Kohlrausch Williams Watts Equation Research Articles

Temperature dependent magnetic and electrical transport properties of lanthanum and samarium substituted nanocrystalline nickel ferrite and their hyperthermia applications

Structural, optical, temperature dependent magnetic and electrical properties have been investigated for the nanocrystalline NiFe1.97RE0.03O4 (RE = La3+ and Sm3+) compound. Without any signs of a secondary REFeO3 phase, the Rietveld refinement reveals a single-phase spinel structure possessing cubic symmetry for current samples. The decrease in lattice constant has been observed as a result of RE ions substitution. The TEM micrographs reveal nanosized particles with an average size of 35 ± 3 nm and 32 ± 3 nm for La3+ and Sm3+ substituted samples. EDX spectra of both samples show good compositional homogeneity. HRTEM micrographs of both samples show well resolved lattice fringes and their inter-planar spacing matches with that obtained from the Rietveld analysis of the XRD patterns. The concentration of Fe2+ and Fe3+ ions has been estimated from the XPS spectra analysis and it is found to be ∼ 22% and 78% for NiFe1.97La0.03O4 and, 20% and 80% for NiFe1.97Sm0.03O4 compound. The optical energy band gap for rare earth substituted samples is found to be more than that of pure nickel ferrite. The value of saturation magnetization (Ms) and magneto-crystalline anisotropy constant (K1) estimated from the “Law of Approach to Saturation” equation for rare earth substituted samples are found to be less than that of pure nickel ferrite. However, an enhanced value of coercivity has been observed with RE substitution. ZFC (zero field cooling) and FC (field cooling) DC magnetization curves measured at 100 Oe in the temperature range of 60–400 K reveal a combination of weak and intermediate forms of magnetic interaction between the particles for both samples. Temperature dependent analysis of saturation magnetization and coercivity employing modified Bloch’s law and Kneller’s relation supports the nanomagnetic behavior of both samples. Under an AC magnetic field of 14.92 kA/m and frequency 337 kHz, the SAR and ILP values have been found to be ∼ 331 W/g and 4.22 nHm2/kg for NiFe1.97La0.03O4 and, ∼ 241 W/g and 3.21 nHm2/kg for NiFe1.97Sm0.03O4. The dielectric relaxation data have been analyzed at various temperatures ranging from 40 to 300 0C over the frequency range 100 Hz-1 MHz using electrical impedance spectroscopy. The dielectric constant for rare earth substituted samples is found to be more and their AC conductivity is observed to be less than that of pure nickel ferrite. The analysis of temperature dependent AC conductivity employing Jonscher’s power law suggests that the charge carrier’s conduction mechanism of both samples follows the small polaron hopping mechanism below 200 0C, thereafter; it follows the correlated barrier hopping mechanism. The activation energy estimated by imaginary impedance spectra is found to be 0.411 eV and 0.398 eV for NiFe1.97La0.03O4 and NiFe1.97Sm0.03O4 which is more than that of pure nickel ferrite. The Cole-Cole plots at different temperatures suggest the presence of non-Debye-type relaxation. The modeling of Cole-Cole plots with equivalent circuits for both samples confirms the contribution of both grain and grain boundary in electrical conduction. The estimated stretching exponential factor by fitting the modified KWW (Kohlrausch-Williams-Watts) equation to the imaginary modulus curve reveals relatively more dipole-dipole interaction in NiFe1.97Sm0.03O4 than that of the La3+ substituted sample.

Unexpected non-monotonic changing in the heterogeneity of glasses during annealing

The heterogeneity of glasses has critical influences on the properties. How heterogeneity evolves during annealing is an intriguing cutting-edge question. In this work, the heterogeneity of the annealed metallic and polymer glasses has been studied systematically by using stress relaxation and nanoindentation tests. The stress relaxation processes are analyzed using Kohlrausch-Williams-Watts (KWW) equation. We surprisingly find that the heterogeneous factor βKWW in KWW equation does not change monotonously but increases first and then decreases along with the annealing time. The two-stage process implies that glasses do not evolve as expected toward the more homogeneous glassy state but become homogeneous first and then more heterogeneous. This is further verified by the evolution of critical shear stress for local plasticity. It is revealed that the two-stage process is correlated with different relaxation modes, which is further interpreted using a phenomenological model. These findings not only give insights into understanding the nature of glasses, but also are useful for designing glasses with superior properties.

