Adam-Gibbs Theory Research Articles

Thermodynamic universality of configurational entropy in glass-forming liquids

Glass is a liquid-like disordered material but behaves mechanically like a solid. Ubiquitous in nature and important in technology, the vitreous state manifests its presence from window glass, polymers, to optical fiber, and almost all kinds of materials have ability to form glass. Significant progress has been made in understanding the nature of the phenomenon, yet the issue remains a major scientific challenge. Here we propose one concise, explicit thermodynamic expression in both temperature and pressure for the configurational entropy of the Adam-Gibbs theory, and show its excellent universal description of experimental data. The formulation generalizes the most important equations in the field such as the VFT equation, judiciously unifies for the first time the two key thermodynamic variables in one form, has non-divergence which resolves the long-standing Kauzmann paradox, tentatively provides a sound foundation addressing the mutual effects of temperature and pressure, and predicts the glass transition as a second-order phase transition. This approach should thus offer an organizing principle to rationalize the vast body of dynamic properties and advance researches on the thermodynamics including the glass transition of glass-forming substances.

The viscosity of planetary tholeiitic melts: A configurational entropy model

The viscosity (η) of silicate melts is a fundamental physical property controlling mass transfer in magmatic systems. Viscosity can span many orders of magnitude, strongly depending on temperature and composition. Several models are available that describe this dependency for terrestrial melts quite well. Planetary basaltic lavas however are distinctly different in composition, being dominantly alkali-poor, iron-rich and/or highly magnesian. We measured the viscosity of 20 anhydrous tholeiitic melts, of which 15 represent known or estimated surface compositions of Mars, Mercury, the Moon, Io and Vesta, by concentric cylinder and parallel plate viscometry. The planetary basalts span a viscosity range of 2 orders of magnitude at liquidus temperatures and 4 orders of magnitude near the glass transition, and can be more or less viscous than terrestrial lavas. We find that current models under- and overestimate superliquidus viscosities by up to 2 orders of magnitude for these compositions, and deviate even more strongly from measured viscosities toward the glass transition.We used the Adam–Gibbs theory (A–G) to relate viscosity (η) to absolute temperature (T) and the configurational entropy of the system at that temperature (Sconf), which is in the form of logη=Ae+Be/TSconf. Heat capacities (CP) for glasses and liquids of our investigated compositions were calculated via available literature models. We show that the A–G theory is applicable to model the viscosity of individual complex tholeiitic melts containing 10 or more major oxides as well or better than the commonly used empirical equations. We successfully modeled the global viscosity data set using a constant Ae of −3.34±0.22 log units and 12 adjustable sub-parameters, which capture the compositional and temperature dependence on melt viscosity. Seven sub-parameters account for the compositional dependence of Be and 5 for Sconf. Our model reproduces the 496 measured viscosity data points with a 1σ root-mean-square deviation (rmsd) of 0.12 log units across 13 orders of measured melt viscosity. The model performed well in predicting the viscosity of lunar and martian melts not used in calibration, and should be used to calculate lava flow velocities and fluxes for anhydrous basaltic volcanism on other moons and planets.

Modelling configurational entropy of silicate melts

The Adam-Gibbs theory provides a robust connection between the transport or relaxation properties of melts and their thermochemical properties. In its expanded form:logη=A+BTScTg+CpclnTTgthe equation has adjustable unknown parameters A, B and Sc (Tg) which can be estimated from experimental estimates of configurational heat capacity (Cpc), glass transition temperature (Tg) and viscosity (η). Here, we use recently published datasets for anhydrous and hydrous silicate melts and glasses (N~50) for which there are measurements of log η and calorimetric measurements of Cpc and Tg. Our fitting strategy follows the approach developed by previous workers with the sole exception that we assume all silicate melts converge to a common, but unknown, high temperature limit to melt viscosity (e.g., A=log η∞). Our optimal value for A is −3.51±0.25. A consequence of a common, high-temperature limit to silicate melt viscosity is that the corresponding model values of glass transition temperature (Tg12), melt fragility (m), and the ratio Cpc/Sc are constrained to lie on a single plane approximated as:CpcSc=−Tg12243399−m15.518+0.996thereby establishing a quantitative connection between calorimetric and rheological measurements. Lastly, we show a good correspondence between values of Tg12 and fragility (m) from this Adam-Gibbs based model of melt viscosity and values predicted by the GRD viscosity model for multicomponent silicate melts (cf. Giordano et al., 2008).

