Broadband Dielectric Spectroscopy Data Research Articles

Machine learning-assisted equivalent circuit identification for dielectric spectroscopy of polymers

Polymers have become indispensable across fields of application, and understanding their structure–property relationships and dynamic behaviour is essential for performance optimization. Polymer membranes, particularly ion exchange membranes, play a crucial role in renewable energy conversion technologies, fuel cells, solar energy conversion, and energy storage. In this context, broadband dielectric spectroscopy (BDS) offers a powerful, non-destructive approach to investigate the electrical response and relaxation dynamics of polymers. These properties are investigated by parametrizing the system’s impedance response in terms of a network of circuit elements, i.e. the electrical equivalent circuit (EEC), whose impedance resembles the one of the system under investigation. However, the determination of the EEC from BDS data is challenging due to system complexity, interdependencies of circuit elements, and researcher biases. In this work, we propose a novel approach that incorporates a convolutional neural network (CNN) model to predict the EEC topology. By reducing user bias and enhancing data analysis, this approach aims to make BDS accessible to both experienced users and those with limited expertise. We show that the combination of machine learning and BDS provides valuable insights into the dynamic behaviour of polymer membranes, thus facilitating the design and characterization of tailored polymers for various applications. We also show that our model outperforms state-of-the-art machine learning methods with a top-5 accuracy of around 80% for predicting the circuit topology and a parameter fitting error as low as 0.05%.

Modeling the Interface Between Phases in Dense Polymer‐Carbon Black Nanoparticle Composites by Dielectric Spectroscopy: Where Are We Now and What are the Opportunities?

AbstractThe macroscopic properties of polymer nanocomposites (PNC) rely largely on the interphase between the polymer chains and the filler particles. One significant difficulty to solve this issue is to quantitatively model the structure‐property correlations due to the interfacial region in these complex materials. While dielectric spectroscopy (DS) measurements are routinely used to characterize the effective permittivity of filled polymers, fitting standard effective medium models and mixing equations to these data remains notoriously difficult to interpret. This is due to the absence of explicit reference to internal length scales characterizing the interfaces in the PNC. As an illustrative example, a two‐level homogenization framework is proposed which enables the extraction of useful information on the impact of a thin interphase confined on a nanometer length scale based on broadband DS data. This model leads to new ways of tuning the interphase so as to optimize the material's response to electric field, a situation relevant for electromagnetic shielding. This approach provides guidance on how to observe directly and experimentally the actual properties of the interface between the phases (as opposed to model‐based inference). Aside from its secure physical foundation in the theory of effective medium, a significant advantage of this approach is that a genetic algorithm (GA) technique applied to this physics‐based model enables the uniqueness of the fit parameters to be considered, as the GA method is robust in terms of finding globally optimum solutions, therefore placing confidence in non‐universal values of the percolation exponents. Recent work in physics‐informed machine learning indicates that the effective dielectric properties of PNC with many degrees of freedom due to their complex morphology can be described by considering only a few degrees of freedom describing the interface features between the phases in these composites.

Studying the Intermolecular Interactions, Structural Dynamics, and Non-Equilibrium Kinetics of Cilnidipine Infiltrated into Alumina and Silica Pores.

In the present study, the behavior of the calcium channel blocker cilnidipine (CLN) infiltrated into silica (SiO2) and anodic aluminum oxide (AAO) porous membranes characterized by a similar pore size (d = 8 nm and d = 10 nm, respectively) as well as the bulk sample has been investigated using differential scanning calorimetry, broadband dielectric spectroscopy (BDS), and Fourier-transform infrared spectroscopy (FTIR) techniques. The obtained data suggested the existence of two sets of CLN molecules in both confined systems (core and interfacial). They also revealed the lack of substantial differences in inter- and intramolecular dynamics of nanospatially restricted samples independently of the applied porous membranes. Moreover, the annealing experiments (isothermal time-dependent measurements) performed on the confined CLN clearly indicated that the whole equilibration process under confinement is governed by structural relaxation. It was also found that the βanneal parameters obtained from BDS and FTIR data upon equilibration of both confined samples are comparable (within 10%) to each other, while the equilibration constants are significantly different. This finding strongly emphasizes that there is a close connection between the inter- and intramolecular dynamics under nanospatial restriction.

