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.

The glass transition phenomenon is one of key challenges of the modern material science, condensed matter physics and soft matter physics12345. For the latter it constitutes even the general reference for dynamics in the variety of systems within this category5. Glass transition physics is also recognized as one of key references for the general science of collective phenomena, aimed to discover properties emerging from complex correlations6. The practical significance of the glass transition extends from glass7, petroleum8, plastics9, pharmaceutical10 and food industries11 to geophysics12 and issues related to environmental protection9.

However, in the last decade experimental results appeared that significantly disrupted much of the established wisdoms in glass transition physics. First, Hecksher et al.13 presented analysis of the evolution of the primary relaxation time in 42 supercooled low molecular weight glass forming liquids and noted a clear preference for parameterization without a “finite-temperature” divergence. This coincided with the earlier discovery of Tanaka14 that “dynamic” and “thermodynamic” estimates of the ideal glass Kauzmann temperature15, located below the glass temperature T, differ qualitatively.

These findings became a kind of “experimental Rosetta Stone”, inspiring qualitatively new theoretical searches in the glass transition physics34616171819202122.

In this report, 42 experimental data-sets from the paper by Hecksher et al.13 are re-analysed. Due to the implementation of the novel, “model free” analysis it is shown that for each set of these data the dynamics is associated with the finite temperature divergence, contradicting the key conclusion of ref. 13. Subsequently, the analysis is extended for 13 data-sets covering also liquid crystals, plastic crystals, spin glass-like systems, and polymers. Basing on results obtained it is indicated that the proper strategy for the ultimate insight into dynamics of glass forming systems may be comprehensive studies of different categories of glass formers.

The new “model free” approach, explores the reciprocal of the Dyre-Olsen (DO) activation energy temperature index 1/I = [−dlnΔE/dlnT]−1, where ΔE(T) defines the temperature-dependent apparent activation energy23. A preference for parameterization with the finite-temperature divergence is clearly shown and the novel metric characterizing arbitrary glass former is proposed2324. Finally, the novel way of determining the ideal glass Kauzmann temperature (T) which solves the fundamental puzzle of Tanaka14 is proposed.

As mentioned above, the basic artifact constituting the check point for theoretical models of the glass transition is the optimal parameterization of the evolution of primary relaxation time τ(T) or viscosity η(T) upon approaching T, appeared to be elusive. The most basic feature of previtrification processes is the dramatic increase of the apparent activation energy what gives rise to the general super-Arrhenius equation (SA)346: where R denotes the gas constant. Parallel equations are valid for viscosity, diffusion oefficient, and resistivity325. For ΔE(T) = ΔE = const one obtains the simple Arrhenius relation.

This research report focuses on τ(T) behavior, which can be estimated with particularly high resolution and reliability via modern broad band dielectric spectroscopy from coordinates of primary relaxation loss curves peaks3. However, conclusions presented below extend also for the other aforementioned dynamic properties. Unfortunately, the general SA eq. (1) is not directly applicable, due to the unknown form of ΔE(T) evolution. Consequently, alternative equations have been used. The most dominant is the Vogel-Fulcher-Tammann (VFT) dependence3262728: where D denotes the fragility strength coefficient. Experiments for organic molecular glass forming liquid glass yield most often T0 ≈ T − 30K.

The coefficient D is considered as one of the most important metrics of fragility, which orders SA dynamics of molecularly different glass forming systems32930. Assuming a “universal value” for the prefactor τ0 = 10−14 s and τ(T) = 100 s one obtains relation D ≈ 590/(m − 16), where is the basic fragility metric2930.

The unique position of the VFT equation is also associated with the fact that it became a key checkpoint for basic glass transition theories/models3461421. The most notable is Adam-Gibbs theory331, in which the ultraviscous liquid consists of a number of independently relaxing regions, composed of a group of atoms or molecules that can rearrange cooperatively. On cooling toward T the configurational entropy of the system diminishes as the size of the cooperatively rearranging regions (CRR) grows progressively larger, leading to an increase in the structural relaxation time, expressed via331: where Δμ defines the free energy barrier between CRRs, S is the configurational entropy related to the difference between the entropy of the metastable supercooled liquid state and the corresponding equilibrium crystal, and A is a constant. Combining eqs. (1) and (3) one obtains: ΔE(T) ∝ 1/S(T).

