Light scattering and dielectric relaxation studies of glass forming liquids

Extended Abstract: Glass forming organic liquids and polymers exhibit long range density fluctuations with correlation length ξ in the range of 10–300 nm at temperatures above T_g (1 - 6). This follows from dynamic and static light scattering experiments revealing some unexpected features, which cannot be explained on the basis of conventional liquid state theories: (i) In static light scattering the intensity I(q → 0) is no longer proportional to the isothermal compressibility, (ii) This excess scattering I_exc shows a strong q-dependence (q = (4π/Λ.)sin(θ/2)) corresponding to a correlation length ξ in the above mentioned range, (iii) The Landau-Placzek ratio I_Rayleigh/2I_Brillouin is much too high compared with the results of light scattering theories, (iv) In photon correlation spectroscopy a new ultraslow hydrodynamic mode (Γ ˜ q²) is detected with relaxation rates Γ about 10⁻⁶ to 10⁻⁹ lower than those of the α-process at a given temperature. In order to explain these observations, a two-state fluid model is proposed, which starts from the coexistence of “liquid-like” and “aperiodic solid-like” regions within the liquids. Such ideas have been discussed many times before, so for example A.R. Ubbelohde (7) speculates about “anticrystalline” clusters in liquids. Molecular dynamics simulations of atomic liquids showed that long range orientational fluctuations appear upon supercooling (8). A preferred icosahedral ordering is observed (9) and the number of icosahedral clusters increases with decreasing temperature (10). In connection with the interpretation of the dynamics of supercooled liquids different “two-state” models have been proposed (11 - 15). For the explanation of the light scattering results we propose that the molecules in the different dynamic states (“liquid” or “solid”) aggregate during annealing of the liquid at temperatures above T_g. Experiments showed that the equilibration times can be rather long (3 - 5), but nevertheless the liquids exhibiting long range density fluctuations are in the state of lowest free energy. We claim that our observations are the first experimental proof of the existence of such different dynamic states, which have been discussed many times before. The extended secondary clusters can also be detected by ultra small angle X-ray scattering.     

The new insight into dynamic crossover in glass forming liquids from the apparent enthalpy analysis

One of the most intriguing phenomena in glass forming systems is the dynamic crossover (T(B)), occurring well above the glass temperature (T(g)). So far, it was estimated mainly from the linearized derivative analysis of the primary relaxation time τ(T) or viscosity η(T) experimental data, originally proposed by Stickel et al. [J. Chem. Phys. 104, 2043 (1996); J. Chem. Phys. 107, 1086 (1997)]. However, this formal procedure is based on the general validity of the Vogel-Fulcher-Tammann equation, which has been strongly questioned recently [T. Hecksher et al. Nature Phys. 4, 737 (2008); P. Lunkenheimer et al. Phys. Rev. E 81, 051504 (2010); J. C. Martinez-Garcia et al. J. Chem. Phys. 134, 024512 (2011)]. We present a qualitatively new way to identify the dynamic crossover based on the apparent enthalpy space (H(a) (')=dlnτ/d(1/T)) analysis via a new plot lnH(a) (') vs. 1∕T supported by the Savitzky-Golay filtering procedure for getting an insight into the noise-distorted high order derivatives. It is shown that depending on the ratio between the "virtual" fragility in the high temperature dynamic domain (m(high)) and the "real" fragility at T(g) (the low temperature dynamic domain, m = m(low)) glass formers can be splitted into two groups related to f < 1 and f > 1, (f = m(high)∕m(low)). The link of this phenomenon to the ratio between the apparent enthalpy and activation energy as well as the behavior of the configurational entropy is indicated.     

