=1 and l=2. Specifically, at omegatau(alpha)>1, where the susceptibility is dominated by the so-called excess wing, the NMR and light scattering spectra (both l=2) rather coincide with each other and are about three times more intense than the dielectric (l=1) spectrum. This is explained by assuming that the high frequency dynamics correspond to only small-angle excursions. Below T(g), dielectric and NMR susceptibility compare well and exhibit an exponential temperature dependence.     

Rheological and Electrokinetic Properties of Sodium Montmorillonite Suspensions

Because of their particular electric surface properties and crystal structure, most clay minerals possess a very high ion exchange capacity. Furthermore, the surface charge distribution is anisotropic: while faces of the laminar clay particles have a negative, pH-independent charge, edges may be positive or negative, depending on pH. In this work, we propose to contribute new data on particle-particle interaction and charge distribution, by means of measurements of the low-frequency dielectric dispersion (LFDD) of the clay suspensions. Because of the nonspherical shape of clay particles, there are no theoretical models capable of explaining the experimental relaxation spectra. Hence, we limit ourselves to obtaining indirect information by comparing LFDD spectra in different experimental conditions. The quantities of interest in LFDD are the value of the low-frequency dielectric constant, epsilon'(r)(0), and the characteristic or relaxation frequency, omega(cr). These two parameters were measured varying the weight fraction, straight phi, of clay (0.5, 1, and 1.5% w/v) and the pH of the dispersion medium (5, 7, and 9), while maintaining the ionic strength constant ([NaCl]=10(-4) M). It was found that the characteristic relaxation frequency of the dielectric constant was pH-dependent, with a significant minimum at pH 7 in all cases. The results are interpreted as the superposition of two independent relaxation phenomena, associated with edges and faces. With respect to the weight fraction influence, we have found a linear behavior of epsilon'(r)(0) with straight phi at pH 9, indicating the existence of no significant interaction between particles. However, at pH 7 a slight deviation of linearity is observed, and at pH 5 we observe a clearly nonlinear behavior, indicating a stronger degree of interaction between particles. This is in good agreement with the initial assumption that at acid pH values, the electric surface charge of faces is negative, whereas the edges possess a positive charge, thus favoring attractive face-to-edge interaction. Copyright 2000 Academic Press.     

Occurrence of an Intermediate Relaxation Process in Water-in-Oil Microemulsions below Percolation: The Electrical Modulus Formalism

The dielectric and conductometric spectra of water-in-oil microemulsions below percolation in the frequency range from 1 MHz to 1.8 GHz have been analyzed on the basis of the electrical modulus formalism. In the frequency range investigated, this approach clearly evidences the presence of a particular polarization mechanism, resulting in a well-defined dielectric dispersion, located between that due to the orientational polarization of the bulk aqueous phase and that due to the ionic structure of the interface, usually occurring in heterogeneous systems. This polarization mechanism has been attributed to the "in-phase" correlation displacement of surfactant polar head groups surrounding each water droplet dispersed in the oil phase. This mechanism differs from the usual interfacial Maxwell-Wagner effect. The advantage of the electrical modulus formalism, in comparison with the analysis of the directly measured quantities, the permittivity epsilon'(omega), and the total electrical conductivity sigma(omega), are briefly discussed. Copyright 2001 Academic Press.     

Effects of T-tubules on dielectric spectra of skeletal muscle simulated by boundary element method with two-dimensional models

In order to investigate the origin of large intensity the alpha-relaxation in skeletal muscles observed in dielectric measurements with extracellular electrode methods, effects of the interfacial polarization in the T-tubules on dielectric spectra were evaluated with the boundary-element method using two-dimensional models in which the structure of the T-tubules were represented explicitly. Each model consisted of a circular inclusion surrounded by a thin shell corresponding to the sarcolemma. The T-tubules were represented by simplified two types of invagination of the shell: straight invagination along the radial directions, and branched one. Each of the models was subjected to two kinds of calculations relevant to experiments with the extracellular and the intracellular electrode methods. Electrical interactions between the cells were omitted in the calculations. Both calculations showed that the dielectric spectra of the models contained two relaxation terms. The low-frequency relaxation term assigned to the alpha-relaxation depended on the structure of the T-tubules. Values of the relaxation frequency of the alpha-relaxation obtained from the two types of calculations agreed with each other. At the low-frequency limit, the permittivity obtained from the extracellular-electrode-type calculations varied in proportion to the capacitance obtained from the intracellular-electrode-type ones. These results were consistent with conventional lumped and distributed circuit models for the T-tubules. This confirms that the interfacial polarization in the T-tubules in a single muscle cell is not sufficient to explain the experimental results in which the intensity of the alpha-relaxation in the extracellular-electrode-type experiments exceeded the intensity expected from the results of the intracellular-electrode-type experiments. The high-frequency relaxation term that was assigned to the beta-relaxation was also affected by the T-tubule structure in the calculations relevant to the extracellular-electrode-type experiments.     

