High-pressure specific-heat spectroscopy at the glass transition in o-terphenyl

On the Segmental Dynamics and the Glass Transition Behavior of Poly(2-vinylpyridine) in One- and Two-Dimensional Nanometric Confinement

Geometric nanoconfinement, in one and two dimensions, has a fundamental influence on the segmental dynamics of polymer glass-formers and can be markedly different from that observed in the bulk state. In this work, with the use of dielectric spectroscopy, we have investigated the glass transition behavior of poly(2-vinylpyridine) (P2VP) confined within alumina nanopores and prepared as a thin film supported on a silicon substrate. P2VP is known to exhibit strong, attractive interactions with confining surfaces due to the ability to form hydrogen bonds. Obtained results show no changes in the temperature evolution of the α-relaxation time in nanopores down to 20 nm size and 24 nm thin film. There is also no evidence of an out-of-equilibrium behavior observed for other glass-forming systems confined at the nanoscale. Nevertheless, in both cases, the confinement effect is seen as a substantial broadening of the α-relaxation time distribution. We discussed the results in terms of the importance of the interfacial energy between the polymer and various substrates, the sensitivity of the glass-transition temperature to density fluctuations, and the density scaling concept.

Temperature and pressure dependence of the alpha relaxation in ortho-terphenyl

Molecular dynamics (MD) simulations of ortho-terphenyl using an all-atom model with the optimized potentials for liquid simulations (OPLS) force field were performed both in the high temperature Arrhenian region and at lower temperatures that include the onset of the super-Arrhenian region. From the MD simulations, the internal energy of both the equilibrium liquid and crystal was determined from 300 K to 600 K and at pressures from 0.1 MPa to 1 GPa. The translational and rotational diffusivities were also determined at these temperatures and pressures for the equilibrium liquid. It is shown that within a small offset, the excess internal energy Ū_x from the MD simulations is consistent with the experimentally determined excess internal energy reported earlier [Caruthers and Medvedev, Phys. Rev. Mater. 2, 055604, (2018)]. The MD mobility data {including extremely long-time 1 atm simulations from the study by Eastwood et al. [J. Phys. Chem. B 117, 12898, (2013)]} were combined with experimental data to form a unified dataset, where it was shown that in both the high temperature Arrhenian region and the lower temperature super-Arrhenian region, the mobility is a linear function of 1/Ū_x(T,p), albeit with different proportionality constants. The transition between the Arrhenian and super-Arrhenian regions is relatively sharp at a critical internal energy Ū_x ^α. The 1/Ū_x(T,p) model is able to describe the mobility data over nearly 16 orders-of-magnitude. Other excess thermodynamic properties such as excess enthalpy and excess entropy (i.e., the Adam-Gibbs model) are unable to unify the pressure dependence of the mobility.

Connecting 1D and 2D Confined Polymer Dynamics to Its Bulk Behavior via Density Scaling

Under confinement, the properties of polymers can be much different from the bulk. Because of the potential applications in technology and hope to reveal fundamental problems related to the glass-transition, it is important to realize whether the nanoscale and macroscopic behavior of polymer glass-formers are related to each other in any simple way. In this work, we have addressed this issue by studying the segmental dynamics of poly(4-chlorostyrene) (P4ClS) in the bulk and upon geometrical confinement at the nanoscale level, in either one- (thin films on Al substrate) or two- (within alumina nanopores) dimensions. The results demonstrate that the segmental relaxation time, irrespective of the confinement size or its dimensionality, can be scaled onto a single curve when plotted versus ρ^γ/T with the same single scaling exponent, γ = 3.1, obtained via measurements at high pressures in bulk. The implication is that the macro- and nanoscale confined polymer dynamics are intrinsically connected and governed by the same underlying rules.