Depolarized light scattering versus optical Kerr effect. II. Insight into the dynamic susceptibility of molecular liquids

We have previously discussed [J. Chem. Phys. 125, 114502 (2006)] that optical Kerr effect (OKE) and depolarized light scattering (DLS) data of molecular liquids reveal, each in their native domain, the same characteristic signatures of the glass transition dynamics; in particular, the intermediate power law of OKE is equivalent with the excess wing of the frequency-domain data, long since known in dielectric spectroscopy. We now extend the discussion to show that the excess wing is an equally common feature in DLS. We further discuss the time-temperature superposition property of OKE data in relation to our DLS and literature dielectric-spectroscopic results, and the merits of their mode coupling theory analyses. Spectroscopic signatures of a liquid-crystal-forming system (nematogen) are discussed in the same frame.     

On the relaxation theory of glass transition in liquids

A method for calculating the constant in the main equation of glass transition (which relates the relxation time and the cooling rate near the glass transition temperature) with consideration given to the temperature dependence of the activation energy in this region is proposed. A modification of the main glass transition equation is considered. Application of this equation to the relaxation spectrometry of amorphous polymers and inorganic glasses is discussed.     

Temperature dependence of the Landau-Placzek ratio in glass forming liquids

Here, we studied Rayleigh-Brillouin light scattering in ten different glass-forming liquids (α-picoline, toluene, o-toluidine, ethanol, salol, glycerol, dibutyl phthalate, o-terphenyl, propylene carbonate, and propylene glycol). For each of these liquids it was found that the Landau-Placzek ratio is in a good agreement with the theory at high temperatures and significantly exceeds the theoretical prediction below a certain temperature. Transition between the two temperature regimes occurs near T(A), where T(A) is crossover point from an Arrhenius-like to a non-Arrhenius behavior for the α-relaxation time dependence on temperature. Increase of the Landau-Placzek ratio relative to the theoretical prediction below T(A) seems to be the universal feature of glass-formers. We suggest that formation of locally favored structures in liquids below T(A) causes observed excess of the Landau-Placzek ratio.     

The Adam-Gibbs equation and the out-of-equilibrium alpha relaxation of glass forming systems

The temperature dependence of the alpha-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam-Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam-Gibbs equation, for polymers the experimental activation energy values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam-Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity of the Adam-Gibbs equation for describing the temperature dependence of the time scale of the alpha-relaxation also out of equilibrium, at least for fragile glass formers.     

Dynamic light scattering in mixed alkali metaphosphate glass forming liquids

We report the first ever photon correlation spectroscopy performed on single alkali and mixed alkali metaphosphate glasses at refractory temperatures above the glass transition. We find not only a significant decrease in the glass transition temperature but also a decrease in fragility for the mixed alkali composition as compared with the single akali glasses. We argue that structural relaxation in these polymeric oxide glasses is largely controlled by the cross linking cations and that the changes in fragility that we observed are a reflection of changes in the cooperativity of structural relaxation wrought by the substantial decrease in the ion mobility that accompanies the mixing of alkali ions.     

Relaxation time dispersions in glass forming metallic liquids and glasses

Relaxation time dispersions in glass forming metallic liquids of diverse fragility characters were reviewed mainly based on mechanical relaxations. The compilation of the stretching exponents revealed the common nonexponential dynamic features among the metallic liquids. The time-temperature-superposition law of the relaxation profiles was identified with an average stretching exponent around 0.5 at low frequency regions near the glass transitions. No notable correlation of the stretching parameter with alloy composition was discerned. The construction of the frequency dependence of the stretching exponent across the whole range of liquid dynamics revealed a striking similarity of the nonexponential dynamics between metallic and fragile molecular liquids.     

Thermodynamics of viscous flow and elasticity of glass forming liquids in the glass transition range

The elastic moduli of glasses from different chemical systems, including oxide, chalcogenide, oxynitride, and metallic, were investigated through the glass transition (T(g)), typically from 0.4 to 1.3 T(g). These data were used to interpret the temperature sensitivity of the shear viscosity coefficient obtained on the same materials. The relevant Gibbs free activation energy was estimated from the apparent heat of flow by means of the temperature dependence of the shear elastic modulus. The activation entropy associated with the viscous flow was also derived and was found to correlate with the fragile versus strong character of the glass forming liquids. Finally, the physicochemistry of the flow process was described on the basis of the glass network de-structuration which shows up through the temperature dependence of Poisson's ratio, and an expression for the shear viscosity coefficient is proposed which is chiefly based on the high temperature elastic behavior.     

