Interdependence of primary and Johari-Goldstein secondary relaxations in glass-forming systems

We report evidence from broadband dielectric spectroscopy that the dynamics of the primary alpha- and secondary Johari-Goldstein (JG) beta-processes are strongly correlated in different glass-forming systems over a wide temperature T and pressure P range, in contrast with the widespread opinion of statistical independence of these processes. The alpha-beta mutual dependence is quantitatively confirmed by (a) the overall superposition of spectra measured at different T-P combinations but with an invariant alpha-relaxation time; (b) the contemporary scaling of the isothermal-pressure and isobaric-temperature dependences of the alpha-and beta-relaxation times as plotted versus the reduced variable Tg(P)/T where Tg is the glass transition temperature. These novel and model-independent evidences indicate the relevance of the JG relaxation phenomenon in glass transition, often overlooked by most current theories.     

Primary and secondary dielectric relaxations in semi-crystalline and amorphous starch

The thermally stimulated depolarization current technique, TSDC, has been used to study the dielectric relaxations in cassava starch on semi-crystalline and amorphous samples. The A-type structure was observed by WAXS experiments and the variation of the crystallinity as a function of the moisture content, h, was followed on native starch. Retrogradation of the amorphous sample occurred at room temperature after 4 weeks in a closed vessel with a water activity 97.3%. In these conditions the humidity content reached a value of 28.5 wt% dry base and the crystallinity degree was comparable to that of the native starch. Three secondary relaxation modes were detected and attributed to short range orientations of polar groups and to main chain restricted motion. The influence of the moisture plasticization effect on the relaxation parameters of the local modes, was determined by decomposing the global TSDC curve in elementary Debye peaks with Arrhenius relaxation times. The main relaxation, α, which is proposed to be the dielectric manifestation of the dynamic glass transition, sweeps a wide temperature interval around room temperature as the sample dries, shifting to higher temperatures as a result of the plasticization of the polysaccharide by water molecules. The α peak deconvolution lead to the 2D relaxation time distribution and Vogel-Tammann-Fulcher parameters were obtained confirming the cooperative character of this mode. The transformed sample showed a bimodal distribution of segmental relaxation times that is interpreted as the existence of a heterogeneous amorphous phase: the mobile one which is similar to the original disordered phase present in semi-crystalline native starch and a more restricted one originated by the disruption of the crystalline lamellae during the pre-gelatinization process.     

Dynamics of glass-forming liquids. XII. Dielectric study of primary and secondary relaxations in ethylcyclohexane

The dynamics of ethylcyclohexane are investigated by high resolution dielectric spectroscopy aiming to characterize the relevant relaxational features of this simple system in its fluid, supercooled liquid, and glassy states. The dielectric signature of structural relaxation is a primary loss peak with amplitude Deltaepsilon=0.01, and a secondary loss process is found in the glassy state. This beta relaxation is compared with a "slow" process revealed by ultrasonics and with previously found gamma and chi processes in similar materials containing the cyclohexyl group. The results suggest that this secondary process is an intramolecular mode rather than a Johari-Goldstein process, consistent with its persistence in the liquid state at slow relaxation times which exceed those of the alpha process. The dielectric activity of such a slow process requires that the dipole magnitude changes with the intramolecular transition, whereas a change in dipole direction only would be masked by the faster structural relaxation.     

The effect of water on the secondary dielectric relaxations in nylon 66

Dielectric data were taken on nylon 66 at several moisture levels at frequencies from 10 to 10⁵ Hz and temperatures from ?70°C to room temperature. Moisture increases the frequency and the peak height for the β relaxation and reduces its activation energy. The peak height of the γ relaxation is reduced by moisture and shifts to slightly higher frequencies with little change in activation energy. The β relaxation follows the pattern of Jonscher and Ngai for a cooperative many-body process. The γ relaxation is slightly broader than a Debye relaxation and approaches that model quite closely as the temperature is increased. The high-frequency end of the β relaxation overlaps the γ relaxation.     

