Computer simulation study of thermodynamic scaling of dynamics of 2Ca(NO3)2·3KNO3

Molecular dynamics (MD) simulations of the glass-former 2Ca(NO(3))(2·3KNO(3), CKN, were performed as a function of temperature at pressures 0.1 MPa, 0.5 GPa, 1.0 GPa, and 2.0 GPa. Diffusion coefficient, relaxation time of the intermediate scattering function, and anion reorientational time were obtained as a function of temperature and densitiy ρ. These dynamical properties of CKN scale as ρ(γ)∕T with a common value γ = 1.8 ± 0.1. The scaling parameter γ is consistent with the exponent of the repulsive part of an effective intermolecular potential for the repulsion between the atoms at shortest distance in the equilibrium structure of liquid CKN, Ca(2+), and oxygen atoms of NO(3)(-). Correlation between potential energy and virial is obeyed for the short-range terms of the potential function, but not for the whole potential including coulombic interactions. Decoupling of diffusion coefficient and reorientational relaxation time from relaxation time take place at a given ρ(γ)∕T value, i.e., breakdown of Stokes-Einstein and Debye-Stokes-Einstein equations result from combined thermal and volume effects. The MD results agree with correlations proposed between long-time relaxation and short-time dynamics, lnτ ∝ 1∕, where the mean square displacement concerns a time window of 10.0 ps. It has been found that scales as ρ(γ)∕T above and below the glass transition temperature, so that thermodynamic scaling of liquid dynamics can be thought as a consequence of theories relating short- and long-time dynamics, and the more fundamental scaling concerns short-time dynamical properties.     

Thermodynamic scaling of polymer dynamics versus T-T(g) scaling

A thermodynamic scaling law for the relaxation times of complex liquids as a function of temperature and volume has been proposed in the literature: τ(T,V) = f(TV(γ)), where γ is a material-dependent constant. We test this scaling for six materials, linear polystyrene, star polystyrene, two polycyanurate networks, poly(vinyl acetate), and poly(vinyl chloride), and compare the thermodynamic scaling to T-T(g) scaling, where τ = f(T-T(g)). The thermodynamic scaling law successfully reduces the data for all of the samples; however, polymers with similar structures but different glass transition (T(g)) and pressure-volume-temperature (PVT) behavior, i.e., the two polycyanurates, cannot be superposed unless the scaling law is normalized by T(g)V(g) (γ). On the other hand, the T-T(g) scaling successfully reduced data for all polymers, including those having similar microstructures. In addition, the T-T(g) scaling is easier to implement since it does not require knowledge of the PVT behavior of the material. The relationship between T(g)V(g) (γ)∕TV(γ) and T-T(g) scaling is clarified and is found to be weakly dependent on pressure.     

Density scaling of the transport properties of molecular and ionic liquids

Casalini and Roland [Phys. Rev. E 69, 062501 (2004); J. Non-Cryst. Solids 353, 3936 (2007)] and other authors have found that both the dielectric relaxation times and the viscosity, η, of liquids can be expressed solely as functions of the group (TV?(γ)), where T is the temperature, V is the molar volume, and γ a state-independent scaling exponent. Here we report scaling exponents γ, for the viscosities of 46 compounds, including 11 ionic liquids. A generalization of this thermodynamic scaling to other transport properties, namely, the self-diffusion coefficients for ionic and molecular liquids and the electrical conductivity for ionic liquids is examined. Scaling exponents, γ, for the electrical conductivities of six ionic liquids for which viscosity data are available, are found to be quite close to those obtained from viscosities. Using the scaling exponents obtained from viscosities it was possible to correlate molar conductivity over broad ranges of temperature and pressure. However, application of the same procedures to the self-diffusion coefficients, D, of six ionic and 13 molecular liquids leads to superpositioning of poorer quality, as the scaling yields different exponents from those obtained with viscosities and, in the case of the ionic liquids, slightly different values for the anion and the cation. This situation can be improved by using the ratio (D∕T), consistent with the Stokes-Einstein relation, yielding γ values closer to those of viscosity.     