Identifying interfacial failure mode in aerospace adhesive bonds by broadband dielectric spectroscopy

The most widely accepted test for bond durability analysis in aerospace metal-bonded structures is the bondline corrosion test introduced in the late 90s. Little progress has been made however on non-destructive testing methods that allow determining the bond quality after years of use. Here, a non-destructive method based on dielectric spectroscopy is introduced to evaluate the state of a metal-adhesive-metal bond exposed to salt fog spray up to 180 days. Several samples were evaluated with broadband dielectric spectroscopy (BDS), floating roller peel (FRP) tests and bondline corrosion (BLC) after exposure to salt fog spray test for different times. Relaxation processes and conductivity phenomena extracted from the BDS data (e.g. apparent conductivity relaxation time (τmax) using electric modulus) are found to correlate well with the bond strength measured in peel test and BLC progression. The BDS-based protocol was able to identify the local interfacial degradation stages in a non-destructive mode and with high resolution. The protocol has the potential to be further developed into a test method for durability on coupon level.

Insight from high-pressure dielectric studies into molecular dynamics of the itraconazole-glycerol mixture in smectic and isotropic phases.

We present here the results of high-pressure broadband dielectric spectroscopy (BDS) measurements for a mixture of liquid-crystalline drug itraconazole (ITZ) and glycerol (GLY) at a critical concentration of 5% w/w in which the nematic order is eliminated. In the investigated system, smectic-A to isotropic phase transition leaves a clear fingerprint on the dielectric response, allowing for a phase diagram creation using BDS data. By following the α-relaxation dynamics under different thermodynamic conditions, we provide insights into the effect of pressure on temperature and the phenomenology of smectic-A to the isotropic phase transition. Additional measurements of specific volume as a function of pressure and temperature provide us with a deeper insight into material properties that could be analyzed comprehensively via the equation of state. We proved the validity of the density scaling concept, showing that the mixture's complexity does not exclude thermodynamic scaling of dynamic properties related to the α-process in the smectic-A phase. The low value of scaling exponent γ = 2.00 ± 0.02 and a high ratio of the activation energy at constant volume, EV, to the activation enthalpy at constant pressure, HP, indicate that temperature is a dominant variable controlling α-relaxation dynamics in the ordered smectic-A phase of the ITZ-GLY mixture.

Critical Role of the Interfacial Layer in Associating Polymers with Microphase Separation

Polymers with dynamic (transient) bonds, often called associating polymers, have been attracting significant attention in recent years due to their unique viscoelastic properties, self-healing ability, and recyclability. Nevertheless, understanding the mechanisms and the factors controlling their macroscopic properties remains limited due to the higher complexity introduced by the dynamic bonds. In this study, small-angle X-ray scattering (SAXS), broadband dielectric spectroscopy (BDS), and rheology were applied to unravel the structure and dynamics of telechelic associating polymers with different molecular weights. SAXS measurements revealed phase separation of the functional end groups with an average cluster size of ∼2–3 nm and the distance between clusters controlled by the chain length. Borrowing the interfacial layer model analysis of BDS data from the polymer nanocomposite field, we demonstrated the presence of an interfacial polymer layer with a thickness of ∼0.7–0.9 nm surrounding these clusters. Rheological measurements showed quantitatively that the presence of the interfacial layer significantly alters the viscoelastic behavior of these materials, indicating the crucial role of the interfacial layer in defining the macroscopic mechanical properties of the studied telechelic materials. The presented results emphasize that phase separation of the functional groups in associating polymers leads to very significant changes of the viscoelastic properties, opening a promising avenue in the design of novel functional materials.

Relaxation processes in a polymer composite for bulk heterojunction: A dielectric spectroscopy study

Poly[N-9″-hepta-decanyl-2,7-carbazole-alt-5,5-(4ʹ,7ʹ-di-2-thienyl-2ʹ,1ʹ,3ʹ-benzothiadiazole)] (PCDTBT) and its blend with [6,6]-phenyl C71-butyric acid methyl ester (PCBM) available for photovoltaic application were investigated with Fourier transform infrared spectroscopy (FTIR), atomic force microscopy (AFM), and broadband dielectric spectroscopy (BDS). In the BDS spectra, the molecular dynamics, polarization, and conductivity processes were identified, analyzed, and discussed for both PCDTBT and the PCDTBT/PCBM blend. The dielectric constant of the blend was successfully predicted when the dielectric constants of PCDTBT and PCBM and their weight ratio in the blend were taken into account. Enhanced dc conductivity due to increased charge carrier mobility was detected in the blend. The energetic offset of the photovoltaic blend under study was shown to be directly estimated from the BDS data.

