Does the entropy and volume dependence of the structural α-relaxation originate from the Johari–Goldstein β-relaxation?

Conventional theories of glass transition are focussed on reproducing the thermodynamic and dynamic properties of the structural α-process. However, in the last decade a class of secondary relaxations, called the Johari–Goldstein (JG) β-relaxations, has attracted attention in view of the existence of various correlations and similarities of its properties with the structural α-process. These experimental evidences suggest that the secondary process may play a fundamental role in glass transition, and any theory of glass transition would be incomplete until the inter-relations between the JG β-relaxation and the structural relaxation have been considered. In this paper, some significant experimental results showing several general and nontrivial connections between structural relaxation and JG β-relaxation are reported. In particular, these connections indicate that, like the structural relaxation, the JG β-relaxation is entropy and volume dependent. The experimental facts are consistent with the results of the coupling model.     

Semi-interpenetrating polymer networks based on polyurethane and poly(2-hydroxyethyl methacrylate): Dielectric study of relaxation behavior

The study of molecular dynamics by broadband dielectric spectroscopy (BDS) is presented for polyurethane (PU), poly(2-hydroxyethyl methacrylate) (PHEMA) and for semi-IPNs based on PU and PHEMA synthesized by photopolymerization. The dielectric properties were performed in wide range of frequencies and temperatures with the goal to establish the relation between the relaxations and the structure. Five relaxation phenomena were finally detected for PHEMA : γ-, βsw-, β-relaxations at low temperatures and α-relaxation at 150 °C at high frequencies plus ionic conductivity relaxation which starts at 0 °C. For semi-IPNs the overlapping of γ- and βsw-relaxations of PHEMA (?125/?75 °C), then with increasing the temperature α-relaxation in PU (?75/0 °C), next ionic conductivity relaxation which starts at 0 °C, and finally the α-relaxation of PHEMA (+125/+170 °C) were detected. The α-relaxation of PHEMA in semi-IPNs shifts to lower temperatures and became broader with increasing amount of PU due to incomplete phase separation in the system and formation of interphases. The dielectric relaxation phenomena were fitted with Havriliak–Negami equation. Activation energy, τ_o and α parameters were calculated. For α-relaxations corresponding dielectric characteristics have been determined from Vogel–Fulcher–Tammann equation. The relaxation map for investigated PU, PHEMA and semi-IPNs was built.     

The slow β-relaxation observed in Ce-based bulk metallic glass-forming supercooled liquid

Dynamic mechanical relaxation measurements are performed on a Ce-based metallic supercooled liquid close to its glass transition temperature T_g. An obvious excess wing is observed both in the temperature and frequency dependent loss modulus curves by the calculation the relaxation time of the α-relaxation in supercooled liquid with the fit by the combination of the Kohlrausch–Williams–Watts and Vogel–Fulcher–Tamman equation. The results indicate that the slow β-relaxation process exists in the metallic liquid and arises from the small-scale translational motions of atoms that are linked in its metastable islands.     

Dielectric spectroscopy of natural rubber-cellulose II nanocomposites

Nanocomposite materials obtained from natural rubber (NR) reinforced with different amounts of cellulose II nanoparticles (in the range of 0 to 30 phr) are studied by dielectric spectroscopy (DS). For comparative purposes the pure materials, NR and cellulose, are also investigated. The dielectric spectra of the nanocomposites exhibit: (a) two overlapped α-relaxations associated respectively with the dynamic glass transitions of NR (faster process) and of the lipid present in NR; (b) a β-relaxation associated with local chain dynamics of cellulose and (c) a relaxation process associated to the presence of traces of water in cellulose. The spectra exhibit conductivity phenomena at low frequencies and high temperatures. The samples were also studied in the dry state. An explanation is given concerning the cellulose effect on the dielectric properties of the dry and wet nanocomposites.     

Predicting the changes of relaxation dynamics with various modifications of the chemical and physical structures of glass-formers

One merit of the coupling model (CM) is its relevance to experiments as demonstrated by its ability to rationalize, explain, and sometimes predict experimental data, particularly those on dynamics. It also predicts the changes of relaxation dynamics with various modifications of the chemical and physical structures of glass-formers. The modifications considered include application of pressure, nano-confinement, crosslinking, copolymerization, mixing with another glass-former, and various changes including molecular structure, tacticity, and molecular weight. The relaxation dynamics addressed include the secondary Johari–Goldstein β-relaxation, and the primary structural α-relaxation, and also the chain modes in the case of polymers. The changes of these relaxation mechanisms and their relations to each other with modification of chemical and physical structures are predicted and the predictions compare favorably with experimental data.     

