Gaussian excitations model for glass-former dynamics and thermodynamics

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter model to the experimental data on excess entropy and heat capacity shows that "fragile" behavior, indicated by a sharply rising excess heat capacity as the glass transition is approached from above, occurs in anticipation of a first-order transition--usually hidden below the glass transition--to a "strong" liquid state of low excess entropy. The distinction between fragile and strong behavior of glass formers is traced back to an order of magnitude difference in the Gaussian width of their excitation energies. Simple relations connect the excess heat capacity to the Gaussian width parameter, and the liquid-liquid transition temperature, and strong, testable, predictions concerning the distinct properties of energy landscape for fragile liquids are made. The dynamic model relates relaxation to a hierarchical sequence of excitation events each involving the probability of accumulating sufficient kinetic energy on a separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and the known correlation of kinetic with thermodynamic fragility, both follow from the way the rugged landscape induces fluctuations in the partitioning of energy between vibrational and configurational manifolds. A relation is derived in which the configurational heat capacity, rather than the configurational entropy of the Adam-Gibbs equation, controls the temperature dependence of the relaxation times, and this gives a comparable account of the experimental observations without postulating a divergent length scale. The familiar coincidence of zero mobility and Kauzmann temperatures is obtained as an approximate extrapolation of the theoretical equations. The comparison of the fits to excess thermodynamic properties of laboratory glass formers, and to configurational thermodynamics from simulations, reveals that the major portion of the excitation entropy responsible for fragile behavior resides in the low-frequency vibrational density of states. The thermodynamic transition predicted for fragile liquids emerges from beneath the glass transition in case of laboratory water and the unusual heat capacity behavior observed for this much studied liquid can be closely reproduced by the model.     

Two-Gaussian excitations model for the glass transition

We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between T(g) and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.     

Temperature, pressure, and isotope effects on the structure and properties of liquid water: a lattice approach

We present a lattice model to describe the effect of isotopic replacement, temperature, and pressure changes on the formation of hydrogen bonds in liquid water. The approach builds upon a previously established generalized lattice theory for hydrogen bonded liquids [B. A. Veytsman, J. Phys. Chem. 94, 8499 (1990)], accounts for the binding order of 1/2 in water-water association complexes, and introduces the pressure dependence of the degree of hydrogen bonding (that arises due to differences between the molar volumes of bonded and free water) by considering the number of effective binding sites to be a function of pressure. The predictions are validated using experimental data on the temperature and pressure dependence of the static dielectric constant of liquid water. The model is found to correctly reproduce the experimentally observed decrease of the dielectric constant with increasing temperature without any adjustable parameters and by assuming values for the enthalpy and entropy of hydrogen bond formation as they are determined from the respective experiments. The pressure dependence of the dielectric constant of water is quantitatively predicted up to pressures of 2 kbars and exhibits qualitative agreement at higher pressures. Furthermore, the model suggests a--temperature dependent--decrease of hydrogen bond formation at high pressures. The sensitive dependence of the structure of water on temperature and pressure that is described by the model rationalizes the different solubilization characteristics that have been observed in aqueous systems upon change of temperature and pressure conditions. The simplicity of the presented lattice model might render the approach attractive for designing optimized processing conditions in water-based solutions or the simulation of more complex multicomponent systems.     

Landscapes and fragilities

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth, and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.     

Ionic melts with waterlike anomalies: thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.     

