Spontaneous decrease in the heat capacity of a glass

Understanding temperature-modulated calorimetry through studies of a model system

Temperature modulated calorimetry is widely used but still raises some fundamental questions. In this paper we study a model system as a test sample to address some of them. The model has a nontrivial spectrum of relaxation times. We investigate temperature-modulated calorimetry at constant average temperature to precise the meaning of the frequency-dependent heat capacity, its relation with entropy production, and how such measurements can observe the aging of a glassy sample leading to a time-dependent heat capacity. The study of the Kovacs effect for an out-of-equilibrium system shows how temperature-modulated calorimetry could contribute to the understanding of this memory effect. Then we compare measurements of standard scanning calorimetry and temperature-modulated calorimetry and show how the two methods are complementary because they do not observe the same features. While it can probe the timescales of energy transfers in a system, even in the limit of low-frequency temperature-modulated calorimetry does not probe some relaxation phenomena which can be measured by scanning calorimetry, as suggested by experiments with glasses.

Highly sensitive pseudo-differential ac-nanocalorimeter for the study of the glass transition

We present a nanocalorimeter designed for the measurement of the dynamic heat capacity of thin films. The microfabricated sensor, the thermal conditioning of the sensor, as well as the highly stable and low noise electronic chain allow measurements of the real and imaginary parts of the complex specific heat with a resolution Δ C/C of about 10(-5). The performances of this quasi-differential nanocalorimeter were tested on a model of polymeric glass-former, the polyvinyl acetate (PVAc). The high stability and low noise of the device are essential for accurate studies on non-equilibrium slow relaxing systems such as glasses.

Non-exponential relaxation, fictive temperatures, and dispersive kinetics in the liquid-glass-liquid transition range of acetaminophen, sulfathiazole, and their mixtures

To investigate the effects of added molecular heterogeneity on the hysteretic features of liquid-glass-liquid transition, we studied acetaminophen, sulfathiazole, and three of their mixtures by calorimetry, and determined the T(g) and the fictive temperature, T(f), from changes in the enthalpy and entropy on the cooling and heating paths, as well as the non-exponential parameter, β(cal). We find that, (i) T(f) for cooling is within 1-3 K of T(f) for heating and both are close to T(g), (ii) the closed loop entropy change in the liquid-glass-liquid range is negligibly small, (iii) T(g) and T(f) increase on increasing sulfathiazole in the mixture, (iv) β(cal) first slightly increases when the second component is added and then decreases, and (v) ageing causes deviations from a non-exponential, nonlinear behavior of the glass. In terms of fluctuations in a potential energy landscape, adding a solute heterogeneity would shift the state point to another part of the landscape with a different distribution of barrier heights and a different number of minima accessible to the state point. Part of the change in β(cal) is attributed to hydrogen-bond formation between the two components. Ageing changes the relaxation times distribution, more at short relaxation times than at long relaxation times, and multiplicity of relaxation modes implied by β(cal) < 1 indicates that each mode contributing to the enthalpy has its own T(g) or T(f). β(cal) differs from β(age) determined from isothermal ageing, and the distribution parameter of α-relaxation times would differ from both β(cal) and β(age).

Fictive temperature, structural relaxation, and reality of residual entropy

By determining the fictive temperature, Tf, in two ways from the same Cp data, we investigate whether the residual entropy, Sres, of a glass could be an artifact of using the Cp d ln(T) integral in the glass-liquid temperature range. Although the integral gives only the upper and lower limits of the real entropy change, it is still useful and is distinguished as Delta(sigma). We determine Tf(sigma) from Delta(sigma) and the usual TfH from the Cp dT integral for two metal alloy glasses, a basalt composition glass and a spray-quenched propylene glycol glass from the available data, and find that Tf9sigma is about the same as TfH within errors. To substantiate it, we report a differential scanning calorimetry study performed during cooling of the Mg65Cu25Tb10 and Pd40Ni10Cu30P20 melts and on heating their glassy states at the same rates. In addition, we simulate Cp-T plots from a known model for nonexponential, nonlinear relaxation and analyze the data. The quantity Delta(sigma) on cooling the liquid and heating the glass differs negligibly; that is, net change in a temperature cycle between glass and its melt is close to zero, a characteristic of a nearly reversible change. We conclude that spontaneous enthalpy release has little effect on the entropy change determined from the Cp d ln(T) integral and, contrary to recent suggestions, Sres is real.