Physical Ageing of Amorphous Poly(lactic acid)-Indapamide System Studied by Differential Scanning Calorimetry.

The process of isothermal and non-isothermal physical ageing of amorphous polylactide (PLA) with the active pharmaceutical ingredient, indapamide (IND), was investigated. A PLA-IND system with a 50/50 weight ratio was obtained and characterized using differential scanning calorimetry (DSC). In the 50/50 (w/w) mixture, two glass transitions were observed: the first at 64.1 ± 0.3 °C corresponding to the glass transition temperature (Tg) of PLA, and the second at 102.6 ± 1.1 °C corresponding to the Tg of IND, indicating a lack of molecular mixing between the two ingredients. The PLA-IND system was subjected to the isothermal physical ageing process at different ageing temperatures (Ta) for 2 h. It was observed that the highest effect of physical ageing (enthalpy relaxation change) on IND in the PLA-IND system occurred at Ta = 85 °C. Furthermore, the system was annealed for various ageing times at 85 °C. The relaxation enthalpies were estimated for each experiment and fitted to the Kohlrausch-Williams-Watts (KWW) equation. The KWW equation allowed for the estimation of the relaxation time and the parameter describing the distribution of relaxation times of the isothermal physical ageing process of IND in the PLA-IND system. The physical ageing of the PLA-IND mixture (50/50) was also discussed in the context of heat capacity. Moreover, the activation energy and fragility parameters were determined for the PLA-IND (50/50) system.

Electrical transport properties of nanocrystalline and bulk nickel ferrite using complex impedance spectroscopy: a comparative study

In this work, the comparative study on the electrical transport properties of nanocrystalline nickel ferrite (NiFe2O4) and its bulk counterpart has been carried out in detail by using complex impedance spectroscopy in a wide range of frequencies (100 Hz–1 MHz) and temperatures (40 °C–320 °C). The dispersive nature of the dielectric constant and loss factor is explained by the Maxwell-Wagner model and Koop’s phenomenological theory. The value of the dielectric constant for nanocrystalline nickel ferrite is found to be more as compared to its bulk counterpart. The frequency variation dielectric permittivity is well fitted with the modified Debye formula, which suggests the presence of multiple relaxation processes. The temperature dependent ac conductivity follows Jonscher’s universal power law and reveals the presence of multiple transport mechanisms from small polaron hopping (SPH) to correlated barrier hopping (CBH) mechanism near 200 °C. The estimated values of Mott parameters are found to be satisfactory. Thermally activated relaxation phenomena have been confirmed by scaling curves of imaginary impedance () and modulus (). The comparison between the and spectra indicates that both long-range and short-range movement of charge carriers contribute to dielectric relaxation with short-range charge carriers predominating at low temperatures while long-range charge carriers are dominating at high temperatures. Analysis of the semicircular arcs of Nyquist plot indicates the presence of grain boundary contribution to the electrical conduction process for the nanocrystalline sample at high temperatures. The non-Debye type of relaxation has been examined by stretching exponential factor (β) which has been estimated by fitting the modified KWW (Kohlrausch-Williams-Watts) equation to the imaginary electric modulus curve. The value of β is found to be strongly temperature dependent and its value for the nanocrystalline sample is less than that of the bulk system which is explained on the basis of dipole-dipole interaction.