Microviscosity effects on the vibrational relaxation rates in molecular liquids

The isotropic Raman band of the CO stretching mode of the N,N-dimethylformamide (DMF) molecule has been studied as a function of solvents' hydrodynamic properties. The effect of solvent viscosity on linewidth (Γ_iso) has been studied in detail, particularly using the theory of microviscosity. Modifications have been made in the ƒ(ϱ, η, n) parameter which relates the vibrational relaxation rate with viscosity, density and dispersion energy on the basis of microviscosity.     

The glass transition and the distribution of voids in room-temperature ionic liquids: a molecular dynamics study

The glass transition in prototypical room temperature ionic liquids has been investigated by molecular dynamics simulations based on an Amber-like empirical force field. Samples of [C(4)mim][PF(6)], [C(4)mim][Tf(2)N], and [C(3)mim][Tf(2)N] have been quenched from the liquid phase at T = 500 to a glassy state at T ～ 0 K in discontinuous steps of 20 K every 1.2 ns. The glass temperature estimated by simulation (T(g) = 209 K for [C(4)mim][PF(6)], T(g) = 204 K for [C(4)mim][Tf(2)N], and T(g) = 196 K for [C(3)mim][Tf(2)N]) agrees semi-quantitatively with the experimental values (T(g) = 193÷196 K for [C(4)mim][PF(6)], T(g) = 186÷189 K for [C(4)mim][Tf(2)N], and T(g) = 183 K for [C(3)mim][Tf(2)N]). A model electron density is introduced to identify voids in the system. The temperature dependence of the size distribution of voids provided by simulation reproduce well the experimental results of positron annihilation lifetime spectroscopy reported in G. Dlubek, Y. Yu, R. Krause-Rehberg, W. Beichel, S. Bulut, N. Pogodina, I. Krossing, and Ch. Friedrich, J. Chem. Phys. 133, 124502 (2010), with only one free parameter needed to fit the experimental data.     

Diamagnetic susceptibility of liquid crystalline copolyesters: Study of molecular relaxation

The diamagnetic susceptibility of a series of random copolyesters, P(HB/HN), of 4-hydroxybenzoic acid (HBA) with 2-hydroxy-6-naphtoic acid (HNA) has been investigated, both, as a function of composition and temperature. It is shown that the molecular susceptibility of the uniaxially oriented samples linearly decreases with HB content. Results are discussed in terms of the increase in magnetic anisotropy occurring with the introduction of the HN groups. Furthermore, the temperature dependence of the specific susceptibility has been investigated. The diamagnetic susceptibility of these copolymers rises at the beginning of the solid-liquid crystalline transition. Above this temperature, the specific susceptibility exhibits a conspicuous time-dependent behavior which is a function of the temperature at the mesophase. After long storage times at the mesophase, and upon cooling at room temperature, the susceptibility shows values which approach those of a macroscopically isotropic state, i.e., a state with no overall preferred orientation. X-ray diffraction measurements confirm a relaxation mechanism of the molecular orientation occurring at temperatures above the melting point. A similar relaxation process is observed for samples with an initial planar orientation. © 1996 John Wiley & Sons, Inc.     

