Universal critical-like scaling of dynamic properties in symmetry-selected glass formers

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.

Critical Insight into Pretransitional Behavior and Dielectric Tunability of Relaxor Ceramics

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with "weakly discontinuous" local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of "dielectric constant" changes with the "diffused maximum" near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the "glassy" dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the "deep" ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic "critical & activated" evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes.

The impact of ionic contribution to dielectric permittivity in 11CB liquid crystal and its colloids with BaTiO3 nanoparticles

The report shows the temperature behavior of the real part of dielectric permittivity in the static (dielectric constant) and low-frequency (LF) domains in bulk samples of 11CB and its BaTiO₃-based nanocolloids. The study covers the isotropic liquid (I), nematic (N), smectic A (SmA), and solid crystal (Cr) phases. For each phase, the dominance of pretransitional fluctuations, significantly moderated by nanoparticles, is shown. The authors consider separate focuses on the dielectric constant [Formula: see text] evolution in the static domain, yielding mainly response from permanent dipole moment and its arrangement, and in the low-frequency (LF) domain [Formula: see text] (where [Formula: see text] is for the real part of dielectric permittivity in the LF domain), which is associated solely with ionic-related polarization mechanisms. All of these led to new experimental evidence concerning I-N, N-SmA, and SmA-solid transitions, focusing on the strength and extent of pretransitional effects, critical exponents, and phase transitions discontinuities. The strong evidence for pretransitional effects near the SmA-Cr transition is notable, particularly regarding [Formula: see text]. Studies are supplemented by the discussion of DC electric conductivity-a parameter also related to the LF domain. Finally, the validity of the relation [Formula: see text] (where f stands for frequency, and A is a constant parameter), often used for discussing dielectric spectra in LC compound and its nanocolloids in the LF domain, is examined.

The fluctuation-driven dielectric properties of liquid crystalline 8OCB and its nanocolloids

Results of broadband dielectric spectroscopy studies in liquid crystalline octyloxycyanobiphenyl (8OCB) and its colloids with BaTiO₃ nanoparticles (paraelectric, diameter d = 50 nm) are presented. Studies were carried out in isotropic liquid, nematic, smectic A and solid crystalline phases. They are supported by derivative-based and distortion-sensitive analyses, revealing a set of universal scaling patterns for temperature evolution of static and dynamic dielectric properties. All these yielded evidence for a pretransitional fluctuation impact on the dielectric constant, primary relaxation time, loss curve maximum and translational-orientational decoupling associated with anomalous values of the fractional Debye-Stokes-Einstein (DSE) exponent 0.2 < S < 2.2. The evidence for critical like changes in a distribution of relaxation times is shown. For mesophases, a tiny addition of nanoparticles causes permanent orientation of LC molecules, leading even to a 16% increase of the dielectric constant above a maximal value in pure 8OCB. A split of two regions, dominated by pre-isotropic and pre-smectic fluctuations, is evidenced. Model explanations for detected phenomena, particularly in the isotropic liquid phase, are presented. New evidence for a premelting effect in the solid phase is also shown.

New paradigm for configurational entropy in glass-forming systems

We show that on cooling towards glass transition configurational entropy exhibits more significant changes than predicted by classic relation. A universal formula according to Kauzmann temperature [Formula: see text] is given: [Formula: see text], where [Formula: see text]. The exponent [Formula: see text] is hypothetically linked to dominated local symmetry. Such a behaviour is coupled to previtreous evolution of heat capacity [Formula: see text] associated with finite temperature singularity. These lead to generalised VFT relation, for which the basic equation is retrieved. For many glass-formers, basic VFT equation may have only an effective meaning. A universal-like reliability of the Stickel operator analysis for detecting dynamic crossover phenomenon is also questioned. Notably, distortions-sensitive and derivative-based analysis focused on previtreous changes of configurational entropy and heat capacity for glycerol, ethanol and liquid crystal is applied.