Dynamic Heterogeneity and Cooperative Length Scale at Dynamic Glass Transition in Glass Forming Liquids

Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter research. However, recently great advances have been made within the framework of the Adam–Gibbs theory on the connection between cooperatively rearranging regions, or dynamic heterogeneities, i.e., domains of the supercooled liquid whose relaxation is highly correlated. The growth of the size of these dynamic domains is now believed to be the driving mechanism for different experimental parameters like relaxation times and viscosity of supercooled liquid approaching the glass transition. Recent studies have shown the evolution of cooperative motions in supercooled liquids using different experimental tools and models. In this work, broadband dielectric spectroscopy and modulated temperature differential scanning calorimetry were carried out on six different amorphous glass-forming systems in order to scan a wide range of relaxation times and temperatures...

Atomistic Molecular Insight into the Time Dependence of Polymer Glass Transition.

The most atomistic molecular details of polymer glass transition were analyzed through the frozen torsions in our molecular dynamics simulations. Different observation times were used to determine the frozen fractions and frozen chain lengths. The glass transition temperature was found to coincide well with the temperature at which the frozen fractions were reduced to 1/e. The frozen chain segments grow as the temperature decreases in a similar way with that of linear polymerization, and the inverse number-average frozen chain length leads to the formulation of configuration entropy during glass transition. The ideal glass transition temperature extrapolated to zero configuration entropy corresponds well with those reported in the literature, and the relation between the relaxation time and the configuration entropy shows perfect agreement with the Adam-Gibbs theory around the glass transition temperature. Volume spanning clusters are formed at the low temperature end, which might serve as a premature prototype for the formation of the "ideal glassy state" with limited accessible configurations.

The interplay between grain boundary structure and defect sink/annealing behavior

We present a series of results from atomistic simulations in three different materials (3 crystal structures) that demonstrate that the multiplicity of grain boundary (GB) structures at fixed macroscopic GB degrees of freedom is both extremely large and ubiquitous. The GB energy vs. misorientation curve that is commonly discussed is in fact a wide band, with many GB states very close in energy. The existence of so many GB states suggests that GB configurational entropy Sc is important for GB properties. We demonstrate that the GB Sc consists of two major contributions, one of which is geometric in nature and one that depends on bonding. We then show how this concept can be employed to predict GB relaxation dynamics by analogy with Adam-Gibbs theory, originally derived to predict the properties of glass forming liquids. Finally, we apply these predictions to understand GB denuded zone size during irradiation.

The Influence of TiO2 Addition on the Modulus of Rupture of Alumina-Magnesia Refractory Castables

The addition of TiO2 to alumina-magnesia refractory castables could accelerate the in situ spinel and calcium hexa-aluminate (CA6) formation and change the phase evolution, which will have direct effect on the overall modulus of rupture values. The cold (CMOR) and hot (HMOR) modulus of rupture, thermal expansion, and elastic modulus of alumina-magnesia refractory castables with different amounts of TiO2 were measured. The correlation of CMOR, theoretical strength, fracture toughness, and the fractal dimension of the fracture surface for these compositions were investigated. HMOR data were described using the model based on Varshni approach and Adam-Gibbs theory. The influence of TiO2 addition on the modulus of rupture of alumina-magnesia refractory castables was related to microcracks derived from expansive phase formation and pore filling or viscous bridging due to the presence of liquid phase at high temperature. The contribution of the above factors to the modulus of rupture for castables varied with the temperature.