Temperature-dependent dielectric properties of CsPb2Br5: a 2D inorganic halide perovskite

Two dimensional (2D) CsPb2Br5 have been successfully synthesized via the chemical precipitation method. Detailed structural, morphological, optical, and dielectric studies of these materials have been performed. These 2D CsPb2Br5 plates (of thickness around 200–300 nm) are ascribed to a tetragonal lattice system with I4/mcm space group. The dielectric attributes such as dielectric constant, electrical modulus, loss factor, and the DC, and AC conductivities, are observed to be varying appreciably with temperature over an extensive frequency window of 10 Hz–50 MHz. The Nyquist plots are investigated using the Maxwell–Wagner equivalent circuit model, which shows the impact of grains and grain boundaries on the overall impedance. Both the free charge conductivity and space charge increase with an increment in temperature, as revealed from the modified Cole–Cole plot. The relaxation time and relaxation mechanism of 2D CsPb2Br5 are estimated using the Kohlrausch–Williams–Watts equation. Variation in DC conductivity and relaxation time, as a function of temperature, closely resembles Arrhenius’ behavior. Value of activation energy calculated from the DC conductivity corroborates with the same derived from relaxation time. The observation of high dielectric constant and nominal dielectric loss for CsPb2Br5 perovskite offers enormous potential in energy harvesting and storage devices.

Surface Chemistry Study of the Interactions of Sesame Oil with Meibomian Films.

A possible approach for the treatment of meibomian gland disease (MGD) can be the supplementation of meibomian gland secretion (MGS) with nonpolar lipids (NPL) rich plant oils. Sesame oil (SO), approximately equal in monounsaturated fat (oleic acid, 40% of total) and polyunsaturated fat (linoleic acid, 42% of total), has shown multiple health benefits due to its anti-inflammatory and antioxidant effects. Thus, the interactions between SO and MGS in surface layers deserve further study. Therefore, pseudobinary films were formed with controlled MGS/SO molar ratios (0%, 10%, 30%, 50%, and 100% SO) at the air/water surface of the Langmuir trough over phosphate buffered saline (pH 7.4) subphase. Surface pressure (π)-area (A) isotherms and Brewster angle microscopy observations showed nonideal interactions where SO aggregates with MGS and complements the NPL stratum of the meibomian layers. The analysis of stress relaxation transients with Kohlrausch–Williams–Watts equation revealed that the supplementation of fixed amount of MGS with excess lipids via SO altered the dilatational elasticity of the films as reflected by the increase of the exponent β. Thus, SO with its unique combination of high oxidative stability and abundance of long polyunsaturated acyl chains might be a useful supplement to MGS layers.

Dynamic mechanical response of ZrCu-based bulk metallic glasses

The thermal stability and the dynamic mechanical relaxation behavior of (Zr50Cu40Al10)100-xDyx (at.%) (x = 0 or 2) metallic glasses were investigated by differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). In the case of the (Zr50Cu40Al10)100-xDyx (x = 0 or 2) metallic glasses, atomic mobility increases by introduction of the Dy element. The activation energy of the the main a relaxation process and fragility index were discussed according to the DMA measurements. With the help of the time-temperature superposition (TTS) principle, the master curves of the model alloys were established, the Kohlrausch-Williams-Watts (KWW) function and quasi-point defects (QPD) theory were used to descirbe the master curves of the metallic glasses. The characteristic parameters related to microstructural heterogeneity in the KWW equation and the QPD model, Kohlrausch exponent βKWW and the correlation factor χ were evaluated. In parallel, the elastic, viscoelastic and viscoplastic responses of the model alloys have been analyzed based on the DMA results. Our investigations demonstrated that introduction of the Dy increases the structure heterogeneity of the (Zr50Cu40Al10)100-xDyx (x = 0 or 2) glassy system, which plays an important role in tailoring the dynamic relaxation behavior and mechanical properties of the metallic glasses.

Effect of minor addition on dynamic mechanical relaxation in ZrCu-based metallic glasses

The dynamic mechanical behavior of Zr50-xCu34Ag8Al8Pdx (x = 0 and 2) bulk metallic glasses was probed by mechanical spectroscopy. The results suggest that microalloying retards the relaxation dynamics. The physical aging was analyzed considering a model based on the variation of the concentration of flow units and the Kohlrausch-Williams-Watts (KWW) equation. In the current study, the characteristic parameters of the two models, βc and βaging, reflect the faster annihilation of flow units at higher temperature and the increase of dynamic heterogeneity with temperature, respectively. The mechanical relaxation spectrum was also analyzed. Based on the KWW equation and the quasi-point defect model, replacing Zr with a small amount of Pd can slightly increase the dynamic inhomogeneity and reduce the defect concentration. The analysis according to the HN function suggests that the addition of Pd increases the relaxation time. However, it does not significantly alter the shape of the relaxation time distribution.

