Molecular-dynamics study of supercooled ortho-terphenyl

Dynamic heterogeneities in a supercooled diatomic molecular system

Dynamic heterogeneities in a supercooled system of diatomic molecules with an associated dipole moment have been investigated. To this end, three-time correlation functions have been evaluated. Correlations between molecular displacements performed during consecutive time intervals are apparent at low temperatures in the beta -relaxation regime, whereas they tend to disappear during the alpha -relaxation regime. These correlations maximize when the deviation from Gaussian dynamics takes a maximum, and they reveal the existence of different dynamic domains. Directionality of translational motions has also been studied. At low temperatures, and in the beta -relaxation zone, the molecular vector displacement in a given time interval has an important component in the opposite direction of the vector displacement corresponding to the initial time interval. The amplitudes associated with this quasi-oscillatory behavior become larger as the system is cooled. Dynamic heterogeneities in reorientation have been observed in the beta -relaxation regime, and it has been obtained that molecules that perform faster translational motions experience faster reorientational motions too. This effect increases as temperature decreases.

Computational probes of molecular motion in the Lewis-Wahnström model for ortho-terphenyl

We use molecular dynamics simulations to investigate translational and rotational diffusion in a rigid three-site model of the fragile glass former ortho-terphenyl, at 260 K< or =T< or =346 K and ambient pressure. An Einstein formulation of rotational motion is presented, which supplements the commonly used Debye model. The latter is shown to break down at supercooled temperatures as the mechanism of molecular reorientation changes from small random steps to large infrequent orientational jumps. We find that the model system exhibits non-Gaussian behavior in translational and rotational motion, which strengthens upon supercooling. Examination of particle mobility reveals spatially heterogeneous dynamics in translation and rotation, with a strong spatial correlation between translationally and rotationally mobile particles. Application of the Einstein formalism to the analysis of translation-rotation decoupling results in a trend opposite to that seen in conventional approaches based on the Debye formalism, namely, an enhancement in the effective rate of rotational motion relative to translation upon supercooling.

A comparative molecular simulation study of the glass former ortho-terphenyl in bulk and freestanding films

We performed molecular dynamics simulations of the low-molecular weight organic glass former ortho-terphenyl in bulk and freestanding films. The main motivation is to provide molecular insight into the confinement effect without explicit interfaces. Based on earlier models of ortho-terphenyl we developed an atomistic model for bulk simulations. The model reproduces literature data both from simulations and experiments starting from specific volume and diffusivity to mean square displacement and radial distribution functions. After characterizing the bulk model we form freestanding films by the elongation and expansion method. These films give us the opportunity to study the dynamical heterogeneity near the glass transition through in-plane mobility and reorientation dynamics. We finally compare the model in bulk and under confinement. We found qualitatively a lower glass transition temperature for the freestanding film compared to the bulk.

Nonequilibrium thermodynamics of glasses

We consider the nonequilibrium thermodynamics of glasses from various perspectives. For the commonly used equilibriumlike approach based on Gibbs' fundamental form with an additional pair of conjugate variables, we discuss possible choices of the independent out-of-equilibrium variable and we illustrate some implications by concrete results for a well-known exactly solvable lattice model. The choice of variables is further illuminated from the complementary atomistic perspective offered by the inherent-structure formalism. A general formalism of nonequilibrium thermodynamics is employed (i) to derive the standard equilibriumlike approach, (ii) to formulate two self-contained levels to describe glassy dynamics and thermodynamics, and (iii) to offer guidance for future simulations of glasses. The thermodynamic approach suggests to introduce four-point correlation functions associated with structural rearrangements after imposed deformations, which might offer a possibility to detect a growing length scale at the glass transition without employing any dynamic information.

Molecular Dynamics Study of Translational and Rotational Diffusion in Liquid Ortho-terphenyl

NVT molecular dynamics simulations were performed on liquid o-terphenyl as a function of temperature in the range 320-480 K. Computed translational diffusion coefficients displayed the non-Arrhenius behavior expected of a fragile glass-forming liquid and were in good, semiquantitative agreement with experimental results. Rotational correlation functions calculated for various vectors within the molecule exhibited a very short time (0-1 ps) initial decay, followed by a reversal, which corresponds to free reorientation within the "solvent" cage prior to collision with a wall. Rotational correlation times of three orthogonal vectors fixed on the central benzene were close to equal at all temperatures, indicating nearly isotropic overall molecular reorientation. The average correlation times exhibited a non-Arrhenius temperature dependence and were in very good agreement with experimental values derived from 2D and 1H NMR relaxation times. Correlation times of vectors located on the lateral phenyl rings were used to calculate the "spinning" internal rotation diffusion coefficients, which were approximately twice as great as the overall rotational diffusion constants, indicating rapid internal rotation of the phenyl side groups over wide ranges of angle in the liquid.

