Enthalpy Relaxation Experiments Research Articles

Analysis of TNM model calculation for enthalpy relaxation based on the fictive temperature model and the configurational entropy model

Enthalpy relaxation experiments were conducted for polystyrene samples at different annealing temperatures below glass transition temperature (Tg) using a differential scanning calorimeter. The framework of Tool-Narayanaswamy-Moynihan approach was applied to reproduce experimental traces with two models of the structural relaxation times; those are the generalized Arrhenius type characterized by fictive temperature (Tf model) and the configurational entropic type (Sc model). The calculation data of the heat capacity (cp) obtained from the two models were analysed on the basis of the parameter – geometry relationship, in which three factors were given to the geometry of the Tg shoulder and overshoot appeared in cp curve. It was found that both the horizontal shift and the broadening of Tg shoulder occur interdependently in the cp curve calculation of Sc model, while they are almost independent in the calculation of Tf model. In addition, the analysis revealed the process of producing cp overshoot in Tg shoulder, which is expected to be instructive in the optimized cp calculation.

Physicochemical properties and storage stability of lutein microcapsules prepared with maltodextrins and sucrose by spray drying.

The purpose of this study was to determine the physicochemical properties of lutein microcapsules. Nine types of lutein microcapsules were prepared in order to determine their encapsulation efficiency and yield. Results show that lutein microcapsules with maltodextrin M040 and sucrose at the weight ratio of 3:1 (designated as M040:1) had the highest encapsulation efficiency (90.1%) among the lutein microcapsules, as well as a higher encapsulation yield (90.4%). The onset glass transition temperatures (Tgi ) and the surface dents of the lutein microcapsules decreased as the dextrose equivalent value of maltodextrin and the weight ratio of sucrose increased. Enthalpy relaxation experiments were conducted for the lutein microcapsules M040:1 at (Tgi - 5) , (Tgi - 10), and (Tgi - 15) °C, and the obtained data were fitted to the Kohlrausch-Williams-Watts model. Results show that the mean relaxation time (τ) (316 h) of M040:1 lutein microcapsules aged at (Tgi - 15) °C was greater than the τ (161 h) at (Tgi - 10) °C and τ (60.5 h) at (Tgi - 5) °C. Effects of temperature and oxygen transmission rates for package film on the storage stability of M040:1 lutein microcapsules were also investigated. Findings show that rates of lutein degradation and color change increased by an order of magnitude as storage temperature (4 to 97 °C) and oxygen transmission rate of the package film (0.018 to 62.8 cc/m(2) day) increased. These results suggest that lutein is highly unstable and susceptible to thermal and oxidative degradations. However, microencapsulation with appropriate wall materials of higher relaxation time and high oxygen barrier packaging can increase the storage life.

Improving the mechanical properties of Zr-based bulk metallic glass by controlling the activation energy for β-relaxation through plastic deformation

The mechanism of plastic deformation in bulk metallic glasses (BMGs) is widely believed to be based on a shear transformation zone (STZ). This model assumes that a shear-induced atomic rearrangement occurs at local clusters that are a few to hundreds of atoms in size. It was recently postulated that the potential energy barrier for STZ activation, WSTZ, calculated using the cooperative shear model, is equivalent to the activation energy for β-relaxation, Eβ. This result suggested that the fundamental process for STZ activation is the mechanically activated β-relaxation. Since the Eβ value and the glass transition temperature Tg of BMGs have a linear relation, that is, because Eβ ≈ 26RTg, the composition of the BMG determines the ease with which the STZ can be activated. Enthalpy relaxation experiments revealed that the BMG Zr50Cu40Al10 when deformed by high-pressure torsion (HPT) has a lower Eβ of 101 kJ/mol. The HPT-processed samples accordingly exhibited tensile plastic elongation (0.34%) and marked decreases in their yield strength (330 MPa). These results suggest that mechanically induced structural defects (i.e., the free volume and the anti-free volume) effectively act to reduce WSTZ and increase the number of STZs activated during tensile testing to accommodate the plastic strain without requiring a change in the composition of the BMG. Thus, this study shows quantitatively that mechanically induced structural defects can overcome the compositional limitations of Eβ (or WSTZ) and result in improvements in the mechanical properties of the BMG.

