Hans Sillescu

Heterogeneity at the glass transition: a review

Theoretical concepts and experimental evidence of heterogeneity in glass-forming liquids and polymers are reviewed. The main purpose is to provide an introduction to theoretical developments and recent experiments which have led to rapidly increasing knowledge. Realizing that there is no consensus in regard to the various scenarios of the glass transition starting from rather different assumptions we try to give a balanced overview although we also compare and interrelate some of the approaches. The experimental part describes recent nuclear magnetic resonance, dielectric, and optical experiments from which dynamically distinguishable subensembles can be selected thus proving the existence of a well defined dynamical heterogeneity.

Translational and rotational diffusion in supercooled orthoterphenyl close to the glass transition

Self diffusion coefficients in supercooled orthoterphenyl (OTP) have been determined down toDt=3·10−14 m2s−1 using a1H-NMR technique applying static field gradients up to 53T m−1 In a range of more than two decades theDt values agree with those of photochromic tracer molecules of the same size determined by forced Rayleigh scattering down to the glass transition temperatureTg. A change of mechanism is found for translational diffusion atTc≈1.2Tg whereDt is proportional to the inverse shear viscosityη−1 atT>Tc butDt ∼ηξ with ξ=0.75 atT<Tc. Rotational correlation times determined by2H-NMR stimulated echo techniques in deuterated OTP remain proportinal toη−1 down toTg. Our results are discussed in relation with mode coupling theory and with models of cooperative motion at the glass transition.

Solid echoes in the slow-motion region

Abstract NMR lineshapes obtained by Fourier transform of the solid-echo decay are compared with those from the free-induction decay in the slow-motion region where the motional correlation times are of the same order as the reciprocal anisotropic spin interactions. The theory has been worked out explicitly for the example of two-site exchange in an I = 1 spin system that applies, e.g., to 1 H or 2 D NMR of water molecules flipping by 180° about the twofold axis. Large differences are found in the region where the time between the two 90° pulses of the solid-echo sequence is comparable with the motional correlation time. The intensity of the solid echo is reduced by a factor R > 0.5 relative to the free-induction decay for the example of anisotropic motion considered. Much smaller reduction factors are obtained for isotropic reorientation by small- or large-angle rotational jumps.

Translational and rotational molecular motion in supercooled liquids studied by NMR and forced Rayleigh scattering

It has been shown that translational diffusion coefficients, Dt, in the supercooled van der Waals liquids, orthoterphenyl, phenolphthaleindimethylether, and salol, have a weaker temperature dependence than the shear viscosity, η, at T ≲ 1.2Tg and can be described by Dt ∼ η−χ with χ < 1 whereas Dr ∼ η−1 applies for the mean rotational diffusion coefficients, Dr, down to the glass transition temperature, Tg. This apparent decoupling of translational and rotational motion has been discussed in relation with possible anomalous short time diffusion, spatial heterogeneity, and cooperative molecular motions close to Tg.

Theory of Molecular Reorientation in Liquids: Magnetic Spin Resonance Line Shapes

The Debye model of rotational Brownian motion and the rotational random jump model have been extended to allow for time fluctuations of the rotational diffusion constant and the jump rate constant, respectively. The treatment is applicable to experimental situations which are conventionally described in terms of a distribution of correlation times and to systems where molecular reorientation is complicated, e.g., by rapid chemical exchange processes. Correlation functions for spin relaxation are discussed in some detail and are compared with the corresponding correlation functions for dielectric relaxation. In particular, the ESR (or NMR) line shape is given for a simple example of very slow reorientation where the rotational correlation time is comparable with the spin relaxation time. In this case, the Debye model and the jump model yield different line shapes, and further changes occur if environmental fluctuations are considered. Details are given for fluctuations described by an Uhlenbeck–Ornstein pr...

Dynamic light scattering study of concentrated microgel solutions as mesoscopic model of the glass transition in quasiatomic fluids

