A resolution for the enigma of a liquid’s configurational entropy-molecular kinetics relation

First-principles study of the specific heat of glass at the glass transition with a case study on glycerol

The standard method to determine the transition temperature (T_g) of glasses is the jump in the specific heat,ΔCp. Despite its importance, standard theory for this jump is lacking. The difficulties include lack of proper treatment of the specific heat of liquids, hysteresis, and the timescale issue. The first part of this paper provides a non-empirical method for calculating the specific heat in the glass transition. The method consists of molecular dynamics (MD) simulations based on density-functional theory (DFT) and thermodynamics methods. Calculation of the total energy, which is the heart of DFT, is the most general method for obtaining specific heat for any state of matters. The influence of energy dissipation processes on specific heat is treated by adiabatic MD simulations. The problems of hysteresis and the timescale are alleviated by restricting the scope of calculations to equilibrium states only. The second part of this paper demonstrates the validity and usefulness of the methods by applying to the specific-heat jump of glycerol. By decomposingΔCpinto contributions of the structural, phonon, and thermal expansion energies, an appropriate interpretation for the specific-heat jump has been established: the major contribution toΔCpis the change in the structural energy. From this, a neat energy diagram about the glass transition is obtained. An outcome of this study is verification of the empirical relationship between the fragility and the specific-heat jump. These two quantities scale to the ratiok=Tg/ΔTg, whereΔTgis the width of the transition, through which the two quantities are interrelated.

Tuning the dynamic fragility of acrylic polymers by small molecules: the interplay of molecular structures

This report studied changes in the dynamic fragility (m) of poly(butyl methacrylate) (PBMA) by introducing guest hindered phenols capable of forming two or three intermolecular hydrogen bonds (inter-HBs) per molecule with the host polymer. The small molecules effectively decrease the m value, even if they apparently increase the glass transition temperature (T_g) of mixtures. The reduction in m was confirmed by enthalpy relaxation in two aspects: adding the guest molecule leads to a stronger cooling rate dependence of the limiting fictive temperature together with an apparent increase in aging rate of PBMA hybrids at low concentrations. By varying the molecule size and steric hindrance of the hydroxyl group on the hindered phenols, we clarified that m is primarily governed by the strength of inter-HB interactions, while the T_g value of mixtures depends on a combined effect of additive bulkiness and HB interaction. The anomalous dynamics was further rationalized not only by the HB-induced flexibility balance between side groups and backbone, but also by the reduction of cooperative rearranging sizes and alleviation of long-chain connectivity in such HB-driven hybrids.

Liquid-solid directional composites and anisotropic dipolar phases of polar nanoregions in disordered perovskites

Using temperature-resolved dielectric spectroscopy in the range of 75-320 K we have inspected the solid-like and liquid-like arrangements of nanometric dipoles (polar nanoregions) embedded in sodium-enriched potassium-tantalate-niobate (KNTN), a chemically-substituted complex perovskite crystal hosting inherent substitutional disorder. The study of order versus direction is carried out using Fröhlich entropy measurements and indicates the presence of four long-range symmetry phases, two of which are found to display profoundly anisotropic features. Exotic phases are found for which the dipoles at one fixed temperature manifest a liquid reorientational response along one crystal axis and a solid-like behavior along another axis. The macroscopic anisotropy observed in the sequence of different phases is found to match a microscopic order-disorder sequence typical of nominally pure perovskites. Moreover, experimental demonstration of the onset of a frozen state above transitions is provided.

Energy landscape-driven non-equilibrium evolution of inherent structure in disordered material

Complex states in glasses can be neatly expressed by the potential energy landscape (PEL). However, because PEL is highly multi-dimensional it is difficult to describe how the system moves around in PEL. Here we demonstrate that it is possible to predict the evolution of macroscopic state in a metallic glass, such as ageing and rejuvenation, through a set of simple equations describing excitations in the PEL. The key to this simplification is the realization that the step of activation from the initial state to the saddle point in PEL and the following step of relaxation to the final state are essentially decoupled. The model shows that the interplay between activation and relaxation in PEL is the key driving force that simultaneously explains both the equilibrium of supercooled liquid and the thermal hysteresis observed in experiments. It further predicts anomalous peaks in truncated thermal scanning, validated by independent molecular dynamics simulation.