The AG eq. (3) can be transformed to the VFT form assuming S = S0(1 − T/T) and T0 = T31. The latter denotes the extrapolated below T temperature for which entropies of the ultraviscous liquids and the “ground, stable” crystalline state matches3631. This “ideal glass transition temperature”, often recalled as the Kauzmann temperature (T)15, is recognized alternatively as one of the most fundamental or controversial properties of glass forming liquids34621. Basically, T is estimated from thermodynamic heat capacity studies, but the above discussion opened the route for the much more experimentally convenient estimations via the VFT equation346. This formed the basis for research regarding the coincidence of the “thermodynamic” and “dynamic” estimations of T. The ultimate answer to this question is closely related to one of the most basic problems of glass transition physics, namely, if the vitrification is associated with a hidden phase transition well below the laboratory T7. A milestone result was reported in 2003 by Tanaka14, who compiled experimental data for 18 ultraviscous liquids and concluded that: “…T0 systematically increases from unity with a decrease in the fragility (i.e.: D), contrary to the common belief…”. In subsequent years this result had been reduced to the generalized message13: “…Tanaka presented a compilation of data showing that T0 = T” and became a significant source of questioning even the experimental existence of T. In 2008 Hecksher et al.13 carried out fitting comparison of τ(T) data for 42 glass forming low molecular weight organic liquids in the ultraviscous domain. They showed notable prevalence of parameterization via two formal functions (FF) without the “finite temperature” “divergence” over the VFT parameterization. In their conclusions, Hecksher et al.13 stated: “The observation that data are well fitted by the VFT equation was used to justify a search for models with a dynamic divergence. Our findings indicate that this is probably not a fruitful route. Thus, with Occam's razor in mind —‘it is vain to do with more what can be done with fewer’—we suggest that in the search for the correct theory for ultraviscous liquid dynamics, theories not predicting a dynamic divergence of the VFT form should be focused on.”

Refs. 13,14 became very influential references for searching new paths in glass transition physics and stimulating the search of new equations portraying τ(T) or η(T) SA evolution without a finite temperature divergence. The possible lack of the finite temperature divergence below T and then also the non-existence of the Kauzmann temperature in “dynamic” τ(T) link or η(T) studies significantly questioned also the hypothetical connection between the glass transition and phase transitions/critical phenomena physics41617181920.

The essential importance of problems discussed above, particularly Kauzmann temperature, has been clearly strengthen in the recent review4: “…It would be a major theoretical accomplishment to identify logically airtight tests that could establish whether the glass transition in a given system or model is caused by a dearth of entropy or by purely kinetic constraints. This would enable a currently lacking unambiguous distinction between correlations, such as are observed between kinetics and thermodynamics in many glass-forming systems, and causal relations…”.

The response to the above fundamental questions is the focus of the current report. First, the same 42 sets of data as used by Hecksher et al.13 for ultraviscous low molecular weight liquids (L), have been re-analyzed. The assembly of experimental results was supplemented by 13 sets of τ(T) data from the authors in ref. 23, covering also glass forming polymers (P), liquid crystals (LC), orientationally disordered crystals (ODICs, plastic crystals) and spin-glass-like systems (SGLs). It is notable that the main-stream discussion of “previtreous” dynamics focuses on (L) and (P) cases, and the rest of systems are often considered as separate issues in glass transition physics3. This is particularly notable for the SGLs case. As in ref. 13 the analysis was carried out in the low-temperature dynamic domain for , where T denotes the dynamic crossover temperature. The up-to-date discussion related to the latter can be found in ref. 22.

In this report we show the existence of a new singular temperature 0 < T < T and the new, local symmetry related parameter n, characterizing arbitrary glass former and indicative for the finite-temperature divergent dynamics. All these lead to the explanation of the discrepancy between T0 (VFT) and T (Kauzmann) temperatures noted by Tanaka14 and indicates a new dynamic and model-free way of analysis of dynamics in ultraviscous/ultraslowing glass forming systems.