Designing generalized statistical ensembles for numerical simulations of biopolymers

Conformational properties of polymers, such as average dihedral angles or molecular alpha-helicity, display a rather weak dependence on the detailed arrangement of the elementary constituents (atoms). We propose a computer simulation method to explore the polymer phase space using a variant of the standard multicanonical method, in which the density of states associated to suitably chosen configurational variables is considered in place of the standard energy density of states. This configurational density of states is used in the Metropolis acceptance/rejection test when configurations are generated with the help of a hybrid Monte Carlo algorithm. The resulting configurational probability distribution is then modulated by exponential factors derived from the general principle of the maximal constrained entropy by requiring that certain average configurational quantities take preassigned (possibly temperature dependent) values. Thermal averages of other configurational quantities can be computed by using the probability distributions obtained in this way. Moments of the energy distribution require an extra canonical sampling of the system phase space at the desired temperature, in order to locally thermalize the configurational degrees of freedom. As an application of these ideas we present the study of the structural properties of two simple models: a bead-and-spring model of polyethylene with independent hindered torsions and an all-atom model of alanine and glycine oligomers with 12 amino acids in vacuum.     

A comparison between the bond-strength-coordination number fluctuation model and the random walk model of viscosity

We have studied the temperature dependence of the viscosity of some polymeric materials by using both, the bond-strength-coordination number fluctuation model and the random walk model. The results reveal that both models show an excellent agreement with the experimental data. For the random walk model, two equations corresponding to two temperature regimes (low-T and high-T) separated by the critical temperature T _c, which is difficult to determine, are needed to describe the temperature dependence of the viscosity of a fragile system, whereas for the bond-strength-coordination number fluctuation model, a single equation with clear physical meaning describes the temperature dependence of the viscosity of both, the fragile and strong systems. We have also studied the relationship between the normalized temperature range of cooperativity and the fragility index. A theoretical expression for the relationship has been derived based on the bond-strength-coordination number fluctuation model. The comparison with the experimental data shows a good agreement, leading to the conclusion that the kinetic properties of glass forming liquids and the cooperativity of molecular relaxations are correlated.     

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.     

Environmental swap energy and role of configurational entropy in transfer of small molecules from water into alkanes

We studied the effect of segmented solvent molecules on the free energy of transfer of small molecules from water into alkanes (hexane, heptane, octane, decane, dodecane, tetradecane, and hexadecane). For these alkanes we measured partition coefficients of benzene, 3-methylindole (3MI), 2,3,4,6-tetrachlorophenol (TeCP), and 2,4,6-tribromophenol (TriBP) at 3, 11, 20, 33 [corrected], and 47 degrees C. For 3MI, TeCP, and TriBP the dependence of free energy of transfer on length of alkane chains was found to be very different from that for benzene. In contrast to benzene, the energy of transfer for 3MI, TeCP, and TriBP was independent of the number of carbons in alkanes. To interpret data, we used the classic Flory-Huggins (FH) theory of concentrated polymer solutions for the alkane phase. For benzene, the measured dependence of energy of transfer on the number of carbons in alkanes agreed well with predictions based on FH model in which the size of alkane segments was obtained from the ratio of molar volumes of alkanes and the solute. We show that for benzene, the energy of transfer can be divided into two components, one called environmental swap energy (ESE), and one representing the contribution of configurational entropy of alkane chains. For 3MI, TeCP, and TriBP the contribution of configurational entropy was not measurable even though the magnitude of the effect predicted from the FH model for short chain alkanes was as much as 20 times greater than experimental uncertainties. From the temperature dependence of ESE we obtained enthalpy and entropy of transfer for benzene, 3MI, TeCP, and TriBP. Experimental results are discussed in terms of a thermodynamic cycle considering creation of cavity, insertion of solute, and activation of solute-medium attractive interactions. Our results suggest that correcting experimental free energy of transfer by Flory-Huggins configurational entropy term is not generally appropriate and cannot be applied indiscriminately.     

玻璃化液体中构型熵与展宽弛豫函数关系的研究

The relationship between the transport properties and thermodynamic properties in glass forming liquids was investigated. The configurational entropy of Adam-Gibbs theory on cooperatively rearranging regions and the theoretic function derived from extremal value model were used to propose a brief that non-exponential stretched exponent in KWW form relaxation function is equal to the relative configurational entropy of cooperatively rearranging region in liquids, and is inversely proportional to the critical number of molecules occurring configurational transformation in a cooperatively rearranging region. Therefore, the new physical significance on glassy configuration is imposed on the stretched exponent, and theoretical developments and empirical correlations between the structural relaxation and configurational entropy are established. Further, an improved expression of β(T) was proposed to eliminate the deviation of the fit by using Vogel-Fulcher-Tammann equation from viscosity data at higher temperatures, which conforms well over 200 K temperature range. The improvement on β(T) is correspondent to the improvement on the difference in thermal capacities between isobaric and isochoric processes.     