Strategies to address low drug solubility in discovery and development

Drugs with low water solubility are predisposed to low and variable oral bioavailability and, therefore, to variability in clinical response. Despite significant efforts to "design in" acceptable developability properties (including aqueous solubility) during lead optimization, approximately 40% of currently marketed compounds and most current drug development candidates remain poorly water-soluble. The fact that so many drug candidates of this type are advanced into development and clinical assessment is testament to an increasingly sophisticated understanding of the approaches that can be taken to promote apparent solubility in the gastrointestinal tract and to support drug exposure after oral administration. Here we provide a detailed commentary on the major challenges to the progression of a poorly water-soluble lead or development candidate and review the approaches and strategies that can be taken to facilitate compound progression. In particular, we address the fundamental principles that underpin the use of strategies, including pH adjustment and salt-form selection, polymorphs, cocrystals, cosolvents, surfactants, cyclodextrins, particle size reduction, amorphous solid dispersions, and lipid-based formulations. In each case, the theoretical basis for utility is described along with a detailed review of recent advances in the field. The article provides an integrated and contemporary discussion of current approaches to solubility and dissolution enhancement but has been deliberately structured as a series of stand-alone sections to allow also directed access to a specific technology (e.g., solid dispersions, lipid-based formulations, or salt forms) where required.

Adam-Gibbs relation for glass-forming liquids in two, three, and four dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

Glass transition and fragility in the simple molecular glassformer CS(2) from CS(2)-S(2)Cl(2) solution studies

With an interest in finding the fragility for a simple, single component, molecular glassformer, we have determined the dielectric relaxation and glass transition behavior for a series of glasses in the CS(2)-S(2)Cl(2) and CS(2)-toluene systems. Crystallization of CS(2) can be completely avoided down to the composition 20 mol% second component, and the fragility proves almost independent of CS(2) content in each system. Since the glass temperature T(g) obtained from both thermal studies and from dielectric relaxation (using T(g,diel)=T(tau=100 s)) is quite linear over the whole composition range in each system, and since relaxation time data for pure CS(2) fall on the same master plot when scaled by the linearly extrapolated T(g) value, we deduce that pure CS(2) has the same high fragility as the binary solutions. The value is m=86, as for ortho-terphenyl (OTP). Based on observations of independent studies for the vibrational density of states (VDoS) (of inherent structures for OTP and instantaneous, at-temperature structures for CS(2)), we attribute the high fragility to an excess vibrational heat capacity (defined by C(p) (vib, excess)=dS(vib, excess)/d ln T) originating in the behavior of the low frequency modes of the VDoS (the boson peak modes). Both low frequency DoS and anharmonicity increase with increasing temperature, augmenting the configurational entropy drive to the top of the system energy landscape. The surprising implication is that fragility is determined in the vibrational, not configurational, manifold of microstates.

Origin of the enthalpy features of water in 1.8 nm pores of MCM-41 and the large C(p) increase at 210 K

It is shown that exothermic and endothermic features of dH(m)/dt observed on heating rapidly precooled and slowly precooled states of water in 1.8 nm pores of MCM-41 and the unusually large increase in the specific heat in the 210-230 K range [M. Oguni, Y. Kanke, S. Namba, and AIP Conf, Proc. 982, 34 (2008)] are inconsistent with kinetic unfreezing of a disordered solid, or glass softening. The exotherm is attributable to the melt's gradual conversion to distorted icelike structures and the endotherm to the reverse process until their fractional amounts reach a reversible equilibrium on heating. The large increase in C(p,m) with T is attributed to the latent heat, similar to that seen on premelting of fine grain crystals. The available calorimetric data on freezing and melting and the pore-size dependence of the features support this interpretation. The findings also put into question a conclusion from neutron scattering studies that in 1.8 nm pores water undergoes a structural and kinetic transition at approximately 225 K while remaining a liquid.

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.

