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 spectra broadening as the signature of dipole-matrix interaction. I. Water in nonionic solutions

Whenever water interacts with another dipolar entity, a broadening of its dielectric relaxation occurs. Often this broadening can be described by the Cole-Cole (CC) spectral function. A new phenomenological approach has been recently presented [A. Puzenko, P. Ben Ishai, and Y. Feldman, Phys. Rev. Lett. 105, 037601 (2010)] that illustrates a physical mechanism of the dipole-matrix interaction underlying the CC behavior in complex systems. By considering the relaxation amplitude Δε, the relaxation time τ, and the broadening parameter α, one can construct a set of 3D trajectories, representing the dynamic behavior of different systems under diverse conditions. Our hypothesis is that these trajectories will contribute to a deeper understanding of the dielectric properties of complex systems. The paper demonstrates how the model describes the state of water in aqueous solutions of non-ionic solutes. For this purpose complex dielectric spectra for aqueous solutions of D-glucose and D-fructose are analyzed.     

Dielectric Study of Homogeneity in Some Binary Liquids in Their Supercooled State

In this work, we report a dielectric study of some binary mixtures in their supercooled region over a frequency range of 10⁶ to 10^–3 Hz. Differential scanning calorimetry measurements have been made above 100K. The samples studied here are DL-lactic acid (88% in aqueous solution), binary mixtures of dimethyl sulfoxide and acetic acid, of propylene glycol and cyclohexanol, and of 4-methyl-3-heptanol and tritolyl phosphate. The frequency dispersion of the relaxation spectra and the temperature dependence of the relaxation process have been critically examined for heterogeneity. The mixtures of dimethyl sulfoxide and acetic acid reveal a 1:1 complex formation. Some evidence of heterogeneity was found only in mixtures of 4-methyl-3-heptanol and tritolyl phosphate. For comparison, we have also studied liquid mixtures of isopropylbenzene with small quantities of acetone or fluorobenzene. These mixtures showed no signs of heterogeneity, although the relaxation spectra are broader than the spectrum of pure isopropylbenzene.     

Heterogeneous thermal excitation and relaxation in supercooled liquids

We investigate a phenomenological model which rationalizes the effects of dielectric hole burning on the basis of heterogeneous dielectric and specific heat relaxation in supercooled liquids. The quantitative agreement between model predictions and dielectric hole-burning observations is lost if the assumption of correlated dielectric and thermal relaxation times is removed from the model. This suggests that dynamically distinct domains in real liquids are associated with a time constant which characterizes both the structural and thermal relaxation behaviors. The calculations demonstrate that the observed burn-induced modifications reflect the spectral selectivity and persistence time of the fictive temperatures within these domains, and that 100 or more cycles of the sinusoidal burn field can be required to saturate the heat accumulated in the slow degrees of freedom. It is also shown that the recovery of dielectric holes is entirely accounted for by the model, and that the persistence times do not provide direct insight into rate exchange processes. Additionally, the model predicts that the heating effects considered here are a significant source of nonlinear dielectric behavior, even in the absence of deliberate frequency selective hole burning.     

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.     

Dielectric Relaxation Study of Chloro Group with Associative Liquids. II. 1,2-Dichloroethane with Methanol, Ethanol, and 1-Propanol

Frequency spectra of the complex permittivity for 1,2-dichloroethane–alcohol binary mixtures have been determined over the frequency range 10 MHz to 20 GHz at 15, 25, 35, and 45°C, using the time-domain reflectometry (TDR) technique, for 11 compositions of each 1,2 dichloroethane–alcohol system. The alcohols used in the study were methanol, ethanol, and 1-propanol. The relaxation in these systems can be described by a single relaxation time using the Debye model. The static dielectric constant, relaxation time, the corresponding excess dielectric properties, Kirkwood correlation factor, and Bruggeman factor of the mixtures have been determined. The static dielectric constants for the mixtures have been fitted with the modified Bruggeman model.     

Dielectric properties for the binary mixture of dimethylsuphoxide and dimethylacetamide with 2-nitrotoluene at microwave frequencies

The dielectric properties of various organic solvents and binary solvent mixtures at different temperatures over the frequency range of 10 MHz–20 GHz, are investigated using the time domain reflectometry technique, at various temperatures from 15 to 45 °C. These solvent mixtures—dimethylacetamide–2-nitrotoluene and dimethylsulphoxide–2-nitrotoluene as well as pure solvents display a Debye type dispersion. Their frequency-dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters, for these solvent systems at various temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The static permittivity increases with increase in volume percentage of 2-nitrotoluene in dimethylacetamide as well as dimethylsulphoxide whereas the relaxation time decreases for both the systems.     

