Genuine Johari–Goldstein β-relaxations in glass-forming binary mixtures

Broadband dielectric spectroscopy measurements were performed on glass-forming binary mixtures, composed of rigid polar molecules dissolved at low concentration in apolar viscous solvent (tristyrene). Dielectric spectra were dominated by the polar molecule contribution, so enabling the study of its dynamic behavior. A well resolved secondary relaxation, not attributable to internal degrees of freedom, was visible in both the liquid and glassy states: for its intermolecular nature, it can be called a ‘genuine’ Johari–Goldstein (JG) relaxation, in the sense that it is a local and non-cooperative process but entailing the motion of the molecule as a whole. Among our results, the following ones are noteworthy: (a) polar systems in the neat state showed an excess wing that became a well resolved JG-peak on mixing with the apolar solvent; (b) the time-scale distance between structural and JG loss peak increased with the apolar solvent fraction; (c) broader the structural loss peak was, larger was the separation in the frequency scale between structural and JG peak; (d) the JG relaxation time showed a non-Arrhenius temperature behavior above T_g, paralleling that of the structural relaxation time. All the results can be rationalized in the framework of Coupling Model.     

Dielectric spectroscopy of low-losses sugar lyophiles: III: The influence of moisture on the dielectric response of freeze-dried lactose

This paper presents the results of a dielectric spectroscopy study of freeze-dried lactose with a range of moisture contents. Dielectric properties were measured over a wide range of frequency (10⁻¹ to 10⁶ Hz) and temperature (−120 °C to 120 °C). Four relaxation processes were analysed with respect to moisture content and corresponding relaxation mechanisms were suggested. Two processes (γ and β) were observed in the sub-T_g range of temperature and another two processes were observed near to and above the glass transition temperature, T_g. The relatively high-frequency γ-process was ascribed to the mobility of pendant hydroxymethyl groups and exhibited only a weak dependence on moisture content. The most moisture sensitive process was the second sub-T_g (Johari-Goldstein) β-process, whereby the relaxation time changed by 2 orders of magnitude as the moisture was increased by 7%. Also the third process (α-relaxation, near T_g) was sensitive to moisture content and was in good agreement with DSC data measured for freeze-dried lactose. The fourth process was a proton percolation process at the micro-crystals formed at the surface of amorphous particles during heating at the temperatures higher than T_g and shows the moisture dependence.     

Reversible structural relaxation and crystallization of Zr62Al8Ni13Cu17 bulk metallic glass

The effect of pre-treatment above glass transition temperature (T_g) on the reversible structural relaxation in a Zr₆₂Al₈Ni₁₃Cu₁₇ bulk metallic glass at sub-T_g annealing has been investigated. It is found that the enthalpy relaxation can be well described by a stretched exponential function. A free-volume model can only qualitatively simulate the process of enthalpy recovery. Sub-T_g heat treatments after enthalpy recovery have almost no effect on the following crystallization, which can be accelerated when critical clusters are formed for a longer time annealing.     

Physical ageing and the Johari-Goldstein relaxation in molecular glasses

Based on some of our earlier dielectric relaxation studies during structural relaxation of molecular glasses, we describe certain features specific to the change in the Johari-Goldstein (JG) relaxation and examine their consequences for understanding of the molecular mechanism of the JG process. The parameter for the distribution of relaxation times increases slightly (loss curve becomes narrower) and the relaxation rate either remains constant or increases on ageing. In all cases, contribution to permittivity from the JG relaxation, Δε_JG decreases with time, with a rate constant k according to a relation, Δε_JG (t) = Δε_JG (t → ∞) − [Δε_JG (t = 0) − Δε_JG ( t → ∞)][1− exp[−(kt)]. This reduces to an equation of the type Δε_JG(t) = a + b exp(− kt) where a and b are constants of the glass as well are dependent on the thermal history of quenching of the glassy system. On decreasing the temperature, the relaxation rate for a rigid molecular glass follows the Arrhenius equation in a range that extends from liquid to glass, but deviates from it as a result of structural relaxation of the two alcohols, while the distribution of relaxation times decreases. The variation of Δε_JG with temperature shows an increase in slope on heating through T_g or else a deep and broad minimum before T_g is reached and the slope increases are remarkably similar to the changes observed for volume and thermodynamic properties on heating a glass. These findings need to be considered for a molecular mechanism in the potential energy view of JG relaxation, in analyzing the physical ageing of the α-relaxation process. It is argued that a recent suggestion for considering the JG relaxation within the picture of potential energy landscape may not be inconsistent with its molecular origin and dynamics in localized regions of structurally inhomogeneous glass. But there is still need to determine how the apparent dynamic heterogeneity evident from the broad distribution of the JG relaxation times can be reconciled with the dynamic heterogeneity used to explain less-broad spectra of the α − relaxation process.     