A Calorimetric Investigation of Thermodynamic andMolecular Mobility Contributions to the Physical Stability of Two Pharmaceutical Glasses

The purpose of this work was to investigate the contribution of thermodynamics and mobility to the physical stability of two pharmaceutical glasses with similar glass transition temperatures (Tg), by comparing configurational thermodynamic quantities and molecular relaxation time constants (tau) at temperatures below Tg. Ritonavir and nifedipine were chosen as model glasses because they show excellent and poor physical stability, respectively. Although ritonavir and nifedipine have similar Tg values (50 and 46 degrees C, respectively), amorphous ritonavir is quite stable while nifedipine has been reported to crystallize at temperatures as low as 40 degrees C below Tg. Modulated temperature differential scanning calorimetry (MTDSC) was used to characterize both crystalline phases and freshly prepared glasses. The glasses were then annealed at Tg-Ta = 25 degrees C while monitoring the extent of relaxation and heat capacity change as a function of time via MTDSC. Configurational thermodynamic quantities (Gc, Hc, and Sc) and molecular relaxation time constants, tau, were calculated from the calorimetric data. Interestingly, the Gibbs free energy driving force for crystallization was nearly identical for the two compounds. The largest differences were found in the configurational entropy (Sc) values for the fresh glasses and in the Sc values over time. Configurational entropy values were approximately 50% higher for ritonavir. The tau values of freshly prepared glasses indicated that both materials had similar initial mobility at the annealing temperatures and the temperature dependence of tau was approximately Arrhenius, regardless of age. Although initial tau values were similar, the tau values after 3 days annealing were approximately sixfold greater for ritonavir. The relatively poor physical stability of nifedipine compared to ritonavir is attributed to both the lower entropic barrier to crystallization for fresh and annealed glass, and higher molecular mobility in aged glasses of nifedipine. These observations below Tg are consistent with the previous work on physical stability of amorphous pharmaceuticals performed above Tg.

Correlation between Quasielastic Raman Scattering and Configurational Entropy in an Ionic Liquid

Low-frequency (5-200 cm(-1)) Raman spectra are reported for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, [bmim]PF(6), in glassy, supercooled liquid, and normal liquid phases (77-330 K). Raman spectra of [bmim]PF(6) agree with previous results obtained by optical Kerr effect spectroscopy and molecular dynamics simulation. Both the superposition model and the coupling model give reasonable fit to low-frequency Raman spectra of [bmim]PF(6). The configurational entropy of [bmim]PF(6) has been evaluated as a function of temperature using recently reported data of heat capacity. The calculated configurational entropy is inserted in the Adam-Gibbs theory for supercooled liquids, giving a good fit to non-Arrhenius behavior of viscosity and diffusive process, with the latter revealed by a recent neutron scattering investigation of [bmim]PF(6). There is a remarkable linear dependence between intensity of quasielastic Raman scattering and configurational entropy from 77 K up to the melting point of [bmim]PF(6). This correlation offers insight into the nature of dynamical processes probed by low-frequency Raman spectra of ionic liquids.

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

The dielectric relaxation spectra of D-sorbitol glass have been studied in real time during annealing at 221.1 K, which is 47 K below its T(g) of 268 K. As the glass structurally relaxes during annealing, features of the Johari-Goldstein (JG) relaxation change with time: (i) the relaxation strength decreases, (ii) the relaxation peak at 48 Hz shifts to a higher frequency, and (iii) the relaxation spectra become narrower. All seem to follow the relation p proportional, variant exp[-(kt)(n)], where p is the magnitude of a property, k the rate constant, and t the time. The parameter n may well be less than 1, but this could not be ascertained. It is proposed that shift of the relaxation peak to a higher frequency and narrowing of the relaxation spectra occur when local, loosely packed regions of molecules in the glass structure collapse nonuniformly and the relaxation time of some of the molecules in the collapsed state becomes too long to contribute to the JG-relaxation spectra. Consequently, the half width of the spectra decreases, and the relaxation peak shifts to a higher frequency. Molecules whose diffusion becomes too slow after the local regions' collapse would contribute to the alpha-relaxation spectra and thus the net relaxation strength would increase on structural relaxation. It is argued that these findings conflict with the NMR-based conclusions that motion of all molecules in the glass and supercooled liquid contributes to the faster relaxation process.

Entropy theory of polymer glass formation revisited. I. General formulation

A generalized entropy theory of glass formation is developed by merging the lattice cluster theory for the thermodynamics of semiflexible polymer melts at constant pressure with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy. Since experimental studies have suggested that the relative rigidity of the chain backbone and the side groups is an essential parameter governing the nature of glass formation in polymers, we incorporate this rigidity disparity parameter, along with monomer structure, into our new theoretical description of the polymer fluid thermodynamics. Our entropy theory is compared with alternative theories that describe the rate of structural relaxation in glass-forming liquids in terms of an activated rate process.