Analogy of the slow dynamics between the supercooled liquid and supercooled plastic crystal states of difluorotetrachloroethane

Slow dynamics of difluorotetrachloroethane in both supercooled plastic crystal and supercooled liquid states have been investigated with molecular dynamics simulations. The temperature and wave-vector dependence of collective dynamics in both states are probed using coherent dynamical scattering functions S (Q,t). Our results confirm the strong analogy between molecular liquids and plastic crystals for which alpha-relaxation times and nonergodicity parameters are controlled by the nontrivial static correlations S (Q), as predicted by the mode coupling theory.

Effect of chemical structure on the isobaric and isochoric fragility in polychlorinated biphenyls

Pressure-volume-temperature data, along with dielectric relaxation measurements, are reported for a series of polychlorinated biphenyls (PCB), differing in the number of chlorine atoms on their phenyl rings. Analysis of the results reveals that with increasing chlorine content, the relaxation times of the PCB become governed to a greater degree by density rho relative to the effect of temperature T. This result is consistent with the respective magnitudes of the scaling exponent gamma yielding superpositioning of the relaxation times measured at various temperatures and pressures, when plotted versus rho(gamma)/T. While at constant (atmospheric) pressure, fragilities for the various PCB are equivalent, the fragility at constant volume varies inversely with chlorine content. Evidently, the presence of bulkier chlorine atoms on the phenyl rings magnifies the effect which the density has on the relaxation dynamics.

Energy landscapes for cooperative processes: nearly ideal glass transitions, liquid-liquid transitions and folding transitions

We describe basic phenomenology in the physics of supercooling liquids at constant volume (most simulations), and at constant pressure (most laboratory experiments) before focusing attention on the exceptional cases that exhibit liquid-liquid phase transitions on constant-pressure cooling. We give evidence for point defects in glasses and liquids near T(g). Models based on defects predict transitions with density gaps in constant-pressure systems. We describe the energy landscape representation of such systems. Water, in these terms, is post-critical, and its nearly ideal glass formation can be related to nucleation-free protein 'funnel-folding'. For nucleated folding of proteins, a pseudo-gap should be present. Experimental methods of distinguishing between alternative folding scenarios are described.

The Role of Hydrogen Bonding in Supercooled Methanol

The role of hydrogen bonding on the microscopic properties of supercooled methanol has been analyzed by means of molecular dynamics simulations. Thermodynamic, structural, and dynamical properties have been investigated in supercooled methanol. The results have been compared with those of an ideal methanol-like system whose molecules have the same dipole moment as the methanol but lack sites for hydrogen bonding. Upon cooling the methanol samples, translational relaxation times increase more rapidly than reorientational ones. This effect is much more important when hydrogen bonds are suppressed. Suppression of hydrogen bonds also results in lower critical temperatures for diffusion and for several characteristic relaxation time constants. The anisotropy of individual dynamics and the existence of dynamical heterogeneities have also been investigated.

Structural relaxation in supercooled orthoterphenyl

We report molecular-dynamics simulation results performed for a model of molecular liquid orthoterphenyl in supercooled states, which we then compare with both experimental data and mode-coupling-theory (MCT) predictions, aiming at a better understanding of structural relaxation in orthoterphenyl. We pay special attention to the wave number dependence of the collective dynamics. It is shown that the simulation results for the model share many features with experimental data for real system, and that MCT captures the simulation results at the semiquantitative level except for intermediate wave numbers connected to the overall size of the molecule. Theoretical results at the intermediate wave number region are found to be improved by taking into account the spatial correlation of the molecule's geometrical center. This supports the idea that unusual dynamical properties at the intermediate wave numbers, reported previously in simulation studies for the model and discernible in coherent neutron-scattering experimental data, are basically due to the coupling of the rotational motion to the geometrical-center dynamics. However, there still remain qualitative as well as quantitative discrepancies between theoretical prediction and corresponding simulation results at the intermediate wave numbers, which call for further theoretical investigation.