Relaxation time of polypropylene glycol and polypropylene glycol dimethylether-like polymers in terms of fluid-phase temperature and pressure dependent hole fraction

We present a model explaining relaxation time of PPG (polypropylene glycol) and PPGM (polypropylene glycol dimethylether) as representative compounds, with different molecular weights, PPG2 (Mw=2kgmol−1), PPG3 (Mw=3kgmol−1), PPGM1 (Mw=1kgmol−1), and PPGM2 (Mw=2kgmol−1), as a function of hole fraction at various fluid phase temperatures and high pressures. Proposed model based on the structural relaxation behavior of chain molecules given by “thermo-occupancy” function in terms of temperature and temperature–pressure dependent hole fraction is discussed and compared with the free volume model. The former is the most universal behavior than the latter in terms of temperature and pressure. We discuss activation energy parameter and transmission coefficient for the species in terms of chain length and end groups such as dimethylether. Scaling relaxation time parameter in the proposed model has similar trend with relaxation time parameter of Adam–Gibbs theory.

Generalized Entropy Theory of Glass Formation in Polymer Melts with Specific Interactions

Chemical structure has been long recognized to greatly influence polymer glass formation, but a general molecular theory that predicts how chemical structure determines the properties of glass-forming polymers has been slow to develop. While the generalized entropy theory (GET) explains the influence of various molecular details on polymer glass formation, the application of the GET has heretofore been limited to the use of the simplest polymer model in which all united atom groups within the monomers of a species interact with a common monomer averaged van der Waals energy. However, energetic heterogeneities are ubiquitous within the monomers of real polymers, and their implications for polymer glass formation remain to be investigated theoretically. This paper uses an extension of the GET to explore the influence of energetic heterogeneities within monomers upon the nature of polymer glass formation. This extension of the GET is achieved by combining the Adam–Gibbs theory relating the structural relaxation time to the configurational entropy with a recent significant extension of the lattice cluster theory for polymer melts with specific interactions, in particular, for melts where three distinct van der Waals interaction energies are required to describe the energetic heterogeneities within monomers. The present paper focuses on establishing general trends for the variation of characteristic properties of glass formation, such as the isobaric fragility parameter mP and the glass transition temperature Tg, with molecular details, such as the specific interactions and chain stiffness. Our computations confirm that the previously used model with monomer averaged interactions correctly captures general trends in the variation of mP and Tg with various molecular parameters. More importantly, adjustment of the energetic heterogeneities within monomers alone are shown to provide an efficient mechanism for tailoring the properties of glass-forming polymers. The variations of polymer properties along iso-fragility and iso-Tg lines are illustrated as important design tools for exhibiting the combined influence of specific interactions and chain stiffness.

Modified Adam–Gibbs models based on free volume concept and their application in the enthalpy relaxation of glassy polystyrene

Vogel–Fulcher–Tammann (VFT) equation based on free volume concept is used extensively to describe the temperature dependence of relaxation time of polymer above the glass transition temperature Tg, but failed in fitting the enthalpy relaxation data across the glass transition region. Under the line of the Adam–Gibbs theory on temperature dependence of cooperative relaxation property, two equations based on the free-volume theory of glass transition, free-volume (FV) and modified free-volume (FVM) equations, were proposed and applied to fit the enthalpy relaxation data of PS. Compared with the VFT equation, the fitting quality of FV equation is improved greatly and similar to that of the extensively used Tools–Narayanaswamy–Moynihan (TNM) and Adam–Gibbs (AG) models. The fitting quality of FVM equation is improved further and better than that of TNM and AG models, as well as Macedo model with the same number of fitting parameters, especially on the prediction of the limit fictive temperatures.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion.

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

Interfacial Dynamic Length Scales in the Glass Transition of a Model Freestanding Polymer Film and Their Connection to Cooperative Motion

Nanoscale confinement alters the dynamics of glass-forming liquids in films of order 100 nm in thickness. A common hypothesis for the origin of this long range posits that interfacial dynamics propagate into the film via cooperatively rearranging regions (CRRs). However, the precise nature of the dynamic interface remains uncertain, and its identification with CRRs has yet to be firmly established. Based on results from coarse-grained molecular dynamics simulations of a freestanding polymer film, here we show that an apparent qualitative discrepancy between computational and several experimental measures of the interfacial dynamic length scale results from a difference in definition and not from a difference in underlying behavior of experimental and simulated systems. We then show that the computational definition exhibits a direct correspondence with the expected behavior of CRRs as predicted by the Adam–Gibbs theory, and we suggest that it should be possible to extract this length scale from experimental measurements.

