From Single-Particle to Collective Dynamics in Supercooled Liquids (original) (raw)
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Unique Dynamic Correlation Length in Supercooled Liquids
2010
We present a direct comparison of the number of dynamically correlated molecules in the shear-mechanical and dielectric relaxations of the following seven supercooled organic liquids: triphenylethylene, tetramethyl-tetraphenyl-trisiloxane, polyphenyl ether, perhydrosqualene, polybutadiene, decahydroisoquinoline, and tripropylene glycol. For each liquid we observe that the numbers of dynamically correlated molecules in the shear and in the dielectric relaxation are proportional. We show that this proportionality can be explained by the constancy of the decoupling index of the shear and dielectric relaxation times in conjunction with time-temperature superposition. Moreover the value of this proportionality constant is related to the difference in stretching of the shear and dielectric response functions. The most significant deviations from unity of this constant are found in a liquid with strong hydrogen bonds and in a polymer.
Contribution to Understanding of the Molecular Dynamics in Liquids
The Journal of …, 2007
The dielectric relaxation spectroscopy is used for studying the orientational molecular dynamics in the isotropic (I) and nematic (N) phases of two mesogenic liquids composed of the molecules of similar structure and length, but of an essentially different polarity: n-heptylcyanobiphenyl, C 7 H 15 PhPhCN, 7CB (molecular dipole moment µ ≈ 5D) and 4-(trans-4′-n-hexylcyclohexyl)isothiocyanatobenzene, C 6 H 13 CyHxPhNCS, 6CHBT (µ ≈ 2.5D); advantageously, the temperatures of the I-N phase transition for the two compounds are very close to each other (T NI ) 316.6 ( 0.2 K). It is shown that regardless of the differences in polarity of 7CB and 6CHBT molecules and their abilities in dipolar aggregation, the values and temperature dependences of the relaxation time (corresponding to the rotational diffusion of the molecules around their short axis) are very close to each other, in both the isotropic and nematic phases of the liquids studied. Therefore, the data show that the dielectric relaxation processes occurring in dipolar liquids in the isotropic and nematic states lead through the rotational diffusion of individual molecules and the diffusion seems to be not influenced by the intermolecular interactions.
2011
The nonlinear dielectric susceptibilities χ (1) 3 (ω,T) and χ (3) 3 (ω,T), corresponding respectively to the first-and third-harmonic responses, have been measured in supercooled glycerol close to the glass transition temperature T g. By analyzing the two contributions to the nonlinear response, saturation of the polarization and glassy correlations, we show that the first one is dominant at low frequencies and verify the scaling prediction of Bouchaud and Biroli [Phys. Rev. B 72, 064204 (2005)] in what concerns the second one. Such a detailed investigation allows an accurate determination of the temperature dependence of the average number of correlated molecules N corr (T).
Molecular Correlations in a Supercooled Liquid
1998
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 which can be predicted on the basis of the C_{2v}-symmetry of the molecule. The analysis of the MD--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.
Structural and entropic modes in supercooled liquids: experimental and theoretical investigation
Journal of Physics-condensed Matter, 2003
We studied the relaxation processes of glycerol by a transient grating experiment with polarization selectivity and optical heterodyne detection. The density response of supercooled glycerol, for a wavevector q = 0.63 µm −1 , has been studied in that temperature range (T = 200-340 K), where the rearrangement of the structure (α-relaxation) and thermal diffusion occur on the same timescale. A strong interaction between the two modes is observed, manifesting in a dip in the T dependence of the apparent thermal conductivity and in a flattening of the apparent α-relaxation time upon cooling. A parameter-free thermohydrodynamic model for the long-time response is developed. The model is capable of quantitatively reproducing the data and of explaining the observed phenomenology.
Molecular mode-coupling theory for supercooled liquids: Application to water
Physical Review E, 1999
We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory ͑MCT͒ originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the q-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with ''exact'' results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones. ͓S1063-651X͑99͒06210-8͔
Physical Review E, 1998
A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T c , where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T c agrees with that found earlier for the orientational dynamics within the error bars. In the β-regime of MCT the factorization of space-and time dependence is satisfactorily fulfilled for both types of correlations. The first scaling law of ideal MCT holds in the von Schweidler regime, only, since the validity of the critical law can not be confirmed, due to a strong interference with the microscopic dynamics. In this first scaling regime a consistent description within ideal MCT emerges only, if the next order correction to the asymptotic law is taken into account. This correction is almost negligible for q = q max , the position of the main peak in the static structure factor S(q), but becomes important for q = q min , the position of its first minimum. The second scaling law, i.e. the time-temperature superposition principle, holds reasonably well for the self and collective density correlators and different values for q. The α-relaxation times τ (s) q and τ q follow a power law in (T − T c ) over 2 -3 decades. The corresponding exponent γ is weakly q-dependent and is around 2.55. This value is in agreement with the one predicted by MCT from the value of the von Schweidler exponent but at variance with the corresponding exponent γ ≈ 1.6 obtained for the orientational correlators C (s) 1 (t) and C 1 (t), studied earlier.
Proceedings of the National Academy of Sciences, 2015
Significance Supercooled liquids are believed to exhibit spatially heterogeneous dynamics, where molecular mobility within a given spatial region may differ from that of a neighboring region, potentially by orders of magnitude. If supercooled liquids are ergodic, such that the spatial average of all regions with distinct dynamics equals the time average of a given region, these regions of distinct dynamics must interchange over time. With an appropriate probe, similar in size and mobility to the host, single-molecule measurements can provide direct access to these spatial and temporal variations. Here, such a probe is used, revealing how relaxation dynamics are distributed in time and space and directly demonstrating ergodicity of a prototypical glass former down to the glass transition temperature.
Qualitatively different collective and single-particle dynamics in a supercooled liquid
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
The equations of fluctuating nonlinear hydrodynamics for a two component mixture are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. Using these nonlinear equations we construct the basic equations of the mode coupling theory (MCT) and consequent ergodic-nonergodic (ENE) transition in a binary mixture. The model is also analyzed in the one component limit of the mixture to study the dynamics of a tagged particle in the sea of identical particles. According to the existing MCT, dynamics of the single-particle correlation is slaved to that of the collective density fluctuations and, hence, both correlations freeze simultaneously at the ENE transition. We show here from a nonperturbative approach that at the ENE transition, characterized by the freezing of the long time limit of the dynamic correlation of collective density fluctuations to a nonzero value, the tagged-particle correlation still decays to zero. Our result implies t...
Heterogeneous relaxation in supercooled liquids: A density functional theory analysis
The Journal of Chemical Physics, 2001
Recent time domain experiments which allow selective study of the relaxation of slower subpopulations among the distributions of local, inhomogeneous regions, have shown the existence of a length scale (∼2–3 nm) beyond which the liquid behaves like a homogeneous liquid. Here we use the density functional theory to calculate the probability of creating a soft localized density fluctuation (density droplet). Theoretical calculation shows that the free energy penalty for creating a local inhomogeneity of small size is much less than that for a large size and that a dense supercooled system is unlikely to sustain inhomogeneity of a length, lf, which is larger than 5σ, where σ is the molecular diameter. We have calculated both the equilibrium and the nonequilibrium (subsequent to photobleaching) orientational correlation functions with the theoretically obtained inhomogeneous distributions. The nonequilibrium distribution relaxes at a slower rate. A simple two state exchange model has be...