Molecular mobility, thermodynamics and stability of griseofulvin's ultraviscous and glassy states from dynamic heat capacity

PURPOSE

To determine the calorimetric relaxation time needed for modeling griseofulvin's stability against crystallization during storage.

METHODS

Both temperature-modulated and unmodulated scanning calorimetry have been used to determine the heat capacity of griseofulvin in the glassy and melt state.

RESULTS

The calorimetric relaxation time, tau cal, of its melt varies with the temperature T according to the relation, tau cal [s] = 10(-13.3) exp [2, 292 /(T[K] - 289.5)] , and the distribution of relaxation times parameter is 0.67. The unrelaxed heat capacity of the griseofulvin melt is equal to its vibrational heat capacity.

CONCLUSIONS

Griseofulvin neither crystallizes on heating to 373 K at 1 K/h rate, nor on cooling. Molecular mobility and vibrational heat capacity measured here are more reliable for modeling a pharmaceutical's stability against crystallization than the currently used kinetics-thermodynamics relations, and molecular mobility in the (fixed structure) glassy state is much greater than the usual extrapolation from the melt state yields. Molecular relaxation time of the glassy state of griseofulvin is about 2 months at 298 K, and longer at lower temperatures. It would spontaneously increase with time. If the long-range motions alone were needed for crystallization, griseofulvin would become more stable against crystallization during storage.

Relaxation during polymerization on slow heating and the vibrational heat capacity of the polymers

The real and imaginary components of the complex heat capacity, C(p) (') and C(p) ("), and C(p,app) have been measured in real time during the linear chain polymerization on 12 K/h heating of six different (partially) polymerized states of a stoichiometric mixture of cyclohexylamine and diglycidyl ether of bisphenol A. Their C(p,app) shows a sigmoid shape rise with different onset temperatures T(onset), which is followed by a deep exotherm as the viscosity decreases and further polymerization occurs at different rates. The rates of their enthalpy decrease on polymerization determined by subtracting C(p) (') from C(p,app) differ but C(p) (') and C(p,app) of their final states are the same. The relaxation time increases with polymerization and decreases with an increase in T. C(p) (') rises in a sigmoid shape manner, and C(p) (") shows a peak when the relaxation time of the polymerized state is equal to the inverse of the temperature modulation frequency, whether polymerization occurs or not. The unrelaxed or vibrational heat capacity C(p,vib) of the polymers at T>T(onset) is close to C(p) of their glassy state at T<T(onset), showing that C(p) difference between the equilibrium liquid and its glass is mostly configurational. This contradicts a calculation showing that C(p,vib) change of a polymer at T(g) is generally approximately 20% of the total C(p) change.

Determining vibrational heat capacity and thermal expansivity and their change at glass-liquid transition

The vibrational parts of a liquid's heat capacity Cp and thermal expansion coefficient alpha may be determined from dynamic measurements. The Cp data for Pd40Ni40P20 and 0.4 Ca(NO3)(2).0.6 KNO3 have been analyzed accordingly, and it is found that change in the vibrational part at liquid-glass transformation is negligible. Analysis for alpha of poly(styrene) leads to the same conclusion. There is no discontinuity in the vibrational parts of Cp and alpha on structural unfreezing in the Tg range, and hence the change in Cp and alpha at Tg is almost entirely due to change in the configurational part. Crystallization decreases the vibrational part not because the molecular mobility is lost but because the density increases.

Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb)

The authors report the results of temperature-dependent Brillouin scattering from both transverse and longitudinal acoustic waves, heat capacity studies as well as room temperature Raman scattering studies on M2O-MgO-WO3-P2O5 glasses (M=K,Rb). These results were used to obtain information about structure and various properties of the studied glasses such as fragility, elastic moduli, ratio of photoelastic constants, and elastic anharmonicity. They have found that both glasses have similar properties but replacement of K+ ions by Rb+ ions in the glass network leads to decrease of elastic parameters and P44 photoelastic constant due to increase of fragility. Based on Brillouin spectroscopy they show that a linear correlation between longitudinal and shear elastic moduli holds over a large temperature range. This result supports the literature data that the Cauchy-type relation represents a general rule for amorphous solids. An analysis of the Boson peak revealed that the form of the frequency distribution of the excess density of states is in agreement with the Euclidean random matrix theory. The reason of the observed shift of the maximum frequency of the Boson peak when K+ ions are substituted for Rb+ ions is also briefly discussed.

Thermal conductivity of a polymerizing liquid

Thermal conductivity kappa of seven polymerizing liquids has been measured in real time at different temperatures, and calorimetry and dielectric spectroscopy of one liquid are performed to help interpret the results. As a covalently bonded linear chain or a network structure in the liquid grows, kappa of the Debye equation initially increases with the polymerization time t(polym) as the molecular weight, density, and sound velocity increase, as on cooling a liquid. The measured kappa reaches a maximum and then decreases, thus showing a peak at a certain t(polym) and finally becomes constant, which is not the true behavior of steady state kappa. The dielectric relaxation time of the covalently bonded structure at the t(polym) for the kappa peak is less than 5 s and the extent of polymerization is below the vitrification plateau value. The peak height increases when the pulse time for kappa measurement is increased. An increase in the liquid's temperature shifts the kappa peak to a shorter t(polym). Liquid compositions polymerizing rapidly show a similar shift, and those polymerizing slowly or whose viscosity does not reach a high enough value show a small kappa peak or none. The kappa peak may be an artifact of the time dependence of heat capacity during the pulse time used for the kappa measurement, as proposed for glasses and supercooled liquids, similar to the changes in other properties observed as an artifact of kinetic freezing/unfreezing. For a polymerizing liquid, the peak may additionally arise when the rate of increase in the elastic modulus becomes equal to the rate of decrease in equilibrium Cp. In either case, its appearance does not distinguish the Brownian motions' slowing on polymerization from that on cooling or compressing a liquid.

Dielectric relaxation and elasticity during polymerization

A molecular kinetics-elasticity relation has been investigated by using real time dielectric spectroscopy of a diepoxide-triamine liquid mixture polymerizing at 298 K. As the liquid polymerized, the dielectric relaxation time tau increased linearly with the exponential of the known value of the instantaneous shear modulus G(infinity), in agreement with the elastic model for viscous flow but without the effect of temperature. Thus the structure-dependent effect on the Brownian motions are separated from the temperature-dependent effect. In this time-dependent process, increase in G(infinity) may be compensated by an increase in T, thereby keeping G(infinity) and tau constant. In the potential energy landscape paradigm, a polymerizing liquid's state point, like a normal liquid's on cooling, continuously shifts to deeper and lower energy minima of higher curvature, but the shift occurs irreversibly to other parts of the total energy landscape, thus adding a reaction coordinate to the landscape. A minimum in the energy landscape corresponding to a structure formed by polymerization may be identical to a minimum in another landscape corresponding to another structure.