Enthalpy relaxation near the glass transition for comb-like polymer: Power law relaxation revealed by DSC experiment

A series of enthalpy relaxation experiments at different ageing temperatures was conducted on a sample of poly(cyanobiphenyl hexylacrylate) with variation in the molecular weight using a DSC technique. The value of the relaxation function (ϕ) was obtained as a function of the ageing time (tA) from the experimental results using the excess enthalpy in the limit of infinity of tA and that of the given tA. The double logarithmic plot of −lnϕ and tA was constructed to determine the functional form of the relaxation function. Two possible forms are found, the stretched exponential and the power law forms, which suggests that the functional form varies continuously between these two according to the ageing experiment. The activation energy spectrum was derived for the two functional forms, which show the distribution of the activation energy of the molecular process controlling the decrease in enthalpy. It was revealed that, for the spectrum based on the power law relaxation, the overwhelming fraction of the relaxation processes is at the lower energy side and the population of the process decreases rapidly toward the higher energy side.

Aging of amorphous raspberry powder: Enthalpy relaxation and fragility

Enthalpy relaxation experiments were conducted in freeze-dried raspberry powder at 5, 10 and 15 °C below its onset glass transition temperature ( T gi ) using differential scanning calorimetry (DSC). The statistical differences in T gi for the raspberry powders aged at ( T gi − 5), ( T gi − 10), and ( T gi − 15) from 6 to 96 h were not significant ( p > 0.05). The non-exponential behavior of enthalpy relaxation in raspberry powder was fitted with the Kohlrausch–Williams–Watts (KWW) model. The mean relaxation time constant ( τ) (1017.4 h) for raspberry powder aged at the temperature ( T gi − 15) was greater than the τ (147.1 h) at ( T gi − 5). The KWW model parameter β values for freeze-dried raspberry powders were greater than the β values of pure food constituents. The activation energy for enthalpy relaxation in the glassy state was determined as 145.4 kJ/mol by approximating with the Arrhenius equation. The dependence of mean relaxation time on temperature followed an Arrhenius behavior indicating raspberry powder is a strong system. Several approaches were used to classify raspberry powder into strong/fragile system. There is a difference among fragility parameters of raspberry powders determined using selected methods.

Study of the kinetics of free volume in Zr 45.0Cu 39.3Al 7.0Ag 8.7 bulk metallic glasses during isothermal relaxation by enthalpy relaxation experiments

Enthalpy relaxation experiments were conducted to study the kinetics of free volume in Zr 45.0Cu 39.3Al 7.0Ag 8.7 bulk metallic glasses (BMGs) during isothermal relaxation using differential scanning calorimetry (DSC) at the temperature within the range from 648 to 684 K. Stretched exponential relaxation functions and the Šesták–Berggren SB ( m, n) model were employed to analyze the kinetics of free volume. It is found that the relaxation time decreases from 2643.5 to 242.8 s while the Kohlrausch exponents increase from 0.717 to 0.892 in the investigated temperature range. The activation energy fluctuates slightly in the course of the relaxation process and its mean value is determined to be 239.7 kJ/mol. By fitting the first derivative of the conversion degree as a function of annealing time using the Šesták–Berggren SB ( m, n) model, it is found that the values of m at all annealing temperatures are very small and can be approximated as zero. The values of the pre-exponential factors Z and the kinetic parameter n are found to be slightly varying with the annealing temperature, indicating the complexity of the kinetics of the isothermal relaxation. Finally, an approximate rate equation describing the kinetics of free volume during isothermal relaxation is proposed.

Quantification of the free volume in Zr 45.0Cu 39.3Al 7.0Ag 8.7 bulk metallic glasses subjected to plastic deformation by calorimetric and dilatometric measurements

Zr 45.0Cu 39.3Al 7.0Ag 8.7 bulk metallic glasses (BMGs) were prepared using suction casting technique. Plastic deformations were carried out by cold rolling and high-pressure torsion (HPT). The absolute contents of free volume in the as-cast, preheated and deformed samples were determined by differential scanning calorimetry (DSC) and dilatometry using the free volume model (FVM). The parameters required in the FVM are experimentally determined to be b = 0.107, β = 642.1 kJ/mol, D * = 10.3 and T 0 = 496.9 K, respectively. The equilibrium free volume determined by these parameters is in good agreement with that calculated from previous enthalpy relaxation experiments, showing the reliability of the values of the parameters. It is found that the content of free volume in the as-cast sample is 0.533% with respect to the atomic volume of the BMG. The free volume in the HPT deformed sample is determined to be 0.672%, which is the largest among all the samples. The excess free volume introduced by cold rolling is found to increase with the deformation strain and show weak strain rate dependent behavior. Finally, attempts are made to simulate the experimental DSC curve using a bimolecular kinetics in the flow defect model. However, the result shows that the kinetics of free volume may be more complicated than as described as a bimolecular process.

