Heat Capacity Step Research Articles

Glass transition under confinement-what can be learned from calorimetry

Calorimetry is an effective analytical tool to characterize the glass transition and phase transitions under confinement. Calorimetry offers a broad dynamic range regarding heating and cooling rates, including isothermal and temperature modulated operation. Today 12 orders of magnitude in scanning rate can be covered by combining different types of calorimeters. The broad dynamic range, comparable to dielectric spectroscopy, is especially of interest for the study of kinetically controlled processes like crystallization or glass transition. Accuracy of calorimetric measurements is not very high. Commonly it does not reach 0.1% and often accuracy is only a few percent. Nevertheless, calorimetry can reach high sensitivity and reproducibility. Both are of particular interest for the study of confined systems. Low addenda heat capacity chip calorimeters are capable to measure the step in heat capacity at the glass transition in nanometer thin films. The good reproducibility is used for the study of glass forming materials confined by nanometer sized structures, like porous glasses, semicrystalline structures, nanocomposites, phase separated block copolymers, etc. Calorimetry allows also for the frequency dependent measurement of complex heat capacity in a frequency range covering several orders of magnitude. Here I exclusively consider calorimetry and its application to glass transition in confined materials. In most cases calorimetry reveals only a weak dependence of the glass transition temperature on confinement as long as the confining dimensions are above 10 nm. Why these findings contradict many other studies applying other techniques to similar systems is still an unsolved problem of glass transition in confinement.

Reverse calorimetry of a supercooled liquid: Propylene carbonate

Using propylene carbonate as an example for a glass-forming liquid with generic behaviour, a technique based on dielectric relaxation experiments at high electric fields is reviewed and explained in unprecedented detail. Analogous to microwave heating, the sample absorbs energy from the field, and the resulting configurational changes are measured and linked to the configurational modes of the heat capacity. Evidence is provided for the heterogeneous nature of the slow degrees of freedom that are responsible for the heat capacity step near T g. Moreover, the thermal and dielectric relaxation times are not only subject to the same overall dispersion, but are locally correlated and the dielectric and thermal time constants are identical within a 15% margin. Only for the fastest few percent of the thermal relaxation times can deviations from these correlations be found.

Influence of Crystal Polymorphism on the Three-Phase Structure and on the Thermal Properties of Isotactic Poly(1-butene)

The influence of crystal polymorphism on the three-phase structure of isotactic poly(1-butene) (PB-1) is discussed. Crystallization of PB-1 from the melt yields the tetragonal phase, known as form II. Upon storage, it spontaneously transforms to the trigonal form I. The chain motion within the crystalline parts varies strongly with the crystal structure and affects the coupled amorphous parts. The form II−form I solid−solid transformation is accompanied by a change in the thermal properties that involves all parts of the three-phase structure. The increased density and thermal stability of the crystals cause a higher rigidity of the coupled amorphous phases. In form I PB-1, the mobile amorphous phase (MAF) has a reduced heat capacity step at the glass-transition temperature that occurs at a slightly broadened temperature. The RAF is coupled more strongly to the rigid form I crystals and relaxes at higher temperatures compared with the polymer containing modification II crystals, which are conformationally disordered. Both polymorphs display only little reversibility of the melting process. It is almost negligible in form I PB-1 and more conspicuous in the form II crystals. The different behavior arises from the varied recrystallization kinetics, which is limited in extent for the trigonal polymorph.

Calorimetric Glass Transition of Poly(2,6-dimethyl-1,5-phenylene oxide) Thin Films

The glass transition of poly(2,6-dimethyl-1,5-phenylene oxide) (PPO) films with thickness ranging from about 6 nm (approximately half of radius of gyration, Rg) to 330 nm (∼29 Rg) was studied by the recently developed differential alternating current chip calorimeter with sensitivity on the order of tenths of a pJ K−1. No thickness dependence of the glass temperature Tg was found for this polymer. Tgs of all the films measured in the available frequency range (∼0.5 to ∼1000 Hz) can be fit by a single Vogel−Fulcher−Tammann function in the activation plot within an uncertainty of ±3 K, thus showing no deviation from the common VFT behavior even for the thinnest film. There is also no detectable change in the shape or width of the step in heat capacity at Tg. Finally, we found that calorimetric relaxation strength at the glass transition was proportional to the thickness of the film within an uncertainty of about 25%. Consequently, we estimate the thickness of the layer deviated from the bulky behavior to be...

Measuring the Configurational Heat Capacity of Liquids

A high electric field impedance experiment on supercooled molecular liquids is employed to transfer energy to the slow modes by absorption from the field and detect the increase of their "configurational temperature", T(cfg), via the change of the relaxation times. This allows us to determine the configurational heat capacity, which accounts for most of the excess heat capacity for stronger liquids, but for only half of the heat capacity step in the case of more fragile systems. It is also observed that T(cfg) gradually approaches the phonon temperature on the structural relaxation time scale.

