New Interpretation of Glass Formation in Isomeric Substances: Shifting from Melting‐Point to Melting‐Entropy

Abstract Revealing the critical thermodynamic parameters determining the glass formation of substances is of great significance for understanding the glass transition and guiding the composition design of glass‐forming materials. Nevertheless, the direct access to glass‐forming ability (GFA) by thermodynamics for various substances remains to be substantiated. The strategy to seek the fundamental properties of glass formation is explored several decades ago, as pioneered by Angell, arguing that the GFA in isomeric xylenes depends on the low lattice energy manifested by the low melting point. Here, an in‐depth study is advanced using two more isomeric systems. Surprisingly, the results do not constantly support the reported relationship between the melting point and glass formation among isomeric molecules. Instead, molecules with enhanced glass formability are featured by the properties of low melting entropy without exception. Comprehensive studies of isomeric molecules find that the low melting entropy is roughly accompanied by the low melting point, explaining the apparent link between melting point and glass formation. Progressively, the viscosity measurements of the isomers uncover a strong dependence of the melting viscosity on melting entropy. These results emphasize the significance of the melting entropy in governing the glass formability of substances.


Introduction
Glassy materials are of crucial importance in industries and engineering by virtue of a number of unique properties in practical applications, [1][2][3] but understanding glass formation has been a DOI: 10.1002/advs.202206389 challenge for decades. [4,5] There are considerable criteria involved in the evaluation of the ability of glass formation of various substances, among which the kinetic viscosity (or relaxation time and diffusion coefficient D [6] ) of melts, in particular, melting viscosity m , is a widely accepted parameter. [7][8][9][10] It is also portrayed by two independent variables of the kinetic fragility m [11,12] and the reduced glass temperature T rg , [7] which is the ratio of the glass temperature T g and melting point T m . In contrast, there have been many thermodynamic quantities proposed to associate with glass formation, such as the Gibbs free energy difference of liquids and crystals in the undercooling regions ΔG, [13] interface energy , [14,15] bond energy E b , [16] mixing enthalpy ΔH mix , [17] formation enthalpy ΔH f , [18] mixing entropy ΔS mix , [19] configurational entropy ΔS conf , [20] vibrational entropy ΔS vib , [21] and mismatch entropy S mis . [22] Yet, these criteria are mainly applicable for evaluating the glass formation in specific alloys, and the application to more materials is challenging. Hence, a consensus remains to be clarified to pinpoint a fundamental thermodynamic parameter capable of evaluating the glass formation and guiding the composition design of glassy materials.
To seek such a fundamental thermodynamic property in governing the glass formation of substances, a simple but effective strategy is to focus on isomeric molecules because the difference in intermolecular interactions is trivial, which assists in presenting the smeared influence of other variables on the glass formation. Angell pioneered a study for the first time to understand the glass transition of three xylene isomers, proposing the low T m principle for the glass formation in molecular isomers. [23] This principle holds that the lattice of substances with high glass-forming ability (GFA) usually has poor crystal packing manifested by the low lattice energy E latt , leading to low T m . Scrutinizing the thermodynamic data of the three xylene isomers found that m-xylene (m-X) with the lowest T m (219.6 K) has the best GFA, while T m of o-xylene (o-X) and p-xylene (p-X) is higher (247.8 K for o-X and 286.4 K for p-X), [24] accompanied by the successively decreased glass formability. It is obvious that a relationship between GFA and T m appears in the isomeric systems. As expected, this argument of the importance of low T m for glass formation can find more support from some criteria, for instance, the empirical rules of T g /T m [7] and T b /T m , [25] where T b is the boiling point. Also, the combined criterion of m /T m 2 [26] in evaluating the glass formation of oxide glasses is proposed. Intuitively, lowering T m or T l (liquidus temperature) is advantageous to the glass formation. Similarly, for multicomponent glassy materials such as metallic alloys, the glass formation and composition design are mainly guided