Sub-Tg relaxations due to dipolar solutes in nonpolar glass-forming solvents

It is well known that rigid dipolar solutes (in smaller quantity) dispersed in a nonpolar glassy matrix exhibit a sub-T(g) (or beta(s)) relaxation due to the solute often designated as Johari-Goldstein (JG) relaxation, which is intermolecular in nature. In this article, we report the results of our study of such a sub-T(g) process in a wide variety of dipolar solutes in different glassy systems using dielectric spectroscopy over a frequency range of 20-10(6) Hz down to a temperature of 77 K. The T(g) of these solutions are determined using differential scanning calorimetry. The solvents used in this study are o-terphenyl (OTP), isopropylbenzene (IPB), and methylcyclohexane. In the case of rigid molecular solutes, like mono-halogen benzenes, the activation energy (DeltaE(beta)) of the beta(s) process is found to increase with decreasing T(g) of the solvent, with a corresponding decrease in the magnitude of the beta(s) process. In the case of more symmetrical molecular solute, for example, tert-butylchloride, the change in DeltaE(beta) is not very appreciable. These results emphasize the importance of the size of the cage of the host matrix in the relaxation of the solute molecules. We have also studied the sub-T(g) relaxation(s) due to some flexible molecular solutes, viz., 1butylbromide, 1hexylbromide, 1butylacetate, and benzylacetate. These solutes in IPB matrix exhibit only one relaxation, whereas in OTP matrix they exhibit an additional sub-T(g) process, which may be identified with a JG type of relaxation. These observations lead us to the conclusion that the beta process observed in the glassy states of these pure solutes is predominantly intramolecular in nature.     

Secondary relaxations and electrical conductivity in hyperbranched polyester amides

Broadband dielectric spectroscopy is used to investigate molecular dynamics and charge transport in three hyperbranched polyester amides with hydroxyl, phenyl, and stearate terminal groups. At higher temperatures, the dielectric spectra are interpreted in terms of hopping conduction in a spatially randomly varying energy landscape, whereas two secondary dipolar relaxations attributed to librations of the terminal and amide groups dominate the low temperature regime. Despite a shift of more than 3 decades in the dc conductivity upon variation of the end groups, the Barton–Nakajima–Namikawa relation is shown to hold. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1651–1657, 2010     

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.     

Mechanical and dielectric relaxations in liquid crystalline copolyesters

Dynamic mechanical measurements in tension and torsion on oriented tapes and monofilaments of a range of liquid crystalline polyesters have been combined with dielectric measurements to obtain a molecular understanding of the relaxation processes. This paper extends our previous work [1,2,3] on polyesters of hydroxybenzoic acid (HBA) and hydroxynaphthoic acid (HNA) to related polymers containing dihydroxynaphthalene (DHN) and terephthalic acid (TPA) or biphenyl (BP) and TPA in place of the HNA. It confirms the association of the β and γ processes with naphthyl and phenyl moieties but shows that the processes cannot be due simply to the independent motions of single units.     

TSC and dielectric study of multiple relaxations in poly-L-proline

The thermally stimulated current (TSC) technique has been used to perform a detailed study of the complex relaxation modes observed in poly-L -proline II. Each mechanism has been resolved into elementary processes, each well described by using the assumption of a single relaxation time following an Arrhenius equation. This resolution allows us to predict the complex dielectric constant for temperatures between 77 and 400°K and frequencies between 10^?6 and 10⁴ Hz. In the range where experimental results are available, the predicted energy losses are in very good agreement with those measured by DC transient experiments, the pendulum technique without contacting electrodes, and the AC bridge. We discuss the probable origin of the various relaxation modes. The relaxation observed at the highest temperature may be attributed to electrons trapped at the boundaries between paracrystalline and crystalline regions. From the changes in the relaxations caused by bound water, we conclude that there are two types of water interacting with the macromolecular substrate. With increasing water content, the relaxation modes observed may first be due to water tightly bound between two carbonyl groups of adjacent chains and second, to increased stiffness of the poly-L -proline chain from more mobile water.     