Data analysis

Hecksher et al.13 indicated that a direct comparison of the fitting quality of experimental τ(T) data may not be a decisive route. They proposed to apply the activation energy temperature index, introduced earlier by Dyre and Olsen (DO)24: This can serve as the alternative metric of fragility, with a form recalling the Grueneisen parameter23. However, there is a basic problem with determining ΔE(T) from τ(T) experimental data. The derivative procedure, sometimes used erroneously, yields an apparent activation enthalpy: instead of ΔE(T)33. So, the latter has to be calculated directly from eq. (1) via: , as it was done in in ref. 13. Unfortunately, this procedure requires prior knowledge of the prefactor τ0. Hecksher et al.13 assumed two universal values of τ0 = (10−14, 10−13)s for each of 42 tested ultraviscous liquids. Such values are often considered as “universal/averaged” prefactors, and have also some theoretical justification31330. Notwithstanding, in practice the analysis based on the VFT parameterization showed a broader range of 10−16 s < τ0 < 10−10 s33. The improper value of τ0 assumed for a given system could therefore yield notable biasing in the evolution of ΔE(T).

In this report a novel procedure introduced recently is employed23. It is based on the numerical solution of the differential equation 23, resulting directly from eq. (1), which avoids the requirement of knowing the prefactor in advance. The description of the employed procedure, avoiding the a priori knowledge of the prefactor τ0, is presented in the Supplementary Information.

We also employ the recent authors' finding23 that the reciprocal of the DO index in the ultraviscous/ultraslowing domain follows a linear dependence for basic relations employed for τ(T) parameterization: VFT262728, Avramov-Baessler (AB)3435, Waterton-Mauro (WM, MYEGA)2036 and the critical-like (Crit.)3337. The last one, obeying in LCs and ODICs, is particularly important for the current paper222337: where . This equation is optimal for liquid crystals (LC, ϕ ≈ 9), ODICs (ϕ = 9 − 15), selected clearly uniaxial low molecular liquid (LMW), polymers (P) for which ϕ = 9 − 12 and spin-glass-likes systems (SGLs) where ϕ = 9 − 12222337. For the latter it is often assumed, by convention, that T = T3.

Basing on refs. 13,23 one can write the following set of equations: where FF1 and FF2 are “formal functions”, without the physical background, introduced by Hecksher et al.13 to show superiority of the description without the finite-temperature divergence (below T) over the VFT parameterization. The “crit.” case is for the asymptotic approximation.

The MYEGA (WM)20 equation is given via and the AB36 relation by . Is notable that relations in eq. (7), related to formal functions (FF1 and FF2) proposed by Hecksher et al.13, do not follow the linear behavior, i.e. 1/I(T) ≠ aT + b. For the VFT and “critical-like” dependences 1/I(T) is the linear function for which both a ≠ 0 and b ≠ 0. For AB equation 1/I(T) = 1/(D − 1) = b = const and for MYEGA (WM) dependence 1/I(T) = (1/C)T = aT. The list of systems for which τ(T) experimental data are analyzed in the given report is presented in Table 1, where abbreviations, full names, and symbols used in plots are listed.

Table 1

Glass-forming liquids collected from refs. 13 and 23 which are included in the present analysis. The system abbreviations, name of each liquid as well as the symbol are listed. The symbols are those used in Figs. 1–2. More detailed information is provided in the Supplementary Information