Deciphering the Dynamics of Organic Nanoaggregates with AIEE Effect and Excited States: Lipophilic Benzothiadiazole Derivatives as Selective Cell Imaging Probes

An aggregation-induced emission enhancement (AIEE) effect in fluorescent lipophilic 2,1,3-benzothiadiazole (BTD) derivatives and their organic nanoaggregates were studied. A set of techniques such as single-crystal X-ray, dynamic light scattering (DLS), electron paramagnetic resonance (EPR), UV-vis, fluorescence, and density functional theory (DFT) calculations have been used to decipher the formation/break (kinetics), properties, and dynamics of the organic nanoaggregates of three BTD small organic molecules. An in-depth study of the excited-state also revealed the preferential relaxation emissive pathways for the BTD derivatives and the dynamics associated with it. The results described herein, for the first time, explain the formation of fluorescent BTD nanoaggregate derivatives and allow for the understanding of their dynamics in solution as well as the ruling forces of both aggregation and break processes along with the involved equilibrium. One of the developed dyes could be used at a nanomolar concentration to selectively stain lipid droplets emitting an intense and bright fluorescence at the red channel. The other two BTDs could also stain lipid droplets at very low concentrations and were visualized preferentially at the blue channel.

‘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.

Cooperative behavior of molecular motions giving rise to two glass transitions in the same supercooled mesophase of a smectogenic liquid crystal dimer

In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer α-(4-cyanobiphenyl-4'-yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py) throughout both nematic and smectic-A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition (T_{g}) temperatures: The higher T_{g} is due to the freezing of the molecular motions responsible for the relaxation mode with the lowest frequency (μ_{1L}); the lower T_{g} is due to the motions responsible for the two relaxation modes with highest frequencies (μ_{1H} and μ_{2}), which converge just at their corresponding T_{g}. It is shown how the three modes follow a critical-like description via the dynamic scaling model. The two modes with lowest frequencies (μ_{1L} and μ_{1H}) are cooperative in the whole range of the mesophases, whereas the highest frequency mode (μ_{2}) is cooperative just below some crossover temperature. In terms of fragility, at the glass transition, the ensemble (μ_{1H}+μ_{2}) presents a value of the steepness index and μ_{1L} a different one, meaning that fragility is a property intrinsic to the molecular motion itself. Finally, the steepness index seems to have a universal behavior with temperature for the dielectric relaxation modes of liquid crystal dimers, being almost constant at high temperatures and increasing drastically when cooling the compound down to the glass transition from a temperature about 3/4T_{NI}.

Fragility and basic process energies in vitrifying systems

The concept of 'fragility' constitutes a central point of the glass transition science serving as the 'universal' metric linking previtreous dynamics of qualitatively distinct systems. Finding the fundamental meaning of fragility is the 'condicio sine qua' for reaching the long expected conceptual breakthrough in this domain. This report shows that fragility is determined by the ratio between two fundamental process energies, viz. the activation enthalpy and activation energy. The reasoning, avoiding any underlying physical model, is supported by the experimental evidence ranging from low molecular weight liquids and polymers to plastic crystals and liquid crystals. All these lead to the new general scaling plot for dynamics of arbitrary glass former. The limited adequacy of broadly used so far semi-empirical relationships between fragility and the activation energy is shown. Results presented remain valid for an arbitrary complex system and collective phenomena if their dynamics is described by the general super-Arrhenius relation.

Divergent dynamics and the Kauzmann temperature in glass forming systems

In the last decade the challenging analysis of previtreous behavior of relaxation time (τ(T)) in ultraviscous low molecular weight liquids led to the conceptual shift of the glass transition physics toward theories not predicting a “finite-temperature” divergence. This “breakthrough” experimental finding was strengthened by the discovery that “dynamic” (i.e. from τ(T) fitting) and “thermodynamic” estimations of the “ideal glass” (Kauzmann) temperature do not match, what in fact questioned its existence. In this report, due to the novel way of analysis based on the transformation of τ(T) experimental data to the activation energy temperature index form, the clear prevalence of the “finite-temperature” divergence is proved. The obtained “dynamic” singular temperatures clearly coincide with “thermodynamic” estimations of the Kauzmann temperature, thus solving also the second mystery. The comprehensive picture was obtained due to the analysis of 55 experimental data-sets, ranging from low molecular weight liquids and polymers to liquid crystal and plastic crystals.