using phase diagrams by pining the composition of the lowest liquidus temperature, particularly the eutectic points. [27,28] The temperature-oriented composition design strategy has been prevalent for finding practically new glassy materials. However, a question as to whether the temperature-oriented strategy is the most fundamental needs to be clarified, because no specific correlation between T l and GFA can be verified if one considers all types of glass-forming substances. [12] Theoretically, T l in phase diagrams is determined by the balance of the Gibbs free energies of liquid and crystal phases. Alternatively, a close inspection reveals the importance of melting entropy ΔS m and intermolecular interaction in determining the slope of T l in a eutectic phase diagram. [29] In this work, we re-checked the relation between T m and glass formation in isomeric molecules by exploring more systems, as shown in Figure 1. As the melting thermodynamics and melting viscosity are determined, the results do not show the advantage of low T m for the glass formation. In contrast, the importance of melting entropy ΔS m is revealed to connect closely to the glass formation. In particular, we found a strong dependence of ΔS m on the liquid viscosity determined at T m . In-depth analyses emphasize that ΔS m can serve as an indicator to understand the glass formation and guide the composition design. Figure 2 shows the calorimetric melting traces of the two sets of isomers. T m is recorded using the onset temperature of the melting traces. The melting enthalpy ΔH m is obtained by integrating the melting peak area, and the melting entropy ΔS m is quantified by the equation of ΔS m = ΔH m /T m . [30] The thermodynamic values are consistent with the reported ones in literature. [31,32] All thermodynamic characteristic quantities determined by experiments are listed in Table 1. Figure 3 shows the DSC cooling and subsequent heating curves of the two isomeric systems to monitor the glass transition behaviors. For dichlorobenzophenone isomers, vitrification occurs in both 2,2′-dichlorobenzophenone (2,2′-D) and 2,4′-dichlorobenzophenone (2,4′-D) at the highest accessible cooling rate of the calorimeter of ≈120 K min −1 , but 4,4′dichlorobenzophenone (4,4′-D) crystallized totally, indicating the worst GFA with the critical cooling rate R c higher than 120 K min −1 . To distinguish the GFA of 2,2′-D and 2,4′-D, a slower cooling rate of 80 K min −1 was applied while keeping the same reheating rate at 20 K min −1 . As seen in Figure 3a, 2,2′-D underwent partial crystallization, while the 2,4′-D remained completely vitrified. During reheating, the glass transition of 2,2′-D and 2,4′-D is detected at 215.33 and 225.56 K, as shown in Figure 3b, while the 4,4′-D directly melt at its T m . In subsequent testing of 2,4′-D, it was found to form a complete glass at a slower cooling rate of 10 K min −1 . Thus, R c of 2,2′-D and 2,4′-D are determined to be ≈80 and lower than 10 K min −1 , respectively. Similar experiments were performed on the indole-carboxaldehyde isomers. The results show that indole-5-carboxaldehyde (I-5-C) and indole-7-carboxaldehyde (I-7-C) can form glasses at the highest accessible cooling rate, but the indole-4-carboxaldehyde (I-4-C) isomer is completely crystallized. Then a melt-quenching experiment with a cooling rate of 80 K min −1 was applied on I-5-C and I-7-C, presented in Figure 3c. It is found that I-7-C is partially crystallized, while the I-5-C is entirely vitrified, showing the highest GFA. Figure 3d shows T g of I-5-C (241.24 K) and I-7-C (215.50 K), meanwhile I-4-C only detects the melting signal. Subsequent experiments show that R c of I-5-C is about 20 K min −1 . Figure 4 shows the viscosity results of the molecular melts measured at T m as a function of shear rate. The viscosity of all Table 1. Thermodynamic, kinetic, and structural data of three sets of isomers including melting points T m , melting enthalpy ΔH m , melting entropy ΔS m , melting viscosity m , beads, critical cooling rate R c , liquid density at T m , and the glass-forming ability (GFA) ranking of isomers.  samples tends to reach constants when the shear rate exceeds 50 s −1 , indicating the nature of Newtonian fluids, [33,34] and giving the viscosity values m in the stable stage. Among the two sets of isomers, 2,4′-D (5.75 mPa s) and I-5-C (5.21 mPa s) have the highest m values accompanied by their best GFA in each isomeric family. For comparison, m of three xylenes was obtained based on the reported results [35] guided by the Vogel-Fulcher- [30] where A, B and T 0 are constants. The fittings are shown in Figure 5, giving m of xylene isomers to be 1.74, 1.95, and 0.71 mPa s for o-X, m-X, and p-X, respectively. It can be immediately seen that m-X with the highest GFA has the largest m value. Table 1 summarizes the thermodynamic and kinetic data of the isomers. To determine the accurate R c values, which express the GFA of glass formers most directly, a calculation is introduced by referring to the experimental results. The calculated critical cooling rates R c calc of three sets of isomers can be reached from the melting viscosity in terms of the quantitative relationship proposed by Sarjeant and Roy, [36] R calc