The Johari-Goldstein β-relaxation of glass-forming binary mixtures

The present paper shows, by means of broadband dielectric measurements, that the primary α- and the secondary Johari-Goldstein (JG) β-processes in binary mixtures are strongly correlated. This occurs for different polar rigid probes dissolved in apolar glass-forming solvents, over a wide temperature and pressure range.We found that the coupling parameter n = 1 − β_KWW and the ratio between α- and β-relaxation time reduce on increasing the size of the solute solved within the same apolar matrix. Moreover, such a ratio is invariant when calculated at different combinations of P and T maintaining either the primary or the JG relaxation times constant. Dielectric spectra measured at different T-P combinations but with an invariant α-relaxation time are well superposed in both the α- and β-frequency ranges. Experimental results can be rationalized by Coupling Model equation.     

Effect of orientation and crystallization on dielectric and mechanical relaxations in uniaxially stretched poly(ethylene naphthalene 2,6 dicarboxylate)(PEN) films

Microstructural analysis (crystallinity, orientation) have been performed on stretched and isothermally crystallized poly(ethylene naphthalene 2,6 dicarboxylate)(PEN) films. The crystallinity ratios are higher at drawing temperatures below T_g than above T_g, and for similar draw ratios, a higher orientation can be obtained at drawing temperature below T_g than above T_g. The molecular mobility study by dielectric relaxation spectroscopy (DRS) and mechanical relaxation spectroscopy (MRS) was carried out as a function of draw ratio (λ) and drawing temperature (T_draw). Drawing in glassy state apparently splits the α-relaxation into two components: an α-low component which exhibits a strongly accelerated dynamics but this relaxation process is masked by microstructural rearrangements occurring while heating followed by an α-high relaxation process. The two sub-glass processes (β and β¹) are influenced by the drawing in the glassy state. This can be observed from the increase of relaxation amplitudes and was related to a high disorder in the amorphous phase that is induced by drawing below glass transition temperature. Drawing at 160 °C induces the opposite trend associated with crystallization and confinements effects. Differences in viscoelasticity behaviour were found by MRS in tensile mode parallel and perpendicular to stretching direction. As a result, when comparing oriented and crystallized samples with the same crystallinity ratios, a strong effect of morphology on the location and amplitude of the three relaxations of PEN can be found.     

The defect diffusion model and the properties of glasses and liquids

Several previously unexplained relaxation phenomena are interpreted quantitatively in terms of the defect diffusion model (DDM). These include widely different pre-exponentials, exponents and consequently fragility. In addition, the DDM is used to give a qualitative explanation of many properties that glasses and liquids exhibit. This includes interpretations of the glass transition (T_g), the liquid–liquid transition (T_B), the crystalline melting temperature (T_m), and the different values of the characteristic temperature, T_C, that some materials exhibit for different types of physical measurements. Next, qualitative explanations of the origin of secondary relaxations such as the excess wing and the β relaxation are given. In addition, the boson peak is discussed in terms of the DDM. Finally, it is pointed out that in the DDM, universality is embodied in the defects i.e. free volume.     

Johari-Goldstein relaxation as the origin of the excess wing observed in metallic glasses

Measurements of the shear loss modulus G″ of amorphous Zr₆₅Al_7.5Cu_27.5 at 5.4 kHz were reported by Rösner, Samwer and Lunkenheimer. They observed that the measured G″ are in excess of the contribution from the α-relaxation, indicating the existence of an ‘excess wing’ in amorphous metals like that found in molecular glass-formers. They speculated that the excess wing found in amorphous metal is due to the presence of an unresolved Johari-Goldstein (JG) secondary relaxation. In this work, the coupling model is used to calculate the temperature T_JG at which the JG relaxation frequency coincides with the experimental frequency of the isochronal measurement. The location of T_JG is well within the temperature range where the excess wing of Zr₆₅Al_7.5Cu_27.5 appears at 5.4 kHz. Hence, the result supports the assertion of Rösner et al. that the excess wing found in the metallic glass originates from the intrinsic JG relaxation.     