Dielectric Dispersion and Electric Relaxation Processes Induced by Ionic Conduction in Formamide, 2-Aminoethanol and Their Binary Mixtures

The complex dielectric permittivity, ionic conductivity, electric modulus and impedance spectra of the dipolar molecules formamide (FA), 2-aminoethanol (AE) and their binary mixtures were investigated in the frequency range from 20 Hz to 1 MHz at 303.15 K. Debye-type distributions of the frequency dependent electric modulus and complex impedance were found, corresponding to an ionic conduction relaxation process in the upper frequency regime of the spectra, whereas a spike in the impedance spectra at low frequencies confirms the contribution of an electrode polarization (EP) relaxation process induced by ionic conduction. Due to the high static permittivity of FA, its ionic conductivity was found more than one order of magnitude higher than that of the AE, which is also shown by the comparative values of their EP and ionic conductivity relaxation times. The dependences of dc ionic conductivity values of the binary mixtures on their relaxation times and static permittivity were explored. The concentration dependent static permittivity and the relaxation times led us to infer the formation of a 1:1 H-bonded stable complex between FA and AE molecules with reduction in the number of effective parallel-aligned dipoles.     

Dielectric studies of a 5-n-alkyl-2-(4'-isothiocyanatophenyl)- 1,3-dioxane (nDBT) homologous series (n=4-10)

The results of dielectric studies of seven members of a 5-n-alkyl-2-(4'-isothiocyanatophenyl)- 1,3-dioxane (nDBT) homologous series (n=4-10) in the isotropic and smectic A phases are presented. The complex dielectric permittivity, epsilon* (nu) = epsilon'(nu) - iepsilon' (nu), was measured with the aid of two experimental set-ups: an impedance analyser (10kHz-13 MHz) and a dielectric time domain spectrometer (TDS, 10 MHz-4 GHz). This allowed two main relaxation processes in both the phases studied to be separated: the low frequency (l.f.) process connected with molecular reorientations around the short axes, and the high frequency (h.f.) process connected with the rotations around the long axes. The measured dielectric increments enabled us to estimate the value and direction of the dipole moment of the nDBT molecules. The l.f. relaxation process in the isotropic and smectic A phases of the nDBT compounds exhibits some peculiar features which distinguish the materials from other similar substances. The observed decrease of the relaxation times and activation enthalpy with increasing n is discussed in relation to the molecular arrangements in the smectic layers.     

Dielectric properties of a protein-water system in selected animal tissues

Dielectric spectroscopy has been applied to study aspects of the organization of water in selected animal tissues (tendon, bone and horn). The measurements of the relative permittivity epsilon' and the dielectric loss epsilon' were carried over the frequency range of 10-100 kHz and at temperatures from 22 to 240 degrees C. The water content was 10% for bone and horn, and 22% for tendon by mass at room temperature at a relative humidity of 70%. The temperature dependencies of epsilon' and epsilon' reveal distinctively the temperature ranges corresponding to the release of water in temperatures up to about 200 degrees C for all tissues and the melting of the crystalline structure only for tendon and horn, above this temperature. The frequency dependencies of epsilon' and epsilon' show a remarkable dispersion in the low-frequency at selected temperatures up to 200 degrees C for all tissues due to the release of the loosely and strongly bound water. The results were discussed in terms of the interfacial (Maxwell-Wagner) polarization and polarization mechanism involving hopping charge carriers interacting with the bound water molecules. The information on the effect of temperature, water content and frequency of the electromagnetic field on the dielectric behaviour of the tissues studied is of importance in the design and construction of medical diagnostic or therapeutic instruments based on the use of electric signals.     

The use of dielectric spectroscopy for the characterization of polymer-induced flocculation of polystyrene particles

The flocculation of colloidal suspensions is an important unit operation in many industries, as it greatly improves the performance of solid separation processes. The number of available techniques for evaluating flocculation processes on line is limited, and most of these are only functional in dilute suspensions. Thus, techniques usable for flocculation characterization in high-solids suspensions are desirable. This study investigates the use of dielectric spectroscopy to monitor the flocculation of polystyrene particles with a cationic polymer. The frequency-dependent permittivity is modeled and the model parameters are used to describe the particle aggregation. The results show a peak in the modeled time constants of the dielectric relaxation at the onset of flocculation. Further, the adsorption of polymeric flocculant onto the particle surface results in a reduction in particle charge, evident as a decrease in the magnitude of the dielectric dispersion. The use of dielectric spectroscopy is found to be valuable for assessing flocculation processes in high-solids suspensions, as changes in parameters such as floc size and charge can be detected.     