Discussion
where k B is the Boltzmann constant, v is the molar volume calculated from molecular weight and density. In order to gain the precise v values, liquid densities of the isomers at melting points are used. For isomeric xylene, the density values can be reached by using the density at room temperature together with densitytemperature relations (−8.59 × 10 −4 K −1 for o-X, −8.81 × 10 −4 K −1 for m-X, and −8.89 × 10 −4 K −1 for p-X). [35] For the other two families of molecular isomers, the calculated results are in the same order of magnitude as the experimental results when using the liquid densities at T m s. Earlier studies have also examined and confirmed the reliability of this formula. [37][38][39][40][41][42] Inspecting experimental and calculated R c together with m of the isomers shown in Table 1, it is immediately seen that low T m does not always suggest the enhanced GFA for each isomeric family studied here. This is somehow a surprise and arises a question as to whether there is a thermodynamic parameter, which can predict the glass formation more accurately.
In Angell′s studies, [43] the interpretation of the highest GFA of the meta isomer emphasizes the lowest lattice energy E latt with the lowest T m . [23] E latt depends on intermolecular interaction force and molecular packing fashion, indicating that low E latt is accompanied by relatively loose packing structures with low T m . Decreased T m is critical in enhancing m , which hinders the migration and rearrangement of molecules or atoms during nucleation and growth and inhibits the precipitation of crystal phases from the liquid, consequently favoring glass formation. [6] Thus, the low T m effect on glass formation is an indication of the unique crystal phases and the slow liquid kinetics.
Yet, the correlation between T m and the glass formation becomes challenging when more materials are involved for comparison. Simple examples are metal alloys, for which there is no direct correlation between low T l and GFA. [12,44] Moreover, holding the consensus of the kinetic criterion of the glass formation that m is the dominant factor in determining glass formation, [7][8][9][10]   Melting viscosities m were calculated by extrapolating the curves to melting points T m of xylene isomers. Viscosity data are cited from elsewhere. [35] the relation of both T l and the Gibbs free energy of liquid and solid phases together with their difference of ΔG l-s to m remains vague.
Earlier studies of small-molecule glass formers found that T g is positively correlated with the boiling point T b , which can largely express the intermolecular interaction. [45] This implies that T g can also serve as an indicator of interaction force, as emphasized in earlier studies. [46] By contrast, T m depends on intermolecular interaction forces and the crystal packing fashion. Based on Angell's argument of the advantage of low T m for the glass forma-tion together with the interpretation of the relationship of T m and unique crystalline structures of isomeric glass formers, one can expect a large proportion of low-frequency vibration modes due to the low lattice energy and the low crystalline packing efficiency. This would suggest higher vibrational entropy in such crystals. [47] When assuming that the entropy of different liquid alloys has no pronounced difference due to the disordered states at individual melting points, the low melting entropies ΔS m would be expected for the isomers with high GFA. With the thermodynamic data of each group of isomeric molecules listed in Table 1, it is evident that ΔS m shows a closer correlation with GFA. A similar conclusion can also be reached if one inspects the thermodynamic results of glass-forming metal alloys by Busch's group, showing that low ΔS m favors glass formation. [48,49] It is also seen in Table 1 that isomeric molecules with lower melting entropies basically hold higher glass transition temperatures. Similar observations have been reported in earlier studies of poly ( -caprolactone) and nylon-6, which hold the virtually identical conformations, [50,51] and