Crystallization kinetics of ultraviscous acetaminophen by heat capacity and enthalpy measurements and diffusion control.

Crystallization kinetics of ultraviscous acetaminophen has been studied at 308.2, 318.2, and 328.2 K by measuring the heat capacity, C(p), and the heat release in real time up to a period of 2.5 days. C(p) decreases according to an inverted sigmoid-shape curve, and the heat released increases according to a similar shape. The extent of crystallization determined from the two measurements differs, thus indicating that the interfacial liquid's C(p) may be slightly different from that of the bulk liquid. Both the excess C(p) of the liquid over the crystal phase and the corresponding excess enthalpy decrease with decrease in the temperature. The kinetics of crystallization follows the Kolmogorov-Johnson-Mehl-Avrami relation, alpha(cryst)(t) = 1 - exp(-kt(m)). The logarithm of the rate constant, ln k, increases from -40.78 at 308.2 K to -32.85 at 328.2 K, and m from 3.60 to 3.83. The product of k and the calorimetric relaxation time remains constant with changing temperature thus showing that the two are inversely related. This shows that crystallization may be diffusion-controlled in the ultraviscous melt. The C(p) data indicate that slow crystallization of melt produces acetaminophen's (monoclinic) form I. Several effects usually overlooked in the crystallized kinetics formalisms have been described.

Specific heat relaxation of an alcohol and implications for dielectric comparison.

The dynamic and the apparent specific heats of 5-methyl-2-hexanol were measured in its vitrification temperature range during its cooling and then heating at the same and exceptionally slow rates of 12 K/h and 60 K/h. The relaxation time determined from dynamic measurements is 48 s at 149.8 K. The relaxation time estimated from the onset of the apparent C(p)-endotherm measured on heating is found to be inconsistent with that determined from dynamic C(p) measurements. The fitting of a nonexponential nonlinear relaxation model to the C(p,app) data shows that beta varies slightly with the heating rate, and this is attributed to contributions to temperature-dependent energy from change in the hydrogen-bond population. The unrelaxed C(p) of the ultraviscous liquid is closer to that of its glassy state, thus showing that the vibrational part of C(p) does not increase in a sigmoid-shape manner when the glass structure kinetically unfreezes on heating. The results have implications for use of calorimetry in inferring the dielectric relaxation mechanism.

Configurational specific heat of molecular liquids by modulated calorimetry.

The specific heat of a liquid varies as its structure and molecular vibrational frequencies vary with the temperature. We report the magnitude of the structural or configurational part C(p,conf) for five molecular liquids by measuring their dynamic and the apparent specific heats, and find that the unrelaxed or vibrational specific heat, of the equilibrium liquid, is not greatly different from that of the nonequilibrium glass. Therefore, the vibrational part of the specific heat C(p,vib) does not change substantially when a glass becomes an ultraviscous liquid. This contradicts the inference that there is a large sigmoid-shape (discontinuous) increase in C(p,vib) as the structure of a glass kinetically unfreezes on heating above its T(g), and further that C(p,conf) is 20%-50% of the net C(p) change at the glass transition.

Calorimetric relaxation in pharmaceutical molecular glasses and its utility in understanding their stability against crystallization.

Glassy states of three pharmaceuticals, acetaminophen, griseofulvin, and nifedipine, and an acetaminophen-aspirin (1:1 mol) alloy were made by slow cooling of the melt and studied by calorimetry. Measurements were performed by cooling and heating at significantly slow rates of 20 K/h, which were comparable to the rate used in adiabatic calorimetry. The results were modeled in terms of a nonexponential, nonlinear structural relaxation. The calorimetric relaxation of all four pharmaceutical samples were less nonexponential than those of polymeric or inorganic glasses, and this finding was attributed to additional contributions to energy change that would arise from temperature and time dependent variation in the hydrogen bond population, the extent of isomerization, and/or the ionic equilibria that exist in these materials. Four calculated and relevant parameters for the pharmaceutical samples were, ln A = -183, beta = 0.75, x = 0.4, and Delta h* = 457 kJ/mol for acetaminophen, ln A = -170, beta = 0.75, x = 0.45, and Delta h* = 516 kJ/mol for griseofulvin, ln A = -189, beta = 0.69, x = 0.39, and Delta h* = 503 kJ/mol for nifedipine, and ln A = -160, beta = 0.70, x = 0.50, and Delta h* = 363 kJ/mol for the acetaminophen-aspirin alloy. The significance of these parameters and, in particular, their values are discussed in the context of the stability of the pharmaceuticals against crystallization and compared against the significance of the localized motions of the JG relaxation in the same context. Acetaminophen was found to be significantly more prone to crystallization on heating than the other two pharmaceuticals as well as the acetaminophen-aspirin alloy.

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.

Vibrational and configurational heat capacity of poly(vinyl acetate) from dynamic measurements.

The complex heat capacity C(p) (*) of poly(vinyl acetate) has been measured at 20.95 mrads modulation frequency during the cooling as well as on heating at 24, 8, and 2 Kh and during cooling at 0.5 Kh. The study is complemented with (the rate-dependent) C(p,app) measured during cooling and heating at 60, 24, and 8 Kh. At low temperatures, the real component of C(p) (*) yields the unrelaxed C(p) or C(p,vib), the vibrational part of C(p). It is found to be indistinguishable from C(p,glass) and lies on a line extrapolated to its equilibrium melt's temperature. At T near T(g),DeltaC(p)(=C(p,melt)-C(p,glass)) shows no detectable contribution from C(p,vib). The finding conflicts with a modified entropy theory calculation [E. A. DiMarzio and F. Dowell, J. Appl. Phys. 50, 6061 (1979)], which had predicted that approximately 27% of DeltaC(p) of poly(vinyl acetate) at T near T(g) is vibrational in origin and the remainder configurational. At T

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

Composition dependence and the nature of endothermic freezing and exothermic melting.

