Broadband dielectric spectroscopy (BDS) research on the molecular motion of various substances, such as molecular liquids and polymers in liquid to solid states, has been popular over the past two decades, for example, [21, 22]. Research has shown that the α-relaxation with a relaxation time τ _α of nanosecond order or shorter is generally observed at relatively high temperatures where substances are in the liquid state. τ _α increases with decreasing temperature, and one or more secondary relaxations on the high-frequency side of the α-relaxation appear. The multiple relaxations frequently observed in various polymers were conventionally called α-, β-, and γ-relaxations in order of increasing frequency. In addition to them, the normal mode relaxation originating from the overall rotational motion of polymer appears at a frequency lower than that of the α-relaxation if the polymer has components of dipole moment parallel to its main chain. The α-relaxation has been found to show common characteristics in various substances. The α-relaxation has an asymmetric shape of its dielectric loss plotted against the logarithm of frequency, that is, broader at high frequencies than at low frequencies with respect to the loss peak, and τ _α exhibits a VFTH temperature dependence. The VFTH temperature dependence of τ _α corresponds to the increase in the apparent activation energy of the reorientational motion of molecules with decreasing temperature. The extent of the change in the apparent activation energy, i.e., the deviation from the Arrhenius temperature dependence of τ _α, has been evaluated using the fragility [23], i.e., the steepness index [24] m. m is defined as the slope at the glass transition temperature T _g on the plane of log τ _α vs inverse temperature, 1/T, normalized by 1/T _g, as
A material with a large m value is fragile glass and that with a small m is strong glass. These terms of “fragile” and “strong” do not express the real mechanical strength or fragility of the materials but present the information of the degree of change in the apparent activation energy with temperature. The change in the apparent activation energy is generally interpreted to be due to the change in the cooperativity of molecular motion contributing to the relaxation process. These characteristics indicate that the α-relaxation is caused by the cooperative motion of many molecules and that the molecular motion causing the α-relaxation is the origin of the glass transition. Thermal measurements revealed that the glass transition is observed at temperatures at which τ _α = 100–1,000 s. Because of this, such temperatures have been generally defined as the glass transition temperature T _gα in dynamics observation. On the other hand, the relaxation time of secondary relaxations of polymers, such as β- and γ-relaxations, has weak temperature dependence than that of α-relaxation and generally exhibits an Arrhenius temperature dependence with a constant apparent activation energy. The Arrhenius equation is given by
where τ _∞Arr is the pre-exponential factor corresponding to τ at infinitely high temperature, R the gas constant, and ΔE the apparent molar activation energy. Therefore, β- and γ-relaxations are considered to be caused by the intramolecular motion of, for example, freely moving side chains, which is more local than that in the case of α-relaxation. Johari and Goldstein demonstrated that β-relaxation occurs on the high-frequency side of α-relaxation, even in molecular liquids with no degree of freedom within a molecule, and that it is not always caused by the local intramolecular motion [25, 26].

In recent years, secondary relaxations have been classified into the Johari-Goldstein (JG) relaxation, as the elementary process of α-relaxation and local β-relaxation caused by other local molecular motions [27]. The primitive relaxation defined by the coupling model is the precursor of the cooperative α-relaxation [28–31], but it is a local process. The coupling model predicted the relationship between the primitive relaxation time τ ₀ and the relaxation time of the α-relaxation τ _α as
Here, t _c is the crossover time from independent relaxation to cooperative relaxation and is approximately 2 ps for small molecular liquids [31] and n is the coupling constant and is the exponent of the stretched exponential function and determines the asymmetric broadening of the shape of α-relaxation in the dielectric loss spectrum in the Kohlrausch function, i.e., the time dependence of the response function of α-relaxation, as
Equation (9.5) enables τ ₀ to be calculated from τ _α using the coupling constant n. Thus, this attribute of the primitive relaxation is shared with the JG relaxation, and it can be expected that the primitive relaxation time τ ₀ is approximately located near the relaxation time τ _JG of the JG relaxation at various temperatures and pressures [32, 33]. It was found that τ₀(T, P) ≈ τ _β(T, P) holds in many glass formers having the JG relaxations [32, 33]. The examination of τ ₀(T, P) ≈ τ _β(T, P) by comparing the measured τ _β and the calculated τ ₀ at ambient pressure reveals that they are nearly the same at various temperatures [32, 34]. Then the JG relaxation is a precursor or local step of the cooperative α-relaxation. Similarly to the α-relaxation, the JG relaxation is universally observed in various substances, not only in polymers but also in low-molecular-weight molecular liquids even in the case with no degree of freedom within molecules. The JG relaxation exhibits symmetric behavior with respect to the loss peak. Similarly to the α-relaxation time, the JG relaxation time shows VFTH or at least non-Arrhenius temperature dependence above T _g and Arrhenius temperature dependence with a constant apparent activation energy below T _gα. Secondary relaxations other than JG relaxation are attributed to the local intramolecular motion of molecules with an internal degree of freedom, similar to the motion of part of the polymer side chains, and are not directly related to the glass transition [27].