show the negative relation between ΔS m and T g . Our recent studies of various glass formers have also implied that there are other thermodynamic parameters than T l or T m that could determine the glass formation. [12,29,30] Figure 6 presents a quantitative connection between ΔS m and GFA expressed by R c calc for the three sets of isomers. The correlations are quite acceptable, confirming the significance of low ΔS m in mediating the glass formation of materials, compared with several reported thermodynamic ones. [17][18][19][20][21][22][23] This is not an exception since there is increasing evidence reported in recent studies that ΔS m has a series of correlations with glass formation related properties. For instance, studies of eutectic systems with negative heat of mixing ΔH mix show a deficit in ΔS m , [52] where negative ΔH mix is generally regarded as an essential condition for glass-forming systems. [53] Moreover, based on the metallic www.advancedsciencenews.com www.advancedscience.com compounds of low ΔS m , glassy materials have been successfully designed and prepared such as a semiconductor glass of Ga 2 Te 3 -SnTe [54] and bulk metallic glasses of (Zr 40 Ti 40 Ni 20 ) 100-x Be x . [55] Theoretically, the Gibbs free energy difference ΔG l-s between liquid and solid phases is associated with glass formation due to its nature of the crystallization driving force. ΔG l-s can be expressed in terms of [13] ΔG l − s = ΔS m ΔT + f(ΔT), where ΔT is the degree of supercooling relative to T m , and f (ΔT) is the higherorder function. Lower ΔG l-s is required to suppress the crystallization, corresponding directly to a lower ΔS m . [56] Similarly, the studies of the crystal growth in melts found that the system with low ΔS m has a lower growth rate, [57] favoring to suppress crystallization and, thus, enhancing the glass formation. The significance of ΔS m on the glass formation mentioned above allows for the conclusion that ΔS m might be able to serve as a fundamental thermodynamic property and to make contribution to the glass formation, compared with a number of reported thermodynamic ones. [17][18][19][20][21][22][23] Earlier studies have revealed that the melting entropy ΔS m of materials is a crucial thermodynamic quantity involved in many aspects of crystals and liquids such as crystal growth, [57] crystal structure, [58] and clustering in liquids. [59] Yet, one more key question needs to be addressed regarding how glass formation thermodynamics and kinetics work jointly in governing the glass formation. Given the fact that glassforming compositions can be guided by phase diagrams in the vicinity of the composition of deep eutectics, it can be inferred that thermodynamics can independently guide the glass formation, since phase diagrams can be interpreted by the thermodynamic Gibbs free energy of liquids and crystals. Moreover, a close inspection of the liquidus in phase diagrams, it can be easily found that the melting entropy is the fundamental property to control the slope of the liquidus, and a low melting entropy usually arises a high slope, favoring the occurrence of deep eutectics. [29] Alternatively, one can understand the glass formation from the perspective of kinetics. Commonly, it is accepted that kinetic melting viscosity m is a dominant quantity in governing the glass formation. [6,60] This indicates that kinetics can basically determine the glass formation, as evidenced by Equation (1), suggesting the dominant effect of the kinetics on the glass formation. Such a paradox of the glass-forming thermodynamics and kinetics might find its solution by seeking certain correlation between the two aspects. Albeit the viscosity of glass formers has not been well explained, [61] there are indeed some clues presenting links between viscosity and thermodynamic quantities. For instance, Adam-Gibbs established the dependence of melt viscosity on configurational entropy ΔS conf , [20] which is a faction of the liquid-crystal entropy difference, which becomes ΔS m at T m . Also, Greet and Magill found that melt viscosity can be interpreted by melting entropy ΔS m . [62] Nevertheless, establishing a direct correlation between ΔS m and m in different types of materials keeps a tremendous challenge, because melting entropy ΔS m depends numerically on molecular structure, indicating that ΔS m of a molecule with more atoms would be higher. This leads to a consequence that ΔS m of molecules with different atom number is not comparable with regard to the glass formation. This differs much from the kinetic quantities such as melting viscosity m , which is numerically independent of the atom number of molecules.