Hydrogen bond strength and network structure effects on hydration of non-polar molecules

We measure the solvation free energy, Δμ*, for hard spheres and Lennard-Jones particles in a number of artificial liquids made from modified water models. These liquids have reduced hydrogen bond strengths or altered bond angles. By measuring Δμ* for a number of state points at P = 1 bar and different temperatures, we obtain solvation entropies and enthalpies, which are related to the temperature dependence of the solubilities. By resolving the solvation entropy into the sum of the direct solute-solvent interaction and a term depending on the solvent reorganisation enthalpy we show that, although the hydrophobic effect in water at 300 K arises mainly from the small molecular size, its temperature dependence is anomalously low because the reorganisation enthalpy of liquid water is unusually small. We attribute this to the strong tetrahedral network which results from both the molecular geometry and the hydrogen bond strength.     

Molecular motions in amorphous ibuprofen as studied by broadband dielectric spectroscopy

The molecular mobility of amorphous ibuprofen has been investigated by broadband dielectric relaxation spectroscopy (DRS) covering a temperature range of more than 200 K. Four different relaxation processes, labeled as alpha, beta, gamma, and D, were detected and characterized, and a complete relaxation map was given for the first time. The gamma-process has activation energy E a = 31 kJ.mol (-1), typical for local mobility. The weak beta-relaxation, observed in the glassy state as well as in the supercooled state was identified as the genuine Johari-Goldstein process. The temperature dependence of the relaxation time of the alpha-process (dynamic glass transition) does not obey a single VFTH law. Instead two VFTH regimes are observed separated by a crossover temperature, T B = 265 K. From the low temperature VFTH regime, a T g (diel) (tau =100 s) = 226 K was estimated, and a fragility or steepness index m = 93, was calculated showing that ibuprofen is a fragile glass former. The D-process has a Debye-like relaxation function but the temperature dependence of relaxation time also follows the VFTH behavior, with a Vogel temperature and a pre-exponential factor which seem to indicate that its dynamics is governed by the alpha-process. It has similar features as the Debye-type process observed in a variety of associating liquids, related to hydrogen bonding dynamics. The strong tendency of ibuprofen to form hydrogen bonded aggregates such as dimers and trimers either cyclic or linear which seems to control in particular the molecular mobility of ibuprofen was confirmed by IR spectroscopy, electrospray ionization mass spectrometry, and MD simulations.     

THz reflection spectroscopy of liquid water

We report an investigation of the temperature-dependent far-infrared spectrum of liquid water. We have employed a new experimental technique based on ultrashort electromagnetic pulses (THz pulses). This technique allows for fast and reliable data of both index of refraction and absorption coefficient for highly absorbing liquids. The temperature dependence reveals an enthalpy of activation corresponding to 2.5 kcal/mol, in agreement with recent Raman experiments, but lower than the enthalpy observed in dielectric relaxation experiments. This demonstrates that part of the orientational relaxation in liquid water takes place without breaking of hydrogen bonds with bonding energy of 5 kcal/mol, as suggested in recent theoretical model.     

Comparing landscape calculations with calorimetric data on ortho-terphenyl, and the question of the configurational fraction of the excess entropy

Mossa et al. [Phys. Rev. E 65, 041205 (2002)] have calculated the total and configurational entropies of supercooled ortho-terphenyl liquid using the potential-energy landscape formalism and a simplified model of the intermolecular potential. I show here that the agreement of their calculated configurational entropy with the experimental data depends on what is assumed about the configurational fraction of the excess entropy and its temperature dependence. In particular, if the configurational fraction is taken as 0.70 and independent of temperature the agreement is excellent; if a marked temperature dependence of that fraction inferred from calorimetric data is assumed the agreement is only fair at best. This marked temperature dependence of the configurational fraction also implies some implausible behavior of contributions to the excess entropy at the Kauzmann temperature, but no obvious reason for disregarding it presents itself.     