Communication: High pressure specific heat spectroscopy reveals simple relaxation behavior of glass forming molecular liquid

The frequency dependent specific heat has been measured under pressure for the molecular glass forming liquid 5-polyphenyl-4-ether in the viscous regime close to the glass transition. The temperature and pressure dependences of the characteristic time scale associated with the specific heat is compared to the equivalent time scale from dielectric spectroscopy performed under identical conditions. It is shown that the ratio between the two time scales is independent of both temperature and pressure. This observation is non-trivial and demonstrates the existence of specially simple molecular liquids in which different physical relaxation processes are both as function of temperature and pressure/density governed by the same underlying "inner clock." Furthermore, the results are discussed in terms of the recent conjecture that van der Waals liquids, like the measured liquid, comply to the isomorph theory.

Affinity and its derivatives in the glass transition process

The thermodynamic treatment of the glass transition remains an issue of intense debate. When associated with the formalism of non-equilibrium thermodynamics, the lattice-hole theory of liquids can provide new insight in this direction, as has been shown by Schmelzer and Gutzow [J. Chem. Phys. 125, 184511 (2006)], by Möller et al. [J. Chem. Phys. 125, 094505 (2006)], and more recently by Tropin et al. [J. Non-Cryst. Solids 357, 1291 (2011); ibid. 357, 1303 (2011)]. Here, we employ a similar approach. We include pressure as an additional variable, in order to account for the freezing-in of structural degrees of freedom upon pressure increase. Second, we demonstrate that important terms concerning first order derivatives of the affinity-driving-force with respect to temperature and pressure have been previously neglected. We show that these are of crucial importance in the approach. Macroscopic non-equilibrium thermodynamics is used to enlighten these contributions in the derivation of C(p),κ(T), and α(p). The coefficients are calculated as a function of pressure and temperature following different theoretical protocols, revealing classical aspects of vitrification and structural recovery processes. Finally, we demonstrate that a simple minimalist model such as the lattice-hole theory of liquids, when being associated with rigorous use of macroscopic non-equilibrium thermodynamics, is able to account for the primary features of the glass transition phenomenology. Notwithstanding its simplicity and its limits, this approach can be used as a very pedagogical tool to provide a physical understanding on the underlying thermodynamics which governs the glass transition process.

The role of the isothermal bulk modulus in the molecular dynamics of super-cooled liquids

Elastic models imply that the energy expended for a flow event in ultra-viscous matter coincides with the elastic work required for deforming and re-arranging the environment of the moving entity. This is quite promising for explaining the strong non-Arrhenius behavior of dynamic quantities of fragile super-cooled liquids. We argue that the activation volume obtained from dielectric relaxation and light-scattering experiments for super-cooled liquids should scale with the Gibbs free energy of activation, with a proportionality constant determined by the isothermal bulk modulus and its pressure derivative, as described by an earlier thermodynamic elastic model. For certain super-cooled liquids the bulk compression transpiring in the local environment, as governed by the isothermal bulk modulus, play a significant role in the reorientational dynamics, with far-field density fluctuations and volume changes avoided by shear deformation.

Bond Strength-Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids

The Vogel-Fulcher-Tammann (VFT) equation has been used extensively in the analysis of the experimental data of temperature dependence of the viscosity or of the relaxation time in various types of supercooled liquids including metallic glass forming materials. In this article, it is shown that our model of viscosity, the Bond Strength-Coordination Number Fluctuation (BSCNF) model, can be used as an alternative model for the VFT equation. Using the BSCNF model, it was found that when the normalized bond strength and coordination number fluctuations of the structural units are equal, the viscosity behaviors described by both become identical. From this finding, an analytical expression that connects the parameters of the BSCNF model to the ideal glass transition temperature T₀ of the VFT equation is obtained. The physical picture of the Kohlrausch-Williams-Watts relaxation function in the glass forming liquids is also discussed in terms of the cooperativity of the structural units that form the melt. An example of the application of the model is shown for metallic glass forming liquids.

Idealized glass transitions under pressure: dynamics versus thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.