To explore the correlation between ΔS m and m for different types of glass formers, a concept of normalized ΔS m by beads is proposed and applied successfully in our recent studies. [30] The beads concept was initially proposed by Wunderlich [63] to describe intramolecular degrees of freedom and quantified by the number of rotatable units, having an equivalent physical implication to the number of excitable degrees of freedom per molecule. [64,65] Recent reports have also indicated that the beads value of molecules may be identified by measuring OH bond orientation polarization using infrared spectra. [66] Figure 7 presents the relation of normalized ΔS m and m for the isomeric systems studied in this work together with xylene isomers, as represented in our previous study. [30] The link between m and ΔS m is www.advancedsciencenews.com www.advancedscience.com observed for glass formers such as metals, [5,[67][68][69][70][71][72][73][74][75] aromatic, [76][77][78][79][80][81] alcohols, [47,82,83] and pharmaceuticals. [30,[83][84][85] Since isomers have the same beads values, the normalization does not change the relation between ΔS m and m . This holds true in each isomeric system, showing lower ΔS m corresponds to higher m and stronger GFA.
In addition to the studies of the glass formation thermodynamics and kinetics, structural consideration for the glass formation has been also extensively studied from the perspective of the similarity and difference of liquid and crystal structures. For example, recent studies have proposed that crystal nuclei are not born randomly but induced in regions of high crystal-like bondorientational order in a supercooled liquid, and the manipulation of the crystallization kinetics was achieved by controlling the degree of liquid preordering. [86,87] It seems that the appearance of a crystal-like structure in the liquid is beneficial to nucleation. Note that the similarity or the difference in the structures of the liquid and its crystals can be reflected by the melting thermodynamics, in particular, the melting entropy. [58,59] Finally, the advantages of using isomers to clarify the fundamental thermodynamic quantity in mediating the glass formation should be highlighted, in particular, for understanding the contributions made by enthalpy and entropy. Among molecular isomers, the difference in enthalpy is markedly reduced, and, thus, the entropy effect on the glass formation can be well resolved. In contrast, for the conventional comparison of the GFA among various materials with a large difference in melting points, the entropy effect was usually smeared because of the large difference in enthalpy, and thus, the independent contributions made by enthalpy and entropy are hardly achieved.

Conclusion
Isomeric molecules were selected to identify the key thermodynamic quantity in determining the glass formation. With the reported results, the critical issue of the glass formation thermodynamics is clarified, indicating that the melting entropy is more correlated with the glass formation than the melting point of a system, and the GFA of the systems with low melting entropy is stronger. Experimental evidence also demonstrates that for the glass-forming systems, the melting entropy has a close connection to melting viscosity, indicating that the melting entropy of a system not only serves as the driving force of crystallization, but has an impact on the glass formation by regulating the kinetic viscosity. Thus, the melting entropy of a system is a fundamental thermodynamic parameter in determining glass formation.
A Perkin-Elmer differential scanning calorimeter (Diamond DSC) was used to measure the glass transition and melting behaviors. The DSC equipment was calibrated with indium and cyclohexane. Powder samples were sealed in aluminum pans and melted at a heating rate of 10 K min −1 from T m −30 K to T m +30 K to probe melting processes. Varied quenching rates were performed for samples to determine the crystallization tendency of the molecules from their melt states. The glassy states were attained by quenching the molten samples to low temperatures at the highest cooling rate (≈120 K min −1 ), [52] and then reheating was performed to get the glass transition signals at a fixed heating rate of 20 K min −1 . Based on the accessible cooling rates for the glass formation in the isomers, the ranking of GFA can be reached, as listed in Table 1. Smaller number corresponds to enhanced GFA. To obtain the liquid densities, Archimedes principle was applied by monitoring the weight change of a tungsten rod immersed into the liquid isomers heated to 30 K above T m to ensure complete melting. And the density of the molecular liquids was calculated by, [88] = 0 (m 0 − m 1 ) m 1 where 0 is the density of the tungsten rod, m 0 is the actual weight of the tungsten rod, and m 1 is the weight of the tungsten rod immersed into the liquids.
The kinetic viscosity was determined using the MCR-302 rheometer from Anton Paar equipped with the pp25 parallel plates. The samples were placed between two parallel plates spaced by a distance of 4 mm and heated to 10 K above their T m . The molten samples were isothermally maintained for 5 min to guarantee complete melting. Then the temperature was decreased and stabilized to the corresponding T m of each sample, and a shear rates of 0.01-200 s −1 were applied to the samples.