Diluting the hydrogen bonds in viscous solutions of n-butanol with n-bromobutane: a dielectric study

Glass-forming monohydroxy alcohols exhibit not only a structural relaxation but also a slower, single-exponential Debye-type relaxation process which already freezes in the liquid phase. By using dielectric spectroscopy, we study how these relaxations evolve when the aprotic alkyl halide n-bromobutane is added to n-butanol, thereby diluting the hydrogen-bond network. The structural relaxation times smoothly vary over the concentration range of this completely miscible binary system. The Debye process remains unaffected by the dilution of the OH groups up to n-bromobutane mole fractions of about 50%. For larger hydroxy dilutions, it turns rather abruptly into a feature which develops significant spectral broadening and it becomes faster. In the dilute limit, the decoupling between the time scale of the Debye process and that of the structural relaxation amounts to almost 6 decades when extrapolated to the glass transition temperature. This relatively large, strongly concentration dependent decoupling is interpreted in analogy to normal modes in polymers. The present results suggest that the structural and the Debye-like responses of monohydroxy alcohols are unrelated.     

A new approach to explain concentration-dependent changes of isotropic Raman line width in the associated binary mixtures

We report on a new empirical relationship to explain the concentration-dependent isotropic Raman line width changes of a vibrational mode in uniform binary mixtures. The factors contributing to the intrinsic line width and several other broadening mechanisms are, in general, concentration-dependent. Concentration fluctuation in a microscopic volume and microviscosity are the two factors that are known to cause a concentration-dependent line width variation. These two factors combined in a specific manner successfully explain the variation of the line width with concentration strongly associated with binary systems. A readily usable empirical relationship for line width is suggested. It has been demonstrated that it can successfully explain the line width variation with concentration in a given class of hydrogen-bonded systems taking some representative binary mixtures.     

Complex Permittivity Spectra of Binary Pyridine–Amide Mixtures Using Time–Domain Reflectometry

Frequency spectra of the complex permittivity for pyridine–amide binary mixtures have been determined over the frequency range 10 MHz to 10 GHz, at 5, 15, 25, and 40°C, using the time–domain reflectometry method, for 11 compositions of each pyridine–amide system, e.g., formamide, N-methylformamide, and N,N-dimethylformamide. The relaxation in these systems can be described by a single relaxation time using the Debye model. The static dielectric constant, relaxation time, the corresponding excess dielectric properties, Kirkwood correlation factor, and molar activation energy of the mixtures have been determined. The excess permittivity is found to be positive in the amide-rich region and negative in the pyridine-rich region. The excess inverse relaxation time is negative, except in the pyridine-rich region. The static dielectric constants for the mixtures have been fitted with the modified Bruggeman model. The temperature-dependent relaxation times show the expected Arrhenius behavior.     

Dielectric Study of n-Butyl Acetate–Alcohol Mixtures by Time-Domain Reflectometry

Using picosecond time-domain reflectometry (TDR), dielectric relaxation studies have been carried out on binary mixtures of n-butyl acetate with methanol, ethanol, and 1-propanol, over the frequency range from 10 MHz to 20 GHz, at various concentrations and temperatures. The excess permittivity, excess inverse relaxation time, Kirkwood correlation factor, and thermodynamic parameters have been obtained. The excess permittivity for all the systems is negative. The values of static permittivity and relaxation time decrease with an increase in the percentage of n-butyl acetate in the mixtures.     

Dielectric Relaxation and Thermodynamic Studies of Binary Mixtures of 2-Nitrotoluene with Primary and Secondary Alcohols at Different Temperatures

The dielectric complex spectra of 2-nitrotoluene with primary or secondary alcohol binary mixtures were studied over the frequency range of 10 MHz to 20 GHz for the whole solute mole fraction range at four different temperatures. An unusual suppression phenomenon was observed in the real and imaginary parts of the mixture complex spectrum, which are smaller than those for the pure alcohols, at low solute concentrations. The dielectric constant and dielectric relaxation time values were obtained by fitting the complex dielectric spectrum data to the single Debye model using a non-linear least squares method. The dielectric constant of mixtures decrease with the increasing mole fraction of 2NT in both the primary alcohols and secondary alcohols; the dielectric relaxation time decreases for all the five binary systems. Using the dielectric data, derived dielectric parameters, namely: the excess dielectric constant, excess inverse relaxation time, effective Kirkwood correlation factor, molar activation enthalpy and molar activation entropy, were calculated. The non-linear variation of permittivity (?₀) reveals the change in size and shape of hetero-molecular complex due to intermolecular H-bond interaction. The negative variation of the excess permittivity constant confirms that the dipoles form multimer structures with anti-parallel ordering of unlike dipoles. The molar activation enthalpy was found to be higher at 0.2 mol fraction of 2NT for primary alcohol binary system. To confirm the molecular function group interaction, a FT-IR spectroscopy study was carried out at 298 K. The FT-IR analysis confirmed the formation of hydrogen bonds between the hydrogen atom of hydroxyl groups of the alcohols and the oxygen atom of nitro groups of 2NT in the binary mixtures.     