The amount of immobilized polymer in PMMA SiO 2 nanocomposites determined from calorimetric data

For semicrystalline polymers there is an ongoing debate at what temperature the immobilized or rigid amorphous fraction (RAF) devitrifies (relaxes). The question if the polymer crystals are melting first and simultaneously the RAF devitrifies or the RAF devitrifies first and later on the crystals melt cannot be answered easily on the example of semicrystalline polymers. This is because the crystals, which are the reason for the immobilization of the polymer, often disappear (melt) in the same temperature range as the RAF. For polymer nanocomposites the situation is simpler. Silica nanoparticles do not melt or undergo other phase transitions altering the polymer–nanoparticle interaction in the temperature range where the polymer is thermally stable (does not degrade). The existence of an immobilized fraction in PMMA SiO 2 nanocomposites was shown on the basis of heat capacity measurements at the glass transition of the polymer. The results were verified by enthalpy relaxation experiments below the glass transition. The immobilized layer is about 2 nm thick at low filler content if agglomeration is not dominant. The thickness of the layer is similar to that found in semicrystalline polymers and independent from the shape of the nanoparticles. Nanocomposites therefore offer a unique opportunity to study the devitrification of the immobilized fraction (RAF) without interference of melting of crystals as in semicrystalline polymers. It was found that the interaction between the SiO 2 nanoparticles and the PMMA is so strong that no devitrification occurs before degradation of the polymer. No gradual increase of heat capacity or a broadening of the glass transition was found. The cooperatively rearranging regions (CRR) are either immobilized or mobile. No intermediate states are found. The results obtained for the polymer nanocomposites support the view that the reason for the restricted mobility must disappear before the RAF can devitrify. For semicrystalline polymers this means that rigid crystals must melt before the RAF can relax.

Thermodynamic properties of Pd-based glass-forming alloys

Undercooled liquids of the easy glass-forming alloys Pd–Ni–P and Pd–Cu–Ni–P (Pd40Ni40P20, Pd40Ni10Cu30P20, Pd43Ni10Cu27P20) have an extra-ordinary stability against crystallization allowing for direct calorimetric measurements of this metastable state. The liquid alloys can be undercooled consistently into the glassy state at moderate cooling rates of about 0.2 K/s and heat capacity measurements have been performed covering the undercooling regime from the melting temperature to the glass transition temperature. The thermodynamic functions of the alloys in dependence on temperature were evaluated. The isentropic temperature, TK, often interpreted as the low temperature limit of the liquid state, was determined from the excess entropy. Enthalpy relaxation experiments show that the addition of Cu leads to an increase in the fragility of the Pd-based alloys.

Solid-state characteristics of amorphous sodium indomethacin relative to its free acid.

Having previously studied the amorphous properties of indomethacin (IN) as a model compound for drugs rendered amorphous during processing, we report on the formation and characterization of its sodium salt in the amorphous state and a comparison between the two systems. Sodium indomethacin (SI) was subjected to lyophilization from aqueous solution, rapid precipitation from methanol solution, and dehydration followed by grinding to produce, in each case, a completely amorphous form. The amorphous form of SI was analyzed using DSC, XRD, thermomicroscopy and FTIR. The method of scanning rate dependence of the glass transition temperature, Tg, was used to estimate the fragility of the SI system. Enthalpy relaxation experiments were carried out to probe the molecular mobility of the SI system below Tg. The amorphous form of SI formed by different methods had a Tg equal to 121 degrees C at a scanning rate of 20 degrees C/min. This compares with a Tg for indomethacin of 45 degrees C. Estimation of fragility by the scanning rate dependence of Tg indicates no significant differences in fragility between ionized and unionized forms. Enthalpy relaxation measurements reveal very similar relaxation patterns between the two systems at the same degree of supercooling relative to their respective Tg values. The amorphous form of SI made by various methods has a Tg that is about 75 degrees C greater than that of IN, most likely because of the greater density and hence lower free volume of SI. Yet, the change of molecular mobility as a function of temperature relative to Tg is not very different between the ionized and unionized systems.

Physical aging studies of amorphous linear polyesters. Part II. Dependence of structural relaxation parameters on the chemical structure