Differential AC‐chip calorimeter for glass transition measurements in ultrathin films

AbstractA differential AC‐chip calorimeter capable of measuring the step in heat capacity at the glass transition in nanometer‐thin films is described. Because of the differential setup, pJ/K sensitivity is achieved. Heat capacity can be measured for sample masses below 1 ng in broad temperature range as needed for the study of the glass transition in nanometer‐thin polymeric films. Relative accuracy is sufficient to investigate the changes in heat capacity as the step at the glass transition of polystyrene. The step is about 25% of the total heat capacity of polystyrene. The calorimeter allows for the frequency dependent measurement of complex heat capacity in the frequency range from 1 Hz to 1 kHz. The glass transition in thin polystyrene films (50–4 nm) was determined at well‐defined experimental time scales. No thickness dependency of the glass transition temperature was observed within the error limits (±3 K)—neither at constant frequency (40 Hz) nor for the trace in the activation diagram (1 Hz–1 kHz). © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2996–3005, 2006

Fragility and thermodynamics in nonpolymeric glass-forming liquids

For nonpolymeric supercooled liquids, the empirical correlation m = 56Tg DeltaCp(Tg)/DeltaHm provides a reliable means of correlating dynamic and thermodynamic variables. The dynamics are characterized by the fragility or steepness index m and the glass transition temperature Tg, while thermodynamics enter in terms of the heat capacity step DeltaCp at Tg and the melting enthalpy DeltaHm. The combination of the above correlation with the 23 rule for the Tg/Tm ratio yields an expression, m = 40DeltaCp(Tg)/DeltaSm, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via DeltaCp(Tg)/DeltaSm also reveals that the slopes in Kauzmann's original DeltaS(T)/DeltaSm versus T/Tm plot reflect the fragility concept [Chem. Rev. 43, 219 (1948)], so long as Tm/Tg = 1.5. For the many liquids whose excess heat capacity is a hyperbolic function of temperature, we deduce that the fragility cannot exceed m = 170, unless the Tg/Tm = 2/3 rule breaks down.

γ‐Radiation‐induced graft copolymerization of acrylic acid onto poly(ethylene terephthalate) films: A study by thermal analysis

AbstractThe grafting of acrylic acid onto poly(ethylene terephthalate) films with γ radiation was carried out. The effects of different parameters, such as the monomer concentration, inhibitor concentration, and irradiation dose, on the grafting yield were investigated. The grafting yield depended on these parameters, and its maximum value was obtained at a 1.5% inhibitor concentration and a 40% monomer concentration. The obtained grafting films were characterized with water swelling measurements, differential scanning calorimetry, and thermogravimetric analysis. The results of differential scanning calorimetry showed decreases in the heat capacity step and the glass‐transition temperature with increasing grafting yield. The ability of poly(ethylene terephthalate) to crystallize and the size of the crystalline domains were affected by the grafting. The grafted poly(ethylene terephthalate) that was obtained was tested as an ion exchanger for copper, nickel, cobalt, and lead. The capacity of the grafted films for ion recovery was dependent on the grafting yield. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 198–203, 2006

Heat Capacity and Glass Transition of Crystalline Pentachloronitrobenzene

Abstract The heat capacity of crystalline pentachloronitrobenzene was measured by adiabatic calorimetry between 6 and 303 K. A large step in heat capacity was detected around 185 K; this is attributed to a glass transition corresponding to freezing of structural disorder. The observed glass transition temperature was similar to that estimated from the temperature dependence of the dielectric relaxation due to molecular reorientation around the “sixfold axis” of the benzene core.

Ac Calorimetry and EPR Study on Metal–Insulator Transition and Glass Transition in an Organic Conductor with Double-Column Structure, (DIMET)2BF4*

Successive metal–insulator transitions in (DIMET) 2 BF 4 were studied by chopped-light ac calorimetry and electron paramagnetic resonance (EPR) measurement. An anomaly due to the metal–insulator transitions has been clearly detected in ac calorimetry between 20 and 35 K. In contrast to other double-column salts (DMET) 2 BF 4 and (DMET) 2 ClO 4 , successive metal–insulator transitions detected in transport properties are shown to be thermodynamic phase transitions. The EPR detected an anomaly only for the lowest transition around 12 K. The properties of the metal–insulator transitions are compared among the DIMET and DMET salts having the double-column structure. A frequency-dependent step in heat capacity was detected around 110 K. The step-like anomaly is attributed to a glass transition due to freezing of the intramolecular motion of the ethylene group in the ET moiety within a DIMET molecule.

