THE THIRD LAW OF THERMODYNAMICS. EVIDENCE FROM THE SPECIFIC HEATS OF GLYCEROL THAT THE ENTROPY OF A GLASS EXCEEDS THAT OF A CRYSTAL AT THE ABSOLUTE ZERO

Effects of Assisting Solvents on Purification Efficiency in the Layer Melt Crystallization of Glycerol

The efficiency of layer melt crystallization for the selective separation of glycerol from a glycerol-diethylene glycol mixture containing 4 wt % of diethylene glycol was evaluated using solvent-free and solvent-aided approaches. The effect of 1-butanol and the binary solvent of 1-butanol and acetone with a total molar composition of 25 mol % on the crystal growth kinetics and the purity of the final product was studied at different undercooling degrees and crystallization yields. The melting point temperature of the mixtures was predicted by using the modified UNIFAC Dortmund model. The addition of both a single and binary solvents significantly increased the crystal growth rate and purity of the final product compared to crystallization from the solvent-free mixture. Additionally, higher crystal growth rates and product purity were observed in the binary solvent system compared to those in the single solvent system at the same degree of undercooling. The second stage of solvent-aided crystallization resulted in glycerol with a purity above 99.5 wt %, depending on the type of solvent used and the rate of crystal growth.

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.

Hydrophilic and Hydrophobic Effects on the Structure and Themodynamic Properties of Confined Water: Water in Solutions

NMR spectroscopy is used in the temperature range 180–350 K to study the local order and transport properties of pure liquid water (bulk and confined) and its solutions with glycerol and methanol at different molar fractions. We focused our interest on the hydrophobic effects (HE), i.e., the competition between hydrophilic and hydrophobic interactions. Nowadays, compared to hydrophilicity, little is known about hydrophobicity. Therefore, the main purpose of this study is to gain new information about hydrophobicity. As the liquid water properties are dominated by polymorphism (two coexisting liquid phases of high and low density) due to hydrogen bond interactions (HB), creating (especially in the supercooled regime) the tetrahedral networking, we focused our interest to the HE of these structures. We measured the relaxation times (T1 and T2) and the self-diffusion (DS). From these times, we took advantage of the NMR property to follow the behaviors of each molecular component (the hydrophilic and hydrophobic groups) separately. In contrast, DS is studied in terms of the Adam–Gibbs model by obtaining the configurational entropy (Sconf) and the specific heat contributions (CP,conf). We find that, for the HE, all of the studied quantities behave differently. For water–glycerol, the HB interaction is dominant for all conditions; water–methanol, two different T-regions above and below 265 K are observable, dominated by hydrophobicity and hydrophilicity, respectively. Below this temperature, where the LDL phase and the HB network develops and grows, with the times and CP,conf change behaviors leading to maxima and minima. Above it, the HB becomes weak and less stable, the HDL dominates, and hydrophobicity determines the solution.

Hierarchy of Relaxation Times and Residual Entropy: A Nonequilibrium Approach

We consider nonequilibrium (NEQ) states such as supercooled liquids and glasses that are described with the use of internal variables. We classify the latter by the state-dependent hierarchy of relaxation times to assess their relevance for irreversible contributions. Given an observation time τobs, we determine the window of relaxation times that divide the internal variables into active and inactive groups, the former playing a central role in the NEQ thermodynamics. Using this thermodynamics, we determine (i) a bound on the NEQ entropy and on the residual entropy and (ii) the nature of the isothermal relaxation of the entropy and the enthalpy in accordance with the second law. A theory that violates the second law such as the entropy loss view is shown to be internally inconsistent if we require it to be consistent with experiments. The inactive internal variables still play an indirect role in determining the temperature T(t) and the pressure P(t) of the system, which deviate from their external values.

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

Slow rheological mode in glycerol and glycerol–water mixtures

Glycerol–water mixtures were studied at molar concentrations ranging from x_gly = 1 (neat glycerol) to x_gly = 0.3 using shear mechanical spectroscopy.