Origin of the dynamic transition upon pressurization of crystalline proteins

We study the role of hydration water in the dynamic transition of low-hydrated proteins upon pressurization found recently (Meinhold, L.; Smith, J. C. Phys. Rev. E 2005, 72, 061908). Clustering and percolation of water in the hydration shells of protein molecules in crystalline Staphylococcal nuclease are analyzed at various pressures. The number of water molecules in the hydration shell increases and the hydrogen-bonded network of hydration water spans with increasing pressure. The dynamic transition of protein occurs when the spanning water network exists with the probability of about 50% and hydration water shows large density fluctuations. Formation of a spanning water network upon pressurization promotes protein dynamics as in the case of the dynamic transition with increasing hydration. Properties of hydration water in various thermodynamic states and their influence on biological function are discussed.

Pressure effects on the α and α′ relaxations in polymethylphenylsiloxane

In some polymers, in addition to the usual structural alpha relaxation, a slower alpha' relaxation is observed with a non-Arrhenius temperature dependence. In order to understand better the molecular origin of this alpha' relaxation in poly(methylphenylsiloxane) (PMPS) we have studied, for the first time, the pressure dependence of its relaxation time, together with the usual temperature dependence, by means of dynamic light scattering (DLS). For the same material the alpha relaxation was also studied by means of DLS and dielectric spectroscopy (DS) in broad temperature and pressure ranges. We find that the temperature dependence of both alpha and alpha' relaxation times, at all pressures studied, can be described by a double Vogel-Fulcher-Tammann (VFT) law. The pressure dependence of the characteristic temperatures Tg (glass transition temperature) and T0 (Vogel temperature) as well as the activation volumes for both alpha and alpha' processes are very similar, indicating, that both relaxation processes originate from similar local molecular dynamics. Additionally, for both alpha and alpha' relaxations the combined temperature and pressure dependences of the relaxation times can be described using a parameter Gamma=rhon/T with the same value of the exponent n.

A new interpretation of dielectric data in molecular glass formers

Literature dielectric data of glycerol, propylene carbonate, and ortho-terphenyl show that the measured dielectric relaxation is a decade faster than the Debye expectation but still a decade slower than the breakdown of the shear modulus. From a comparison of time scales, the dielectric relaxation seems to be due to a process which relaxes not only the molecular orientation but also the entropy, the short range order, and the density. On the basis of this finding, we propose an alternative to the Gemant-DiMarzio-Bishop extension of the Debye picture.

Cluster kinetics of pressure-induced glass formation

A prior correlation model for glass formation based on cluster-size distribution kinetics is here extended to account for pressure effects as well as temperature effects. The model describes how rapidly cooling or compressing a liquid or colloid leads to structural arrest and a consequent sharp rise in viscosity or dielectric relaxation time. In addition to activation energies, we include activation volumes in the rate coefficients for monomer-cluster addition and dissociation and cluster aggregation and breakage. The approach leads to scaled pressure correlations and plots for viscosity that reveal strong and fragile glass behavior, and agree with experimental data. A simple relationship among viscosity, attractive interparticle energy, and particle volume fraction displays how hard spheres with attractive forces can vitrify at small particle densities.

Pressure dependence of the glass temperature in supercooled liquids

The description of the pressure evolution of the glass temperature Tg(p) based on experimental data for diethyl phtalate is discussed. First, parameterizations of Tg(P) experimental data applied are briefly given. Then a novel relation based on the modified Simon-Glatzel equation is proposed. Its applications may result in the appearance of the asymptotic temperature (theta) and the asymptotic pressure (pi) previously postulated [E. Donth,, Springer Series in Material Sci. II (Springer, Berlin, 1998), Vol. 48, pp. 6, 375]. The asymptotic pressure is hidden in the negative pressure domain. Such asymptotic behavior was absent for parameterizations of Tg(p) data in glassy liquids applied up to now.