Scaling of the hysteresis in the glass transition of glycerol with the temperature scanning rate

By measuring the dependences of the temperature-dependent primary ("alpha") dielectric relaxation time behavior on the temperature scanning rate for the glass-forming glycerol, we study the scaling of hysteresis at the glass transition in glycerol. Based on the Vogel-Fulcher-Tammann (VFT) expression and the Angell's fragility concept, notable correlations of the systematic kinetic fragility, and of the hysteresis effect in the vitrification∕fusion "alpha"-relaxation process of glycerol, with the temperature scanning rate, were reasonably analyzed and discussed. It was observed that the kinetic fragility m and the apparent glass-transition temperature hysteresis width ΔT(g)(a), respectively, scaled the temperature scanning rate q as m ≈ α(m)q(-γ) and ΔT(g)(a) ≈ A(0) + αq(β), at which the exponents, γ and β, were suggested to be characteristic of the resistance to the structure change or fragility change of the system during the glass transition. The observed scaling laws are quite similar to the scaling power law for the thermal hysteresis in the first-order phase transition (FOPT) of solids, providing a significant insight into the hysteresis effect in the glass transition of the glass-forming liquids.     

The inflection point in the pressure dependence of viscosity under high pressure: a comprehensive study of the temperature and pressure dependence of the viscosity of propylene carbonate

The pressure dependence of the prototypical glass-former propylene carbonate has been investigated over a broad range of temperature and pressure that were inaccessible in previous investigations using dielectric spectroscopy. We find that the viscosity measurements validate the scaling relation, eta(T,V)=J(TV gamma), with a scaling parameter gamma close to that found from dielectric relaxation measurements. In the pressure dependence of the viscosity, we observe an inflection point in the log eta versus P response, similar to that found previously for other materials. However, this inflection has never been observed in dielectric relaxation measurements. Using the scaling property above, it is possible to determine the behavior of the dielectric relaxation time in this otherwise inaccessible experimental range and compare it with the viscosity measurements. We find that the behaviors of eta and tau are very similar, and a very good agreement between the function phi P calculated for these two quantities is found. Starting from the validity of the scaling properties, we show that the inflection point in the pressure dependence of the viscosity can be attributed to the convolution of the pressure dependences of the compressibility kappa T and the apparent activation energy at constant volume EV.     

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein β-relaxation time, τ(β), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(β) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnstr?m model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.     

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Viscosities eta and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV(gamma), where the exponent gamma is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of gamma for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing gamma in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) with thermodynamic conditions.     

Scaling of the segmental relaxation times of polymers and its relation to the thermal expansivity

Segmental relaxation times of polymers measured at various temperatures and pressures can be superposed as a function of temperature, using a shift factor equal to the specific volume raised to a power. The material-specific scaling exponent can be linked to the nature of the intermolecular repulsive potential for the material. We show the relationship of this scaling exponent to the thermal expansivity of the material, and how it can be used to sort out the different contributions to the temperature dependence of the local dynamics.     

Comment on: "Disentangling density and temperature effects in the viscous slowing down of glass forming liquids" [J. Chem. Phys. 120, 6135 (2004)

Recently, Tarjus et al. [G. Tarjus, D. Kivelson, S. Mossa, and C. Alba-Simionesco, J. Chem. Phys. 120, 6135 (2004)] concluded from a review of data for a variety of glass formers that the supercooled dynamics are almost invariably dominated by temperature T, rather than by density rho. By including additional published data into such a compilation, we show that for van der Waals molecular liquids, the dynamics near T(g) are in fact governed as much by density as by temperature. Moreover, relaxation times measured at various temperatures and pressures can be superimposed by plotting as a function rho(gamma)/T. This scaling form can arise from an assumed inverse power law for the intermolecular repulsive potential, with gamma a material constant. (c) 2004 American Institute of Physics.     

Slow magnetic relaxation and electron delocalization in an S = 9/2 iron(II∕III) complex with two crystallographically inequivalent iron sites

The magnetic, electronic, and Mo?ssbauer spectral properties of [Fe(2)L(μ-OAc)(2)]ClO(4), 1, where L is the dianion of the tetraimino-diphenolate macrocyclic ligand, H(2)L, indicate that 1 is a class III mixed valence iron(II∕III) complex with an electron that is fully delocalized between two crystallographically inequivalent iron sites to yield a [Fe(2)](V) cationic configuration with a S(t) = 9∕2 ground state. Fits of the dc magnetic susceptibility between 2 and 300 K and of the isofield variable-temperature magnetization of 1 yield an isotropic magnetic exchange parameter, J, of -32(2) cm(-1) for an electron transfer parameter, B, of 950 cm(-1), a zero-field uniaxial D(9∕2) parameter of -0.9(1) cm(-1), and g = 1.95(5). In agreement with the presence of uniaxial magnetic anisotropy, ac susceptibility measurements reveal that 1 is a single-molecule magnet at low temperature with a single molecule magnetic effective relaxation barrier, U(eff), of 9.8 cm(-1). At 5.25 K the Mo?ssbauer spectra of 1 exhibit two spectral components, assigned to the two crystallographically inequivalent iron sites with a static effective hyperfine field; as the temperature increases from 7 to 310 K, the spectra exhibit increasingly rapid relaxation of the hyperfine field on the iron-57 Larmor precession time of 5 × 10(-8) s. A fit of the temperature dependence of the average effective hyperfine field yields |D(9∕2)| = 0.9 cm(-1). An Arrhenius plot of the logarithm of the relaxation frequency between 5 and 85 K yields a relaxation barrier of 17 cm(-1).     