Microwave dielectric spectra and molecular relaxation in formamide-N,N-dimethylformamide binary mixtures

The dielectric dispersion and absorption spectra of formamide (FA), N,N-dimethylformamide (DMF) and their binary mixtures are investigated in the frequency range of 500 MHz to 20 GHz at 30 °C in view of the organic synthesis by microwaves heating using amides solvents. The concentration dependent values of molecular reorientation relaxation times lower than that of the ideal mixing behaviour have been attributed to the cooperative dynamics of H-bonded FA–DMF structures. The molar ratio of stable adduct is 2:1 of FA to the DMF, which is determined from the concentration dependent excess static dielectric constant and the relaxation time plots of these binary mixtures. Electrode polarization effect and ionic conduction in FA and DMF were investigated from their dielectric dispersion spectra in the low frequency region of 20 Hz to 1 MHz.     

Dielectric and shear mechanical alpha and beta relaxations in seven glass-forming liquids

We present shear mechanical and dielectric measurements taken on seven liquids: triphenylethylene, tetramethyltetra-phenyltrisiloxane (Dow Corning 704 diffusion pump fluid), polyphenyl ether (Santovac 5 vacuum pump fluid), perhydrosqualene, polybutadiene, decahydroisoquinoline (DHIQ), and tripropylene glycol. The shear mechanical and dielectric measurements are for each liquid performed under identical thermal conditions close to the glass transition temperature. The liquids span four orders of magnitude in dielectric relaxation strength and include liquids with and without Johari-Goldstein beta relaxation. The shear mechanical data are obtained by the piezoelectric shear modulus gauge method giving a large frequency span (10(-3)-10(4.5) Hz). This allows us to resolve the shear mechanical Johari-Goldstein beta peak in the equilibrium DHIQ liquid. We moreover report a signature (a pronounced rise in the shear mechanical loss at frequencies above the alpha relaxation) of a Johari-Goldstein beta relaxation in the shear mechanical spectra for all the liquids which show a beta relaxation in the dielectric spectrum. It is found that both the alpha and beta loss peaks are shifted to higher frequencies in the shear mechanical spectrum compared to the dielectric spectrum. It is in both the shear and dielectric responses found that liquids obeying time-temperature superposition also have a high-frequency power law with exponent close to -12. It is moreover seen that the less temperature dependent the spectral shape is, the closer it is to the universal -12 power-law behavior. The deviation from this universal power-law behavior and the temperature dependencies of the spectral shape are rationalized as coming from interactions between the alpha and beta relaxations.     

Dielectric relaxation study of hexamethylphosphoramide–1,4-dioxane mixtures using time domain reflectometry (TDR) technique

Dielectric relaxation study on hexamethylphosphoramide–1,4-dioxane binary mixtures has been carried out at 16 concentrations over the frequency range of 10?MHz to 30?GHz at different temperatures using time domain reflectometry technique. The mixtures exhibit a principal dispersion of the Debye relaxation type at microwave frequencies. The concentration-dependent static dielectric constant, excess dielectric properties and thermodynamic parameters have been determined. The hydrogen-bonded theory is applied to compute the Kirkwood correlation factors for the mixture. The average numbers of the hydrogen bonds between hexamethylphosphoramide–hexamethylphosphoramide and hexamethylphosphoramide–1,4-dioxane pairs are estimated from the dielectric constant.     

Diluent effects on the Debye-type dielectric relaxation in viscous monohydroxy alcohols

With the recognition that the Debye-type dielectric relaxation of liquid monohydroxy alcohols does not reflect the structural relaxation dynamics associated with the viscous flow and the glass transition, its behavior upon dilution is expected to differ from that of real alpha-processes. We have investigated the Debye-type dielectric relaxation of binary alcohol/alkane mixtures across the entire concentration range in the supercooled regimes. The focus is on 2-ethyl-1-hexanol in two nonpolar liquids, 3-methylpentane and squalane, which are more fluid and more viscous than the alcohol, respectively. The Debye relaxation is found to occur only for alcohol mole fractions x > 0.2 and is always accompanied by a non-Debye relaxation originating from the alcohol component. Prior to its complete disappearance, the Debye relaxation is subject to broadening. We observe that the Debye dynamics of 2-ethyl-1-hexanol is accelerated in the more fluid 3-methylpentane, while the more viscous squalane leads to longer Debye relaxation times. The present experiments also provide evidence that the breakdown of the Debye relaxation amplitude does not imply the absence of hydrogen-bonded structures.     