No	Systems	Full name	Symbol
1	3Ph1P	3-phenyl-1-propanol
2	3Sty	3-styrene
3	5-PP	5-polyphenyl-ether
4	AFEH	2-phenyl-5-acetomethyl-5-ethyl-1,3-dioxocyclohexane
5	BePh	benzophenone
6	BN	butyronitrile
7	BP2IB	biphenyl-2yl-isobutylate
8	BPC	3,3,4,4benzophenonetetra carboxylic dianhydride
9	Cum	isopropyl-benzene
10	dBAF	dibutyl-ammonium-formide
11	DBP	dibutyl-phtalate
12	DC704	tetraphenyl-tetramethyl-trisiloxane
13	DCHMMS	dicyclohexyl-methyl-2-methylsuccinate
14	DEP	diethyl-phtalate
15	DHIQ	decahydroisoquinoline
16	dIBP	di-iso-butyl-phtalate
17	DMP	dimethyl-phtalate
18	DOP	dioctyl-phtalate
19	DPG	dipropylene-glycol
20	DPGDME	dipropylene-glycol-dimethyl-ether
21	EH	2-ethyl-hexylamine
22	ER	diglycidyl-ether-of-bisphenol A (epoxyresin)
23	FAN	3-fluoro-aniline
24	Gly	glycerol
25	KDE	cresolphthalein-dimethylether
26	mTC	m-tricresyl-phosphate
27	MTHF	2-methyl-tetrahydrofurane
28	mTol	m-toluene
29	OTP	o-terphenyl
30	PDE	phenolphthalein-dimethylether
31	PG	1,2-propandiol (propylene-glycol)
32	PHIQ	perhydroisoquinoline
33	PPG	polypropylene-glycol
34	PT	pyridine-toluene
35	Sal	phenyl-salicylate (salol)
36	SB	sucrose-benzonate
37	Sqa	squalane
38	TCP	tricresyl-phosphate
39	tNB	trisnaphthylbenzene
40	TPE	triphenyl-ethylene
41	TPG	tripropylene-glycol
42	Xyl	xylitol
43	C8-OH	cyclooctanol
44	C7-OH	cycloheptanol
45	Cnc6	cyanocyclohexane
46	Cnadm	cyanoadamantane
47	NPANPG0.30	neopentylalcohol – neopentylglycol(32%)
48	SG	Ferrofluid with 5% of Fe1-xCx (x = 0,2 0,3)
49	8*OCB	isooctylcyanobiphenyl
50	E7	eutectic mixture of 4 nematic LC
51	5*OCB	Isopentylcyanobiphenyl
52	Srb	sorbitol
53	PS700	Polystyrene(Mw ≈ 700)
54	Prop	1-Propanol
55	Eth	Ethanol

The analysis based on derivation of experimental data always leads to a notable scatter in the output. To reduce this artifact, an innovative numerical analysis based on the Savitzky-Golay numerical filtering idea, introduced in refs. 22,23, was applied.

Results and discussion

Fig. 1 presents the evolution of the reciprocal of the DO index determined from τ(T) data for 42 molecular liquids explored earlier in Hecksher et al.13 report. For all ultraviscous systems the linear behavior of 1/I(T) = b + aT takes place. Such behavior proves that using of FF1 and FF2 functions for these systems, suggested as optimal one in ref. 13, is unjustified. (see the non-linear temperature dependence for eqs. 6, 7)

Figure 1

Reciprocal temperature dependence of the DO index.

The analysis has been done using the same sets of τ(T) experimental data by Hecksher et al.13. The figure is divided in two different temperature ranges (a) and (b) as was reported by Hecksher et al.13. Characteristics of liquids related to the given symbol are presented in Table 1.

Fig. 2 shows that coefficients a ≠ 0 and b ≠ 0 for all system presented in Fig. 1. Hence, in each case the evolution of τ(T) is associated with the finite temperature divergence behaviour23. Fig. 2 contains also results for supplementary 13 glass formers in the ultraslow domain, covering liquid crystals, plastic crystals, polymers and spin glasses23. The linear regression fit can yield values of a and b and subsequently the unequivocal estimations of the singular temperature T via I(T = T)−1 = 0 and the coefficient 23. They can be used as the basic input parameters for the following generalized temperature dependence of the configurational entropy23: The summary of calculated results is presented in the Table in Supplementary Material, where values of n, m, T, and T are given.

Figure 2

Results of the linear regression analysis of 1/I(T) plot for the 55 glass formers under study.

Results are for the ultraviscous/ultraslowing domain. The non-zero values of coefficients a and b for 1/I(T) = aT + b dependence are shown, with error bars, for all experimental sets of experimental data from ref. 13 by Hecksher et al. as well as for data from ref. 23.

The discussion of eq. (8), including the link to the local symmetry and the possibility of unified presentation of experimental data ranging from plastic crystal to liquid crystals via polymers and low molecular liquid crystals is presented in ref. 23.

The graphical summary of key results for all (55) tested glass formers is presented in Fig. 3. There are three characteristic domains in Fig. 3:

Figure 3

Summary of the data dynamics analysis.