Fragility of Glass-Forming Polymer Liquids

The fragility of polymeric glass-forming liquids is calculated as a function of molecular structural parameters from a generalized entropy theory of polymer glass-formation that combines the Adam-Gibbs (AG) model for the rate of structural relaxation with the lattice cluster theory (LCT) for polymer melt thermodynamics. Our generalized entropy theory predicts the existence of distinct high and low temperature regimes of glass-formation that are separated by a thermodynamically well-defined crossover temperature T(I) at which the product of the configurational entropy and the temperature has an inflection point. Since the predicted temperature dependence of the configurational entropy and structural relaxation time are quite different in these temperature regimes, we introduce separate definitions of fragility for each regime. Experimentally established trends in the fragility of polymer melts with respect to variations in polymer microstructure and pressure are interpreted within our theory in terms of the accompanying changes in the chain packing efficiency.

Dielectric Studies of Molecular Motions in Amorphous Solid and Ultraviscous Acetaminophen

The dielectric permittivity and loss spectra of glassy and ultraviscous states of acetaminophen have been measured over the frequency range 10 Hz-0.4 MHz. The relaxation spectra show an asymmetric distribution of times expressed in terms of the Kohlrausch exponent, beta, which remains constant at 0.79+/-0.02 over the 305-341 K range. The dielectric relaxation time increases on cooling according to the Vogel-Fulcher-Tammann equation. However, the values of the parameters are considerably different from the values deduced from earlier work by other researchers using the heat capacity of ultraviscous acetaminophen and relating it to its molecular mobility. The calorimetric glass softening temperature of 296 K obtained from differential scanning calorimetry is close to the value measured from dielectric relaxation. The equilibrium permittivity of ultraviscous acetaminophen decreases on heating like that of a normal dipolar liquid, as anticipated from the Curie law. But, its value decreases rapidly with time when it begins to crystallize. The equilibrium permittivity of this crystal phase is approximately 3.1 at 300 K and increases with temperature, which indicates a partial, orientational-disordering of its structure. The results show limitations of the procedures used in the modeling of the kinetics of molecular motions, that is, estimating physical stability, using thermodynamic considerations based on thermal analyses of the amorphous solid phase of acetaminophen.

The Glass Transition Temperature of Polymer Melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.

On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario for finite dimensional systems, proposed by Kirkpatrick, Thirumalai, and Wolynes (KTW). This allows us to establish clearly a temperature dependent length xi( *) above which the mean-field glass transition picture has to be modified. We argue in favor of the mosaic state introduced by KTW, which leads to the Adam-Gibbs relation between the viscosity and configurational entropy of glass forming liquids. Our argument is a mixture of thermodynamics and kinetics, partly inspired by the random energy model: small clusters of particles are thermodynamically frozen in low energy states, whereas large clusters are kinetically frozen by large activation energies. The relevant relaxation time is that of the smallest "liquid" clusters. Some physical consequences are discussed.

The Adam–Gibbs equation and the out-of-equilibrium α relaxation of glass forming systems

The temperature dependence of the alpha-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam-Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam-Gibbs equation, for polymers the experimental activation energy values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam-Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity of the Adam-Gibbs equation for describing the temperature dependence of the time scale of the alpha-relaxation also out of equilibrium, at least for fragile glass formers.

Slow dynamics of salol: a pressure- and temperature-dependent light scattering study

We study the slow dynamics of salol by varying both temperature and pressure using photon correlation spectroscopy and pressure-volume-temperature measurements, and compare the behavior of the structural relaxation time with equations derived within the Adam-Gibbs entropy theory and the Cohen-Grest free volume theory. We find that pressure-dependent data are crucial to assess the validity of these model equations. Our analysis supports the entropy-based equation, and estimates the configurational entropy of salol at ambient pressure approximately 70% of the excess entropy. Finally, we investigate the evolution of the shape of the structural relaxation process, and find that a time-temperature-pressure superposition principle holds over the range investigated.

Can experiments select the configurational component of excess entropy?

Configurational entropy is frequently used to rationalize the structural dynamics of glass-forming liquids. The main problem with this concept is that it is not directly accessible to experiments. We introduce a procedure to estimate the configurational component of the excess entropy of a liquid --specifically, the configurational-entropy contribution from the structural relaxation process-- through a combined investigation of dynamic and thermodynamic properties as functions of temperature and pressure. We test our method on orthoterphenyl, salol, and glycerol, and find that the fraction of excess entropy that arises from structural configurations is about 70% for all three materials.