Aging of a low molecular weight poly(methyl methacrylate)

Dielectric relaxation of a low molecular weight PMMA was measured in both the equilibrium and glassy states. The intense β process, due to motion of the pendant ester moiety, exhibits a change in T-dependence of both its relaxation time and dielectric strength at T_g, reflecting the coupling of this high frequency process to the backbone conformational changes underlying the α dynamics. Consequently, we can exploit the change in the properties of the β process during physical aging to quantify the α relaxation time and its T-dependence for glassy PMMA. The obtained values, τ_α > 10⁴, are too long for direct measurement.     

Structural relaxation of Ti40Zr25Ni8Cu9Be18 bulk metallic glass

Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ bulk metallic glass has a unique quenched-in nuclei/amorphous matrix structure. The crystallization of quenched-in nuclei, when the experimental isothermal annealing time is within its incubation time, may not disturb the enthalpy relaxation, which makes it have the accordingly common enthalpy relaxation behavior with amorphous materials. The alloy's annealing time dependence of recovery enthalpy follows a stretched exponential function with the mean relaxation time obeying an Arrhenius law. The equilibrium recovery enthalpy ΔH_T^eq, mean relaxation time τ and stretching exponent β are all dependent on the annealing temperature, and generally, a higher annealing temperature comes with a lower value of ΔH_T^eq, τ and a higher value of β. Two parameters, β_g and τ_g, representing the stretching exponent and the mean structural relaxation time at the calorimetric glass transition temperature, respectively, are correlated with glass forming ability and thermal stability, respectively. For Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ BMG, the high value of β_g, which is much higher than 0.84 and approaches unity, reveals its good glass forming ability, while, on the other hand, the low value of τ_g indicates a worse thermal stability compared with typical BMGs.     

Conductivity and dielectric properties of polymer electrolytes PEO:LiN(CF3SO2)2 near glass transition

Results of measurements of PEO:LiN(CF₃SO₂)₂ polymer electrolytes of composition between 12:1 and 1.5:1 EO:Li, performed by impedance spectroscopy, impedance spectroscopy simultaneous with microscope observation, differential scanning calorimetry and X-ray diffraction were analyzed focusing on electrical properties of semicrystalline and rapidly cooled amorphous samples. In the loss spectra measured at low temperature, the occurrence of two dielectric relaxations was evidenced: local (β) and segmental (α). For each of the investigated electrolytes, the temperature dependence of the ionic conductivity and the frequency of α relaxation could be described by the VTF function with the same value of parameter T₀, which indicated close coupling of both phenomena. The local (β) relaxation exhibited an Arrhenius type temperature dependence. With increasing amount of salt, two effects were observed for amorphous samples: an increase of the glass transition temperature T_g affecting the α relaxation and changes of structure of PEO:LiN(CF₃SO₂)₂ complexes reflected in shift of the β relaxation frequency. Crystallization caused decrease of both the ionic conductivity and the strength of dielectric relaxations. The presence of crystalline phase was also reflected in a shift of the T_g of amorphous phase remaining in the system with respect to the T_g of amorphous electrolyte obtained by rapid cooling.     

An electrospray technique for hyperquenched glass calorimetry studies: Propylene glycol and di-n-butyl phthalate

We describe an electrospray technique for in situ preparation, for differential scanning calorimetry study, of samples of molecular liquids quenched into the glassy state on extremely short time scales (hyperquenched). We study the cases of a hydrogen-bonded liquid, propylene glycol, PG and a Van der Waals liquid, di-n-butyl phthalate DBP. Using a fictive temperature method of obtaining the temperature dependence of enthalpy relaxation, we show that the electrospray method yields quenching rates of ∼10⁵ K/s, while the more common method, dropping a sealed pan of sample into liquid nitrogen, yields only 120 K/s. These hyperquenched samples start to relax, exothermically, far below the glass temperature, at a temperature (0.75T_g) where the thermal energy permits escape from the shallow traps in which the system becomes localized during hyperquenching. This permits estimation of the trap depths, which are then compared with the activation energy estimated from the fictive temperature of the glass and the relaxation time at the fictive temperature. The trap depth in molar energy units is compared with the ‘height of the landscape’ for PG, the quasi-lattice energy of the liquid based on the enthalpy of vaporization, and the single molecule activation energy for diffusion in crystals. The findings are consistent with the mechanism of relaxation invoked in a current model of relaxation in glassforming liquids. In the case of di-n-butyl phthalate we investigate the additional question of sub-T_g annealing effects. We find the ‘shadow’ glass transition, (an annealing prepeak) seen previously only in multicomponent mineral and metallic glasses. The phenomenon is important for understanding microheterogeneities in viscous liquid structures.     