Temperature and frequency dependent dielectric response of C3H7NH3PbI3: A new hybrid perovskite

Propylammonium lead iodide (C3H7NH3PbI3), a promising hybrid perovskite, is successfully synthesized by a solgel technique. Structural, optical, and dielectric properties have been studied in detail. The dielectric constant, loss factor, electric modulus, and AC and DC conductivity of this hybrid perovskite exhibit strong temperature dependence over the frequency range of 10 Hz ≤ f ≤ 8 MHz. The Nyquist plot reveals the distinct contributions of grain and grain boundary to the total impedance. The dielectric constant is found to increase with temperature in the high frequency region. The modified Cole–Cole plot shows that the space charge and free charge conductivity increase with the elevation of temperature, whereas the relaxation time decreases with the rise in temperature. From the modified Kohlrausch–Williams–Watts equation, we perceived asymmetrical nature in electric modulus spectra at various temperatures, which corresponds to the non-Debye type nature of perovskite. It has also been found that, with the elevation of temperature, the imaginary part of electric modulus spectra shifts from the non-Debye type toward the Debye type nature, though failing to acquire exact Debye type response, and emerges as a semiconductor material. AC conductivity of PAPbI3 is illustrated on the basis of the correlated barrier hopping (CBH) mechanism. Activation energy estimated from both modulus spectra and DC conductivity matches well, affirming the similarity between relaxation behavior and conduction mechanism. Along with all these, PAPbI3 possesses a high dielectric constant associated with a small dielectric loss, making it a potential candidate for energy harvesting devices.

Description of physical aging kinetics of glassy polymers by interpretation of parameters of the Kohlrausch-Williams-Watts relaxation function via simulation.

The empirical Kohlrausch-Williams-Watts (KWW) relaxation function has been widely used to describe the nonexponential relaxation behavior of glassy polymers during their physical aging. The characteristic relaxation time (τ_{KWW}) and the stretching parameter (β_{KWW}) of the KWW equation are obtained from experimental relaxation data by a curve-fitting procedure. However, knowing the values of KWW parameters is not sufficient to completely characterize the physical aging kinetics of glassy materials in order to compare, for example, the aging rate of different systems. To be able to overcome such problems, at least, an exact interpretation of these parameters is absolutely vital and then it would be quite desirable to convert them into a single relaxation-time constant. This approach, indeed, provides the possibility to directly evaluate and compare the kinetics and aging rate of different systems as well as different methods used for monitoring the physical aging of the same materials. To do these, a method based on the notion of the relaxation spectrum is employed which is modeled via the well-known statistical distribution of log-normal. By detailed numerical simulations, some explicit expressions between KWW parameters with descriptor parameters of the distribution are established. From this point of view, it is tried to interpret τ_{KWW} and β_{KWW} and convert them into a single relaxation-time constant. Finally, the results of suggested simulations are compared with those obtained in the literature.

In situ investigation of the kinetics and microstructure during photopolymerization by positron annihilation technique and NIR-photorheology.

The microstructural free volume evolution during a photopolymerization process was studied on a commercial photopolymer (SPOT LV) in situ by positron annihilation lifetime spectroscopy (PALS) and concomitant NIR-photorheology. Analysis of the positron lifetime spectra revealed a high sensitivity of the PALS technique to the different phases of photopolymerization associated with different reaction rates as well as to the evolution of microstructural free-volume shrinkage, which was described at the molecular level by the Kohlrausch–Williams–Watts equation. The in situ PALS study of microstructural changes in photopolymerization was related to the vitrification (gel point) accompanied by shrinkage stress registered via NIR-photorheology. The simultaneous NIR measurements yield information on the monomer conversion of SPOT LV, which can be correlated to the occurrence of the gel point and the evolution of the microstructural free volume. This combined study allows us to see deeper into the crosslinking process and its influence on the resulting material characteristics.