This paper presents a light scattering study of the dynamics of concentrated solutions of nearly monodisperse (σ≊0.16) spherical micronetwork particles consisting of highly cross‐linked polystyrene dissolved in carbon disulfide, i.e., a ‘‘good’’ solvent. Above volume fractions of φ=0.50 the intermediate scattering function, measured over a time window of 10−7 to 103 s using the ALV5000 correlator, decays in two steps and shows indications of nonergodic behavior for φ≥0.64. Such behavior is typical for glass forming systems and has recently been found close to the glass transition of a hard sphere colloidal system [W. van Megen and P. N. Pusey, Phys. Rev. A 43, 5429 (1991)]. Thus the introduced system can be used for modeling the glass transition of atoms on a mesoscopic scale. The traditional analysis of structural relaxation in terms of a Kohlrausch–Williams–Watts distribution yields a mean relaxation time which follows the empirical Mooney equation as a function of concentration and thus corresponds to Vogel–Fulcher–Tammann behavior. However, the necessity to add an unspecified ‘‘intermediate’’ process between the short and long time KWW decays demonstrates the limitations of this ‘‘pragmatic’’ approach. The mode coupling theory of the glass transition interprets the intermediate scattering function consistently over nearly seven decades in time, the intermediate region corresponding to the crossover from β to α relaxation (von Schweidler law). The critical volume fraction of 0.636 derived by this analysis corresponds to a value of 0.59 for an ideal monodisperse system which is well in accord with other experimental and computer simulation studies of the glass transition of atomic systems.

The molecular dynamics around the glass transition and in the glassy state of molecular organic systems: A 2H−nuclear magnetic resonance study

2H‐nuclear magnetic resonance(NMR)‐spin–lattice relaxation experiments have been performed for studying the crossover from viscous (α process) to secondary (β processes) dynamics in the van der Waals liquid orthoterphenyl and the H‐bridged network glycerol. The essential and general features, observed in both systems, are the following: (a) a dominating α process in the liquid and viscous regime; (b) a change from exponential to nonexponential spin–lattice relaxation as the temperature is lowered below a characteristic temperature above Tg; (c) the existence of a slow (>10−9 s) secondary reorientational process in the highly viscous regime; and (d) the existence of a fast (∼10−12 s) local process in the glassy state. Whereas the slower process is shown to be the one known from dielectric studies, we attribute the fast mode to a β process found in quasielastic neutron scattering.

Nonexponential 2H spin-lattice relaxation as a signature of the glassy state

Abstract High-precision measurements of 2H spin-lattice relaxation on several molecular glass-forming liquids have been performed. As a general feature the following can be stated: At temperatures more than ten to twenty degrees above the calorimetric glass transition temperature Tg the 2H spin-lattice relaxation is exponential; below that temperature regime the relaxation is nonexponential. This crossover from exponential to nonexponential magnetization recovery implies that no common spin temperature caused by spin diffusion exists in a 2H glass. This contrasts 1H spin-lattice relaxation which is found to be strictly monoexponential throughout. The occurrence of nonexponential 2H relaxation serves as a new observable at the glass transition, being a signature of the crossover from ergodic to nonergodic behaviour.

Deuteron n.m.r. study of chain motion in solid polyethylene

Abstract The chain motion in the amorphous regions in linear polyethylene is studied by exploiting various 2 H n.m.r. pulse methods. The experimental techniques employed are described in considerable detail. In particular, the solid echo- and the spin alignment spectra are recorded over a wide range of temperatures (123–393 K) as a function of the pulse spacings. In addition the spin-lattice relaxation times of both polymerization and alignment are given for the crysralline as well as the amorphous regions. The data are analysed in terms of highly constrained conformational motions which generate an exchange of C-H bond directions between 2, 3, or all 4 tetrahedral sites on a diamond lattice. Thus in the temperature interval from the γ-relaxation up to ∼200 K only 2 sites are accessible, whereas a third site is appreciably populated at room temperature. Between 330 K and the melting point the number of conformations accessible to the chain must be high enough to lead to an increasingly isotropic 4 site exchange. The motion remains highly constrained and localized, however, up to the melting region as shown by the analysis of the spin-alignment spectra. The intensity ratio of the deuteron n.m.r. signals from the rigid crystalline and the mobile amorphous regions, respectively, yields the crystallinity of the sample as a function of temperature in remarkable agreement with the results obtained by X-rays. Finally, frequency dependent relaxation of spin alignment due to torsional oscillations of the chains in the crystalline regions is observed and analysed.

Orientational distributions in partially ordered solids as determined from NMR and ESR line shapes

The orientational distribution in partially ordered solids, drawn polymers, etc. is related with NMR and ESR line shapes governed by anisotropic shift, dipolar, or quadrupolar couplings. In principle, the theory yields the complete orientational distribution by numerical deconvolution or spectral fitting procedures. Furthermore, the line shape can be decomposed into subspectra that correspond to the moments of the orientational distribution. The theory is applied to 2D‐NMR line shapes in partially ordered solid benzene, and to ESR nitroxide spin label spectra.