Ion Transport and Interfacial Dynamics in Disordered Block Copolymers of Ammonium-Based Polymerized Ionic Liquids

A series of diblock copolymers bearing a polymerized ionic liquid (polyIL) block (poly(N-(methacryloyloxy)ethyl-N,N-dimethyl-N-ethylammonium bis(trifluoromethylsulfonyl)imide)) and a noncharged block (poly(methyl methacrylate) (PMMA)) or poly(n-butyl methacrylate) (PBuMA)) were studied using differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), wide-angle X-ray scattering (WAXS), and broadband dielectric spectroscopy (BDS) to probe the effect of ion concentration on the morphology and ion transport in these polyelectrolytes. Two majority PMMA block copolymers, having mole ratios of the polyIL of 0.19 and 0.22, exhibited evidence of aggregation indicated by interfacial polarization in the dielectric spectra. The 0.19 mole ratio sample also displayed two distinct glass transitions by DSC. The SAXS measurements showed that no long-range order was present in these samples. The ionic conductivity of these samples were lower than the polyIL homopolymer due to hindered ion transport at the aggregate boundaries. Copolymers with majority polyIL blocks were found to exhibit disorder based on SAXS and DSC measurements. Furthermore, at a mole fraction of 0.91 of the polyIL the ionic conductivity was enhanced by a factor of ca. 1.5 with respect to the polyIL homopolymer, with a similar increase observed for the static dielectric permittivity. The effective number density and mobility of the ions were calculated for these systems from BDS and WAXS data, indicating that the enhancement of the ionic conductivity corresponds to an increase in the density of mobile charge carriers. The higher effective number density of charge carriers correlates with increased static dielectric permittivity, suggesting that ion pair dissociation is the likely mechanism behind the observed enhancement of ion transport. This study showcases the wealth of information that can be obtained from a combination of complementary experimental techniques.

Enhanced dielectric properties induced by loading cellulosic nanowhiskers in natural rubber: Modeling and analysis of electrode polarization

Natural rubber (NR) isolated from Hevea Brasiliens and reinforced with different amounts of cellulose nanowhiskers (extracted from the rachis of date palm tree) was investigated using differential scanning calorimetry and dielectric spectroscopy in the frequency range 0.1 Hz to 1 MHz, and the temperature range −80 to 200 °C. The experimental dielectric data were analysed within the formalisms of dielectric permittivity, complex conductivity and complex modulus. The results were discussed in terms of dc conductivity, interfacial polarization and electrode polarization. The paper aims to investigate especially the electrode polarization observed at low frequency and/or high temperature (LF/HT). It is exhibited that the understanding of the frequency space charge relaxation behaviour trapped close to the material/electrode interface will help one to elucidate the charge dynamics in the quasi static range. So charge carrier concentration and mobility in the sample at high temperature can be evaluated through the electrode polarization modeling of broadband dielectric spectroscopy data.

Ionic Conduction and Dielectric Relaxation in Poly(ethylene carbonate)-Li Salt Electrolytes