Transition from stress-driven to thermally activated stress relaxation in metallic glasses

The short-range ordered but long-range disordered structure of metallic glasses yields strong structural and dynamic heterogeneities. Stress relaxation is a technique to trace the evolution of stress in response to a fixed strain, which reflects the dynamic features phenomenologically described by the Kohlrausch-Williams-Watts (KWW) equation. The KWW equation describes a broad distribution of relaxation times with a small number of empirical parameters, but it does not arise from a particular physically motivated mechanistic picture. Here we report an anomalous two-stage stress relaxation behavior in a Cu46Zr46Al8 metallic glass over a wide temperature range and generalize the findings in other compositions. Thermodynamic analysis identifies two categories of processes: a fast stress-driven event with large activation volume and a slow thermally activated event with small activation volume, which synthetically dominates the stress relaxation dynamics. Discrete analyses rationalize the transition mechanism induced by stress and explain the anomalous variation of the KWW characteristic time with temperature. Atomistic simulations reveal that the stress-driven event involves virtually instantaneous short-range atomic rearrangement, while the thermally activated event is the percolation of the fast event accommodated by the long-range atomic diffusion. The insights may clarify the underlying physical mechanisms behind the phenomenological description and shed light on correlating the hierarchical dynamics and structural heterogeneity of amorphous solids.

Microwave sintered Bi0.90La0.10Fe0.95Mn0.05O3 nanocrystalline ceramics: Impedance and modulus spectroscopy

Multiferroic Bi0.90La0.10Fe0.95Mn0.05O3 (BLFMO) nanoceramics were synthesized by PVA sol-gel method, followed by microwave sintering. The structural, microstructural and electrical properties of BLFMO were investigated. The crystal symmetry and unit cell dimensions were determined from the experimental data using Rietveld analysis. BLFMO revealed only one electroactive region as verified from impedance and modulus spectroscopy. Overlapping large polaron tunneling transport mechanism was observed from AC conductivity analysis. Conduction below 250°C (−30°C≤T≤250°C) was attributed to translational hopping while above 250°C (250°C≤T≤350°C) corresponds to electron hopping between charge defects. The relative permittivity varies from 66 to 203 at 1kHz over the measured temperature range (−150°C≤T≤350°C). The electrical conductivity of the microwave sintered BLFMO has been discussed based on defect reaction with Mn doping. The measured DC conductivity in the range of 10−13S/cm at −130°C to 10−4S/cm at 350°C revealed the insulating behavior of the sample. At room temperature, the DC resistivity of the sample was over ~50MΩcm. The stretching constant (β) obtained from KWW (Kohlrausch-Williams-Watts) equation indicates that the sample inclined towards ideal Debye behavior as the temperature increases.

Intrinsic correlation between β-relaxation and spatial heterogeneity in a metallic glass.

β-relaxation has long been attributed to localized motion of constituent molecules or atoms confined to isolated regions in glasses. However, direct experimental evidence to support this spatially heterogeneous scenario is still missing. Here we report the evolution of nanoscale structural heterogeneity in a metallic glass during β-relaxation by utilizing amplitude-modulation dynamic atomic force microscopy. The successive degeneration of heterogeneity during β-relaxation can be well described by the Kohlrausch–Williams–Watts equation. The characteristic relaxation time and activation energy of the heterogeneity evolution are in accord with those of excess enthalpy release by β-relaxation. Our study correlates β-relaxation with nanoscale spatial heterogeneity and provides direct evidence on the structural origins of β-relaxation in metallic glasses.

Dynamic light scattering in semidilute and concentrated chitosan solutions

Dynamic light scattering was used to monitor relaxation processes in chitosan solutions at concentrations within the semidilute and concentrated regimes, Kohlrausch–Williams–Watts (KWW) equation being successfully fitted to intensity correlation function data. The dependence of KWW equation parameters on chitosan concentration indicated that an increase in concentration from semidilute to concentrated regime resulted in distribution of relaxation rate narrowing; temperature dependence of average relaxation rate indicated that relaxation was an energy activated process, whose parameters were associated to the interaction between chitosan chains (enthalpy of activation) and rigidity of chitosan conformations (pre-exponential factor).