Thermodynamic functions of liquid water calculated from the temperature evolution of the vibration spectrum contour

Configurational contributions of hydrogen bonds to thermodynamic properties of water (internal energy, entropy, and heat capacity) are calculated on the basis of statistical distributions of frequencies of the OH vibrations of liquid water, calculated earlier from the experimental Raman spectra in frameworks of the fluctuation theory of hydrogen bonding. Distributions of the energy of hydrogen bonds are determined. It is shown by comparison with computer experiments that previously established dependence of energy on frequency, E(nu), must be considered in this formalism as the effective energy of hydrogen bonding averaged over those configurations of hydrogen bridge O-H...O which lead to the given frequency nu in the vibrational spectrum. Contribution of van der Waals interactions not affecting the frequency shift to heat capacity is evaluated.     

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.     

Configurational entropy of polyethylene and other linear polymers

The configurational entropy of the polyethylene chain at the melting points calculated in two ways. In both calculations, tetrahedral angles and discrete trans and gauche arrangements of all bonds are assumed, and trans bonds are assumed more stable than gauche by energy U₁. First, calculations are made on chains of up to N = 18 bonds, disallowing all configurations having overlapping atoms, and the result is extrapolated to large N. Second, a calculation is made directly for long chains, with overlaps excluded only over every short chain segment. The results are in almost exact agreement, suggesting that the second method can be safely used with other molecules. The calculated configurational entropy is in line with that suggested by the entropy of fusion, assuming the chains to acquire a configurational freedom in the melt which approaches that of independent chains.     

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.     

Free energy landscape of protein-like chains with discontinuous potentials

In this article the configurational space of two simple protein models consisting of polymers composed of a periodic sequence of four different kinds of monomers is studied as a function of temperature. In the protein models, hydrogen bond interactions, electrostatic repulsion, and covalent bond vibrations are modeled by discontinuous step, shoulder, and square-well potentials, respectively. The protein-like chains exhibit a secondary alpha helix structure in their folded states at low temperatures, and allow a natural definition of a configuration by considering which beads are bonded. Free energies and entropies of configurations are computed using the parallel tempering method in combination with hybrid Monte Carlo sampling of the canonical ensemble of the discontinuous potential system. The probability of observing the most common configuration is used to analyze the nature of the free energy landscape, and it is found that the model with the least number of possible bonds exhibits a funnel-like free energy landscape at low enough temperature for chains with fewer than 30 beads. For longer proteins, the free landscape consists of several minima, where the configuration with the lowest free energy changes significantly by lowering the temperature and the probability of observing the most common configuration never approaches one due to the degeneracy of the lowest accessible potential energy.     

Calorimetric studies of the energy landscapes of glassformers by hyperquenching methods

We consider some of the conditions associated with ergodicity-breaking and vitrification, in particular the equivalent, in quench vitrification, of the ωτ=1 condition that is well-known in relaxation spectroscopy. For a given quench rate, Q=dT/dt, strong liquids are trapped at much higher temperatures, relative to T _g, than are fragile liquids. We relate the trapping of the system during quenches to the multidimensional 'energy landscape' by means of which the configurational microstates of the system are defined. To characterize the energy landscape at energy levels that are usually associated with fluid materials, we use differential scanning calorimetry on hyperquenched glasses. This yields not only the excess potential energies of the states trapped-in during quench Q, but also the trap depths. The latter are found to be much smaller, relative to kT _g, for strong liquids than they are for fragile liquids. This revised version was published online in August 2006 with corrections to the Cover Date.