The analysis focuses on the evolution of the parameter (n) for different groups of compounds. Fig. 3a shows the histograms of liquid systems for both groups of data. Fig. 3b illustrates the evolution of the coefficient (n) arranged according to the nomenclature in Table 1.

n ≈ 3/2 takes place in system with molecular uniaxiality and then local orientation ordering. They are LCs, polymers like polystyrene and selected molecular liquids. These systems obey the critical-like description with a singular temperature T = T

n ≈ 0.2 is obtained for systems with dominating positional symmetry. This is the case of ODICs and SGLs where molecules are positionally ordered in the crystalline network but can more or less freely rotate. These systems obey the critical-like description with the singular temperature T = T

n ≈ 1 is valid exclusively for the VFT equation. It seems that such parameterization is acceptable only for materials with molecular without a specific symmetry. In this case the singular temperature T = T0.

Hence, the generalized configurational entropy eq. (8) is able to capture the dynamics of any glass former discussed in this report, with the power exponent n ranging from ca. 0.2 to 3/2.

It is notable that experimental τ(T) data used by Hecksher et al.13, are characterized by the average value of the coefficient n ≈ 1.2. Hence they are inherently shifted towards the model showing elements of “uniaxial, orientational symmetry,” and the VFT parameterization is inherently non-optimal for the vast majority of molecular liquids discussed in ref. 13. It is worth recalling here that implementation of the linearized derivative based analysis2333 showed that for compounds characterized by n = 1.2 − 1.4 both VFT and critical-like descriptions can yield comparably reliable fits of experimental data. However for n ≈ 1 and n ≈ 3/2 the prevalence of the VFT and critical like parameterizations, respectively, are clear (see also ref. 23).

Results of this report and ref. 23 clearly show that the VFT equation can be considered as the optimal model exclusively for systems characterized by n = 1. Consequently, for supercooled glass forming systems where n ≠ 1 the implementation of the VFT equation can yield only “effective” values of D and T0, and thus the latter must differ from the Kauzmann temperature. This may be recognized as the source of fundamental discrepancy between T0 and T discovered by Tanaka14, as well as noted by him linear dependence between T0/T and D.

Fig. 4b shows that the fundamental discrepancy found by Tanaka can be absent if the “dynamic singular temperature” is determined without an underlying model-equation, i.e. as T from the 1/I(T) plot. In such case, T/T ≈ 1 for glass formers characterized by the arbitrary values of n. The left part of Fig. 4 shows notable discrepancy between T and T0, particularly for “critical-like” borders (n ≈ 0.2 and n ≈ 3/2) and the coincidence when n → 1. Hence the analysis via 1/I(T) plot offers a new tool for estimating the Kauzmann temperature from “dynamic” experimental τ(T) or η(T) data. Fig. 4 also indicates that it is possible to estimate the Kauzmann temperature even for glass forming LCs, ODICs, uniaxial polymers and SGLs: in this case T = T = T.

Figure 4

Comparison among the singular T, T, and T0 temperatures.

Part (a) compares the values of T with T0, where the latter was estimated via the VFT parameterization. Part (b) shows the comparison between the singular temperature estimated via I(T = T)−1 = 0 and values of the Kauzmann temperature taken from ref. 2 by Tanaka. “PS” means positional symmetry, “OS”- is for the orientational symmetry and VFT is linked to the “no-symmetry” (NS) case.

Conclusions

Temperature evolutions of the primary relaxation time τ(T) or viscosity η(T) in the ultraviscous domain are the most often tested and discussed experimental artifact in the glass transition physics. The way of their portrayal is considered as one of key references for still puzzling theoretical modelling34561314151617181920212223242530313233383940. Notwithstanding, amongst glass transition researchers a discouraging conviction exists that comparisons of fitting quality of τ(T) or η(T) data with different model-equations, so far carried out mainly via the residual analysis, is likely not to be conclusive. This is strengthen by the fact that the glass transition occurs at a substantial temperature away from the putative divergence23.