POSS를 함유한 PMMA 박막의 유리전이온도 및 등온 물리적 시효

순수 PMMA와 methacryl-polyhedral oligomeric silsesquioxane(Ma-POSS)를 5 wt% 첨가한 PMMA를 박막(~650 nm)과 초박막(~50 nm)으로 제조하였으며, 유리전이온도(<TEX>$T_g$</TEX>)와 등온 물리적 시효에 미치는 박막의 두께에 미치는 POSS의 첨가 효과를 시차주사열량계(DSC)를 이용하여 조사하였다. 초박막화와 Ma-POSS의 첨가로 인해 <TEX>$T_g$</TEX> 감소가 관찰되었다. 또한 등온 물리적 시효에 의한 엔탈피 완화값(<TEX>${\Delta}H_{Relax}$</TEX>)도 초박막화 Ma-POSS를 첨가하였을 때 감소하였다. 시효시간에 따른 <TEX>${\Delta}H_{Relax}$</TEX> 데이터에 KWW(Kohlrausch-Williams-Watts)식을 적용하여 최대 엔탈피(<TEX>${\Delta}H_{\infty}$</TEX>), 이완시간(<TEX>${\tau}$</TEX>) 그리고 이완시간의 분포상수(<TEX>${\beta}$</TEX>)를 결정하였으며 이를 비교 분석하였다. Thin (~650 nm) and ultrathin (~50 nm) films of neat PMMA and PMMA containing 5 wt% of methacryl-polyhedral oligomeric silsesquioxane were prepared in this work. The effects of film thickness and POSS on glass transition temperature (<TEX>$T_g$</TEX>) and isothermal physical aging were investigated by means of differential scanning calorimetry (DSC). <TEX>$T_g$</TEX> depression was observed as film thickness was decreased and Ma-POSS molecules were incorporated. Enthalpy relaxation (<TEX>${\Delta}H_{Relax}$</TEX>) due to the isothermal physical aging was reduced by ultra-thin film thickness and the addition of Ma-POSS. KWW (Kohlrausch-Williams-Watts) equation was used to fit <TEX>${\Delta}H_{Relax}$</TEX> vs. aging time data providing the fitting parameters; maximum enthalpy recovery (<TEX>${\Delta}H_{\infty}$</TEX>), relaxation time (<TEX>${\tau}$</TEX>) and non-exponentiality parameter (<TEX>${\beta}$</TEX>).

Influence of molecular weight on enthalpy relaxation and fragility of amorphous carbohydrates

► The glass transition temperature increased with increasing molecular weight. ► Mean enthalpy relaxation time increased with increasing molecular weight. ► The KWW equation was able to describe enthalpy relaxation behavior of selected carbohydrates. ► Fragility analysis indicated maltose and maltotriose as strong systems. Enthalpy relaxation and fragility of selected carbohydrates were correlated with their molecular weight. Anhydrous glucose and its oligomers (i.e. maltose and maltotriose) were selected to represent amorphous carbohydrates with increasing molecular weight. The enthalpy relaxation behavior of glucose, maltose and maltotriose was determined at 5 °C below their respective glass transition temperatures using differential scanning calorimetry (DSC). The non-exponential behavior of enthalpy relaxation was fitted with the Kohlrausch–Williams–Watts (KWW) equation. The mean relaxation time constants ( τ ) for glucose, maltose and maltotriose at ( T g − 5) were 16.9, 38.4 and 128.6 h, respectively. The fragility indices ( m ) of glucose, maltose and maltotriose, determined using the DSC glass transition width approach, were 105, 88.1 and 97.6, respectively. The glass transition temperature and mean enthalpy relaxation time increased with increasing molecular weight for the selected carbohydrates studied herein. The greater glass transition temperature and enthalpy relaxation time of maltotriose are attributed to the decreased specific volume, segmental mobility and increased entanglements resulting from its higher molecular weight. Maltotriose may be preferred as an encapsulant or food ingredient to reduce structural relaxation in food formulations during storage.