Identification of dielectric and structural relaxations in glass-forming secondary amides

Dielectric relaxation dynamics of secondary amides is explored in their supercooled state near the glass transition temperature Tg by investigating N-ethylacetamide and its mixtures with N-methylformamide. All the samples are found to exhibit giant dielectric permittivities, reaching over 500 in N-methylformamide-rich mixtures around Tg. For both the neat and binary systems, the predominant relaxation peak is of the Debye-type throughout the viscous regime, which is an unexpected feature for a glass former with intermediate fragility. The present results combined with the earlier reported high-temperature data reveal that the dielectric strength delta epsilon(D) of the Debye relaxation extrapolates to zero at frequencies of 10(10)-10(11) Hz, which is about two orders of magnitude lower than the phonon frequency limit typical of the structural relaxation. This Debye process is remarkably similar to the dielectric behavior of many monohydroxy alcohols, which implies a common nature of purely exponential relaxation dynamics in these liquids. Based on the dielectric properties, we conclude that the Debye relaxation in the secondary amides is not a direct signature of the primary or alpha-relaxation, the latter being obscured at low temperatures due to the relatively low permittivity and close spectral proximity to the Debye peak. As in the case of monohydroxy alcohols, dielectric polarization and structure fluctuate on different time scales in secondary amides. The Kirkwood-Fr?hlich correlation factors for Debye-type liquids are also discussed.     

Anomalous narrowing of the structural relaxation dispersion of tris(dimethylsiloxy)phenylsilane at elevated pressures

Broadband dielectric relaxation measurements of tris(dimethylsiloxy)phenylsilane were made at ambient pressure and at elevated pressures. The data show an anomalous behavior not previously seen in any other glass-formers; namely, the structural alpha-relaxation loss peak narrows with increasing pressure and temperature at constant peak frequency. Interpreted by the coupling model, the effect is due to reduction of intermolecular coupling at elevated pressures. This interpretation has support from the observed decrease of the separation between the alpha-relaxation and the Johari-Goldstein secondary relaxation, as well as the smaller steepness or "fragility" index m of the data obtained at 1.7 GPa than at ambient pressure.     

Relation between the alpha-relaxation and Johari-Goldstein beta-relaxation of a component in binary miscible mixtures of glass-formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Nonresonant dielectric hole burning in neat and binary organic glass formers

Binary mixtures of the molecular glass former 2-picoline in oligostyrene, in which the dielectric response of 2-picoline exhibits a particularly broad distribution of correlation times, are investigated by nonresonant dielectric hole-burning (NDHB) spectroscopy and the results are compared with NDHB in neat systems, in particular, glycerol. It turns out that in both substance classes spectral selectivity is achieved, which indicates that dynamics is heterogeneous, i.e., slow and fast responses coexist in the material. However, in binary systems the position of the spectral modifications is completely determined by the spectral density of the pump field, and thus shifts linearly with burn frequency as expected, also at pump frequencies around the alpha-relaxation maximum. It is shown that in binary systems the lifetime tau(rec) of the spectral modifications is determined by the burn frequency omega(p) and exceeds its inverse by about one order of magnitude, indicating long-lived dynamic heterogeneity. The data are described in terms of a previously suggested model of dynamically selective heating, which was extended to include intrinsic nonexponential relaxation. It turns out that the spectral broadening in binary mixtures is not only due to pronounced dynamic heterogeneity, but partially also due to intrinsic broadening of the relaxation function.     

Phthalocyanine with a giant dielectric constant

Compound 1 has been prepared by the reaction of 4-nitrophthalonitrile and trans-2-methoxy-4-(2-nitrovinil)phenol by the common method of nucleophilic substitution of an activated nitro group in an aromatic ring. The metallophthalocyanines 2, 3 were prepared by the reaction of a dinitrile derivative with Co(OAc)(2) or Zn(OAc)(2) in DMSO. The lutetium bis-(phthalocyaninato) complex 4 was obtained by treating the dinitrile derivative with lutetium acetate and DBU in 1-hexanol. The new compounds were characterized by elemental analyses, FT-IR, (1)H-NMR, MALDI-TOF MS and UV/Vis spectral data. The spectroscopic data of the new compounds were in accordance with the structures. The temperature and frequency dependence of dielectric and conduction properties of the spin coated film of compounds (2-4) have been studied by fabricating metal-Pc-metal structures. The results show that compound 2 has giant dielectric constant. At a low range of frequency and room temperature, ε' is found to be equal to 2.33 × 10(6), 1.53 × 10(4) and 1.03 × 10(4) for 2, 3 and 4, respectively. The giant dielectric behavior of 2 is mainly attributed to Maxwell-Wagner polarization. The obtained results also indicated that the frequency dependence of the dielectric permittivity, ε'(ω), exhibits non-Debye type relaxation for all temperatures investigated. The ac conductivity results gave a temperature dependent frequency exponent s. The results were compared with the prediction of the Quantum Mechanical Tunneling and Correlated Barrier Hopping models.     

The universal electro-optic response of charged colloids in low electrolyte suspensions

The large dielectric dispersion of colloids in the low-frequency range, related to polarization of the particle surface electric layer (the alpha-relaxation), has been a subject of scientific interest for decades. In recent papers we advanced the idea that the process of particle surface polarization is partially detected by a second low-frequency relaxation displayed in the frequency domain of particle rotation. The aim of the present paper is to argument this view more consistently. The second low-frequency relaxation is as universal as alpha-relaxation and closely related to it. It is more sensitive to variations in particle electrophoretic mobility than the alpha-relaxation. The paper discusses several aspects concerning the phenomenon: the reasons for its difficult identification as a universal effect; the procedures helping its analysis; and the basic features and the origin of the phenomenon.