Reorientational relaxation of a linear probe molecule in a simple glassy liquid

Computer simulations and mode-coupling theory of glass-forming confined hard-sphere fluids

We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated using the full system of matrix-valued integro-differential equations. We investigate several dynamical properties of supercooled liquids including scattering functions, frequency-dependent susceptibilities, and mean-square displacements. Close to the glass transition, we find quantitative agreement between the coherent scattering function predicted from theory and that evaluated from simulations, which enables us to make quantitative statements on caging and relaxation dynamics of the confined hard-sphere fluid.

Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

The generalized Langevin equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All previous studies have focused either on particle-bath systems with time-independent external forces only, or on the simplified case where only the tagged particle is subject to the external time-dependent oscillatory field. Here we extend the GLE and the corresponding FDT for the more general case where both the tagged particle and the bath oscillators respond to an external oscillatory field. This is the example of a charged or polarizable particle immersed in a bath of other particles that are also charged or polarizable, under an external ac electric field. For this Hamiltonian, we find that the ensemble average of the stochastic force is not zero, but proportional to the ac field. The associated FDT reads as 〈F_{P}(t)F_{P}(t^{'})〉=mk_{B}Tν(t-t^{'})+(γe)^{2}E(t)E(t^{'}), where F_{p} is the random force, ν(t-t^{'}) is the friction memory function, and γ is a numerical prefactor.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

Rotational dynamics and aging in a magnetic colloidal glass

We follow here the freezing of the orientational degrees of freedom of strongly interacting magnetic and charged nanoparticles, as the colloidal glass transition is approached. Using a magnetoinduced birefringence technique, we show that the rotational dynamics drastically slows down following a Vogel-Fulcher law. More precisely, this slowing down occurs above a volume fraction threshold phi*, the value of which depends on the range of electrostatic repulsion between nanoparticles. An interpretation in terms of effective spheres, slightly anisotropic, is proposed. The aging of the rotational dynamics of the more concentrated samples is reported on long time scales, with an exponential growth of the rotational characteristic time with the age t(w) of the sample. An attempt of age rescaling at different volume fractions leads us to introduce a phi-dependent "birth age" t(w)0(varphi) , which diverges analytically at the Vogel-Fulcher volume fraction.

Broadband dielectric spectroscopy on benzophenone: alpha relaxation, beta relaxation, and mode coupling theory

We have performed a detailed dielectric investigation of the relaxational dynamics of glass-forming benzophenone. Our measurements cover a broad frequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass temperature well up into the region of the small-viscosity liquid. With respect to the alpha relaxation this material can be characterized as a typical molecular glass former with rather high fragility. A good agreement of the alpha relaxation behavior with the predictions of the mode coupling theory of the glass transition is stated. In addition, at temperatures below and in the vicinity of T(g) we detect a well-pronounced beta relaxation of Johari-Goldstein type, which with increasing temperature develops into an excess wing. We compare our results to literature data from optical Kerr effect and depolarized light scattering experiments, where an excess-wing-like feature was observed in the 1-100 GHz region. We address the question if the Cole-Cole peak, which was invoked to describe the optical Kerr effect data within the framework of the mode coupling theory, has any relation to the canonical beta relaxation detected by dielectric spectroscopy.

Dielectric spectroscopy in benzophenone: the beta relaxation and its relation to the mode-coupling Cole-Cole peak

We report a thorough characterization of the glassy dynamics of benzophenone by broadband dielectric spectroscopy. We detect a well-pronounced beta relaxation peak developing into an excess wing with increasing temperature. A previous analysis of results from Optical-Kerr-effect measurements of this material within the mode-coupling theory revealed a high-frequency Cole-Cole peak. We address the question if this phenomenon also may explain the Johari-Goldstein beta relaxation, a so-far unexplained spectral feature inherent to glass-forming matter, mainly observed in dielectric spectra. Our results demonstrate that according to the present status of theory, both spectral features seem not to be directly related.

Molecular dynamics study of orientational cooperativity in water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time > 50 ns) [D.P. Shelton, Phys. Rev. B 72, 020201(R) (2005)]. Molecular dynamics simulations of extended simple point charge (SPC/E) water show a large vortexlike structure of the dipole field at ambient conditions surviving over [J. Higo, Proc. Natl. Acad. Sci. U.S.A. 98, 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few picoseconds. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations of the SPC/E model in bulk water for temperatures ranging from ambient 300 K down to the deep supercooled region of the phase diagram at 210 K. First, we calculate the dipole autocorrelation function and find that our simulations are well described by a stretched exponential decay, from which we calculate the orientational autocorrelation time t(alpha). Second, we define a second characteristic time, namely, the time required for the randomization of molecular dipole orientation, the self-dipole randomization time t(r), which is an upper limit on t(alpha); we find that t(r) is approximately equal to 5t(alpha). Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time t(box) of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge L(box). We find that the site-dipole randomization time t(box) is approximately equal to 2.5t(alpha) for L(box) approximately equal to 3 A, i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low T.

Dynamic arrest in a liquid of symmetric dumbbells: Reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.