Thermal conductivity of Glycerol's liquid, glass, and crystal states, glass-liquid-glass transition, and crystallization at high pressures

To investigate the effects of local density fluctuations on phonon propagation in a hydrogen bonded structure, we studied the thermal conductivity κ of the crystal, liquid, and glassy states of pure glycerol as a function of the temperature, T, and the pressure, p. We find that the following: (i) κcrystal is 3.6-times the κliquid value at 140 K at 0.1 MPa and 2.2-times at 290 K, and it varies with T according to 138 × T(-0.95); (ii) the ratio κliquid (p)/κliquid (0.1 MPa) is 1.45 GPa(-1) at 280 K, which, unexpectedly, is about the same as κcrystal (p)/κcrystal (0.1 MPa) of 1.42 GPa(-1) at 298 K; (iii) κglass is relatively insensitive to T but sensitive to the applied p (1.38 GPa(-1) at 150 K); (iv) κglass-T plots show an enhanced, pressure-dependent peak-like feature, which is due to the glass to liquid transition on heating; (v) continuous heating cold-crystallizes ultraviscous glycerol under pressure, at a higher T when p is high; and (vi) glycerol formed by cooling at a high p and then measured at a low p has a significantly higher κ than the glass formed by cooling at a low p. On heating at a fixed low p, its κ decreases before its glass-liquid transition range at that p is reached. We attribute this effect to thermally assisted loss of the configurational and vibrational instabilities of a glass formed at high p and recovered at low p, which is different from the usual glass-aging effect. While the heat capacity, entropy, and volume of glycerol crystal are less than those for its glass and liquid, κcrystal of glycerol, like its elastic modulus and refractive index, is higher. We discuss these findings in terms of the role of fluctuations in local density and structure, and the relations between κ and the thermodynamic quantities.

Low-temperature heat capacities of confined liquid benzene, implying the behavior of ordinary bulk liquids

Isobaric heat capacities C p of benzene confined in silica MCM-41 mesopores with average diameters equal to and smaller than 2.9 nm were measured by precise adiabatic calorimetry. The confined benzene samples revealed no thermal anomaly due to crystallization/fusion and vitrified at low temperatures. The C p curves displayed a hump and a considerably quick decrease on the low-temperature side of the hump as the pore diameter increased. The enthalpy-relaxation effects observed on intermittent heating showed that the anomaly of the C p hump and quick decrease is not assigned to a glass transition. The bend in the temperature dependence of density reported previously was interpreted as corresponding to the quick decrease in C p . We concluded that the anomalous C p and density behaviors originated from the ordering/excitation in the configurational state, close to the ground state, of confined molecular aggregate and proposed a scenario that explains the general C p curves of ordinary bulk supercooled liquids in equilibrium at low temperatures below the glass-transition temperatures.

Model of the cooperative rearranging region for polyhydric alcohols

A simplified model of a hydrogen-bonding network is proposed in order to clarify the microscopic structure of the cooperative rearranging region (CRR) in Adam-Gibbs theory [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. Our model can be solved analytically, and it successfully explains the reported systematic features of the glass transition of polyhydric alcohols. In this model, hydrogen bonding is formulated based on binding free energy. Assuming a cluster of molecules connected by double hydrogen bonds is a CRR and approximating the hydrogen-bonding network as a Bethe lattice in percolation theory, the temperature dependence of the structural relaxation time can be obtained analytically. Reported data on relaxation times are well described by the obtained equation. By taking the lower limit of the binding free energy with this equation, the Vogel-Fulcher-Tammann equation can be derived. Consequently, the fragility index and glass transition temperature can be expressed as functions of the number of OH groups in a molecule, and this relation agrees well with the reported experimental data.

Hydrogen-bond network formation of water molecules and its effects on the glass transitions in the ethylene glycol aqueous solutions: failure of the Gordon-Taylor law in the water-rich range and absence of the T(g) = 115 K rearrangement process in bulk pure water

Enthalpy relaxation processes proceeding in ethylene glycol (EG) aqueous solutions [(EG)(x)(H(2)O)(1 - x)] within silica-gel nanopores were studied by adiabatic calorimetry. While the x = 0.25 solution within pores with diameter of 52 nm showed a glass transition at T(g) = 139 K, ageing of the solution at 160 K caused a phase separation to reveal glass transitions at T(g) = 145 and 160 K for EG-rich and water-rich regions, respectively: the water molecules are understood to form a more developed hydrogen-bond network, and consequently force the EG molecules in between the water-rich regions. The T(g) = 160 K is in good agreement with the T(g) value of the internal (not interfacial) water confined within pores with thickness of 1.1 nm. The ageing further remarkably diminished the T(g) = 115 K glass transition. This indicates that, while the molecules responsible for the glass transition are the mobile water ones forming a lower number of hydrogen bonds than four, the fraction of such water molecules is reduced in association with the development of the network and the glass transition is absent in bulk pure water. When the same x = 0.25 solution was confined within 1.1- and 12 nm pores, the water molecules developed a hydrogen-bond network in the pore centre due to the presence of the pore wall and pushed the EG molecules onto the pore surface even at higher temperatures: the water-rich region gave T(g) = 155 K close to 160 K. It is concluded that the hydrogen-bond network inherent to water structure is developed/collapsed remarkably in the range near x = 0; consequently, the composition dependence of T(g) in the bulk system deviates sharply in the range from the Gordon-Taylor empirical law followed for large x > 0.2.