The enthalpy relaxation of a series of linear amorphous polyesters (poly(propylene isophthalate) (PPIP), poly(propylene terephthalate) (PPTP), poly(ethylene terephthalate) (PETP), and poly(dipropylene terephthalate) (PDPT)) has been investigated by differential scanning calorimetry (DSC). These polyesters have been annealed at equal undercooling below their respective glass transition temperatures, Tg, (Tg − 27°C, Tg − 15°C, and Tg − 9°C) for periods of time from 15 min to 480 h. The key parameters of structural relaxation, namely the apparent activation energy (Δh*), the nonlinearity parameter (x) and the nonexponentiality parameter (β), have been determined for each polyester and related to an effective relaxation rate (1/τeff) and to the chemical structure. We observe that the variation of the structural relaxation parameters shows a trend that is common to other polymeric systems, whereby an increase of x and β corresponds a decrease in Δh*. The comparison of these parameters in PETP and in PPTP gives information about the effect of the introduction of a methyl group pendant from the main chain; the x parameter increases (i.e., a reduced contribution of the structure to the relaxation times), β increases (i.e., a narrow distribution of relaxation times), and Δh* decreases. Additionally, enthalpy relaxation experiments show that a decrease of Δh* correlates with an increase of 1/τeff, when they are measured at a fixed value of the excess enthalpy, δH. The introduction of an isopropyl ether group in PDPT with respect to PPTP decreases both x and β, but increases Δh*, which the rate of relaxation decreases. The ring substitution in PPTP and PPIP originates less significant changes in the structural parameters. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 113–126, 1998

Thermodynamic strength of the glassy state and the maximum enthalpy stored in the propylene glycol-D 2O system

The glassy state of several concentrations of propylene glycol in D 2O is presently characterized by enthalpy relaxation experiments. The existence of a lowest glass transition temperature T s has defined an utmost excess enthalpy that can be stored by the glass during cooling. Similar to the thermal behavior of the shear viscosity for liquids, these T s values are maximum for the binary system with compositions in the range 78–82% ( w/ w) propylene glycol in D 2O, suggesting that these concentrations correspond to the strongest glasses, and provide a higher thermodynamic strength for these glasses. These glasses correspond also to the maximum excess enthalpy that can be stored by the glassy state during cooling. These concentrations present, however, an apparent minimum threshold stress to induce fracture nucleation in the glasses with the definition of a maximum mechanical fragility. The present results underline a problem in the definition of the thermodynamic and mechanical strength of the glassy state as an extension of the fragility definition for liquids.

Enthalpy Relaxation in Poly(propylene oxide)/Poly(ethylene oxide) Blends

Phase behavior in poly(propylene oxide)/poly(ethylene oxide) blends was studied by glass transition observations in conjunction with enthalpy relaxation technique. The results points out that the blend behaves as an inmiscible, phase separated system, nevertheless the displacements of the glass transition temperatures together with the results obtained from enthalpy relaxation experiments show that a polymer–polymer interaction is present.

A comparison between the morphology of semicrystalline polymer blends of poly(ε-caprolactone)/poly(vinyl methyl ether) and poly(ε-caprolactone)/(styrene-acrylonitrile)

The morphology of polymer blends of poly(ε-caprolactone) (PCL) and poly(vinyl methyl ether) (PVME) is compared with that of PCL and a random copolymer of styrene and acrylonitrile (SAN). The main objective is to determine the influence of the glass transition temperature of the amorphous component ( T g,a) on the morphology of the semicrystalline polymer blends. These blends represent the two extreme cases corresponding to T c < T g,a, where T c is the crystallization temperature. The morphology of these blends, with PVME and SAN representing the amorphous components, have been studied by small angle X-ray scattering. For both blends the long period increases with the addition of amorphous polymer, which is a strong indication for an interlamellar morphology. D.s.c. experiments, including enthalpy relaxation, are used to investigate the crystallinity and the interphases. The overall amount of crystallinity in both blends decreases with increasing content of amorphous polymer. However, the fraction of PCL that crystallizes decreases in PCL/SAN and increases slightly in PCL/PVME. Apparently, the addition of the low T g,a PVME improves the crystallization of PCL in accordance with a simple Gamblers Ruin Model type argument. The high T g,a of SAN means this does not occur in PCL/SAN blends. Conventional d.s.c. experiments show an interphase of pure amorphous PCL in PCL/SAN blends and enthalpy relaxation experiments demonstrate its presence in PCL/PVME blends as well.

Influence of annealing and casting solvent on the morphology of poly(ethylene oxide)-b-polystyrene-b-poly(ethylene oxide) triblock copolymer: compatibility effects

The influence of annealing on the morphology of solvent-cast films of poly(ethylene oxide)-b-polystyrene-b-poly(ethylene oxide) (PEO-b-PS-b-PEO) triblock copolymer was studied. The annealing temperature was chosen between the melting temperature of PEO and the glass transition temperature of PS. If the casting solvent is selective for PEO, microphase separation occurs and the crystallinity of the PEO is not affected by annealing. On the other hand, if the casting solvent is a good solvent for both blocks, a dramatic decrease in crystallinity of PEO is observed. This phenomenon is due to compatibility effects. The T g region of the PS-rich phase is shifted towards lower values. This behaviour was elucidated using differential scanning calorimetry combined with enthalpy relaxation experiments.