Molecular dynamics study of the thermal and the density effects on the local and the large-scale motion of polymer melts: scaling properties and dielectric relaxation

Results from a molecular dynamics simulation of a melt of unentangled polymers are presented. The translational motion, the large-scale and the local reorientation processes of the chains, as well as their relations with the so-called "normal" and "segmental" dielectric relaxation modes are thoroughly investigated in wide temperature and pressure ranges. The thermodynamic states are well fitted by the phenomenological Tait equation of state. A global time-temperature-pressure superposition principle of both the translational and the rotational dynamics is evidenced. The scaling is more robust than the usual Rouse model. The latter provides insight but accurate comparison with the simulation calls for modifications to account for both the local chain stiffness and the nonexponential relaxation. The study addresses the issue whether the temperature or the density is a dominant control parameter of the dynamics or the two quantities give rise to comparable effects. By examining the ratio /alphatau//alphaP between the isochronic and isobaric expansivities, one finds that the temperature is dominant when the dynamics is fast. If the relaxation slows down, the fluctuations of the free volume increase their role and become comparable to those of the thermal energy. Detectable cross-correlation between the "normal-mode" and the "segmental" dielectric relaxations is found and contrasted with the usual assumption of independent modes.

Viscosity at the dynamic crossover in o-terphenyl and salol under high pressure

The viscosities of two prototypical glass formers, o-terphenyl and phenyl salicylate (salol), are shown to exhibit a change in their temperature and pressure dependences at a constant value of the viscosity. This is the first evidence of a dynamic crossover in the viscosity induced by pressure. The characteristic value associated with the change in dynamics is material dependent, but independent of temperature and pressure. These results are in accord with the previous finding, for other glass formers, that the dielectric relaxation time assumes a density-independent value at the dynamic crossover.

Adam–Gibbs model for the supercooled dynamics in the ortho-terphenyl ortho-phenylphenol mixture

Dielectric measurements of the alpha-relaxation time were carried out on a mixture of ortho-terphenyl (OTP) with ortho-phenylphenol, over a range of temperatures at two pressures, 0.1 and 28.8 MPa. These are the same conditions for which heat capacity, thermal expansivity, and compressibility measurements were reported by Takahara et al. [S. Takahara, M. Ishikawa, O. Yamamuro, and T. Matsuo, J. Phys. Chem. B 103, 3288 (1999)] for the same mixture. From the combined dynamic and thermodynamic data, we determine that density and temperature govern to an equivalent degree the variation of the relaxation times with temperature. Over the measured range, the dependence of the relaxation times on configurational entropy is in accord with the Adam-Gibbs model, and this dependence is invariant to pressure. Consistent with the implied connection between relaxation and thermodynamic properties, the kinetic and thermodynamic fragilities are found to have the same pressure independence. In comparing the relaxation properties of the mixture to those of neat OTP, density effects are stronger in the former, perhaps suggestive of less efficient packing.

Role of the density in the crossover region of o-terphenyl and poly(vinyl acetate)

The coupling between the reorientation of molecular probes and the density in one low-molar mass glass former [ o -terphenyl (OTP)] and one polymer [poly(vinyl acetate) (PVAc)] is studied in the Goldstein's crossover region where the structural (alpha) and the secondary (beta) relaxations bifurcate. The coupling is found to be strong in OTP and virtually absent in PVAc. The probes sense both the alpha and beta relaxations, and locate their splitting accurately. It is concluded that the density affects the relaxation occurring in the crossover region of OTP but not of PVAc at subnanometer length scales. The findings are compared with recent assessments of the role of the molecular packing close and above the glass transition temperature T(g).

Frequency dependence and equilibration of the specific heat of glass-forming liquids

We have performed molecular dynamics simulations on a glass-forming liquid consisting of a three-dimensional binary mixture of soft spheres. We show that a peak in the specific heat versus temperature can occur because a glassy system that shows no signs of aging progresses so slowly through the energy landscape that the minimum sampling time needed to obtain accurate thermodynamic averages exceeds the observation time. We develop a systematic technique to determine the equilibrium value of the specific heat and the minimum sampling time. Below the temperature of the specific heat peak, the minimum sampling time is orders of magnitude longer than the alpha relaxation time. We find that an equilibrium system that is not undergoing structural relaxation or aging has a frequency dependent specific heat that rises as the frequency decreases. The rise occurs at frequencies corresponding to periods that are long enough for the system to sample statistically independent energies. When the period is comparable to the minimum sampling time, the frequency dependent specific heat reaches a plateau. As a result, the specific heat has a frequency dependence at frequencies orders of magnitude lower than is implied by the inverse alpha relaxation time.