Contributions to the molecular origin of the dielectric relaxation processes in polysaccharides – the high temperature range

For ionic conducting glasses a concept of correlation of electrical conductivity with dielectric relaxation was developed, which was essential for understanding the relaxation processes found for this substance class. This paper describes on attempt to extend the concept for interpreting the so-called σ-relaxation found in all systems of well dried polysaccharides in the solid state at high temperatures. For various cellulose-based materials, starches and other pure polysaccharides it was found that the activation energies of the dc-conductivity and the dielectric σ-relaxations were well correlated and their values were nearly equal (95–110 kJ/mol) for all substances. The shape and the intensity of this relaxation were nearly independent of temperature for one substance. In cellulose derivatives this process can be only observed, if these have sufficient unsubstituted hydroxyl groups. Highly or persubstituted celluloses show no separable σ-relaxation. Two models are discussed for the interpretation of this relaxation process: the first one assumes a local diffusion process of hydrogen ions between high potential barriers in these disordered systems and the second one a conducting pathway through a badly conducting environment in the material.     

Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers

The temperature dependence and relaxation function breadth of segmental dynamics (α-relaxation) for 1,2-polybutadiene and 1,4-polybutadiene are used to predict their respective temperature-dependent terminal relaxation times by unified application of the Ngai coupling model. Literature results for the terminal flow of near-monodisperse linear polybutadienes having widely varying molecular weights are successfully represented using the coupling model by variation of only a single parameter, C, which is the proportionality constant between the longest Rouse relaxation time and the primitive relaxation time which underlies the cooperative segmental process. The value of C varies with molecular weight (M) according to C ∝ M^b where b is found to range from 1.8 to 2.1, in close agreement with the expected exponent of 2. Contrary to experimental data and coupling model predictions, reptation theory predicts identical influences of temperature on Rouse and terminal relaxation processes; we suggest that invoking a temperature dependence for contour length fluctuations, and hence number of effective entanglements per chain, may resolve this deficiency of the tube model.     

Characterization of low temperature dielectric processes in Poly(dicyclohexyl-itaconate)

Thermally stimulated depolarization current experiments (TSDC) have been carried out on poly(dicyclohexyl itaconate) (PDCHI) in the glassy state. The polymer exhibits three relaxation zones in the interval of temperature studied: a δ-relaxation at ∼130 K, a complex γ-process, in the temperature interval of 140 K to 200 K, and the β-process in the range of 210-270 K. The loss factor of PDCHI in the glassy zone has been reproduced from the partial depolarization data by using the elementary relaxation times and activation energies. The results show the existence of at least two relaxation processes in γ- and β-zones. A tentative explanation of the molecular origin of the observed secondary relaxations has been done by means of molecular mechanics (MM). At this respect, we perform a comparison of the relaxational data of PDCHI and those corresponding to PCHMA. This comparison allows us to confirm the relevant role played by the cyclohexyl ring in the δ- and γ-relaxations.     

High-frequency dynamics of type B glass formers investigated by broadband dielectric spectroscopy

We present the results of broadband dielectric spectroscopy on two glass formers with strong Johari-Goldstein β-relaxations. In addition to the α- and β-relaxation dynamics, the extension of the spectra up to 1 THz also allows revealing information on the fast β-process in this class of materials. There is clear evidence for a fast process contributing in the region of the high-frequency loss minimum, which is analyzed in terms of the idealized mode-coupling theory.     