Photostructural relaxation in As–Se–S glasses: Effect of network fragility

The effect of photoinduced structural relaxation in As–S–Se glass is investigated during sub-bandgap irradiation. It is shown that the glass undergoes rapid optically induced structural relaxation upon photoexcitation of bonding electrons. Fragile systems exhibit larger relaxation as expected from their enthalpy profile. This suggests that the process is thermodynamically driven and that the kinetic impediment to relaxation at low temperature is lifted through photoinduced softening of the glass matrix. Activation energy for enthalpy relaxation measurement and an annealing study near T_g show that the photorelaxation effect is not a thermally activated process. The 〈r〉 dependence of photostructural changes is addressed and explained using the energy landscape formalism.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

On the role of the β process as precursor of the α relaxation in aromatic polyesters

By performing broad band dielectric spectroscopy measurements in a series of amorphous aromatic polyesters we show that different fast modes, contributing to the β relaxation, appear at temperatures below the glass transition temperature, T_g. At high temperatures, (T > T_g) the different β modes tend to merge and the data have to be described by a single β peak. We tentatively assign a molecular origin to each of the different β modes. But also we find a strong connection among the merged β processes and the precursor of the structural α relaxation, implying that this relaxation may posses an important degree of intra-segmental cooperativity.     

Aging of oriented polymer glasses

Dimensional (D) and enthalpy relaxation (ΔH) of oriented polymer glasses (PS and PC) have been studied as function of temperature, between T_g and T_g−20 °C, and aging time t, ranging to several weeks. The dimensional relaxation (shrinkage) and enthalpy relaxation curves verify the logarithm law D(t) ∼ H(t) ∼ log t, between an incubation τ_i and a final relaxation time τ_f. The time τ_f to reach the equilibrium (D and ΔH) follows the Vogel–Tamann–Fulcher (VFT) law. Enthalpy relaxation and shrinkage exhibit important differences. Enthalpy relaxation of oriented and isotropic polymers follows the same logarithm law, independent of the draw ratio λ and the mode of deformation, the relaxation time τ_f coincides with the relaxation time of the α segmental motions. Shrinkage depends on λ and the mode of deformation, the relaxation time τ_f is attributed to the normal mode, the relaxation time of the whole chain. Finally the shrinkages of PS and PC show some differences. PC at short aging times presents another type of dimensional relaxation which would be due to the β motions. This would be in close connection with the ductile (PC) and fragile (PS) behavior of these two polymers far below T_g.     

Defect model for the mixed mobile ion effect revisited: An importance of deformation rates

The progress in understanding the behavior of glassy mixed ionic conductors within the concept of the defect model for the mixed mobile ion effect [V. Belostotsky, J. Non-Cryst. Solids 353 (2007) 1078] is reported. It is shown that in a mixed ionic conductor (e.g., mixed alkali glass) containing two or more types of dissimilar mobile ions of unequal size sufficient local strain arising from the size mismatch of a mobile ion entering a foreign site cannot be, in principle, absorbed by the surrounding network-forming matrix without its damage. Primary site rearrangement occurs immediately, on the time scale close to that of the ion migration process, through the formation of intrinsic defects in the nearest glass network. Neither anelastic relaxation below glass transition temperature, T_g, nor viscoelastic or viscous behavior at or above T_g can be expected being observed in this case because the character of the stress relaxation in a wide temperature range is dictated above all by the deformation rates employed locally to the adjacent network-forming matrix. Since the ion migration occurs on the picosecond time scale, the primary rearrangement of the glass network adjacent to an ionic site occurs at rates orders of magnitude higher than those of the critical minimum values, so the matrix demonstrates brittle-elastic response to the arising strain even at temperatures well above T_g, which explains, among other things, why mixed alkali effect is observable in glass melts.     