Evidence for the weak steric hindrance scenario in the supercooled-state reorientational dynamics

We use molecular-dynamics computer simulations to study the translational and reorientational dynamics of a glass-forming liquid of dumbbells. For sufficiently elongated molecules the standard strong steric hindrance scenario for the rotational dynamics is found. However, for small elongations we find a different scenario--the weak steric hindrance scenario--caused by a new type of glass transition in which the orientational dynamics of the molecule's axis undergoes a dynamical transition with a continuous increase of the nonergodicity parameter. These results are in agreement with the theoretical predictions by the mode-coupling theory for the glass transition.

Brillouin scattering study of salol: exploring the effects of rotation-translation coupling

Brillouin scattering in liquids composed of optically and mechanically anisotropic molecules is affected by coupling between rotational and translational dynamics. While this effect has been extensively studied in depolarized (VH) scattering where it produces the "Rytov dip," recent theoretical analyses by Pick, Franosch show that it should also produce observable effects in polarized (VV) scattering [Eur. Phys. J. B 31, 217 (2003)]; 31, 229 (2003)]]. To test this theory, we carried out Brillouin scattering studies of the molecular glassformer salol in the temperature range 210-380 K, including VH-backscattering, VH-90 degrees, and VV-90 degrees spectra. The data were analyzed consistently to determine the effects of rotation-translation coupling on both the polarized and depolarized spectra. A previously unanticipated feature predicted by these authors was observed: a narrow negative region in the q -dependent part of the 90 degrees VV spectra, which we designate as the "VV dip." It is an analog of the Rytov dip observed at high temperatures in the 90 degrees VH spectra, which is also accurately described by this theory. Analysis of the 90 degrees VV spectra was carried out both with and without inclusion of translation-rotation coupling in order to determine quantitatively the role this coupling plays.

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.

Effect of composition changes on the structural relaxation of a binary mixture

Within the mode-coupling theory for idealized glass transitions, we study the evolution of structural relaxation in binary mixtures of hard spheres with size ratios delta of the two components varying between 0.5 and 1.0. We find two scenarios for the glassy dynamics. For small size disparity, the mixing yields a slight extension of the glass regime. For larger size disparity, a plasticization effect is obtained, leading to stabilization of the liquid due to mixing. For all delta, a decrease of the elastic moduli at the transition due to mixing is predicted. A stiffening of the glass structure is found as is reflected by the increase of the Debye-Waller factors at the transition points. The critical amplitudes for density fluctuations at small and intermediate wave vectors decrease upon mixing, and thus the universal formulas for the relaxation near the plateau values describe a slowing down of the dynamics upon mixing for the first step of the two-step relaxation scenario. The results explain the qualitative features of mixing effects reported by Williams and van Megen [Phys. Rev. E 64, 041502 (2001)] for dynamical light-scattering measurements on binary mixtures of hard-sphere-like colloids with size ratio delta=0.6.

Mode-coupling theory for structural and conformational dynamics of polymer melts

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.

Idealized glass transitions for a system of dumbbell molecules

The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic structure variables. The theory is applied to calculate the liquid-glass phase diagram and the form factors for the arrested structure of a system of symmetric dumbbells of fused hard spheres. The static structure factors, which enter the equations of motion as input, are calculated as function of the packing fraction phi and the molecule's elongation zeta within the reference-interaction-site-model and Percus-Yevick theories. The critical packing fraction phi(c) for the glass transition is obtained as nonmonotone function of zeta with a maximum near zeta=0.43. A transition line is calculated separating a small-zeta-glass phase with ergodic dipole motion from a large-zeta-glass phase where also the reorientational motion is arrested. The Debye-Waller factors at the transition are found to be somewhat larger for sufficiently elongated systems than those for the simple hard-sphere system, but the wave-number dependence of the glass-form factors is quite similar. The dipole reorientations for zeta> or =0.6 are arrested as strongly as density fluctuations with wave vectors at the position of the first sharp diffraction peak.

Microscopic dynamics of molecular liquids and glasses: role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phases, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior, which ranges from a simple hard sphere fluid to long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra straight phi"lm(q,omega) and chi"lm(q,omega). In the center of mass spectra straight phi"00(q,omega) and chi"00(q,omega) we found, besides a high frequency peak at omega(hf), a peak at omega(op), about one decade below omega(hf) x omega(op) has almost no q dependence and exhibits an "isotope" effect omega(op) proportional to I(-1/2), with I the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of medium range orientational order. It is shown that some of these features also exist for schematic mode coupling models.

Calcium rubidium nitrate: mode-coupling beta scaling without factorization

The fast dynamics of viscous calcium rubidium nitrate is investigated by depolarized light scattering, neutron scattering, and dielectric loss. Fast beta relaxation evolves as in calcium potassium nitrate. The dynamic susceptibilities can be described by the asymptotic scaling law of mode-coupling theory with a shape parameter lambda=0.79; the temperature dependence of the amplitudes extrapolates to T(c) approximately equal 378 K. However, the frequencies of the minima of the three different spectroscopies never coincide, in conflict with the factorization prediction, indicating that the true asymptotic regime is unreachable.

Mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the alpha process, which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The alpha process for molecules with a large elongation is shown to exhibit an anomalously wide crossover interval between the end of the von Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary nonmonotonically as a function of its elongation.

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.

Mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index l=1 and l=2 near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the alpha process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. 65, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.

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.