Dynamic Heat Capacity and Relaxation Time of Ultraviscous Melt and Glassy Acetaminophen

The real and imaginary components, C'(p) and C''(p), of the complex heat capacity, C*(p)=C'(p)-iC"(p) of supercooled, ultraviscous melt of acetaminophen have been measured at different temperatures during cooling through its vitrification range and during heating through its glass-softening range by using a modulation frequency of 3.3 mHz. From these data, the distribution of relaxation time parameter, beta, and a characteristic (calorimetric or configurational) relaxation time, tau(cal), have been determined. A constant value of 0.65 for beta fits the data, and tau(cal) varies with the temperature according to the Vogel-Fulcher-Tammann equation, tau(cal) = 10(-12.95) exp[1813/(T - 240.5)]. This relation differs significantly from the one deduced by others in which the configurational entropy theory was used to deduce tau(cal). The C'(p) and C''(p) values measured during the cooling of its ultraviscous melt and during the heating of its glassy state show a small hysteresis only at low temperatures. These investigations also provide a comparison of calorimetric and dielectric relaxation times in ultraviscous acetaminophen and highlight the role of faster modes of relaxation at low temperatures in organic, molecular glasses that can help in a better understanding of the crystal nucleation process in glasses at T below their T(g).

Evolution of vibrational properties during a macromolecule’s growth

The elastic constants and vibrational contributions to thermal properties of three polymerizing liquids were investigated by using the available hypersonic velocity measured by Brillouin light scattering in real time. During the addition polymerization to a molecular network structure, Poisson's ratio upsilon(Poisson) decreases approximately according to exp[-(kt(polym))]n, where both k and n are composition dependent. The Debye frequency increases and the corresponding heat capacity, energy, and entropy approaching a limiting value. upsilon(Poisson) of the vitrified polymer continues to decrease but much more slowly, indicating its continued slow polymerization and structural relaxation with time. In the potential energy landscape interpretation, a polymerizing liquid's state point continuously shifts to another landscape's more curved, deeper minima.

Heat capacity of water in nanopores

Heat capacity of controlled amounts of water in Vycor's 2 nm radius pores has been determined in real time during the course of water's isothermal nanoconfinement from bulk state at 358 K, by using temperature-modulated calorimetry. As water transfers from bulk to nanopores via the vapor phase, its heat capacity per molecule increases asymptotically toward a limiting value of 1.4 times the heat capacity of bulk water for 1.8 wt % water in Vycor and 1.04 times for 10.0 wt %. The observations indicate that vibrational and configurational contributions to the heat capacity are highest when the amount of water is insufficient to completely cover the pore wall, and they decrease as more water is present in the nanopores and water clusters form. The heat capacity of water in completely filled nanopores approaches the value for bulk water, thus indicating that the heat capacity varies with the water molecules' position in the nanopores.

Endothermic freezing on heating and exothermic melting on cooling

Generally, a liquid freezes exothermally on cooling and a crystal melts endothermally on heating. Here we report an opposite occurrence--a liquid's endothermic freezing on heating and the resulting crystal's exothermic melting on cooling at ambient pressures. C(p) decreases on freezing and increases on melting, and the equilibrium temperature meets the thermodynamic requirement. Melting on cooling takes longer than freezing on heating. A rapidly cooled crystal state becomes kinetically frozen, evocative of a nonergodic state. Both C(p) and enthalpy relax like those of glasses, though the viscosity is only a few centipoise. The crystal state belongs to energy minima higher than those of the melt, which has consequences for the use of potential-energy landscape, or inherent structures, for a thermodynamic description of a material.

Position-dependent energy of molecules in nano-confined water

Real time decrease in the energy (or enthalpy) measured during confinement of controlled amounts of water in 2 nm radius pores of Vycor shows that exothermic transfer of bulk water to nanopores via the vapour-phase occurred in two stages. In the first stage, at saturation pressure, H2O molecules from the vapour rapidly accumulated in the nanopore channels near the Vycor surface. In the second, at vapour pressure below saturation, the accumulation rate abruptly decreased and water (slowly) diffused and redistributed in the nanopore channels until the vapour pressure equilibrium was attained. The energy decrease per H2O molecule was highest, 14.5 kJ mol(-1), at low amounts when the pore-wall was incompletely covered by H2O. This value approached zero at higher amounts when pores were gradually filled. The results show that the vibrational and configurational contributions to the energy of H2O molecules depend upon their position in the nanopore and these contributions approach their bulk water values at high water concentration, but do not attain those values for completely filled pores.