Dynamics and structure of hydrogen-bonding glass formers: comparison between hexanetriol and sugar alcohols based on dielectric relaxation

Broadband dielectric spectra of supercooled 1,2,6-hexanetriol are presented in order to reveal physical picture behind a glass transition of polyhydric alcohols. It has been reported so far that temperature dependences of alpha relaxation time for sugar alcohols exhibit systematic trend against number of carbon atoms or OH groups per molecule. However, because each molecule is composed of equal number of carbon atoms and OH groups in the case of the reported sugar alcohols, the more dominant parameter to govern the alpha relaxation dynamics has not been discussed. By using a chemical structure of the hexanetriol composed of the deferent number of carbon and OH, it is possible to determine the dominant parameter. From temperature dependence of alpha relaxation times, it is strongly supported that the number of OH groups is the dominant parameter. Furthermore, from an analysis of static dielectric constant, it is suggested that local hydrogen-bonding structure is similar among all polyhydric alcohols. From these two results, a simple picture of the origin of the systematic character is proposed.

Thermodynamic aspects of vitrification

Vitrification is a process in which a liquid begins to behave as a solid during cooling without any substantial change in molecular arrangement or thermodynamic state variables. The physical phenomenon of vitrification is relevant to both cryopreservation by freezing, in which cells survive in glass between ice crystals, and cryopreservation by vitrification in which a whole sample is vitrified. The change from liquid to solid behavior is called the glass transition. It is coincident with liquid viscosity reaching 10(13) Poise during cooling, which corresponds to a shear stress relaxation time of several minutes. The glass transition can be understood on a molecular level as a loss of rotational and translational degrees of freedom over a particular measurement timescale, leaving only bond vibration within a fixed molecular structure. Reduced freedom of molecular movement results in decreased heat capacity and thermal expansivity in glass relative to the liquid state. In cryoprotectant solutions, the change from liquid to solid properties happens over a approximately 10 degrees C temperature interval centered on a glass transition temperature, typically near -120 degrees C (+/-10 degrees C) for solutions used for vitrification. Loss of freedom to quickly rearrange molecular position causes liquids to depart from thermodynamic equilibrium as they turn into a glass during vitrification. Residual molecular mobility below the glass transition temperature allows glass to very slowly contract, release heat, and decrease entropy during relaxation toward equilibrium. Although diffusion is practically non-existent below the glass transition temperature, small local movements of molecules related to relaxation have consequences for cryobiology. In particular, ice nucleation in supercooled vitrification solutions occurs at remarkable speed until at least 15 degrees C below the glass transition temperature.

Free-energy landscape for a tagged particle in a dense hard-sphere fluid

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome, Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.

Novel Method to Detect the Volumetric Glass → Liquid Transition at High Pressures: Glycerol as a Test Case

We report a novel method of detecting the glass --> liquid transition at high pressures, which comprises measuring the relative volume change incurred upon heating glassy samples into the liquid state. We show data on glycerol in the pressure range 0.050-1.00 GPa to demonstrate the viability of the method. The reversible glass --> liquid transition is observed by means of a kink in the relative volume change on heating the sample isobarically, which is attributed to the glass --> liquid transition temperature Tg. This kink can only be observed in the second and subsequent heating cycles since it is superposed by a compaction in the first heating cycle. The isobaric thermal expansivity beta, which is closely related to the first derivative of this curve, shows the features expected for a glass --> liquid transition, including a sharp rise of beta(glass) in a narrow temperature interval to beta(viscous liquid) and an accompanying overshoot effect. Both Tg and the size of the overshoot effect vary in accordance with theory upon changing the ratio of cooling to heating rates. From the shape of this curve the onset, inflection, overshoot peak, and endpoint of the glass --> liquid transition can be extracted, which can be employed to calculate the reduced glass transition width as a measure for the fragility of the liquid. Comparison with literature data allows quantifying the accuracy of the liquid's thermal expansivity beta to be at least +/-10%, while the error in beta is significantly larger for the expansivity of the glassy state. The reproducibility of the glass --> liquid transition temperature Tg is better than +/-2 K. Our glycerol data confirms literature studies showing a nonlinear increase of Tg with increasing pressure (approximately 35 K/GPa on average), which is accompanied by an increase in fragility.