BDS measurements have been carried out in a very wide frequency range of 10 μHz–10 GHz and a temperature range of 80–298 K using various aqueous solutions containing solutes of different concentrations, in which the solution temperature can be decreased to T _g without the crystallization of water (water content ≤40 %). The solutes used were glycerol [35, 36], ethylene glycol [37, 38], ethylene glycol oligomer [39–41], poly(ethylene glycol) [36, 42, 43], propylene glycol and its oligomers [36, 44], poly(propylene glycol) [45], propanol [46], PVP [36, 43, 47–49], poly (vinyl methyl ether) (PVME) [50, 51], fructose [52], and other various materials [38, 43, 53], which have different molecular structures and a wide range of T _g values. Figure 9.2 shows dielectric loss spectra observed for a 65 wt% pentaethylene glycol-water mixture at various temperatures as an example of water mixtures. A single loss peak is observed at temperatures higher than approximately 200 K. Below 200 K, two loss peaks are clearly observed. Despite the differences in the water content and molecular structure of the solutes (including the resulting difference in T _g) in the various aqueous solutions, the relaxation attributed to the motion of water molecules observed in all the solutions showed many common characteristics [53–56]. This water relaxation is called hydration water relaxation or water-specific relaxation [57]. Here, we call it ν-relaxation [55], ν being the initial letter of νερο, which means water in Greek. It was shown that ν-relaxation is the primary dielectric relaxation of water observed in various aqueous solutions at around room temperature, and the shape of the ν-relaxation spectrum depends on the molecular weight of the solute [39, 40, 55, 58–62].

In solutions containing solutes with a low molecular weight, such as alcohols (molecular weight, M _W ≤100), the observed relaxation curve was asymmetric with respect to the loss peak above the separation temperature T _S [39, 40, 55, 59–61], as shown in Fig. 9.3a. Assuming that the relaxation with asymmetric shape is based on the same mechanism as that of α-relaxation, it is interpreted to result from the cooperative motion of small solvent molecules and water molecules. Below T _c, the asymmetric relaxation behaves as α-relaxation, and ν-relaxation, which is not observed above T _S, appears at a higher frequency than α-relaxation [39, 40, 55]. In contrast, in solutions containing solutes with a molecular weight larger than 100, such as synthetic and biological polymers as well as the pentaethylene glycol shown in Fig. 9.2, water relaxation exhibits a symmetric shape on both the high- and low-frequency sides of the loss peak above T _s, as shown in Fig. 9.3b [39, 40, 55, 58–60, 62]. The shape of the ν-relaxation in solutions of high-molecular-weight solutes is different from that for solutions of low-molecular-weight solutes, although water molecules form hydrogen bonds with high-molecular-weight solutes. As shown in Fig. 9.3b, the high-molecular-weight solute molecules (M _W ≥100) behave as obstacles to water molecules and spatially restrict the motion of water molecules. This spatially restricted motion of water molecules shows symmetric behavior, which is considered to be due to a mechanism similar to that which results in the symmetric behavior of the secondary relaxations attributed to the distribution of relaxation time in various local environments. Below T _S, the relaxation observed at above T _S becomes ν-relaxation; on the low-frequency side, a new α-relaxation is observed. Figure 9.4 shows temperature dependences of the relaxation times and strength for the α- and ν-relaxations, i.e., τ _α, τ _ν, Δε _α, and Δε _ν, respectively, for pentaethylene glycol (5EG) solutions as an example of solutions containing a solute with a high molecular weight [39, 55]. The temperature dependence of Δε _ν is also weak below T _g but significantly differs above T _g, similarly to the temperature dependences of enthalpy, entropy, and volume. Δε _α is small at high temperatures because of the less cooperative motion between water and solute molecules. When cooperative motion is enhanced with decreasing temperature below T _c, Δε _α increases but Δε _ν decreases. Below T _g, τ _ν values are similar among various aqueous solutions of different concentrations and independent of the structure and molecular weight of the solute molecules and T _g [54–56]. τ _ν has an Arrhenius temperature dependence, where the plots of relaxation time against the inverse of temperature are linear with an activation energy of approximately 50 kJ/mol. This is because the local motion of water molecules maintains behavior specific to water.