The heat capacity, C(p), and enthalpy and entropy change of alpha-cyclodextrin, H(2)O, and 4-methylpyridine solutions have been studied during their freezing on heating, isothermal freezing, and the solid's melting on cooling. Freezing occurs in several endothermic steps on heating to 383 K and alpha-cyclodextrin rich solutions freeze in four steps. The melting rate becomes slower with decrease in temperature and its steps merge. Decreasing the amount of alpha-cyclodextrin decreases the C(p) change on freezing. The endothermic freezing phenomenon differs from freezing of a pure liquid and is attributed to formation of a solid inclusion compound and its incongruent way of exothermic melting.

Kinetics and thermodynamics of sucrose hydrolysis from real-time enthalpy and heat capacity measurements.

We report a real time study of the enthalpy release and heat capacity during the course of HCl-catalyzed hydrolysis of sucrose to fructose and glucose. Measurements were performed during both isothermal conditions and during slow heating and then cooling at a controlled rate. The reaction rate constant of the first-order kinetics follows an Arrhenius relation with activation energy of 109.2 kJ/mol of sucrose. On hydrolysis, the enthalpy decreases by 14.4 kJ/mol of sucrose at 310 K, and the heat capacity, Cp, increases by 61 J mol-1 K-1 of sucrose in the solution. The enthalpy of hydrolysis decreases with increase in the temperature and DeltaCp on hydrolysis increases. The effects are attributed to change in the configurational and vibrational partition functions as one covalent bond in sucrose breaks to form two molecules, which then individually form additional hydrogen bonds and alter the water's structure in the solution. Cp of the solution increases with temperature less rapidly before sucrose hydrolysis than after it. This may reflect an increase in the configurational contribution to Cp as the hydrogen bond population changes.

Spontaneous liquifaction of isomerizable molecular crystals.

A lattice vacancy raises the energy of the neighboring (flexible) molecule in a crystal, which may be enough to isomerize it to a tautomer that does not fit the lattice site, thus creating a liquidlike local region embedding the vacancy. Similar regions may appear elsewhere in the lattice and the regions may ultimately merge. Thus a crystal may spontaneously liquefy over a period of hours to years at a temperature below its normal melting point. Simultaneous heat capacity and heat absorption measurements of several such molecular crystals show that they spontaneously liquefy at a temperature far below their reputed melting point, according to a non-exponential rate kinetics and a temperature dependent rate constant, and do not crystallize on cooling.

Heat capacity of tetrahydrofuran clathrate hydrate and of its components, and the clathrate formation from supercooled melt.

We report a thermodynamic study of the formation of tetrahydrofuran clathrate hydrate by explosive crystallization of water-deficient, near stoichiometric, and water-rich solutions, as well as of the heat capacity, C(p), of (i) supercooled tetrahydrofuran-H2O solutions and of the clathrate hydrate, (ii) tetrathydrofuran (THF) liquid, and (iii) supercooled water and the ice formed on its explosive crystallization. In explosive freezing of supercooled solutions at a temperature below 257 K, THF clathrate hydrate formed first. The nucleation temperature depends on the cooling rate, and excess water freezes on further cooling. The clathrate hydrate melts reversibly at 277 K and C(p) increases by 770 J/mol K on melting. The enthalpy of melting is 99.5 kJ/mol and entropy is 358 J/mol K. Molar C(p) of the empty host lattice is less than that of the ice, which is inconsistent with the known lower phonon frequency of H2O in the clathrate lattice. Analysis shows that C(p) of THF and ice are not additive in the clathrate. C(p) of the supercooled THF-H2O solutions is the same as that of water at 247 K, but less at lower temperatures and more at higher temperatures. The difference tends to become constant at 283 K. The results are discussed in terms of the hydrogen-bonding changes between THF and H2O.

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).

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.

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.

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.

Thermodynamic functions of water and ice confined to 2 nm radius pores.

The heat capacity C(p) of the liquid state of water confined to 2 nm radius pores in Vycor glass was measured by temperature modulation calorimetry in the temperature range of 253-360 K, with an accuracy of 0.5%. On nanoconfinement, C(p) of water increases, and the broad minimum in the C(p) against T plot shifts to higher temperature. The increase in the C(p) of water is attributed to an increase in the phonon and configurational contributions. The apparent heat capacity of the liquid and partially frozen state of confined water was measured by temperature scanning calorimetry in the range of 240-280 K with an accuracy of 2%, both on cooling or heating at 6 K h(-1) rate. The enthalpy, entropy, and free energy of nanoconfined liquid water have been determined. The apparent heat capacity remains higher than that of bulk ice at 240 K and it is concluded that freezing is incomplete at 240 K. This is attributed to the intergranular-water-ice equilibrium in the pores. The nanoconfined sample melts over a 240-268 K range. For 9.6 wt % nanoconfined water concentration ( approximately 50% of the maximum filling) at 280 K, the enthalpy of water is 81.6% of the bulk water value and the entropy is 88.5%. For 21.1 wt % (100% filling) the corresponding values are 90.7% and 95.0%. The enthalpy decrease on nanoconfinement is a reflection of the change in the H-bonded structure of water. The use of the Gibbs-Thomson equation for analyzing the data has been discussed and it is found that a distribution of pore size does not entirely explain our results.