Metal microcrystal pollutants: the heat resistant, transmissible nucleating agents that initiate the pathogenesis of TSEs?

This paper exposes the flaws in the conventional consensus on the origins of transmissible spongiform encephalopathies (TSEs) which decrees that the protein-only misfolded 'prion' represents the primary aetiological transmissible agent, and then reviews/presents the emerging data which indicates that environmental exposure to metal microcrystal pollutants (sourced from munitions, etc.) represents the heat resistant, transmissible nucleating agents which seed the metal-prion protein (PrP)-ferritin fibril crystals that cause TSE. Fresh analytical data is presented on the levels of metals in ecosystems which support populations affected by clusters of variant Creutzfeldt-Jacob disease (vCJD), sporadic/familial CJD, and the scrapie types of TSE that have emerged in the UK, Sicily, Sardinia, Calabria and Japan. This data further substantiates the abnormal geochemical template (e.g., elevated strontium (Sr), barium (Ba) and silver (Ag)) which was observed as a common hallmark of the TSE cluster ecosystems across North America, thereby supporting the hypothesis that these microcrystals serve as the piezoelectrion nucleators which seed the growth/multireplication of the aberrant metal-PrP-ferritin fibril features which characterise the neuropathology of the TSE diseased brain. A secondary pathogenic mechanism entails the inactivation of the sulphated proteoglycans which normally regulate the mineralisation process. This can be induced by a rogue metal mediated chelation of free sulphur, or by contamination with organo-sulphur pollutants that substitute at natural sulphur bonds, or via a mutation to the S-proteoglycan cell line; thereby enabling the aberrant overgrowth of rogue fibril crystal formations that possess a piezoelectric capacity which compromises the ability of the contaminated individual to process incoming acoustic/tactile pressure waves in the normal way. The crystals transduce incoming sonic energy into electrical energy, which, in turn, generates magnetic fields on the crystal surfaces that initiate chain reactions of free radical mediated spongiform neurodegeneration. Metal microcrystal nucleating agents provide a group of plausible aetiological candidates that explain the unique properties of the TSE causal agent - such as heat resistance, transmissibility, etc. - which the protein-only prion model fails to fulfill. This paper also discusses the possible nutritional measures that could best be adopted by populations living in high risk TSE ecosystems; as a means of preventing the successful implantation of these rogue microcrystals and their consequent hypermineralisation of the soft tissues within the CNS.

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.

Specific heat in a nonequilibrium system composed of Einstein oscillators

In order to understand the behavior of thermodynamic quantities near the glass transition temperature, we put the energy landscape picture and the particle's jump motion together and calculate the specific heat of a nonequilibrium system. Taking the finite observation time into account, we study the observation time dependence of the specific heat. We assume the Einstein oscillators for the dynamics of each basin in the landscape structure of phase space and calculate the specific heat of a system with 20 basins. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time.

Specific heat in nonequilibrium systems

We propose a general framework of calculating the specific heat of the system in nonequilibrium, where the dynamics of the representative point can be separated into fast motion in a basin of energy landscape and the slow stochastic jump motion among basins. We apply this framework to gaseous hydrogen and obtain the observation time (t(obs)) dependence of the specific heat. We find that the specific heat gives the quenched and the annealed one in the limit of t(obs)-->0 and t(obs)-->infinity, respectively. We also investigate the waiting time and the observation time dependence of the specific heat and show that, for shorter waiting time, the observation time must be longer to obtain the same degree of annealing. This tendency is consistent with the observation that the glass transition temperature is higher for faster quenching.

Potts fully frustrated model: thermodynamics, percolation, and dynamics in two dimensions

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore, this transition can be mapped onto a percolation transition. We numerically study the phase diagram in two dimensions (2D) for this model with frustration and without disorder and we compare it to the phase diagram of (i) the model with frustration and disorder and (ii) the ferromagnetic model. Introducing a parameter that connects the three models, we generalize the exact expression of the ferromagnetic Potts transition temperature in 2D to the other cases. Finally, we estimate the dynamic critical exponents related to the Potts order parameter and to the energy.