Distortion-sensitive insight into the pretransitional behavior of 4-n-octyloxy-4'-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4'-cyanobiphenyl (8OCB) with isotropic (I)-nematic (N)-smectic A (SmA)-crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I-N and N-SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid-fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τ(c)(T-T(C))(-φ). In the immediate vicinity of the I-N transition a novel anomaly has been found: Δτ is proportional to 1/(T - T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the 'background behavior'. Experimental results are confronted with the comprehensive Landau-de Gennes theory based modeling.

A universal description of ultraslow glass dynamics

The dynamics of glass is of importance in materials science but its nature has not yet been fully understood. Here we report that a verification of the temperature dependencies of the primary relaxation time or viscosity in the ultraslowing/ultraviscous domain of glass-forming systems can be carried out via the analysis of the inverse of the Dyre-Olsen temperature index. The subsequent analysis of experimental data indicates the possibility of the self-consistent description of glass-forming low-molecular-weight liquids, polymers, liquid crystals, orientationally disordered crystals and Ising spin-glass-like systems, as well as the prevalence of equations associated with the 'finite temperature divergence'. All these lead to a new formula for the configurational entropy in glass-forming systems. Furthermore, a link to the dominated local symmetry for a given glass former is identified here. Results obtained show a new relationship between the glass transition and critical phenomena.

Disentangling molecular motions involved in the glass transition of a twist-bend nematic liquid crystal through dielectric studies

Broadband dielectric spectroscopy spanning frequencies from 10(-2) to 1.9 × 10(9) Hz has been used to study the molecular orientational dynamics of the glass-forming liquid crystal 1",7"-bis (4-cyanobiphenyl-4'-yl)heptane (CB7CB) over a wide temperature range of the twist-bend nematic phase. In such a mesophase two different relaxation processes have been observed, as expected theoretically, to contribute to the imaginary part of the complex dielectric permittivity. For measurements on aligned samples, the processes contribute to the dielectric response to different extents depending on the orientation of the alignment axis (parallel or perpendicular) with respect to the probing electric field direction. The low-frequency relaxation mode (denoted by μ(1)) is attributed to a flip-flop motion of the dipolar groups parallel to the director. The high-frequency relaxation mode (denoted by μ(2)) is associated with precessional motions of the dipolar groups about the director. The μ(1)-and μ(2)-modes are predominant in the parallel and perpendicular alignments, respectively. Relaxation times for both modes in the different alignments have been obtained over a wide temperature range down to near the glass transition temperature. Different analytic functions used to characterize the temperature dependence of the relaxation times of the two modes are considered. Among them, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics on approaching the glass transition.

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

Results of the dual field nonlinear dielectric spectroscopy (NDS) studies in supercooled glass forming epoxy resin EPON 828 are presented. For the NDS, changes of dielectric permittivity induced by DC (rectangular) or AC (sine-wave) pulses of a strong electric field were probed by a weak radio frequency electric field. A clear stretched exponential (x < 1) decay after switching off the DC pulse and a single exponential decay (x = 1) after switching off the AC pulse were found. The same results are presented for preliminary studies in superpressed low molecular glass former di-isobutyl phthalate. This observation may be considered as an argument for the heterogeneous picture of supercooled glass forming materials. The temperature dependences of the stationary responses related to DC and AC strong electric field excitations are also shown. The sensitivity of the applied set up made it possible to detect NDS outputs even for electric fields E(strong) < 10 kV cm(-1), qualitatively weaker than in similar 'nonlinear, dielectric' experimental studies on glass forming materials carried out so far.

