Dual field nonlinear dielectric spectroscopy in a glass forming EPON 828 epoxy resin

Are Critical Fluctuations Responsible for Glass Formation?

The dynamic heterogeneities occurring just before the transition to the glassy phase have been named as the cause of amorphization in supercooled systems. Numerous studies conducted so far have confirmed this hypothesis, and based on it, a widely accepted solution to the puzzle of glass transition has been developed. This report focuses on verifying the existence of a strong pretransitional anomaly near the glass transition Tg. For this purpose, supercooled liquid-crystalline systems with a strong rod-like structure were selected. Based on the obtained experimental data, we demonstrate in this article that the previously postulated dynamic heterogeneities exhibit a critical characteristic, meaning a strong pretransitional anomaly can be observed with the described critical exponent α=0.5. Due to this property, it can be concluded that these heterogeneities are critical fluctuations, and consequently, the transition to the glassy state can be described based on the theory of critical phenomena. To measure the pretransitional anomaly near Tg in supercooled liquid-crystalline systems, broadband dielectric spectroscopy (BDS) and nonlinear dielectric effect (NDE) methods were applied. The exponent α provides insight into the nature and intensity of critical fluctuations in the system. A value of α=0.5 suggests that the fluctuations become increasingly intense as the system approaches the critical point, contributing to the divergence in specific heat. Understanding the role of critical fluctuations in the glass transition is crucial for innovating and improving a wide range of materials for energy storage, materials design, biomedical applications, food preservation, and environmental sustainability. These advancements can lead to materials with superior properties, optimized manufacturing processes, and applications that meet the demands of modern technology and sustainability challenges.

Global population: from Super-Malthus behavior to Doomsday criticality

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r ( t ) or relaxation time τ ( t ) = 1 / r ( t ) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1 ) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ' t / T C - t , whereT C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

Phase Equilibria and Critical Behavior in Nematogenic MBBA-Isooctane Monotectic-Type Mixtures

The transition from the isotropic (I) liquid to the nematic-type (N) uniaxial phase appearing as the consequence of the elongated geometry of elements seems to be a universal phenomenon for many types of suspensions, from solid nano-rods to biological particles based colloids. Rod-like thermotropic nematogenic liquid crystalline (LC) compounds and their mixtures with a molecular solvent (Sol) can be a significant reference for this category, enabling insights into universal features. The report presents studies in 4'-methoxybenzylidene-4-n-butylaniline (MBBA) and isooctane (Sol) mixtures, for which the monotectic-type phase diagram was found. There are two biphasic regions (i) for the low (TP1, isotropic liquid-nematic coexistence), and (ii) high (TP2, liquid-liquid coexistence) concentrations of isooctane. For both domains, biphasic coexistence curves' have been discussed and parameterized. For TP2 it is related to the order parameter and diameter tests. Notable is the anomalous mean-field type behavior near the critical consolute temperature. Regarding the isotropic liquid phase, critical opalescence has been detected above both biphasic regions. For TP2 it starts ca. 20 K above the critical consolute temperature. The nature of pretransitional fluctuations in the isotropic liquid phase was tested via nonlinear dielectric effect (NDE) measurements. It is classic (mean-field) above TP1 and non-classic above the TP2 domain. The long-standing problem regarding the non-critical background effect was solved to reach this result.

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.

Pretransitional Effects of the Isotropic Liquid-Plastic Crystal Transition

We report on strong pretransitional effects across the isotropic liquid-plastic crystal melting temperature in linear and nonlinear dielectric response. Studies were carried out for cyclooctanol (C8H16O) in the unprecedented range of temperatures 120 K < T < 345 K. Such pretransitional effects have not yet been reported in any plastic crystals. Results include the discovery of the experimental manifestation of the Mossotti Catastrophe behavior, so far considered only as a hypothetical paradox. The model interpretations of experimental findings are proposed. We compare the observed pretransitional behavior with the one observed in octyloxycyanobiphenyl (8OCB), typical liquid crystal (LC), displaying a reversed sequence of phase transitions in orientational and translational degrees of order on varying temperature. Furthermore, in its nematic phase, we demonstrate first-ever observed temperature-driven crossover between regions dominated by isotropic liquid and smectic A pretransitional fluctuations. We propose a pioneering minimal model describing plastic crystal phase behavior where we mimic derivation of classical Landau-de Gennes-Ginzburg modeling of Isotropic-Nematic-Smectic A LC phase behavior.