Thermodynamic scaling of diffusion in supercooled Lennard-Jones liquids

The manner in which the intermolecular potential u(r) governs structural relaxation in liquids is a long standing problem in condensed matter physics. Herein, we show, in agreement with recent experimental results, that diffusion coefficients for simulated Lennard-Jones m-6 liquids (8 < or = m < or = 36) in normal and moderately supercooled states are a unique function of the variable rhogamma/T, where rho is density and T is temperature. The scaling exponent gamma is a material specific constant whose magnitude is related to the steepness of the repulsive part of u(r), evaluated around the distance of closest approach between particles probed in the supercooled regime. Approximations of u(r) in terms of inverse power laws are also discussed.     

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids

The recently discovered scaling law for the relaxation times, tau(T,upsilon) = I(Tupsilon(gamma)), where T is temperature and upsilon the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [J. Non-Cryst. Solids 262, 258 (2000)]. In this modification the entropy is calculated by an alternative route. The resulting expression for the variation of the relaxation time with T and upsilon is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy, we find that the scaling exponent gamma can be identified with the Gruneisen constant.     

Molecular dynamics investigation of a density-driven glass transition in a liquid crystal system

Molecular dynamics simulations are carried out to address the density-driven glass transition in a system of rodlike particles that interact with the Gay-Berne potential. Since crystallization occurs in this system on the time scale of the simulations, direct simulation of the glass transition is not possible. Instead, glasses with isotropic orientational order are heated to a temperature T, and the relaxation times by which nematic orientational order develops are determined. These relaxation times appear to diverge at a critical density rho(c); i.e., the system can equilibrate at rhorho(c) (at the temperature T). The relaxation times follow a power-law scaling as the critical density is approached, suggesting that this density-driven glass transition concurs with mode coupling theory.     

Anomalies in supercooled NaCl aqueous solutions: a microscopic perspective

In this work we studied the effect of NaCl on the thermodynamic and dynamic properties of supercooled water, for salt concentrations between 0.19 and 1.33 mol?kg(-1), using molecular dynamic simulations for TIP5P∕E water model and ion parameters specially designed to be used in combination with this potential. We studied the isobaric heat capacity (C(p)) temperature dependence and observed a maximum in C(p), occurring at T(m), that moves to lower temperature values with increasing salt concentration. Many characteristic changes were observed at scaled temperature T∕T(m) ～ 0.96, namely a minimum in the density of the system, a reduction of the slope of the number of hydrogen bonds vs. temperature, and a crossover from Vogel-Tamman-Fulcher to Arrhenius dynamics. Finally, at low temperatures we observed that water dynamics become heterogeneous with an apparently common relationship between the fraction of immobile molecules and T/T(m) for all studied systems.     

Effects of the volume and temperature on the global and segmental dynamics in poly(propylene glycol) and 1,4‐polyisoprene

Published dielectric relaxation measurements for poly(propylene glycol) and 1,4‐polyisoprene are analyzed to determine the relative effects that thermal energy and volume have on the temperature dependence of the normal‐mode relaxation times, and these are compared with their effects on the temperature dependence of the local segmental relaxation times. For both polymers at temperatures well above the glass‐transition temperature, both relaxation modes are governed more by the thermal energy than by the volume, although the latter's contribution is not negligible. Such a result is consistent with an assumption underlying models for polymer viscoelasticity, such as the Rouse and tube models, that the friction coefficient governing motions over large length scales can be identified with the local segmental friction coefficient. Moreover, the relaxation data for both the segmental and normal modes superimpose when expressed as a function of the product of the temperature and volume, the latter being raised to a power. This scaling form arises from an inverse power law for the repulsive part of the intermolecular potential. The value of the exponent on the volume is the same for the normal and segmental motions and for both polymers indicates a relatively soft potential. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4313–4319, 2004     

Intermolecular relaxation in glycerol as revealed by field cycling 1H NMR relaxometry dilution experiments