Thermodynamic Study of Simple Molecular Glasses: Universal Features in Their Heat Capacity and the Size of the Cooperatively Rearranging Regions

We have obtained some universal thermodynamic properties on glass transitions of molecular liquids. The heat capacity C(p) of glassy propene, which was vitrified by using a vapor-deposition technique, was measured with a newly developed adiabatic calorimeter. Propene has the lowest glass transition temperature (T(g)=56 K), the largest C(p) jump at T(g) (C(p)(lq)/C(p)(gl)~2.5), and the lowest residual entropy (S(res)~Rln2) compared with glass-forming molecules measured before. We have analyzed the present data with other hydrocarbon molecules vitrified by liquid quenching and obtained the following results: (1) The excess heat capacities are scaled well by using a Kauzmann temperature T(K), (2) The size of the cooperative rearrangement region (CRR) frozen at T(g) increases with decreasing the temperature difference between T(g) and T(K) (Kauzmann temperature), and (3) The simpler the molecule is, the larger the frozen CRR becomes. These are all supporting the validity of the Adam-Gibbs theory.

Common Origin of Dynamics Heterogeneity and Cooperatively Rearranging Region in Polymer Melts

If some supercooled liquids are cooled further, they freeze into a specific medium state with both properties of liquid-like structure and solid-like hardness, so-called “glass.” The fact that dynamics freeze drastically when there is only a slight change in static structure remains a mystery in solid-state physics. Recently, it has been reported that when a particular kind of glass-forming liquids with two order parameters are cooled rapidly, local crystalline orders with extremely slow dynamics start to emerge when approaching glass transition temperature. This result suggests a concept of “frustration to crystallization” as a physical picture of glass transition. On the other hand, although Adam–Gibbs theory has predicted the existence of cooperatively rearranging region (CRR) as the origin of extreme slowdown in dynamics, CRR is still no more than a hypothetical subsistent to explain the slow dynamics of glass transition. In this study, we found for the first time, local-bond orientational orders, “LBOOs,” which characterize glass transition in polymer melts, one of the most representative glass-forming liquids. Furthermore, we confirmed that monomers composed of LBOOs were concertedly vibrating and indicated that LBOOs can be identified as CRR. In other words, we were able to prove that the LBOOs we have discovered were consistent with both the physical picture of frustration to crystallization and Adam–Gibbs’ theory.

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.

The emergence of cooperative dynamics in polymers as an effect of conformational restrictions: The case of crystallization and an example on heterogeneous confinement

Cooperativity in the segmental dynamics of polymers, as enhanced by crystal confinement, shows up even above the dynamic glass transition. Some related physical aspects are outlined and, on the basis of a statistical mechanical model, these effects are quantitatively analysed. In this model, which extends aspects of the Adam–Gibbs theory for glass formers, the frequency width of the conformational relaxation is intrinsically connected to a finite free energy barrier hindering readjustment. A possible thermodynamic criterion for crystallization arrest then follows from the analysis of dielectric relaxation data available in the literature. Low-temperature cold-crystallized poly(ethylene terephthalate) is then considered in particular; it is found from mechanical and dielectric relaxation analyses that a cooperativity increase accompanies both recrystallization and cooling towards the glass transition temperature. The application of the model to the case of poly(dimethyl siloxane) confined in nanoporous glasses is also illustrated as an example.