Physicochemical characterization of nicergoline and cabergoline in its amorphous state

Formulation of poorly water-soluble crystalline drugs into their more soluble amorphous form is a common approach for improving their bioavailability. In this study, the amorphous forms of nicergoline (NIC) and cabergoline (CAB) were obtained by different methods (melting and precipitation under solvent evaporation). The physicochemical characteristics of the samples were determined by HPLC, differential scanning calorimetry (DSC), thermogravimetry, and X-ray powder diffractometry. The physical stability of the amorphous forms was investigated by DSC by considering how the onset temperature and the enthalpy content at the glass transition vary with aging time and temperature. Using the Kohlrausch–Williams–Watts equation on the data obtained from the experiments, the “mean molecular relaxation time constant” (τ) was estimated. This parameter was used to understand the stability of NIC and CAB in their glassy state at different temperatures, and results showed that their stability is adequate to enable the formulation of these drugs into solid dosage forms.

Structural Relaxation of Salmon Gelatin Films in the Glassy State

The unique property of gelatin to form networks and induce plasticity and elasticity is considered beneficial in the preparation of biopolymer-based packaging materials. However, its use in food products has been limited by some religious groups (Gudmundsson 2002). Gelatins from marine sources have emerged as an alternative, although they are different from mammalian collagen in terms of their biochemical constituents and therefore in their functional properties. It has been shown that cold-water fish collagen can have a lower content of amino acids (~16–18 %) (Gilsenan and Ross-Murphy 2000). Joly-Duhamel et al. (2002) established a positive correlation of the concentration of amino acids, proline (Pro) and hydroxyproline (Hyp), with the melting temperature of native collagen (helix to coil) and gelatin molecular weight with renaturation temperature (coil to helix), suggesting an important effect of biochemical composition on the structure stability of the gel network. An aspect that has not been explored in detail for marine gelatin is the structural stability of these systems at temperatures below their glass transition temperature (T g ). Early studies in glassy carbohydrates by Noel et al. (1999) described the ageing kinetics of maltose in the glassy state in terms of an overshoot in heat capacity on consecutive heating runs using a differential scanning calorimeter (DSC). Badii et al. (2005) evaluated the kinetics of enthalpic relaxation of bovine gelatin state as a function of the difference between ageing temperature and T g . In their later work, the same authors quantified the enthalpic relaxation of the same model system by DSC, correlating enthalpic values with an increase in the elastic modulus (E) obtained by mechanical spectroscopy. Work by Lourdin et al. (2002) described the mechanical relaxation of amorphous potato starch in the glassy state, obtaining characteristic relaxation parameters by the application of the Kohlrausch–Williams–Watts (KWW) model (Eq. 1). Anderssen et al. (2004) discussed the KWW equation in terms of a spectrum of relaxation times describing the ageing of a polymer. The KWW is an equation that can quantitatively describe the kinetics of the relaxation process toward an absolute relaxed state (Anderssen et al. 2004): $$ \phi (t)= \exp \left[-{\left(\frac{t}{\tau_0}\right)}^{\beta}\right] $$ where φ is the relaxation function, t is time, β (0 < β ≤ 1) is the width of the relaxation time distribution spectrum, and τ0 is the characteristic relaxation time, being dependent on temperature and material structure.

Relationship between enthalpy relaxation and water sorption of ball-milled potato starch

This study reports on the enthalpy relaxation and water sorption behaviors of ball-milled potato starch. Ball milling converts the semi-crystalline state of starch to an amorphous state, and a prolonged procedure promotes enthalpy relaxation. It has been reported that prolonged treatment leads to a decrease in starch water sorption. In the present study, ball milling of potato starch was carried out for up to 90h. The relaxed enthalpies and water sorption isotherms were measured by differential scanning calorimetry and equilibrium sorption of water vapor. Enthalpy was found to increase and water sorption to decrease with milling time. The time-dependant increase in enthalpy was found to follow the Kohlrausch–Williams–Watts (KWW) equation. The sorption isotherms were analyzed with a dual-mode sorption model and the concentration, CH′, of Langmuir type sorption sites was found to decrease with time. This decrease was also found to follow the KWW equation. Moreover, a linear relationship was found between the decrease in CH′ and the increase in enthalpy.