State diagrams and sorption isotherms of bacterial suspensions and fermented medium

Physical properties of lactic acid bacteria suspensions were determined by means of state diagrams and sorption isotherms. Differential scanning calorimetry (DSC) was used to establish the thermal transitions of concentrated “fresh” (before freeze-drying) and freeze-dried bacterial suspension equilibrated at different relative humidities. The bacterial cells and the re-suspending medium (fermented culture medium) were studied separately in order to determine each individual effect. No glass transition ( T g) was detected in thermal profiles of washed bacterial cells. Correspondingly, T g curves were similar for fermented medium and bacterial suspension. Simple glass transitions (one heat capacity step) were observed at T g in the case of low moisture samples. For samples containing more than 60.7% water, two steps remained in the glass transition region ( T g1′ and T g2′), even after annealing treatments. Water plasticising effect was well predicted by Gordon–Taylor equation. The invariant point ( C g′, T g′), characteristic of maximally freeze-concentrated samples, was estimated from the intersection of the T g curve and the melting curve T m. A linear relationship was proposed to rapidly predict the T g′ region of complex aqueous solutions, from T g′ values of single solute aqueous solutions. Water sorption properties of fermented medium and bacterial suspension were determined at 25°C and described by the Guggenheim–Anderson–de Boer equation.

The measurement of the glass transition temperature of sucrose and maltose solutions with added NaCl

The effect of added NaCl on the glass transition temperatures of 200 and 300 g kg−1 sucrose and maltose solutions was determined using DSC and capacitance measurements. Negative shifts of around 4 °C were seen upon the addition of 0.1 mol kg−1 NaCl, consistent with the freezing point depression expected for the maximally freeze-concentrated solutions. Changes in the capacitance were seen which matched both the onset of the devitrification event and the main heat capacity step seen in DSC scans. © 2000 Society of Chemical Industry

Thermal Characterization of Polymethyl(α-n-Pentyl)Acrylate

This work presents new results concerning characterization of polymethyl(α-n-pentyl)acrylate polymer by means of thermal analysis. In differential scanning calorimetry investigations, the measured values of Tg, Tf and ΔCp, i.e. the glass transition temperature, the fictive temperature and the heat capacity step at Tg, show that the polymer can be considered as fragile. Thermogravimetric analysis revealed two mass losses, the first, at low temperature, being associated with the evaporation of water molecules, and the second, at high temperature, corresponding degradation of the polymer. This degradation is a two-step phenomenon. Finally, study of the β and the α transitions by elementary and complex TSDC led to the following values: Tβ=−40°C, Tα=36°C, Tc=47°C, τc=2.5 s and ΔH=85 to 165 kJ mol−1.

Calorimetric evaluation of the glass transition in hydrated, linear and branched polyanhydroglucose compounds

By comparing glass transition temperatures, T g, determined by differential scanning calorimetry (midpoint of heat capacity step at 3 °C.mn −1) on powders of varying water contents for different polysaccharides, the influence of molecular weight, degree of branching and (1–4) vs (1–6) glycosidic linkage ratio upon the depression of T g is illustrated, thus extending results of former studies. Due to both of the doubts concerning the heat capacity change of water at its glass transition, when dispersed in such media, and limitations of second-order entropy-based derivations, the effect of water plasticization is described by the Couchman's correlation in its degenerated form, which is similar to the Gordon-Taylor formulation. Strong enthalpy relaxation effects are observed following aging treatments at temperatures below, and even far below T g. This makes it necessary to erase the history of moisture-conditioned samples and, thus, only the second DSC scan results are presented. As expected, linear chains appear to favor chain-chain interactions and induce partial crystallinity; branched molecules display lower T g values, due to chain end effects, as well as flexibility of branching points. The three dihedrals present in α(1–6) linkages seem to depress T g in a similar fashion to internal plasticization. The case of a linear α(1–4) amylose chain bearing (1–6) grafted fructoses is examined as a first step towards tailored structures, designed to optimize mechanical properties and internal plasticization (as for chemically modified polysaccharides) and inhibit recrystallization. The extension to ciliated structures (sparse brushes) is proposed as a target for biosynthesis optimization.

Linearity of heat capacity step near the onset of α glass transition in poly(n‐alkylmethacrylate)s

AbstractDSC measurements around the glass transition in the homologous series of seven poly(n‐alkylmethacrylate)s (alkyl=methyl, ethyl, propyl, butyl, pentyl, hexyl, octyl) are presented. The step height Δcp decreases linearly with the number of n‐alkyl C‐atoms in the side chain. The usual glass step in the DSC curves, e. g. for poly(methylmethacrylate), degenerates to a bend near poly(n‐octylmethacrylate). This finding is discussed as a result of a linear relation between the caloric relaxation strength Δcp and the temperature difference from the α onset Tonset in the splitting region of poly(n‐alkylmethacrylate)s, with Δcp → 0 for T → Tonset. The number of monomeric units per cooperatively rearranging region at Tg decreases from PMMA (Nα∼20) to PnOMA (Nα<5). This demonstrates that the cooperativity at the α onset in poly(n‐alkylmethacrylate)s is very small, as expected from a fluctuation approach to the glass transition.