τ _ν shows different temperature dependences above and below T _g and exhibits VFTH, or at least non-Arrhenius, behavior above T _g. The same features are also clearly seen in fructose-water mixtures [52]. The significantly different temperature dependences of τ _ν and Δε _ν above and below T _g are also observed in the relaxation time and strength of the JG relaxation, which is observed in various substances, not only in aqueous solutions [27]. Therefore, the motion of various substances, including polymers, in aqueous solutions is considered to result from the local motion of water as the elementary process of hydrated solute molecules [56].

The Arrhenius to non-Arrhenius crossover of the relaxation time at around the glass transition temperature is one of the most attractive features of ν-relaxation discovered in this decade. The dielectric behavior of supercooled aqueous solutions of propylene glycol, glycerol, poly-(vinylpyrrolidone) (PVP), and poly(ethylene glycol)s of different molecular weights has been examined for different concentrations [36, 43]. The sub-T _g process due to the reorientational motion of the “confined” water molecules that are part of the matrix and the matrix itself were frozen at T _g. The corresponding dielectric strength shows an appreciable change at T _g, indicating a hindered rotation of water molecules in the glassy phase [36, 43]. Furthermore, the nature of this confined water appears to be anomalous compared with those of most other supercooled confined liquids [43].

It was presented by other authors that because of the non-Arrhenius temperature dependence of water at high temperatures, the mobility of the matrix (origin of the α-relaxation) increases at temperatures above T _g, and water is able to form an extended network and relax in a cooperative manner, as in bulk water [44]. On the other hand, because of the Arrhenius temperature dependence of water at low temperatures, water behaves as if it is confined, i.e., there is local motion of water molecules in the glassy frozen matrix [44]. Then, the crossover temperature is directly related to the glass transition temperature of the mixtures [45, 48, 49, 51]. 18 different water-rich mixtures with very different hydrophilic substances, such as low-molecular-weight organic glass formers, polymers, sugars, and biopolymers (proteins and DNA), were studied by BDS, and the observed non-Arrhenius to Arrhenius crossover seems to be a general feature not only for water solutions but for dynamically asymmetric mixtures [54]. Another interpretation is that the apparent fragile-to-strong transition for supercooled confined water is due to a merged αβ-relaxation at high temperatures and a pure β-relaxation (confined water) below the crossover temperature, while the α-relaxation disappears at low temperatures owing to confinement effects [63].

The change in the temperature dependence of the relaxation time of ν-relaxation is also observed for water in an aqueous layer of 6 Å thickness (equivalent to that of two water molecules) formed by the hydration of Na vermiculite [64, 65], molecular sieves [66], silica hydrogels [67–69], and poly(2-hydroxyethyl methacrylate) [70–73]. Many such characteristics of ν-relaxation are common with those of JG relaxation observed in nonaqueous systems, such as mixtures of van der Waals liquids [56]. The above experimental results led to the conclusion that, in aqueous solutions, ν-relaxation behaves similarly to JG relaxation, although α-relaxation is attributed to the cooperative motion of solute and water molecules.

The observation of the α-relaxation originating from the segmental motion of polymer chains is generally difficult in aqueous polymer solutions since it is masked by the components of electrical conduction and electrode polarization; only ν-relaxation can be observed dielectrically [42, 48, 50, 54]. Temperature dependences of the relaxation process originating from the segmental motion of the polymer main chain (the α-process) were observed in PVP aqueous solution with 4 water molecules/monomeric unit of PVP [49] and in PVME aqueous solutions with 30 wt% water [51] by quasielastic neutron scattering (QENS), but not by BDS. T _g of α-relaxation was determined by DSC and the extrapolation of the relaxation time of α-relaxation to 100–1,000 s. T _g agrees well with the temperature at which the Arrhenius to non-Arrhenius crossover of ν-relaxation occurs. Recently, we have observed the α-relaxation attributed to the local main chain motion of PVP in aqueous solution by dielectric spectroscopy [47], since the PVP was deionized and the contributions of electrode polarization and dc conductivity were reduced. Figure 9.5 shows the inverse temperature dependence of the relaxation times of the α-relaxation of PVP and the ν-relaxation of water in the 65 wt% PVP-water mixture. The relaxation times of the dielectrically observed α-process of PVP [47] are somewhat larger than those determined by QENS [49], as shown in Fig. 9.5. In addition, the Arrhenius to non-Arrhenius transition of ν-relaxation is observed in close proximity to T _g of the dielectric α-relaxation.