Dielectric secondary relaxations in polypropylene glycols

Broadband dielectric measurements of polypropylene glycol of molecular weight M(w)=400 g / mol (PPG 400) were carried out at ambient pressure over the wide temperature range from 123 to 353 K. Three relaxation processes were observed. Besides the structural alpha relaxation, two secondary relaxations, beta and gamma, were found. The beta process was identified as the true Johari-Goldstein relaxation by using a criterion based on the coupling model prediction. The faster gamma relaxation, well separated from the primary process, undoubtedly exhibits the anomalous behavior near the glass transition temperature (T(g)) which is reflected in the presence of a minimum of the temperature dependence of the gamma-relaxation time. We successfully applied the minimal model [Dyre and Olsen, Phys. Rev. Lett. 91, 155703 (2003)] to describe the entire temperature dependence of the gamma-relaxation time. The asymmetric double-well potential parameters obtained by Dyre and Olsen for the secondary relaxation of tripropylene glycol at ambient pressure were modified by fitting to the minimal model at lower temperatures. Moreover, we showed that the effect of the molecular weight of polypropylene glycol on the minimal model parameters is significantly larger than that of the high pressure. Such results can be explained by the smaller degree of hydrogen bonds formed by longer chain molecules of PPG at ambient pressure than that created by shorter chains of PPG at high pressure.     

Specific heat and dielectric relaxations in ultra-thin polystyrene layers

The effect of thickness on the glass transition dynamics in ultra-thin polystyrene (PS) films (4 nm < L < 60 nm) was studied by thin film ac-calorimetry, dielectric spectroscopy (DRS) and capacitive dilatometry (CD). In all PS-films, a prominent α-process was found in both the ac-calorimetric and dielectric response, indicating the existence of cooperative bulk dynamics even in films as thin as 4 nm. Glass transition temperatures (T_g) were obtained from ac-calorimetric data at 40 Hz and from capacitive dilatometry, and reveal a surprising, marginal thickness dependence T_g(L). These results, which confirm recent data by Efremov et al. [Phys. Rev. Lett. 91 (2003)] but oppose many previous observations, is rationalized by differences in film annealing conditions together with the fact that our techniques probe exclusively cooperative dynamics (ac-calorimetry) or allow the effective separation of surface and “bulk”-type mobility (CD). Two other observations, a significant reduction in c_p towards lower film thickness and the decrease in the contrast of the dilatometric glass transition, support the idea of a layer-like mobility profile consisting of both cooperative “bulk” dynamics and non-cooperative surface mobility.     

Deuteration shift of low temperature dielectric relaxations

Polyethylene and paraffin samples at a temperature of 4.2 K exhibited dielectric relaxations as a result of containing v arious phenol derivatives and amines. Four of these dipolar additives caused distinctly faster relaxations in poly(C₂D₄) than in comparable poly(C₂H₄), the difference being 13 to 20%. The amines, like the phenol derivatives reported earlier, also relaxed orders of magnitude more slowly when their labile hydrogens had been deuterium-substituted. A 4-methyl-2, 6-di-tert-butyl phenol sample in which most of the non-labile hydrogens were deuteriums, relaxed more slowly than the normal compound, the relaxation time being 25–30% longer. These results are all explained with the phononassisted tunnelling model and provide new evidence for the validity of this model.     

Dielectric and shear mechanical relaxations in glass-forming liquids: a test of the Gemant-DiMarzio-Bishop model

