Perspective: Nonlinear approaches to structure and dynamics of soft materials

Dielectric and Shear-Mechanical "Humps" in the Nonlinear Response of Polar Glassformers

Many glassformers display electrorheological effects and a pronounced maximum in their frequency dependent nonlinear dielectric response. The latter so-called "hump" feature was often linked to correlated-particle motions and, so far, was not explored in the large-perturbation mechanical response of viscous liquids. To first clarify the electro-viscoelastic coupling in the linear domain, using the modified Gemant, DiMarzio, and Bishop model, it is demonstrated how the small-amplitude shear mechanical response of S-methoxy-PC, a derivative of propylene carbonate, can be related to its complex dielectric permittivity. Then, in the nonlinear regime, a "hump" feature is identified in the rheological third-order shear modulus of S-methoxy-PC and of another polar glassformer, propylene glycol. Thus, the observation of a "hump" in the cubic response of viscous liquids does not necessarily rely on the application of electrical fields.

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

First- and third-order shear nonlinearities across the structural relaxation peak of the deeply supercooled pharmaceutical liquid indomethacin

Nonlinear rheological properties of viscous indomethacin are studied in the frequency range of its structural relaxation, that is, in a range so far inaccessible to standard techniques involving medium-amplitude oscillatory shear amplitudes. The first- and third-order nonlinearity parameters thus recorded using a sequence of small and large shear excitations in a time efficient manner are compared with predictions from rheological models. By properly phase cycling the shear amplitudes, build-up and decay transients are recorded. Analogous to electrical-field experiments, these transients yield direct access to the structural relaxation times under linear and nonlinear shearing conditions. To demonstrate the broader applicability of the present approach, transient analyses are also carried out for the glass formers glycerol, ortho-terphenyl, and acetaminophen.

Long-Range Static and Dynamic Previtreous Effects in Supercooled Squalene-Impact of Strong Electric Field

This article presents evidence for the long-range previtreous changes of two static properties: the dielectric constant (ε) and its strong electric field related counterpart, the nonlinear dielectric effect (NDE). Important evidence is provided for the functional characterizations of ε(T) temperature changes by the ‘Mossotti Catastrophe’ formula, as well as for the NDE vs. T evolution by the relations resembling those developed for critical liquids. The analysis of the dynamic properties, based on the activation energy index, excluded the Vogel–Fulcher–Tammann (VFT) relation as a validated tool for portraying the evolution of the primary relaxation time. This result questions the commonly applied ‘Stickel operator’ routine as the most reliable tool for determining the dynamic crossover temperature. In particular, the strong electric field radically affects the distribution of the relaxation times, the form of the evolution of the primary relaxation time, and the fragility. The results obtained in this paper support the concept of a possible semi-continuous phase transition hidden below T_g. The studies were carried out in supercooled squalene, a material with an extremely low electric conductivity, a strongly elongated molecule, and which is vitally important for biology and medicine related issues.

Quantifying dielectric permittivities in the nonlinear regime

In contrast to the static dielectric permittivity,ε, associated with linear response, its high-field counterpart,ε_E, is not a material specific quantity, but rather depends on the experimental method used to determine the nonlinear dielectric effect (NDE). Here, we defineε_Ein a manner consistent with how high field permittivities are typically derived from a capacitance measurement using high voltages. Based upon characterizing the materials nonlinear behavior via its third order susceptibility,χ₃, the relations between a givenχ₃and the observableε_Eis calculated for six different experimental or theoretical approaches to NDEs in the static limit. It is argued that the quantityχ₃is superior overε_Eor the Piekara factor, (ε_E-ε)/E², because it facilitates an unambiguous comparison among different experimental techniques and it provides a more robust connection between experiment and theory.

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

Relaxation and vibrational properties in metal alloys and other disordered systems

The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxation, the physics of metal alloys is considered where the emergence of power-law exponents has been identified both in the vibrational density of states (VDOS) as well as in density correlations. Also, theoretical frameworks which connect the VDOS to the relaxation behaviour and mechanical viscoelastic response in metallic glasses are reviewed. The same generic interpretative framework is then applied to the case of molecular glass formers where the emergence of stretched-exponential relaxation in dielectric relaxation can be put in quantitative relation with the VDOS by means of memory-function approaches. Further connections between relaxation and vibration are provided by the study of phonon linewidths in liquids and glasses, where a natural starting point is given by hydrodynamic theories. Finally, an agenda of outstanding issues including the appearance of compressed exponential relaxation in the intermediate scattering function of experimental and simulated systems (metal alloys, colloidal gels, jammed packings) is presented in light of available (or yet to be developed) mathematical models, and compared to non-exponential behaviour measured with macroscopic means such as mechanical spectroscopy/rheology.