Heat capacities of TiO 2-bearing silicate liquids: Evidence for anomalous changes in configurational entropy with temperature

The heat capacities of several TiO 2-bearing silicate glasses and liquids containing Cs 2O, Rb 2O, Na 2O, K 2O, CaO, MgO, or BaO have been measured to 1100 K using a differential scanning calorimeter and to 1800 K using a Setaram HT-1500 calorimeter in step-scanning mode. The results for liquids of M 2O-TiO 2-2SiO 2 composition ( M — Na, K, Cs) are compared to those for liquids of M 2O-3SiO 2 composition. The presence of TiO 2 has a profound influence on the heat capacity of simple three-component silicate liquids over the temperature range 900–1300 K. Specifically, replacement of Si 4+ by Ti 4+ leads to doubling of the magnitude of the jump in C p at the glass transion ( T g); this is followed by a progressive decrease in liquid C p for over 400 K, until C p eventually becomes constant and similar to that in Ti-free systems. The large heat capacity step at T g in the TiO 2-bearing melts suggests significant configurational rearrangements in the liquid that are not available to TiO 2-free silicates. In addition, these “extra” configurational changes apparently saturate as temperature increases, implying the completion of whatever process is responsible for them, or the attainment of a random distribution of structural states. Above 1400 K, however, where the heat capacities of TiO 2-bearing and TiO 2-free alkali silicate liquids are similar, their configurational entropies differ by ~3.5 J/g.f.w.-K. The larger configurational entropy of the TiO 2-bearing alkali silicate liquids relative to the TiO 2-free liquids is energetically equivalent to raising the liquid temperature by more than 300 degrees. This result clearly demonstrates the energetic magnitude of the configurational changes apparent in the supercooled liquid region and their impact on the thermodynamic properties of the stable liquid. Consideration of both density measurements on liquids and spectroscopic data on quenched glasses (from the literature) suggests that the anomalous configurational rearrangements may involve the breakdown of alkali and alkaline earth titanate complexes and changes in Ti 4+ coordination.

Modelling of heat capacity–temperature data for sucrose–water systems

The significance of the point of intersection of the ‘ice-melting curve’ and glass-transition curve (measured by coordinates T′g and C′g on a ‘state’ diagram) as a characteristic feature of the behaviour of aqueous solutions of small sugar (and other) molecules on freezing, has been much emphasised in recent years. In consequence, accurate measurement of T′g and C′g for a solute–water system is important, and at present much reliance is placed upon differential scanning calorimetry as a means of achieving this. Recently, however, controversy has arisen regarding the validity of this approach, particularly where studies are restricted to the freezing of dilute solutions. In an attempt to clarify this matter, the present paper focuses on the sucrose–water system, and describes simulation of experimental heat capacity–temperature scan data for a range of sucrose concentrations. The simulations suggest that a true value for C′g can be obtained from DSC scans performed on dilute solutions only if a correction is made for the temperature dependence of the latent heat of melting of ice and, more importantly, the correct heat capacity ‘background’ is known. The simulations also suggest that, in the ideally reversible situation in which the state diagram is followed precisely, the heat capacity step occurring at T′g will contain a substantial extra contribution from initiation of ice dissolution. In real situations, however, as a result of imperfect annealing of samples during preparation, and irreversibility arising during DSC experiments, a separation and broadening of these events occurs, with the practical consequence that the measured temperatures corresponding to them bracket the true T′g value.

Influence of Thermal History on the Glass Transition of Poly(Phenylene Sulfide)

AbstractPPS is increasingly interesting as a high performance polymer material. Recently, Cheng, et al. [1] reported observation of rigid amorphous phase (RAP) in the amorphous phase of semicrystalline PPS using differential scanning calorimetry. Using the heat of fusion from DSC to obtain the degree of crystallinity of the semicrystalline samples, a simple rule of mixtures was applied to calculate the change in heat capacity step. The heat capacity decreased much more than could be accounted for using the measured crystallinity. Thus, these authors assumed the existence of a rigid amorphous phase which did not become liquid-like at Tg. The ratio of heat capacity step at Tg of semicrystalline PPS to that of the purely amorphous polymer was used to find the fraction of amorphous chains that do become liquid-like at Tg. The amount of RAP was then obtained by assuming a three phase model.