The Gemant-DiMarzio-Bishop model, which connects the frequency-dependent shear modulus to the frequency-dependent dielectric constant, is reviewed and a new consistent macroscopic formulation is derived. It is moreover shown that this version of the model can be tested without fitting parameters. The reformulated version of the model is analyzed and experimentally tested. It is demonstrated that the model has several nontrivial qualitative predictions: the existence of an elastic contribution to the high-frequency limit of the dielectric constant, a shift of the shear modulus loss peak frequency to higher frequencies compared with the loss peak frequency of the dielectric constant, a broader alpha peak, and a more pronounced beta peak in the shear modulus when compared with the dielectric constant. It is shown that these predictions generally agree with experimental findings and it is therefore suggested that the Gemant-DiMarzio-Bishop model is correct on a qualitative level. The quantitative agreement between the model and the data is on the other hand moderate to poor. It is discussed if a model-free comparison between the dielectric and shear mechanical relaxations is relevant, and it is concluded that the shear modulus should be compared with the rotational dielectric modulus, 1(epsilon(omega)-n2), which is extracted from the Gemant-DiMarzio-Bishop model, rather than to the dielectric susceptibility or the conventional dielectric modulus M=1epsilon(omega).     

Primary and secondary relaxations in bis-5-hydroxypentylphthalate

Broadband dielectric spectroscopy was used to study the relaxation dynamics in bis-5-hydroxypentylphthalate (BHPP) under both isobaric and isothermal conditions. The relaxation dynamics exhibit complex behavior, arising from hydrogen bonding in the BHPP. At ambient pressure above the glass transition temperature T(g), the dielectric spectrum shows a broad structural relaxation peak with a prominent excess wing toward higher frequencies. As temperature is decreased below T(g), the excess wing transforms into two distinct peaks, both having Arrhenius behavior with activation energies equal to 58.8 and 32.6 kJmol for slower (beta) and faster (gamma) processes, respectively. Furthermore, the relaxation times for the beta process increase with increasing pressure, whereas the faster gamma relaxation is practically insensitive to pressure changes. Analysis of the properties of these secondary relaxations suggests that the beta peak can be identified as an intermolecular Johari-Goldstein (JG) process. However, its separation in frequency from the alpha relaxation, and both its activation energy and activation volume, differ substantially from values calculated from the breadth of the structural relaxation peak. Thus, the dynamics of BHPP appear to be an exception to the usual correlation between the respective properties of the structural and the JG secondary relaxations.     

Shear and dielectric responses of propylene carbonate, tripropylene glycol, and a mixture of two secondary amides

Propylene carbonate and a mixture of two secondary amides, N-methylformamide and N-ethylacetamide, are investigated by means of broadband dielectric and mechanical shear spectroscopy. The similarities between the rheological and the dielectric responses of these liquids and of the previously investigated tripropylene glycol are discussed within a simple approach that employs an electrical circuit for describing the frequency-dependent behavior of viscous materials. The circuit is equivalent to the Gemant-DiMarzio-Bishop model, but allows for a negative capacitive element. The circuit can be used to calculate the dielectric from the mechanical response and vice versa. Using a single parameter for a given system, good agreement between model calculations and experimental data is achieved for the entire relaxation spectra, including secondary relaxations and the Debye-like dielectric peak in the secondary amides. In addition, the predictions of the shoving model are confirmed for the investigated liquids.     

Analysis of dielectric and conductive dispersion above Tg in glass-forming molecular liquids

Dynamics of the nonassociated supercooled liquids N-methyl-epsilon-caprolactam (NMEC) and glycerol in the frequency domain are investigated using full complex-nonlinear-least-squares fitting of immittance spectroscopy data for appreciable temperature ranges above the glass transition. Such fitting, not previously used for these materials, helps to identify physical processes responsible for the data and elements of their common behavior. Several different fitting models were applied to find a physically plausible best-fitting one to distinguish quantitatively between the dielectric effects of dipoles and the conductive effects of mobile ions. The utility of many composite fitting models was investigated, and although a pure conductive-system dispersive (CSD) fitting model led to good but physically unrealistic fits of all data sets, the dielectric-system dispersive (DSD) Davidson-Cole model best fitted the alpha-dispersion part of the responses. Nevertheless, the series combination of such a DSD model and a separate CSD model (one not associated with electrode effects) was found to yield much better fitting of the data for both materials. Although the CSD model plays somewhat the role of the conventional parallel DSD Johari-Goldstein beta-response, it is here in series and arises from mobile impurity-ion effects rather than from dipolar ones. Previous analyses of data of the present and other molecular materials have often involved two DSD models in parallel, but fitting with such a composite model led here to less physically plausible parameter values and ones with appreciably more uncertainties. Surprisingly, the series DSD and CSD composite-model fits led to comparable estimated values of the NMEC and glycerol dielectric strength parameters, as well as to the nearly equal small thermal activation energies of these parameters.     