The role of primitive relaxation in the dynamics of aqueous mixtures, nano-confined water and hydrated proteins

The relaxation scenario in aqueous systems, such as mixtures of water with hydrophilic solutes, nano-confined water and hydrated biomolecules, has been shown to exhibit general features, in spite of the huge differences in structure, chemical composition and complexity. Dynamics, in all these systems, invariably shows at least two relaxations: (i) a slower process, related to cooperative and structural motions of water and solute molecules (in the case of mixtures) or related to interfacial processes in the case of confined water and (ii) a faster process, with non-cooperative character originating from water. The latter has properties including timescale and temperature dependence similar or related in all the aqueous systems. This water-specific relaxation can be identified as the primitive relaxation, or the Johari-Goldstein β-relaxation. The primitive process is the precursor of the many-body relaxation process which increases in length-scale with time until the terminal α-relaxation is reached.Using new experimental data (at atmospheric and high pressure) along with a revision of most of the recent literature on the dynamics of confined water and aqueous mixtures, we show that the two abovementioned relaxation processes are inter-related as evidenced by correlations in their properties. For instance, both relaxation time and dielectric strength of the water-specific relaxation exhibit a crossover from a stronger to a weaker dependence with decreasing T, at the temperature where the slow process attains a very long timescale (> 1 ks) and becomes structurally arrested, exactly analogous to that found for β-relaxation in van der Waals liquids. Moreover, the primitive relaxation of water is shown to play a pivotal role in determining the dynamics of hydrated biomolecules in general, including the “dynamic transition” observed by neutron scattering and Mössbauer spectroscopy. We show that the primitive relaxation of the solvent is responsible for the dynamic transition, even in the case that the solvent is not pure water or an aqueous mixture.     

The effect of transition M metals on the two-stage enthalpy relaxation behavior of (FeM)83P17 amorphous alloys

The anneal-induced relaxation behavior for (FeM)₈₃P₁₇ (M  Cr, Mo, Mn, Co or Ni) amorphous alloys was examined calorimetrically with the aim to clarify the effect of M substitution on the two-stage relaxation previously found by the present authors. Upon heating the sample annealed at temperatures below T_g, a reversible endothermic reaction (enthalpy relaxation) occurs above T_a. The changes in ΔC_p,endo and with T_a show two distinguishable stages only for The FeMoP alloy which exhibits glass transition; a low-temperature peak at a temperature that is lower by about 180 K than T_g and a high-temperature one just below T_g. However, any indication of the high-temperature peak is not detected for the other alloys which crystallize before T_g. From the data of ΔC_p,endo, ΔH_σ,endo and activation energy for the low-temperature peak which has been thought to generate by relaxation of metal atoms, the first-stage relaxation was concluded to become difficult in the order of Ni < Co < Mn < Cr < V < Mo, i.e., with the decrease in the group number of the periodic table. The change in the first-stage enthalpy relaxation behavior with the substitution of Fe by M is interpreted to originate from the change in the mobility (i.e., relaxation time) of metal atoms through the change in the bonding force among the constituent elements.     

Positron annihilation and broadband dielectric spectroscopy: A series of propylene glycols

We report a thorough joint analysis of the behavior of the ortho-positronium lifetime as obtained from positron annihilation lifetime spectroscopy and of the dipolar relaxation spectra investigated by broadband dielectric relaxation spectroscopy in a series of glass-forming propylene glycols including propylene glycol, dipropylene glycol and tripropylene glycol. A number of empirical correlations between the temperature dependence of the ortho-positronium annihilation lifetime, τ₃(T), and the various spectral and relaxational quantities have been found. The phenomenological evaluation of the quasi-sigmoidal τ₃(T) dependence reveals three characteristic temperatures: T_g^PALS, T_b1 = (1.23 − 1.27)T_g^PALS and T_b2 = (1.46 − 1.53)T_g^PALS, which are found to decrease with increasing fragility. The slighter change of slope in the PALS response at T_b1 in this series of propylene glycols appears to be related to the crossover from the α-process to the excess wing or secondary relaxation, found in the dielectric spectra. The onset of the high-temperature plateau in the τ₃(T) plot at T_b2 occurs when τ₃ matches the average relaxation time of the primary α process. Moreover, the plateau region lies in the vicinity of the crossover in the dielectric parameters of the structural relaxation in all the samples, i.e. spectral width and relaxation strength. In addition it is approximately related to a crossover of the α relaxation time τ_α(T) from non-Arrhenius to Arrhenius regime. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in the series of propylene glycols.