Polymer electrolytes such as poly(ethylene oxide) (PEO)-metal salt complexes have attracted much attention as ion-conductive soft materials for novel battery systems, because of their safety compared with liquid electrolytes, their flexibility and their lightweight. However, the conductivity of typical PEO-based electrolytes is limited to approximately 10-5 S/cm at room temperature, and it is extremely difficult to enhance the lithium (cation) transference number. We believe that the development of novel polymers without PEO chains is one solution for improving the conductivity. So we consider polycarbonates that can be obtained by the alternating copolymerization of carbon dioxide with epoxides and comprise novel polymer candidates for electrolytes. Following the first report of the CO2/epoxide copolymer by Tsuruta et al., there has been considerable development of highly active catalysts for effective polymerization. This copolymer is a remarkable macromolecule because it utilizes CO2as a raw material and has excellent properties; it is biodegradable, easily processed and colored, and has high transparency and low oxygen permeability. We have focused on the chemical structure of the copolymer, which has one alternating carbonate group (-O-(C=O)-O-) in each repeating unit of the main chain. The carbonate group has a large dipole moment, and it can dissolve many types of salts. Carbonate-based organic solvents, such as dimethyl carbonate, are used as the electrolyte solution in Li-ion batteries because of their high dielectric constant. Therefore, we think that the carbonate group can provide a suitable structure for the polymer framework. In this study, we report on the use of poly(ethylene carbonate) (PEC) as a matrix for novel ion-conductive polymer electrolytes [1]. We found that the addition of small amount of TiO2 nano-particulates to the PEC-based electrolytes can enhance lithium transference numbers, t +, which are measured using an electrochemical combination method of DC polarization and AC impedance measurements for Li│electrolyte│Li cells. Moreover, we undertook lithium-7 and fluoride-19 NMR spectroscopic and pulsed field gradient (pfg) diffusion measurements on these electrolytes. The values of self-diffusion coefficients of the lithium cation (D Li) and the estimated t + values for PEC-LiFSI-TiO2 were more than 10-7 cm2/s and 0.8 at 60 oC. The Li-ion conductivities (σ at 60 oC × t + estimated from the electrochemical method) of samples PEO20LiFSI, PEC0.53LiFSI and PEC0.53LiFSI-TiO2 (1 wt%) were calculated to be 5.6×10-5, 2.2×10-4 and 4.3×10-4S/cm, which are superior as a structure to polyether as an electrolyte for flexible batteries. On the other hand, there are no detailed information on the ion-conductive behavior of PEC-based electrolytes. So, we used broadband dielectric spectroscopy (BDS) measurement for the investigation of correlation between ionic conduction and dielectric relaxation behavior over the broad range of salt concentration. We measured BDS data and analyzed dielectric spectra using the Havriliak-Negami functions. Fig. 1 shows salt concentration dependence of relaxation peak for PEC-LiTFSI electrolytes at 40 oC. A strong peak indicates α relaxation derived from segmental motion of PEC main chains. As the salt concentration increased, the α relaxation peak shifted to the high frequency region with increasing the peak area, which is opposite to the behavior of typical PEO-based electrolytes (the peak shifts to the lower frequencies) [2]. This means that the PEC-LiTFSI electrolytes show good conductivities at high salt concentrations because of the fast segmental motion with local ion-rich structures. [1] Y. Tominaga et al.,Chem. Commun., 50,4448 (2014). [2] T. Furukawa et al., Electrochim. Acta, 57,139 (2011). Acknowledgment: This work was financially supported by a Grant-in-Aid for Scientific Research (B) of JSPS KAKENHI (25288095), Japan. Fig.1 Salt concentration dependence of relaxation peaks for PEC-LiTFSI at 40 oC. Figure 1

Small and large scale segmental motion in polymers: estimating cooperativity length by ordinary relaxation experiments

We derive a suitable expression for estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymer melts by fitting data worked out by ordinary relaxation experiments carried out in isothermal conditions. As an example, the average CRR size in poly(n-butyl methacrylate) in proximity to the glass transition temperature is derived from a stress relaxation experiment performed by means of an atomic force microscopy setup. Good agreement is found with results in the literature derived from measurements of temperature fluctuations (the so-called Donth method). The temperature dependence of the CRR size is explored for poly(butadiene); in this case the segmental relaxation function is derived through a novel method for the analysis of the efficiency with which free induction decay echoes are refocused in 1H NMR experiments. It is found that the CRR size increases upon cooling. The results derived from the analysis of the NMR data are found to be in satisfactory agreement with those worked out from broadband dielectric spectroscopy data in the literature. © 2015 Society of Chemical Industry

Glass transition cooperativity from broad band heat capacity spectroscopy

Molecular dynamics is often studied by broad band dielectric spectroscopy (BDS) because of the wide dynamic range available and the large number of processes resulting in electrical dipole fluctuations and with that in a dielectrically detectable relaxation process. Calorimetry on the other hand is an effective analytical tool to characterize phase and glass transitions by its signatures in heat capacity. In the linear response scheme, heat capacity is considered as entropy compliance. Consequently, only processes significantly contributing to entropy fluctuations appear in calorimetric curves. The glass relaxation is a prominent example for such a process. Here, we present complex heat capacity at the dynamic glass transition (segmental relaxation) of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in a dynamic range of 11 orders of magnitude, which is comparable to BDS. As one of the results, we determined the characteristic length scale of the corresponding fluctuations. The dynamic glass transition measured by calorimetry is finally compared to the cooling rate dependence of fictive temperature and BDS data. For PS, dielectric and calorimetric data are similar but for PMMA with its very strong secondary relaxation process some peculiarities are observed.