(1)H spin-lattice relaxation rates R(1) = 1/T(1) have been measured for partly deuterated glycerol-h(5) diluted in fully deuterated glycerol-h(0) for progressively lower concentrations of glycerol-h(5). By means of the field cycling (FC) technique relaxation dispersion data, R(1)(ω), have been collected for several temperatures in the frequency range of 10 kHz-20 MHz. In order to disclose the spectral shape of the intra- and intermolecular relaxation, extrapolation of the relaxation data to the zero concentration limit has been performed. The paper confirms that the low frequency excess contribution to the total relaxation rate R(1)(ω) previously reported for several liquids is of intermolecular origin and reflects translational motion, whereas the high-frequency part is attributed to molecular rotation. Thus, intra- and intermolecular relaxation contributions are spectrally separated. The intermolecular relaxation itself contains also a contribution from rotational motion, which is due to non-central positions of the interacting nuclei in the molecule. This eccentricity effect is quantitatively reproduced by treating the intermolecular spectral density as a sum of translational-like (described by the free diffusion model) and rotational-like contributions (described by a Cole-Davidson function). Applying frequency-temperature superposition master curves as well as individual relaxation dispersion data, R(1)(ω), are analyzed. It is demonstrated that, in spite of the rotational influence, the translational diffusion coefficients, D(T), can be extracted from the (1)H relaxation dispersion which gives (1)H NMR relaxometry the potential to become a routine technique determining the diffusion coefficient in liquids.     

Dielectric behavior of some small ketones as ideal polar molecules

The dielectric behaviors of some small symmetric ketone molecules, including acetone, 3-pentanone, cyclopentanone, 4-heptanone, and cyclohexanone, were investigated as a function of temperature (T) over a wide frequency range from 50 MHz (3.14 × 10(8) s(-1), in angular frequency) to 3 THz (1.88 × 10(13) s(-1)). The temperature dependencies of the rotational diffusion times (τ(r)) determined using (17)O NMR spin-lattice relaxation time (T(1)) measurements and viscosities of the ketones were also examined. The obtained temperature dependencies of the parameters for the ketones were compared with those of ideal polar molecules, which obey the Stokes-Einstein-Debye (SED) relationship without the formation of intermolecular dimeric associations and without orientational correlations between dipoles (molecular axes), that is, free rotation. Kirkwood correlation factors (g(K)) of only acetone and 3-pentanone were close to unity over a wide temperature range, whereas those of other ketones were obviously less than unity. These results revealed that no correlations exist between the rotational motions of dipoles in acetone and 3-pentanone, as expected in ideal polar molecules. However, other ketones exhibited orientational correlations in their dipoles because of dipole-dipole interactions via antiparallel configurations. Furthermore, because acetone and 3-pentanone satisfied the SED relationship and because their microscopic dielectric relaxation times (τ(μ)), which were calculated from the determined dielectric relaxation times (τ(D)) via the relationship τ(μ) = τ(D)g(K)(-1), were identical to 3τ(r) and were proportional to Vη(k(B)T)(-1) over the wide temperature range examined, where V, k(B), and η represent the effective molecular volume, Boltzmann's constant, and the viscosity of the liquid molecules, respectively, these two ketone molecules behave as ideal polar molecules. In addition, other ketones not significantly larger than acetone and 3-pentanone in molecular size likely form dimeric intermolecular associations with antiparallel cyclic configurations, which demonstrates the g(K) values less than unity.     

Enhanced translational diffusion of rubrene in sucrose benzoate

The translational diffusion of rubrene in the fragile molecular glass former, sucrose benzoate (SB) (fragility index m approximately 94), has been studied from T(g)+6 K to T(g)+71 K(T(g)=337 K) by using the technique of holographic fluorescence recovery after photobleaching. In the temperature range of the measurements, the translational relaxation functions were observed to decay exponentially, indicating that Fick's law of diffusion governs the translational motion of rubrene in sucrose benzoate. The value of the translational diffusion coefficient D(T) obtained from the 1e time of the translational relaxation function varied from 5.3 x 10(-15) cm2 s(-1) at 343 K to 5.0x10(-9) cm2 s(-1) at 408 K. The temperature dependence of D(T) for diffusion of rubrene in SB is compared with that of the viscosity and the dielectric relaxation time tau(D) of SB. The temperature dependence of D(T) is weaker than that of Teta for T<1.2T(g) but tracks the reciprocal of the dielectric relaxation time 1tau(D) for 1.05T(g)相似文献