Temperature and pressure study of Brillouin transverse modes in the organic glass-forming liquid orthoterphenyl

Transverse Brillouin spectra of orthoterphenyl are measured in the (250-305 K; 0.1-100 MPa) temperature-pressure range, which corresponds to the supercooled phase of this organic glass former. We show that the analysis of these spectra combined with an extrapolation of the reorientation times under pressure leads to an estimate of the static shear viscosity in a pressure range whose validity extends beyond the range of the Brillouin measurements. The relative contributions of temperature and of density to the change of this reorientation time measured along an isobar are extracted from our results in a large temperature range extending from the liquid to the low temperature supercooled state. They appear to be always of the same order of magnitude. It is also shown that in the range of the experiment, the orientational time is depending on a unique parameter built on temperature and density.

Correlation between nonexponential relaxation and non-Arrhenius behavior under conditions of high compression

Photon correlation spectroscopy was used to investigate the behavior of the dynamical properties of 1,1'-di(4-methoxy-5-methyl-phenyl)cyclohexane (BMMPC) at elevated pressures. The fragility of BMMPC measured by the steepness index m(T) is decreasing and the nonexponentiality parameter beta(KWW) is increasing with increasing pressure. This result strongly suggests that the phenomenological correlation between the steepness index and nonexponentionality is also preserved under high compression. The pressure dependence of the structural relaxation times is well characterized by a simple activation volume form. The activation volume continuously increases with decreasing temperature, which is probably due to the increase of cooperativity of the structural relaxation process. Moreover, we found that the glass-transition temperature exhibits a significant dependence on pressure.

Temperature and pressure scaling of the alpha relaxation process in fragile glass formers: A dynamic light scattering study

The dynamics of two fragile glass forming liquids was studied as a function of temperature and pressure using dynamic light scattering. On the basis of measured data we evaluated the pressure and temperature scaling of the alpha relaxation. All the isotherms can be superimposed and form a master curve when the reduced relaxation times are plotted versus reduced pressure. The Kohlrausch-Williams-Watts stretching parameter beta(KWW) is increasing with increasing temperature and decreasing pressure and plotted versus log<tau(KWW)> follows a master curve at all temperatures and pressures studied.

Influence of temperature and pressure on dielectric relaxation in a supercooled epoxy resin

Isothermal and isobaric dielectric measurements of a supercooled epoxy resin have been compared. A simple scaling relates isobaric and isothermal spectra corresponding to the same frequency of the main loss peak. Thus, the main and secondary processes retain a relative weight that is the same under isothermal and isobaric conditions. It is inferred that both pressure and temperature, equivalently, are able to take effect on the relaxation processes, without changing the relaxation mechanism itself. Careful analysis of the structural relaxation time behavior revealed that the traditional free volume equation, where only the macroscopic volume controls the pressure evolution of free volume, is not a suitable description of the data, as well as a Vogel-Fulcher (VF) type pressure dependent function. Based on a derivative method, a different function for describing the bidimensional surface tau(T,P) has been proposed, which accounts for the observed behavior through a nonlinear correction of the critical temperature T0 in the VF law. The function we propose predicts pressure dependencies of the glass transition temperature and fragility which are appealing in view of a comparison with experimental results in this and many other systems. Interesting hints for interpreting the phenomenological results can be obtained within the Adam-Gibbs theory.

Linear response theory for thermodynamic properties

A fluctuation-dissipation theorem, connecting all thermodynamic response functions to equilibrium fluctuations in the microcanonical ensemble, is derived from classical mechanics. This particular problem is not included in the usual linear response scheme, since the relevant perturbations cannot be stated as additional terms in the Hamiltonian. In experiments where the only control parameter is the heat flow, dissipation is present in terms of an entropy flow from the system to the surroundings. As an example, the full frequency-dependent thermodynamic response matrix is extracted from simulations of a supercooled binary Lennard-Jones fluid. This fluid shows rather high relaxation strength of all response functions, except of the adiabatic compressibility. The low frequency limit of all thermodynamic susceptibilities increases as temperature is decreased along an isocore.