On the visco-elastic and dielectric behaviour of two alcohols and their binary mixture

Inter-molecular and intra-molecular interactions in liquids determine the physical properties of the systems. These interactions are understood through the measurement of these physical properties. These become especially important in the case of alcohols in view of the specific type of interactions involved. Study of the variation of dielectric relaxation time with the viscosity of the medium is relevant in drawing certain quantitative conclusions regarding molecular motion and the inter-molecular forces in liquids, liquid mixtures, dilute solutions and multi-component polar solutes in dilute solution. In the absence of a perfect empirical or theoretical equation for the variation of dielectric relaxation time with viscosity, the experimental investigations on different systems can only give an insight. In the present study, the results of dielectric measurements carried out on pure samples of methyl alcohol and propyl alcohol in dilute solutions in different mixed solvents (benzene?+?paraffin) and on binary mixture (1?:?1) of methyl alcohol?+?propyl alcohol are reported. Different parameters determined are presented and these studies indicate that the dielectric behaviour at microwave frequencies favour the concept of dynamic viscosity and a single visco-elastic relaxation time for the systems under study.     

Ideal mixing behavior of the debye process in supercooled monohydroxy alcohols

Glass-forming monohydroxy alcohols exhibit two dielectric relaxation signals with super-Arrhenius temperature dependence: a Debye peak and an asymmetrically broadened alpha-process. We explore the behavior of these distinct relaxation features in mixtures of such liquids by dielectric measurements. The study focuses on the viscous regime of two binary systems: 2-methyl-1-butanol with 2-ethyl-1-hexanol and 1-propanol with 3,7-dimethyl-1-octanol. We find that the logarithmic relaxation time, log(tau), of the Debye peak follows an ideal mixing law (linear change with mole fraction), even in the case of mixing structurally dissimilar components. By contrast, the log(tau) versus mole fraction curve for the alpha-process is nonlinear, indicative of slower structural relaxation relative to the expectation on the basis of ideal mixing behavior. The latter observation is analogous to the effect of composition on viscosity, heat of mixing, and glass-transition temperature, whereas the ideal mixing of log(tau) seen for the Debye peak is the exception. We conclude that the unusual ideal mixing behavior of dielectric relaxation in monohydroxy alcohols is not a result of structural similarity, but rather yet more evidence of the Debye process being decoupled from other dynamic and thermodynamic properties.     

Dynamic structure of poly(vinyl pyrrolidone)/ethyl alcohol mixtures studied by time domain reflectometry

Dielectric studies of poly(vinyl pyrrolidone)/ethyl alcohol (PVP–E) binary mixtures with concentration variations were carried out in the frequency range of 10 MHz to 10 GHz by time domain reflectometry at 15, 25, 35, and 45 °C. One relaxation process, corresponding to ethyl alcohol molecules in the poly(vinyl pyrrolidone) (PVP) matrix, was observed in this frequency range for all the mixtures. The static dielectric constant of the PVP–E mixtures decreased linearly with an increase in the weight fraction of PVP. The observed anomalous increase in the value of the relaxation time (τ) of these mixtures was interpreted by the consideration of the variation in the local structure of self‐associated ethyl alcohol molecules and also the PVP behavior as a geometric constraint for the rotational motion of ethyl alcohol molecules. Furthermore, the τ values of these mixtures were independent of the viscosity. The energy parameters for the dielectric relaxation process (the free energy, enthalpy, and entropy of activation for the dipolar orientation) were determined to confirm the transient behavior of the heterogeneous species due to the breaking and re‐forming of hydrogen bonds with the internal rotation of ? OH groups in the ordered structure of the PVP–E mixtures. On the basis of the evaluated dielectric parameters, the formation of supermolecular structure in the PVP–E mixtures in dynamic equilibrium was sketched and examined by the consideration of the hydrogen bonding between the terminal hydroxyl groups of self‐associated ethyl alcohol flexible chains and the carbonyl groups of monomer units of PVP coiled chains. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1134–1143, 2005     

Dielectric relaxation studies of binary mixtures of N-methylacetamide and N-methylformamide in benzene solutions using microwave absorption data

Using standard microwave X-band technique and by following Gopala Krishna's single frequency (9.90?GHz) concentration variational method, the dielectric relaxation times (τ) and the dipole moments (μ) of dilute solution of N-methylacetamide (NMA), N-methylformamide (NMF) and NMA?+?NMF binary mixtures in benzene solutions have been calculated at different temperatures. The energy parameters for the dielectric relaxation process for NMA?+?NMF binary mixture containing 30?mol% NMF have been calculated at 25, 30, 35 and 40°C and compared with the corresponding viscosity parameters. A good agreement between the free energy of activation from these two sets of values shows that the dielectric relaxation process like the viscous flow process can be treated as the rate process. From relaxation time behavior of NMA and NMF binary mixture in benzene solution, solute–solute types of the molecular association has been proposed.