High-pressure behavior of dielectric constant in a binary critical mixture

An alternative design of the measurement capacitor for high-pressure studies of complex liquids or soft matter systems is presented. Subsequently, results for the precritical anomaly of dielectric constant in 1-nitropropane-octane critical mixture are reported. First, the pressure dependence of the critical consolute temperature T_{C} up to P=0.55GPa was determined and portrayed using the derivative-based analysis. Second, temperature and pressure evolutions of dielectric constant on approaching the critical consolute point at (T_{C}=304.1K and P_{C}=403MPa) were studied. They revealed that the pretransitional anomaly ɛ(P→P_{C}) is notably more pronounced than for ɛ(T→T_{C}). For both paths, the static domain extends even to as low frequency as f=100Hz, whereas for tests under atmospheric pressure, they require at least f=100kHz. The discussion of the impact of correction-to-scaling terms, including the unique case of the pressure paths, is also presented.

‘Quasi-Tricritical’ and Glassy Dielectric Properties of a Nematic Liquid Crystalline Material

Results of dielectric studies in the nematic and isotropic liquid phases of pentylcyanobiphenyl (5CB), a model rod-like liquid crystalline material, are shown. They are based on the discussion of the evolution of dielectric constant ( ε ), its changes under the strong electric field (nonlinear dielectric effect, NDE), and finally, the primary relaxation time. It is shown that changes in ε T and NDE are entirely dominated by the impact of pretransitional fluctuations (pre-nematic and pre-isotropic, respectively) which are associated with the weakly discontinuous character of the isotropic–nematic phase transition. This influence also extends for the low-frequency, ionic species dominated, region. Notable, that the derivative-based and distortions sensitive analysis revealed the tricritical nature of the I-N transition. Although the glass transition in 5CB occurs in the deeply supercooled state at T g ≈ − 68 ° C , the dynamics (changes of the primary relaxation time) follow a previtreous pattern both in the isotropic and in the nematic phase. Finally, the discussion of the ’molecular’ vs. ‘quasi-critical’ characterizations of the isotropic and nematic phases is presented. It shows the evident prevalence of the ‘quasi-critical-picture’, which offers the consistent temperature parameterization in the total tested temperature range.

Universal behavior of the apparent fragility in ultraslow glass forming systems

Despite decades of studies on the grand problem of the glass transition the question of well-defined universal patterns, including the key problem of the previtreous behavior of the primary (structural) relaxation time, remains elusive. This report shows the universal previtreous behavior of the apparent fragility, i.e. the steepness index mP (T > Tg) = d log10τ(T)/d( Tg/T). It is evidenced that mP(T) = 1(T - T*), for T → Tg and  T*= Tg - Δ T*. Basing on this finding, the new 3-parameter dependence for portraying the previtreous behavior of the primary relaxation time has been derived: τ(T) = CΩ((T - T*)/T)-Ω × [exp((T - T*)/T)]Ω. The universality of obtained relations is evidenced for glass formers belonging to low molecular weight liquids, polymers (melt and solid), plastic crystals, liquid crystals, resins and relaxors. They exhibit clear preferences either for the VFT or for the critical-like descriptions, if recalled already used modeling. The novel relation can obey even above the dynamic crossover temperature, with the power exponent Ω ranging between ~17 (liquid crystals) to ~57 (glycerol), what may indicate the impact of symmetry on the previtreous effect. Finally, the emerging similarity to the behavior in the isotropic phase of nematic liquid crystals is recalled.

Pretransitional behavior of the nonlinear dielectric effect for the liquid-solid transition in nitrobenzene

The nonlinear dielectric effect describes changes of dielectric permittivity induced by the strong electric field. This report shows the evidence for the critical-like pretransitional behavior for the liquid-solid transition in the supercooled nitrobenzene. Hallmarks of such behavior extend even above the melting temperature. A method for the analysis of pretransitional effects, avoiding the biasing impact of the noncritical background contribution, is proposed.

Nonlinear dielectric effect in supercritical diethyl ether

Nonlinear dielectric effect (NDE) describes changes of dielectric permittivity induced by a strong electric field in a liquid dielectric. The most classical finding related to this magnitude is the negative sign of NDE in liquid diethyl ether (DEE), recalled by Peter Debye in his Nobel Prize lecture. This article shows that the positive sign of NDE in DEE is also possible, in the supercritical domain. Moreover, NDE on approaching the gas-liquid critical point exhibits a unique critical effect described by the critical exponent ψ ≈ 0.4 close to critical temperature (T(C)) and ψ ≈ 0.6 remote from T(C). This can be linked to the emergence of the mean-field behavior in the immediate vicinity of T(C), contrary to the typical pattern observed for critical phenomena. The multi-frequency mode of NDE measurements made it possible to estimate the evolution of lifetime of critical fluctuations. The new way of data analysis made it possible to describe the critical effect without a knowledge of the non-critical background contribution in prior.

Nonlinear dielectric response at the excess wing of glass-forming liquids

We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the α relaxation where, in agreement with previous reports, a strong increase of dielectric constant and loss is found.

Nonlinear response theory for Markov processes: simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.