A molecular dynamics simulation study of the α- and β-relaxation processes in 1,4-polybutadiene

We have conducted molecular dynamics simulation studies of melts of 1,4-polybutadiene (PBD) using a quantum chemistry-based force field where the rotational energy barriers between conformational states have been reduced (LB-PBD model, where LB indicates lowered barrier). Segmental relaxation in the LB-PBD melts was investigated over a wide range of temperature by monitoring the decay of the torsional autocorrelation function (TACF). The decay of the TACF could not be well-represented by a single stretched (Kohlrausch–William–Watts) exponential indicating the presence of resolvable α- and β-relaxation processes even at the highest temperatures investigated. We found that all or nearly all dihedrals undergo conformational transitions on the time scale of the β-relaxation process. The β-relaxation process was observed to weaken with decreasing temperature due to an increasingly heterogeneous population of conformational states with decreasing temperature on time scales longer than the β-relaxation time but shorter than the α-relaxation time. The heterogeneity in conformational populations is imposed by the matrix which biases the conformational states of individual dihedrals (but not the average over all dihedrals) on time scales shorter than the α-relaxation time. Complete segmental relaxation (α-relaxation) occurred on longer time scales over which all dihedrals are able to populate each conformational state with near-equilibrium probability, a process that requires cooperative motion of the matrix. The β-relaxation process as monitored by the TACF was also found to broaden with decreasing temperature, consistent with an increasingly broad distribution of times required for individual dihedrals to visit each conformational state.     

The influence of low-concentration γ-Fe2O3 magnetic nanoparticles in a poly(ether–b–ester) copolymer matrix on interfacial polarization and glass transition

A new poly(ester–b–ether) copolymer filled with magnetic γ-Fe₂O₃ nanoparticles of low concentration (0.1 and 0.3 wt%) has been synthesized, with poly(ethylene terephthalate) (PET) as a rigid segment and poly(tetraoxymethylene) (PTMO) as the flexible segment at the ratio of 50 wt%. The filler was used in the form of suspension or solid powder. The dielectric spectroscopy results for these materials, in a wide range of frequencies and temperatures, are presented and compared with similar results for a pure polymeric matrix. Two relaxation processes, α and β, have been observed clearly in all samples at about 253 K and 163 K, respectively. The α process was shifted towards the lower temperatures as the nanoparticle content increased, while the β-relaxation was unaffected by the doping. The interfacial polarization effect was observed in the samples with nanoparticles, less pronounced for the larger nanoparticles.     

Slow and fast dynamics in glycerol–water mixtures

We discuss the relaxation dynamics of glycerol–water mixtures as studied by broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC). BDS studies were performed in a frequency range of 1 Hz to 250 MHz at temperatures ranging from 173 to 323 K and DSC measurements were made between 138 and 313 K. The experimental results obtained for the glycerol-rich mixtures in terms of dielectric loss ‘master plots’ suggest that the main dielectric relaxation process, as well as the high frequency ‘excess wing’ and dc-conductivity, follow the same temperature dependence. This result indicates that all of these processes are based on the same physical origin. A new phenomenological relationship for the complex dielectric permittivity is proposed. The structural and dynamic properties of glycerol–water mixtures are discussed. The experimental data for water-rich mixtures show the existence of a critical concentration of 40 mol% of glycerol that relates to the numbers of hydrogen bonds of glycerol and of water molecules. Below this concentration, water cooperative domains appear, coexisting with the glycerol cooperative domains. Below 20 mol% of glycerol, ice nanocrystals appeared that led to three relaxation processes; result from ice, mesoscopic glycerol–water domains, and water on the interface between former two.     

Dynamic properties of solvent confined in silica gels studied by broadband dielectric spectroscopy

We report the results of a broadband (10⁻²–10⁷ Hz) dielectric spectroscopy study on a solvent system (glycerol–water solution) confined in a porous silica matrix. The dielectric relaxation of the system is studied as a function of both temperature (120–280 K) and solvent composition (0–36 glycerol molar percentage), at constant matrix composition. Our data show that glycerol–water systems confined inside silica gel are characterized by a very complex dynamics quite different from that observed in solution, thus indicating that confinement may deeply modify solvent dynamics. Indeed in addition to the relaxation processes similar to those occurring in bulk samples, new dielectric relaxations are detected: two non-collective relaxations, attributed to water molecules strongly interacting with pore surfaces and to the glycerol trapped within the matrix structure, respectively; a relaxation in the glycerol free sample (and in samples at very low glycerol content) almost coincident with that observed in other different confinement conditions and governed by geometrical confinement per se. Moreover, at high glycerol content we observe two non-Arrhenius processes at least 4 order of magnitude slower than solution-like main relaxation; at low glycerol content the two above relaxations merge and show a fragile to strong transition at about 200 K.     

