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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 T K is given: S = S 0 t n , where t = T - T K / T . The exponent n is hypothetically linked to dominated local symmetry. Such a behaviour is coupled to previtreous evolution of heat capacity Δ C P c o n f i g . T = n C / T 1 - T K / T n - 1 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.

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 m P ( T  >  T g ) =  d log 10 τ( T )/ d (  T g / T ). It is evidenced that m P ( T ) = 1( T  −  T *), for T  →  T g and   T *=  T g  − 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 ) =  C Ω (( 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.

The global population P ( t ) (growth from 10,000 BCE to 2023) is discussed in frames of the Verhulst-type scaling, recalling the sustainable development concept. The analysis focuses on the per capita global population growth rate, for which the analytic counterpart is considered: G P ( P ) = ( d P ( t ) P ( t ) ) d t = d l n P ( t ) d t . The focused insight reveals two near- linear domains for G P ( P ) changes: from ~ 700 CE till ~1968 and from ~1968 till 2023. It can be considered a reference pattern for long-term global population changes. For models recalling the Verhulst-type scaling, such analysis indicates that a single pair of growth rate and system resource coefficients ( r , s ) should describe the rise in the global population. However, the Verhulst relation with such effective parameters does not describe P ( t ) changes, which raises the question of whether it is adequate to describe global population changes. Notably is the new way of data preparation, based on their collections from various sources and numerical filtering to obtain a ‘smooth’ optimal set. The changes of P ( t ) were analyzed via the ‘reversed protocol’ analysis, in comparison to the standard pattern, namely: ( i ) first, the linearized, distortions-sensitive transformation of P ( t ) data is carried out; it indicates domains where the validated application of a given scaling equation is possible and yields optimal values of relevant parameters, ( ii ) the final fitting via the selected scaling equation is carried out for identified domains, and using obtained optimal values of parameters. The analysis reveals links between G P ( P ) local ‘disturbations’ and some historical and prehistorical reference events, showing their global scale impacts.

This report discusses the impact of nanoparticles on glass-forming systems composed of a liquid crystalline (LC) mixture E7 and paraelectric BaTiO3 particles (d≈50 nm, globular), tested via broadband dielectric spectroscopy. In the isotropic phase, critical changes in the dielectric constant are shown. They are related to the weakly discontinuous nature of the isotropic–nematic transition. In the nematic phase, two primary relaxation times/processes and DC electric conductivity are considered, down to the glass temperature Tg. The prevalence of portrayals via the ‘double exponential’ MYEGA equation and the critical & activated Drozd-Rzoska relation for dynamic properties are shown. For the primary loss curve, critical-like changes of its maximum (peak) are evidenced: εpeak″∝1/T−Tg* for Tg