Enthalpy space analysis of the evolution of the primary relaxation time in ultraslowing systems

For decades the Vogel-Fulcher-Tammann equation has dominated the description of dynamics of the non-Arrhenius behavior in glass forming systems. Recently, this dominance has been questioned. Hecksher et al. [Nat. Phys. 4, 737 (2008)], Elmatad et al. [J. Phys. Chem. B 113, 5563 (2009)], and Mauro et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 19780 (2009)] indicated superiority of several equations showing no divergence at a finite (nonzero) temperature. This paper shows distortion-sensitive and derivative based empirical analysis of the validity of leading equations for portraying the previtreous evolution of primary relaxation time.

Evidence for critical-like behavior in ultraslowing glass-forming systems

Glass transition constitutes one of main problems of condensed matter physics and material engineering that remains unsolved. The common acceptance of the Vogel-Fulcher-Tammann (VFT) equation for portraying the primary relaxation time or shear viscosity indicated a possible phase transition, hidden below the glass transition temperature (T(g)). Recently Hecksher [Nat. Phys. 4, 737 (2008)] delivered strong empirical arguments that VFT description lacks a direct experimental basis and thus theories not predicting a dynamic divergence should be focused on. We present clear evidence for a superiority of critical-like divergent equation τ(T)=τ(0)(T-T(C))(-ϕ) and T(C)<T(g) for liquid crystalline (LC) glass formers and orientationally disordered crystals (ODIC). Such dependence was already known for spin-glasslike systems and the dynamical scaling model, although the latter was hardly explored so far. The pressure-related behavior is also discussed. Results obtained support arguments for the suggested direct link between critical phenomena and vitrification [Tanaka, Nat. Mater. 9, 324 (2010)]. LCs and ODICs may be considered as simple experimental model systems for the structural glass formers group.

Scaling the dynamics of orientationally disordered mixed crystals

The evolution of the primary relaxation time of orientationally disordered (OD) mixed crystals [(CH(3))(2)C(CH(2)OH)(2)](1-X)[(CH(3))C(CH(2)OH)(3)](X), with 0 < X < or = 0.5, on approaching the glass temperature (T(g)) is discussed. The application of the distortion-sensitive, derivative-based procedure revealed a limited adequacy of the Vogel-Fulcher-Tammann parametrization and a superiority of the critical-like description tau proportional to (T - T(C))(-phi(') ), phi(') = 9-11.5, and T(C) approximately T(g) - 10 K. Basing on these results as well as that of Drozd-Rzoska et al. [J. Chem. Phys. 129, 184509 (2008)] the question arises whether such behavior may be suggested as the optimal universal pattern for dynamics in vitrifying OD crystals (plastic crystals). The obtained behavior is in fair agreement with the dynamic scaling model (DSM) [R. H. Colby, Phys. Rev. E 61, 1783 (2000)], originally proposed for vitrifying molecular liquids and polymers. The application of DSM made it possible to estimate the size of the cooperatively rearranging regions ("heterogeneities") in OD phases near T(g).

Universal pattern for the distribution of relaxation times in the isotropic phase of liquid crystalline n-cyanobiphenyls

A universal pattern emerging from the analysis of the distribution of relaxation times in the isotropic phase of liquid crystalline n-alkylcyanobiphenyls (nCB) from 4CB to 14CB is presented. The increase of the length of nCB molecules causes the high-frequency (short-time) branch of the primary relaxation loss curve to approach the form epsilon(f>fpeak) approximately omega(-n), with n-->1/2 in frequency (omega=2pif) or approximately sqrt[t] in time on cooling toward the isotropic-mesophase "clearing" phase-transition temperature (TC). Recently, such behavior was suggested as a hypothetical universal pattern for diverse glass forming organic liquids on approaching the glass temperature [A. I. Nielsen, T. Christensen, B. Jakobsen, K. Niss, N. B. Olsen, R. Richert, and J. C. Dyre, J. Chem. Phys. 130, 154508 (2009)]. The isotropic phase of rodlike liquid crystalline compounds is considered to be an important experimental model system for studying glassy dynamics since it constitutes a link with the model fluid of hard ellipsoids of revolution.