Crossover (or Kovacs) effect in an aging molecular liquid

We study by means of molecular dynamics simulations the aging behavior of a molecular model of ortho-terphenyl. We find evidence of a nonmonotonic evolution of the volume during an isothermal-isobaric equilibration process, a phenomenon known in polymeric systems as the crossover (or Kovacs) effect. We characterize this phenomenology in terms of landscape properties, providing evidence that, far from equilibrium, the system explores regions of the potential energy landscape distinct from the one explored in thermal equilibrium.

Dynamics and configurational entropy in the Lewis-Wahnström model for supercooled orthoterphenyl

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

Dynamics of supercooled water in configuration space

We study the potential energy surface (PES) sampled by a liquid modeled via the widely studied extended simple point charge (SPC/E) model for water. We characterize the curvature of the PES by calculating the instantaneous normal mode (INM) spectrum for a wide range of densities and temperatures. We discuss the information contained in the INM density of states, which requires additional processing to be unambiguously associated with the long-time dynamics. For the SPC/E model, we find that the slowing down of the dynamics in the supercooled region-where the ideal mode coupling theory has been used to describe the dynamics-is controlled by the reduction in the number of directions in configuration space that allow a structural change. We find that the fraction f(dw) of the double-well directions in configuration space determines the value of the diffusion constant D, thereby relating a property of the PES to a macroscopic dynamic quantity; specifically, it appears that square root D is approximately linear in f(dw). Our findings are consistent with the hypothesis that, at the mode coupling crossover temperature, dynamical processes based on the free exploration of configuration space vanish, and processes requiring activation dominate. Hence, the reduction of the number of directions allowing free exploration of configuration space is the mechanism of diffusion implicitly implemented in the ideal mode coupling theory. Additionally, we find a direct relationship between the number of basins sampled by the system and the number of free directions. In this picture, diffusion appears to be related to geometrical properties of the PES, and to be entropic in origin.

Molecular dynamics simulation of the fragile glass former orthoterphenyl: a flexible molecule model. II. Collective dynamics

We present a molecular dynamics study of the collective dynamics of a model for the fragile glass former orthoterphenyl. In this model, introduced by Mossa, Di Leonardo, Ruocco, and Sampoli [Phys. Rev. E 62, 612 (2000)], the intramolecular interaction among the three rigid phenyl rings is described by a set of force constants whose value has been fixed in order to obtain a realistic isolated molecule spectrum. The interaction between different molecules is described by a Lennard Jones site-site potential. We study the behavior of the coherent scattering functions F(t)(q,t), considering the density fluctuations of both molecular and phenyl-ring centers of mass; moreover we directly simulate the neutron scattering spectra taking into account both the contributions due to carbon and hydrogens atoms. We compare our results with the main predictions of the mode-coupling theory and with the available coherent neutron scattering experimental data.

Is there something of mode coupling theory in orientationally disordered crystals?

Molecular dynamics simulations have been performed on the orientationally disordered crystal chloroadamantane. We stress that universal behavior, relatively well described by the mode coupling theory, is shared by systems whose dynamics are almost completely controlled by translations or rotations. This investigation also shows the existence of a second remarkable dynamical crossover at the temperature Tx>Tc, consistent with a previous NMR and molecular dynamics study [F. Affouard et al., Europhys. Lett. 53, 611 (2001)]. This allows us to support clearly the existence of a "landscape-influenced" regime as recently proposed [S. Sastry et al., Nature 393, 554 (1998)].

Dynamics in a supercooled molecular liquid: theory and simulations

We report extensive simulations of liquid supercooled states for a simple three-site molecular model, introduced by Lewis and Wahnström [Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of orthoterphenyl. The large system size and the long simulation length allow us to calculate very precisely (in a large q-vector range) self-correlation and collective correlation functions, providing a clean and simple reference model for theoretical descriptions of molecular liquids in supercooled states. The time and wave-vector dependence of the site-site correlation functions are compared (neglecting the molecular constraints) with detailed ideal mode-coupling theory predictions. Except for the wave-vector region where the dynamics are controlled by the center of mass (around 9 nm(-1)), the theoretical predictions compare very well with the simulation data.