However, few years ago Dyre et al.1324 proposed an innovative solution of this problem, namely the transformation of τ(T) or η(T) experimental data to the case-sensitive apparent activation energy temperature index form I(T) = −dlnΔE(T)/dlnT. The subsequent analysis of τ(T) data for 42 low molecular weight liquid disqualified the general validity of the VFT parameterization. The successful implementation of FF1 and FF2 formal functions, without a finite temperature divergence, became a new inspiration for the glass transition physics in last years13. This report and the preceding ref. 23 recall this concept, with some notable improvements:

the new way of determining the apparent activation energy ΔE(T) and then I(T), avoiding the biasing impact of τ0 in the SA eq. (1), was introduced (see Supplementary information). It was supported by numerical filtering based on Savitzky-Golay principle23. This routine can yield non-biased values of ΔE(T) and I(T) from τ(T) or η(T) experimental data.

The analysis was focused on the reciprocal of the apparent activation energy temperature index, since it appeared that for all 55 glass formers: 1/I(T) = a + bT with a ≠ 0 and b ≠ 0.

The analysis covered not only a single category of glass formers but also liquid crystals, plastic crystals (ODIC) or even spin-glass-like systems.

Regarding relations without a “finite temperature divergence”: BA3435 or WM (MYEGA)2036 equations are related to coefficients b = 0, a = 0 and FF1 and FF2 functions13 1/I(T) follows a nonlinear dependence (see eqs. 6, 7). Such behavior is in clear disagreement with the experimental evidence presented above. The fact that experimental 1/I(T) dependences follow solely a linear dependence, allow for the unequivocal determining of the “dynamics divergence temperature” via 1/I(T = T) = 0, i.e. T = a/b condition.

The extension of analysis for few categories of glass forms (this report and ref. 23) led to finding a new general metric . Value n ≈ 0.18 is related to ultraslowing systems with dominated positional symmetry (ODICs.) and n ≈ 1.6 for systems with dominated orientational symmetry (LCs, …). For these ultraslowing systems the critical-parameterization yields a reliable approximation (see also ref. 23).

The VFT equation is optimal only for a limited number of glass formers where n = 1. These facts show that direct “fitting goodness” comparisons between VFT and other model equation based on τ(T) or η(T) experimental data for arbitrary selected glass formers are inherently non-conclusive. Values of the coefficient n, the singular temperature T as well as T and fragility m for 55 tested glass formers are given in the Table in Supplementary Information.

It is notable that the VFT relation appears to be the optimal for the limited number of glass forming systems where n = 1. For glass former characterized by n ≠ 1, the VFT equation can serve solely as an empirical, effective, tool for parameterization. Consequently, we postulate that results assuming the general validity of the VFT equation should be reanalyzed, particularly regarding discussions involving T0 or D parameters refs. 3,4,5,6,38,39,40 as well as refs. recalled therein.

Results of this paper also yield the possibility of solving one of the most important cognitive problems of the glass transition physics, namely the discrepancy between the “dynamic”, i.e., based on the VFT equation, and “thermodynamic” (from heat capacity data) estimations of the ideal glass (Kauzmann) temperature. These estimations match if the “dynamic” estimation is based on the model-independent way of analysis, via the 1/I(T) plot. All these can be essential for the theoretical modeling23456 and may also lead to questions regarding features of the amorphous glass state in domains T = T < T < T and T < T. The fundamental plot in ref. 14 by Tanaka showing the linear dependence of T/T0 vs. D, with 0.5 < T < T0 < 2.2, resulted from the mentioned inadequacy of the VFT equation. It is notable that results presented by Tanaka omitted LCs, ODICs or SGLs, where VFT equation cannot yield even the effective reliable parameterization.

Results of this report, supplemented by ref. 23, show that the still dominated in the glass transition and soft matter physics, VFT equation or its parallels like Williams-Landolt-Ferry (WLF) equation, can be considered only as an “effective tool” for portraying experimental data. Their parameters has a clear physical meaning only for the limited number of system characterized by n = 1. Otherwise, values of D and T0 are biased and have the meaning of an “effective fitting parameter”. All these can indicate that numerous research reports based on the general validity of the VFT equation should be reconsidered.

In 1995 Philip W. Anderson, a Nobel Prize-winning physicist, wrote41: “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. …. This could be the next breakthrough in the coming decade.” But the long awaited breakthrough is still postponed…13467. One of clearly formulated reasons is the extremely sophisticated and complex new physics behind the glass transition234567. But the delay of the long awaited breakthrough may be also associated with the model-dependent insight which may bias or even hide fundamental artifacts. In this report we propose the new, model-free route.