On the molecular theory of relaxation processes and the viscoelastic properties of magnetic liquids

The kinetic equations for one-and two-particle distribution functions including the contributions of spatial correlation of density and correlation of velocities were used to obtain equations of generalized hydrodynamics of magnetic liquids, whose transfer coefficients microscopically depended on the spatial and time scales. (The relaxing flows in these equations comprise kinetic and potential parts, which ensures the inclusion of translational and structural relaxation processes.) The system of generalized hydrodynamics equations obtained can be used to study transfer phenomena in magnetic liquids. Smoluchowski equations for binary density n ₂(q ₁, q ₂, t) and binary flow of particles I ₂(q ₁, q ₂, t) were obtained and their general solutions found to construct a closure of the initial kinetic equation for the one-particle distribution function. The asymptotic behavior of these solutions at low frequencies (ω → 0) was analyzed and found to coincide with the long-time asymptotes of autocorrelation functions. The viscoelastic properties of magnetic liquids were studied over a wide range of frequencies in the presence of an external magnetic field H. Microscopic equations for viscosity coefficients and elastic moduli were found and their asymptotic behavior in slow and fast processes considered.     

Examination of dynamic facilitation in molecular dynamics simulations of glass-forming liquids

Using data from molecular dynamics computer simulations of the one-component Dzugutov liquid and of BKS silica in metastable equilibrium supercooled states, we examine ideas introduced by Garrahan and Chandler (GC) in their dynamic facilitation (DF) model of the glass transition. Utilizing a recently introduced measure of DF, we find that DF is important for particle motion in both the supercooled Dzugutov liquid and in the BKS silica melt, that mobility propagates continuously, and that this effect becomes increasingly pronounced with decreasing T. We show that, in both systems, dynamic facilitation is strongest on the time scale of the late-beta relaxation, where clusters of highly mobile neighboring particles escaping from their cages are largest and, except for the silicon atoms in BKS silica, stringlike motion is most prominent. By comparing the two systems, we show that the temperature dependence of one measure of DF as the mode-coupling temperature is approached from high temperature is similar, once the temperature dependence of the structural relaxation time in each system is scaled out.     

Spin-rotation relaxation in liquids for dynamically coherent reorientation

It is estimated that for liquids in which the molecular reorientation is dynamically coherent the nuclear spin relaxation rate due to spin-rotation interaction increases with temperature approximately as T^{$\text{1}\text{2}$}.     

Prevalence for the universal distribution of relaxation times near the glass transitions in experimental model systems: rodlike liquid crystals and orientationally disordered crystals

Recently, Nielsen et al. [J. Chem. Phys. 130, 154508 (2009); Philos. Mag. 88, 4101 (2008)] demonstrated a universal pattern for the high frequency wing of the loss curve for primary relaxation time on approaching the glass transition for organic liquids. In this contribution it is presented that a similar universality occurs for glass-forming liquid crystals and orientationally disordered crystals (plastic crystals). Empirical correlations of the found behavior are also briefly discussed.     

The ultrafast dynamics of hydrogen-bonded liquids: molecular structure-dependent occurrence of normal arrhenius or fractional Stokes-Einstein-Debye rotational diffusive relaxation

The ultrafast rotational-diffusive dynamics of the peptide linkage model compounds N-methylacetamide (NMA), acetamide (Ac), and N,N-dimethylacetamide (DMA) have been studied as a function of temperature using optically heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy. Both NMA and Ac exhibit a non-Arrhenius temperature dependence of the rotational diffusive relaxation time. By contrast, the non-hydrogen-bonding DMA exhibits normal hydrodynamic behavior. The unusual dynamics of NMA and Ac are attributed to the decoupling of single-molecule rotational diffusive relaxation from the shear viscosity via a transition between stick and slip boundary conditions, which arises from local heterogeneity in the liquid due to the formation of hydrogen-bonded chains or clusters. This provides new insight into the structure and dynamics of an important peptide model compound and the first instance of such a phenomenon in a room-temperature liquid. The OHD-OKE responses of carboxylic acids acetic acid (AcOH) and dichloroacetic acid (DCA) are also reported. These, along with the terahertz Raman spectra, show no evidence of the effects observed in amide systems, but display trends consistent with the presence of an equilibrium between the linear and cyclic dimer structures at all temperatures and moderate-to-high mole fractions in aqueous solution. This equilibrium manifests itself as hydrodynamic behavior in the liquid phase.