Relation between the dispersion of α-relaxation and the time scale of β-relaxation at the glass transition

Dielectric spectra of several typical molecular glass-formers, showing one or more secondary processes resolved in the glassy state, have been measured at different temperatures. We found that the genuine Johari–Goldstein β-relaxation is connected to the structural relaxation. In fact, a clear correlation was found between the structural relaxation time, the Johari–Goldstein relaxation time and the dispersion of the structural relaxation (i.e. its Kohlrausch parameter). Moreover, for a group of epoxide oligomers the steepness index is correlated to the broadness of the structural peak and to the time separation between the structural and the Johari–Goldstein relaxation. These results support the idea that the Johari–Goldstein relaxation acts as a precursor of the structural relaxation. A rationale for our results is provided by the coupling model.     

Dielectric properties of water in amorphous mixtures of polymers and other glass forming materials

We report on the dielectric and calorimetric results of water solutions of poly(vinyl methyl ether) (PVME), poly(vinyl pyrrolidone) (PVP), pentaethylene glycol (5EG) and tri-poly(propylene glycol) (3PG) for a temperature range of 130 K up to crystallization. For 3PG and 5EG two relaxation processes (Process I and II) were observed for all the hydration levels whereas for PVME and PVP a single peak was detected (Process II). We will show that the temperature dependence of the relaxation time of Process II, related to water molecules dynamics, presents a crossover at a temperature about the calorimetric glass transition of the whole system. We show that this crossover could be interpreted in terms of confinement effects due to the frozen-in of the whole solution. Finally, in spite of the fact that water molecules are surrounded by different environments, the results are very similar for the all the investigated systems, which suggest a general behavior for confined water. From this finding, we have obtained an intrinsic value of the activation energy for water dynamics in confining environments.     

Characterization and identification of the nature of two different kinds of secondary relaxation in one glass-former

Dielectric measurements were carried out in the van der Waals liquid di-n-octyl phthalate at ambient pressure. Two secondary relaxation processes were found in the dielectric spectra, namely, an excess wing and a γ-process at higher frequencies. It has been established that the excess wing is the universal JG relaxation. Moreover we pointed out that γ-relaxation times show a minimum in temperature dependence. A Minimal Model proposed by Dyre and Olsen was successfully applied to explain this unusual behaviour of the γ-relaxation in di-n-octyl phthalate.     

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.     

Studies of Specific Adsorption Sites for Sodium Ion and Water on the Interface of Mixed Micelles of Novel Type II Lyomesophases

Novel aqueous type II lyotropic mesophases that align in magnetic fields have been synthesized for binary and ternary mixtures of amphiphiles. A system in which major components of the micelle bilayer are decyltrimethylammonium and dodecanoate ions is an aligning mesophase from 100% to 35% dodecanoate, but replacement of the cationic amphiphile with hexadecyltrimethylammonium facilitates the extension to aligning mesophases up to 100% replacement of the dodecanoate ions. A study of sodium and deuterium quadrupole splittings observed in their nuclear magnetic resonance spectra, confirms and extends a three site adsorption theory for sodium ion in the mixed head group interface. The first site is associated with more strongly hydrated ions and head groups and involves adjacent dodecanoate head groups, the second is not so strongly hydrated and involves one dodecanoate group while the third is a weakly bound water at - N(CH₃)⁺ groups and a sodium remote from the interface layer in close to average isotropic motion.

Mixed detergent mesophases of type II, which spontaneously align in the field, have also been synthesized from variable mixtures of hexadecyltrimethylammonium bromide and decylammonium chloride and from mixtures of potassium dodecanoate and sodium decylsulphate. In the mixed cationic system the sodium quadrupole splittings are always low but water is tightly bound to the -NH₃ ⁺ head group. In the anionic detergent mixture sodium appears about as strongly bound to dodecanoate and decylsulphate head groups. In most of the mixed mesophases some decanol is required (maximum 25% of the bilayer) in order to render the desired type II mesophase stable over a range of mixtures of the charged detergents. Specific site adsorption for sodium and water, peculiar to different head groups renders the effect of the added decanol as primarily a convenient diluent in the bilayer to preserve mesophase integrity.