Viscous flow and jump dynamics in molecular supercooled liquids. II. Rotations

The rotational dynamics of a supercooled model liquid of rigid A-B dumbbells interacting via a Lennard-Jones potential is investigated along one single isobar. The time-temperature superposition principle, one key prediction of mode-coupling theory (MCT), was studied for the orientational correlation functions C(l). In agreement with previous studies we found that the scaling of C(l) in a narrow region at long times is better at high-l values. However, on a wider time interval the scaling works fairly better at low-l values. Consistently, we observed the remarkable temperature dependence of the rotational correlation time tau(1) as a power law in T-T(c) over more than three orders of magnitude and the increasing deviations from that law on increasing l (T(c) is the MCT critical temperature). For 0.7<T<2, good agreement with the diffusion model is found. For lower temperatures the agreement becomes poorer, and the results are also only partially accounted for by the jump-rotation model. The angular Van Hove function shows that in this region a meaningful fraction of the sample reorientates by jumps of about 180 degrees. The distribution of the waiting times in the angular sites cuts exponentially at long times. At lower temperatures it decays at short times as t(xi-1), with xi=0.34+/-0.04 at T=0.5, in analogy with the translational case. The breakdown of the Debye-Stokes-Einstein relation is observed at lower temperatures, where the rotational correlation times diverge more weakly than the viscosity.

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode-coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters F(m)(ll('))(q) and the critical amplitudes of the beta relaxation H(m)(ll('))(q) are solved up to a cutoff l(co)=2 without any further approximations. Here l,m are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations that all molecular degrees of freedom vitrify at a single temperature T(c). The theoretical results for the nonergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cutoff on the nonergodicity parameter, we also calculate the nonergodicity parameters for an upper cutoff l(co)=4. In addition, we also propose a method for the calculation of the critical nonergodicity parameter from the liquid side of transition.

Molecular correlations in a supercooled liquid

We present static and dynamic properties of molecular correlation functions S(lmn,l(')m(')n('))(q-->,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode-coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions that can be predicted on the basis of the C(2v) symmetry of the molecule. Analysis of the molecular dynamics results for the static correlators S(lmn,l(')m(')n('))(q-->) reveals that additional relationships between correlators with different signs of n and n(') exist. We prove that for molecules with C(rv) symmetry this unexpected result becomes exact at least for high temperatures.

Molecular dynamics simulation of the fragile glass-former orthoterphenyl: A flexible molecule model

We present a realistic model of the fragile glass-former orthoterphenyl and the results of extensive molecular dynamics simulations in which we investigated its basic static and dynamic properties. In this model the internal molecular interactions between the three rigid phenyl rings are described by a set of force constants, including harmonic and anharmonic terms; the interactions among different molecules are described by Lennard-Jones site-site potentials. Self-diffusion properties are discussed in detail together with the temperature and momentum dependencies of the self-intermediate scattering function. The simulation data are compared with existing experimental results and with the main predictions of the mode-coupling theory.

Apparent finite-size effects in the dynamics of supercooled liquids

Molecular dynamics simulations are performed for a supercooled simple liquid with changing the system size from N=108 to 10(4) to examine possible finite-size effects. Although almost no systematic deviation is detected in the static pair correlation functions, it is demonstrated that the structural alpha relaxation in a small system becomes considerably slower than that in larger systems for temperatures below T(c) at which the size of the cooperative particle motions becomes comparable to the unit cell length of the small system. The discrepancy increases with decreasing temperature.

Orientational relaxation in Brownian rotors with frustrated interactions on a square lattice

We present simulation results on the equilibrium relaxation of Brownian planar rotors based on a uniformly frustrated XY model on a square lattice. The rotational relaxation exhibits typical dynamic features of fragile supercooled liquids including the two-step relaxation. We observe a dynamic crossover from the high-temperature regime with Arrhenius behavior to the low-temperature regime with temperature-dependent activation energy. A consistent picture for the observed slow dynamics can be given in terms of the caging effect and thermal activation across potential barriers in the energy landscapes.

Neutron scattering and molecular correlations in a supercooled liquid

We show that the intermediate scattering function S(n)(q,t) for neutron scattering (ns) can be expanded naturally with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the q dependence, and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor S(n)(q) is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic molecules. The comparison between the exact result for S(n)(q) and different approximations that result from a truncation of the series representation demonstrates its good convergence for the given model system. On the other hand it shows explicitly that the coupling between translational and orientational degrees of freedom of each molecule and rotational motion of different molecules cannot be neglected in the supercooled regime. Further we report the existence of a prepeak in the ns static structure factor of the examined fragile glass former, demonstrating that prepeaks can occur even in the most simple molecular liquids. Besides examining the dependence of the prepeak on the scattering length and the temperature we use the expansion of S(n)(q) into molecular correlation functions to point out the intermediate range orientational order as its principle origin.