Density Scaling and Dynamic Correlations in Viscous Liquids

We use a recently proposed method [Berthier L.; Biroli G.; Bouchaud J.P.; Cipelletti L.; El Masri D.; L'Hote D.; Ladieu F.; Pierno M. Science 2005, 310, 1797.] to obtain an approximation to the 4-point dynamic correlation function from derivatives of the linear dielectric response function. For four liquids over a range of pressures, we find that the number of dynamically correlated molecules, Nc, depends only on the magnitude of the relaxation time, independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant relaxation time and the density scaling property of the relaxation times, and implies that Nc also conforms to the same scaling behavior. For propylene carbonate and salol Nc becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly non-cooperative relaxation.Comment: revisio

Molecular dynamics simulations of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations (mds) were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glass state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the non-ergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the frequency of the JG process increases significantly, eventually subsuming the slower alpha-relaxation. This evolution of the JG-motion into structural relaxation underlies the correlation of many properties of the JG- and alpha-dynamics.Comment: 12 pages, 6 figure

Are polar liquids less simple?

Strong correlation between equilibrium fluctuations of the potential energy, U, and the virial, W, is a characteristic of a liquid that implies the presence of certain dynamic properties, such as density scaling of the relaxation times and isochronal superpositioning of the relaxation function. In this work we employ molecular dynamics simulations (mds) on methanol and two variations, lacking hydrogen bonds and a dipole moment, to assess the connection between the correlation of U and W and these dynamic properties. We show, in accord with prior results of others [T.S. Ingebrigtsen, T.B. Schroder, J.C. Dyre, Phys. Rev. X 2, 011011 (2012).], that simple van der Waals liquids exhibit both strong correlations and the expected dynamic behavior. However, for polar liquids this correspondence breaks down - weaker correlation between U and W is not associated with worse conformance to density scaling or isochronal superpositioning. The reason for this is that strong correlation between U and W only requires their proportionality, whereas the expected dynamic behavior depends primarily on constancy of the proportionality constant for all state points. For hydrogen-bonded liquids, neither strong correlation nor adherence to the dynamic properties is observed; however, this nonconformance is not directly related to the concentration of hydrogen bonds, but rather to the greater deviation of the intermolecular potential from an inverse power law (IPL). Only (hypothetical) liquids having interactions governed strictly by an IPL are perfectly correlating and exhibit the consequent dynamic properties over all thermodynamic conditions.Comment: 14 pages, 8 figure

Connection between dynamics and thermodynamics of liquids on the melting line

The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power law (IPL) potential, most notably the superpositioning of relaxation data as a function of the variable TV{\gamma}, where T is temperature, V the specific volume, and {\gamma} a material constant. A related scaling law, TmVm{\Gamma}, with the same exponent {\Gamma}={\gamma}, links the melting temperature Tm and volume Vm of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid crystals, we determine dynamic and melting point scaling exponents {\gamma} and {\Gamma} for a large number of non-associating liquids. Rigid, spherical molecules containing no polar bonds have {\Gamma}={\gamma}; consequently, the reduced relaxation time, viscosity and diffusion coefficient are each constant along the melting line. For other liquids {\gamma}>{\Gamma} always; i.e., the dynamics is more sensitive to volume than is the melting point, and for these liquids the dynamics at the melting point slows down with increasing Tm (that is, increasing pressure).Comment: 20 pages, 8 figures, 1 tabl

Cooperativity of short-time dynamics revisited

Using molecular dynamics simulations we examine the system size dependence of the fast dynamics in two model glass forming liquids, one of them a Lennard-Jones mixture for which cooperative fast relaxation has been reported. We find no indication of a temperature-dependent dynamic length scale characterizing these fast dynamics; the size effects in the short time range are temperature independent, and the consequence of cutting off of long wavelength acoustic modes. In a molecular liquid exhibiting a clear Johari-Goldstein (JG) relaxation, significant size effects are again present both for the vibrational motion and long-time {\alpha} relaxation (only the latter having a significant temperature dependence), but absent for the JG relaxation.Comment: 8 pages, 4 figure

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently a new approach to the determination of dynamic correlation lengths, {\xi}, for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [L. Hong, V.N. Novikov, and A.P. Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, Tg, the assumption is that the structure of the liquid is frozen at Tg, so that the {\xi} characterize dynamic heterogeneity in the supercooled liquid state. We compare {\xi} from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, {\xi} from Boson peak measurements above Tg have a different, and unrealistic, temperature dependence.Comment: 10 pages, 3 figure