Dynamics of water-alcohol mixtures: Insights from nuclear magnetic resonance, broadband dielectric spectroscopy, and triplet solvation dynamics

We combine (2)H nuclear magnetic resonance (NMR), broadband dielectric spectroscopy (BDS), and triplet solvation dynamics (TSD) to investigate molecular dynamics in glass-forming mixtures of water and propylene glycol in very broad time and temperature ranges. All methods yield consistent results for the α process of the studied mixtures, which hardly depends on the composition and shows Vogel-Fulcher temperature dependence as well as Cole-Davidson spectral shape. The good agreement between BDS and TDS data reveals that preferential solvation of dye molecules in microheterogeneous mixtures does not play an important role. Below the glass transition temperature T(g), NMR and BDS studies reveal that the β process of the mixtures shows correlation times, which depend on the water concentration, but exhibit a common temperature dependence, obeying an Arrhenius law with an activation energy of E(a) = 0.54 eV, as previously reported for mixtures of water with various molecular species. Detailed comparison of NMR and BDS correlation functions for the β process unravels that the former decay faster and more stretched than the latter. Moreover, the present NMR data imply that propylene glycol participates in the β process and, hence, it is not a pure water process, and that the mechanism for molecular dynamics underlying the β process differs in mixtures of water with small and large molecules.

Dynamics at the Polymer/Nanoparticle Interface in Poly(2-vinylpyridine)/Silica Nanocomposites

The static and dynamic properties of poly(2-vinylpyridine)/silica nanocomposites are investigated by temperature modulated differential scanning calorimetry, broadband dielectric spectroscopy (BDS), small-angle X-ray scattering (SAXS), and transmission electron microscopy. Both BDS and SAXS detect the existence of an interfacial polymer layer on the surface of nanoparticles. The results show that whereas the calorimetric glass transition temperature varies only weakly with nanoparticle loading, the segmental mobility of the polymer interfacial layer is slower than the bulk polymer by 2 orders of magnitude. Detailed analysis of BDS and SAXS data reveal that the interfacial layer has a thickness of 4–6 nm irrespective of the nanoparticle concentration. These results demonstrate that in contrast to some recent articles on polymer nanocomposites, the interfacial polymer layer is by no means a “dead layer”. However, its existence might provide some explanation for controversies surrounding the dynamics of poly...

Chain Length Effects on the Dynamics of Poly(ethylene oxide) Confined in Graphite Oxide: A Broadband Dielectric Spectroscopy Study

The dynamics of poly(ethylene oxide) (PEO) intercalated in the subnanometer-spaced graphite oxide (GO) layers is investigated by using broadband dielectric spectroscopy (BDS). To this end, we compare BDS data obtained for PEO chains of increasing lengths, from three monomeric units to several thousand repetitive ethylene oxide units (n = 3–2135). Two relaxations were clearly identified for the confined PEO. The slowest one is proposed to originate from interfacial polarization. It is dependent on the chain length and exhibits a change in activation energy at 247 K, a temperature at which the GO exhibits an interlayer expansion when subjected to an increase in temperature. The fastest relaxation is nearly independent of the chain length, in contrast to the behavior that we found for the β-relaxation of bulk PEO. These results strengthen a previous hypothesis suggesting the emergence of a new set of chain length scales primarily dictated by the presence of anchoring points on the GO substrate upon intercala...

Study of the Dynamic Heterogeneity in Poly(ethylene-ran-vinyl acetate) Copolymer by Using Broadband Dielectric Spectroscopy and Electrostatic Force Microscopy

Dynamic heterogeneities in ethylene–vinyl acetate (EVA) random copolymers were studied using broadband dielectric spectroscopy (BDS) over a broad frequency and temperature range. BDS data for EVA copolymers show relatively broad spectra extending over several frequency decades, which make interpretation of the data complicated. Thus, microscopic dielectric characterizations of the samples were done using single pass electrostatic force microscopy (SP-EFM) images. From these experiments two distinct dielectric contributions were found in the semicrystalline samples. Dielectric spectra of EVA copolymers were fitted using a model based on the SP-EFM images. According to this analysis, the broad dielectric responses of semicrystalline EVA copolymers were constituted from two dielectrically active phases, referred to as the constrained and nonconstrained phases, exhibiting different segmental relaxations. In the constrained phase, vinyl acetate (VA) motions were greatly restricted by crystalline microstructures, whereas in the nonconstrained phase, VA monomers were assumed to be completely free from crystalline effect. The glass transition temperature derived from the dynamics of the VA segments in the constrained phase was found to correspond well with that determined from DSC representing the overall amorphous phase in the more crystallized state. Moreover, crystallinity of the sample obtained using DSC was found to follow a similar variation with temperature to that of the dielectric relaxation strength of the constrained phase of the copolymers. However, at the earlier stage of crystallization, where crystallinity increases rapidly, the dielectric relaxation remains insensitive to it.