Polysiloxane dizwitterionomers. IV. Mechanical and dielectric relaxations

The relaxation behavior of a series of polysiloxane dizwitterionomers has been studied by using dynamic mechanical and dielectric spectroscopy. The temperature range was 100–375 K and the frequency was ca. 1 Hz in the mechanical measurements and 50 Hz–50 kHz in the dielectric measurements. Three relaxation regions, labeled α_s, β, α_z in order of increasing temperature, were observed. The β_s relaxation was assigned to the nonionic portion of the siloxane chain and correlated with the glass transition of polydimethylsiloxane. The β and α_z processes are ionic-related relaxations; β probably originated from the motion of a chain segment carrying a dizwitterion, and α_z, from the collapse of the organization in the ionic domains. Absorbed water exerts a profound influence on relaxation behavior–primarily on α_z ionic relaxation and the relative rigidity of the samples. The water molecules solvate the ions and thus shift the α_z relaxation to lower temperatures. Some aspects of the effect of thermal history on the microphase separation into domains have also been investigated. The results indicate that the organization of the zwitterions in the ionic domains is improved at slow cooling rates.     

Study of dielectric relaxations of anhydrous trehalose and maltose glasses

We investigated the frequency dependent dielectric relaxation behaviors of anhydrous trehalose and maltose glasses in the temperature range which covers a supercooled and glassy states. In addition to the α-, Johari-Goldstein (JG) β-, and γ-relaxations in a typical glass forming system, we observed an extra relaxation process between JG β- and γ-relaxations in the dielectric loss spectra. We found that the unknown extra relaxation is a unique property of disaccharide which might originate from the intramolecular motion of flexible glycosidic bond. We also found that the temperature dependence of the JG β-relaxation time changes at 0.95T(g) and it might be universal.     

Primary and secondary relaxations in bis-5-hydroxypentylphthalate revisited

The molecular structure of bis-5-hydroxypentylphthalate (BHPP) is like dihexyl phthalate but having appended to it two hydroxyl end groups, which contribute additional dipole moments and capacity for hydrogen-bond formation. In a previously published dielectric study of the primary and secondary relaxations of BHPP, it was found that all the dynamic properties are normal except for the anomalously large width of the primary relaxation loss peak. There are two secondary relaxations, the relaxation time of the slower one increases with increasing pressure, whereas that of the faster one is practically insensitive to pressure. Hence, the slower secondary relaxation is the "universal" Johari-Goldstein (JG) [J. Chem. Phys. 53, 2372 (1970); 55, 4245 (1971)] relaxation in BHPP. All is well except if the observed large width of the primary relaxation were an indication of a corresponding large coupling parameter n=0.45 in the coupling model. Then the predicted relations between the primary relaxation time tau(alpha) and the JG relaxation time tau(JG) found previously to hold in many glass formers would be violated. It was recognized that this singular behavior of BHPP is likely due to broadening of the primary loss peak by the overlapping contributions of two independent dipole moments present in BHPP, and the actual coupling parameter is smaller. However, at the time of publication of the previous work there were not enough data to support this explanation. By making broadband dielectric measurements of dibutyl phthalate (DBP) and dioctyl phthalate (DOP) that have chemical structures closely related to BHPP but with only one dipole moment, we show that all their dynamic properties are almost the same as BHPP but the widths of their primary relaxation loss peaks are significantly narrower corresponding to a smaller coupling parameter n=0.34. The new data presented here indicate that the coupling parameter of BHPP is about the same as DBP and DOP, and the predicted relations between tau(alpha) and tau(JG) of BHPP are brought back in agreement with the experimental data.