Modifying Fragility and Collective Motion in Polymer Melts with Nanoparticles

We investigate the impact of nanoparticles (NP) on the fragility and cooperative stringlike motion in a model glass-forming polymer melt by molecular dynamics simulation. The NP cause significant changes to both the fragility and the average length of stringlike motion, where the effect depends on the NP-polymer interaction and NP concentration. We interpret these changes via the Adam-Gibbs (AG) theory, assuming the strings can be directly identified with the abstract "cooperatively rearranging regions" of AG. Our findings indicate that fragility is primarily a measure of the temperature dependence of the cooperativity of molecular motion.

Temperature dependence of intermediate-range orders in the viscosity-temperature relationship of supercooled liquids and glasses

The viscosity-temperature relationship obtained by us for several glasses over a wide temperature range was analyzed by extending the Adam-Gibbs theory to the range below the glass transition temperature (T(g)). The entropy change of the intermediate-range orders (IROs) is discussed on the basis of the theory developed by Prigogine. It is estimated that the time dependence of the vibrational entropy of a glass shows a constant decrease with a smallest change, while that of its configurational entropy is 0, keeping the constant fictive temperature and the isostructural state. The result predicts the decrease of the volume of a glass at the constant time-rate through spontaneous aging at the constant temperature. We also show that the glass transition is a phase transition from an equilibrium Vogel-Fulcher-Tamman state to a nonequilibrium and (meta-)stable Arrhenius state through fluctuations at T(g), and a microscopic feature of the glass transition is the self-organization of the IROs. These findings are extremely useful in analyzing glass and nanomaterial productions because the size of the IROs in the glass state is a few nanometers.

Dynamical heterogeneity in binary mixtures of low-molecular-weight glass formers

Homogeneous diethyl phthalate/phenylphthalein-dimethylether (DEP/PDE) mixtures have been investigated by means of broadband dielectric spectroscopy. Contrarily to the widespread view that homogenous binary mixtures should give rise to a single glass transition, the mixture displays two dynamics giving rise to two glass transitions. Such a finding can be rationalized invoking the self-concentration concept that relies on the localized nature of the glass transition phenomenon. In such a way, the analogy with miscible polymer blends, for which this concept has been introduced, is highlighted. A model based on the combination of the Adam-Gibbs (AG) theory of the glass transition and the self-concentration concept resulted to be fully predictive once the only unknown variable, namely, the glass-former specific parameter (alpha) connecting the characteristic length for the glass transition to the configurational entropy, is extracted applying the model itself to DEP/toluene and DEP/PDE solutions highly concentrated, respectively, in DEP and PDE. The alpha parameter obtained in such a way allows the precise determination of the most probable relaxation time even for those DEP/PDE mixtures displaying a strong overlap of the dielectric response. The model incorporating the self-concentration concept to the AG theory also provides the characteristic length scale for the glass transition for both DEP and PDE. Such a length scale was found to be on the order of 1-2 nm. This is comparable to that obtained for other glass formers.

Evidence of α fluctuations in myoglobin's denaturation in the high temperature region: Average relaxation time from an Adam–Gibbs perspective

In this work, we derive an analytical expression for the relaxation time τ as a function of temperature T for myoglobin protein (Mb, PDB:1MBN) in the high temperature limit ( T > T g = 200 K). The method is based on a modified version of the Adam–Gibbs theory (AG theory) for the glass transition in supercooled liquids and an implementation of differential geometry techniques. This modified version of the AG theory takes into account that the entropic component in protein's denaturation has two major sources: a configurational contribution Δ S c due to the unfolding of the highly ordered native state N and a hydration contribution Δ S hyd arising from the exposure of non-polar residues to direct contact with solvent polar molecules. Our results show that the configurational contribution Δ S c is temperature-independent and one order of magnitude smaller than its hydration counterpart Δ S hyd in the temperature range considered. The profile obtained for log τ( T) from T = 200 K to T = 300 K exhibits a non-Arrhenius behavior characteristic of α relaxation mechanisms in hydrated proteins and glassy systems. This result is in agreement with recent dielectric spectroscopy data obtained for hydrated myoglobin, where at least two fast relaxation processes in the high temperature limit have been observed. The connection between the relaxation process calculated here and the experimental results is outlined.