Molecular dynamics in PBA/PEO miktoarm star copolymers

Molecular dynamics of miktoarm star copolymers consisting of poly(n-butyl acrylate) PBA and polyethylene oxide (PEO) arms was studied by means of Broadband Dielectric Spectroscopy (BDS) and Nuclear Magnetic Resonance (NMR) methods. The spectroscopic studies were performed for three types of copolymers differing in the composition, namely materials containing 76%, 46% and 16% molar fraction of PBA arms. The local processes, described by the Arrhenius law (e.g. the anisotropic rotation of methyl groups and the anisotropic local motions in the PEO chain), were observed for the studied systems below the glass transition temperature. It was found that the investigated PBA/PEO miktoarm star copolymers are characterized by single glass transition, which may result from similar values of glass transition temperatures of the PBA and PEO polymers. The segmental dynamics in the studied systems was quantitatively described by using the Vogel-Fulcher-Tammann (VFT) relation applied to combined NMR and BDS data. Moreover, above the glass transition temperature the interfacial polarization and conductivity phenomena were detected with the BDS method for all systems under study.

Concentration and mobility of charge carriers in thin polymers at high temperature determined by electrode polarization modeling

Charge carrier concentration (n0) and effective mobility (μeff) are reported in two polymer films (<10 μm) and in a very high temperature range (from 200 to 400 °C). This was possible thanks to an electrode polarization modeling of broadband dielectric spectroscopy data. It is shown that the glass transition temperature (Tg) occurrence has a strong influence on the temperature dependence of n0 and μeff. We carry out that n0 presents two distinct Arrhenius-like behaviors below and above Tg, while μeff exhibits a Vogel-Fulcher-Tamman behavior only above Tg whatever the polymer under study. For polyimide films, n0 varies from 1 × 1014 to 4 × 1016 cm−3 and μeff from 1 × 10−8 to 2 × 10−6 cm2 V−1 s−1 between 200 °C to 400 °C. Poly(amide-imide) films show n0 values between 6 × 1016 and 4 × 1018 cm−3 from 270 °C to 400 °C, while μeff varies between 1 × 10−10 and 2 × 10−7 cm2 V−1 s−1. Considering the activation energies of these physical parameters in the temperature range of investigation, n0 and μeff values appear as coherent with those reported in the literature at lower temperature (<80 °C). Surface charge carrier concentrations (nS) are reported and discussed for potential passivation (i.e., surface electrical insulation) applications. Polyimide films appear as good candidates due to nS values less than 1011 cm−2 up to 300 °C.

Multiple relaxation processes versus the fragile-to-strong transition in confined water

Broadband dielectric spectroscopy data on water confined in three different environments, namely at the surface of a globular protein or inside the small pores of two silica substrates, in the temperature range 140 K ≤ T ≤ 300 K, are presented and discussed in comparison with previous results from different techniques. It is found that all samples show a fast relaxation process, independently of the hydration level and confinement size. This relaxation is well known in the literature and its cross-over from Arrhenius to non-Arrhenius temperature behavior is the object of vivid debate, given its claimed relation to the existence of a second critical point of water. We find such a cross-over at a temperature of ~180 K, and assign the relaxation process to the layer of molecules adjacent and strongly interacting with the substrate surface. This is the water layer known to have the highest density and slowest translational dynamics compared to the average: its apparent cross-over may be due to the freezing of some degree of freedom and survival of very localized motions alone, to the onset of finite size effects, or to the presence of a calorimetric glass transition of the hydration shell at ~170 K. Another relaxation process is visible in water confined in the silica matrices: this is slower than the previous one and has distinct temperature behaviors, depending on the size of the confining volume and consequent ice nucleation.

Experimental evidence for fractional time evolution in glass forming materials

The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless it contains only a single stretching exponent. Qualitative and quantitative agreement with dielectric data for glycerol is found that extends into the excess wing. The fits require fewer parameters than traditional fit functions and can extend over up to 13 decades in frequency.