Unveiling the Dependence of Glass Transitions on Mixing Thermodynamics in Miscible Systems

The dependence of the glass transition in mixtures on mixing thermodynamics is examined by focusing on enthalpy of mixing, ΔHmix with the change in sign (positive vs. negative) and magnitude (small vs. large). The effects of positive and negative ΔHmix are demonstrated based on two isomeric systems of o- vs. m- methoxymethylbenzene (MMB) and o- vs. m- dibromobenzene (DBB) with comparably small absolute ΔHmix. Two opposite composition dependences of the glass transition temperature, Tg, are observed with the MMB mixtures showing a distinct negative deviation from the ideal mixing rule and the DBB mixtures having a marginally positive deviation. The system of 1, 2- propanediamine (12PDA) vs. propylene glycol (PG) with large and negative ΔHmix is compared with the systems of small ΔHmix, and a considerably positive Tg shift is seen. Models involving the properties of pure components such as Tg, glass transition heat capacity increment, ΔCp, and density, ρ, do not interpret the observed Tg shifts in the systems. In contrast, a linear correlation is revealed between ΔHmix and maximum Tg shifts.

negative) would help gain insight into the glass transition behaviors in mixtures. Unfortunately, such studies are not accessible, in particular, the effect of small DH mix .
In this work, we studied the glass transitions in binary glass forming molecular systems, and systematic comparison is shown with typical scenarios of small vs. large and positive vs. negative DH mix . A global picture of the DH mix effect on the T g shifts in mixtures is presented. The results are expected to benefit the understanding of the glass transition as well as the precise evaluation of T g in poor glass formers. The composition dependences of T g are plotted in Fig. 3(a) and (b). A markedly negative T g deviation is immediately visible for the mixtures of o-vs. m-MMB, although the deviation is small. In contrast, the evaluation of the T g shift for the system of o-vs. m-DBB in Fig. 3(b) is of a bit difficulty. The fitting with marginally positive deviation or a linear fitting seems to be able to explain the experimental points, as shown by the black solid line and the light cyan solid line. The bottom line for o-vs. m-DBB is that the deviation is, by no means, negative. The pure components' T g s can be evaluated by the numeric extrapolation in Fig. 3 Fig. 4(a) and (b) show the composition dependences of DC p and T g for the system of 12PDA vs. PG over the whole composition, where DH mix maximum of 12PDA vs. PG is recorded to be 23876 J/mol 23 . A remarkably positive T g deviation is seen in the system. The DC p values for 12PDA and PG are determined to be 1.36 and 0.86 J/(g-K) while the T g s to be 146.8 and 169.7 K.

Results
The explanations of the T g values in the mixtures using the CK and GT equations with the extrapolated T g and DC p values of the pure components are presented by the blue dotted (CK) and magenta dash-dot-dot (GT) lines in Fig. 3(a), (b) and Fig. 4(b). It appears that the calculated T g curves in terms of the CK and GT models do not     13,20 . The large discrepancy suggests that, notwithstanding the importance of the properties (T g , DC p and r) of the pure components, the exact explanation of the T gx relationship for most cases asks for more considerations.
The relative T g shift, DT g /T g , for the systems of o-vs. m-MMB, ovs. m-DBB, and 12PDA vs. PG are shown in Fig. 5, where DT g is the T g difference between the measured values and the ones calculated in terms of the linear average of the pure components' T g s. Two more typical systems recorded in our recent work, benzil (BZL) vs. mnitroaniline (MNA) 21 and methyl m-toluate (MMT) vs. methyl otoluate (MOT) 24 , are also included in Fig. 5 to represent the mixing scenarios of larger positive DH mix and ideal mixing, respectively. It is seen in Fig. 5 that the five systems differ greatly in the T g deviations from the ideal mixing rule. The system of 12PDA vs. PG has a remarkably large and positive T g deviation with the maximum DT g /T g being as high as 14.5%. In contrast, the system of BZL vs. MNA has a large and negative T g deviation with the maximum of DT g /T g of 22.3% 21 . For systems with smaller positive or negative DH mix , DT g /T g becomes smaller.

Discussion
The mixing thermodynamics for the BZL vs. MNA system ( Likewise, large and negative DH mix is also detected in the mixtures composed of water and alkoxy alcohols, such as the aqueous systems of 2-methoxyethanol 30 and 2-ethoxyethanol 31 , and large and positive T g deviations are observed in such mixtures 10 . The results in this work allow us to check the presumably quantitative correlation between T g and DH mix in binary mixtures. In addition to the experimental measurements reported here, more T g 8,21,25,29,32 and DH mix values 21-23,33-37 are collected. Fig. 6 shows a plot between DT g /T g and DH mix measured at 298 K for 13 systems with DH mix ranging from 1044 J/mol to 23900 J/mol. Strikingly, a nearly linear correlation is revealed, and positive DT g /T g values of mixtures are found to be enlarged with increasingly negative DH mix . Note that although systems with positive DH mix are relatively fewer, the available data in the three systems basically follow the correlation showing that increasingly positive DH mix corresponds to enhanced negative T g deviation (DT g /T g ). Note that in Fig. 6 there are a few systems that somehow deviate from the master line such as methanol vs. triethylamine 29,33 . This may arise partly from the error in DH mix values, since several different DH mix values can be found for a mixing system 38 . However, the minor errors do not affect the demonstration of the explicit relationship between the thermodynamics and the glass transition behaviors in binary mixtures. Compared with the results in Figs. 3 and 4 expressed by the CK and GT models, Fig. 6 consequently implies that DH mix could be a more decisive factor in affecting the T g behaviors in mixtures. Fig. 6 includes a typical glass forming binary system of 2-ethyl-1hexanol (2E1H) and 2-ethyl-1-hexylamine (2EHA), and the accurate T g data show a large and positive deviation with DT g /T g reaching  5.6% 39 . The enthalpy of mixing in the system is not available. Yet, the value could be roughly evaluated from the mixtures composed of the homologous liquids with similar molecular structures and chemistry. For example, the DH mix maximum at 298 K reaches 22905 J/mol for the system of butyl amine vs. 1-butanol 26 , which is comparable with the value of 22755 J/mol for the system of amylamine vs. 1-butanol 27 . It is seen that the absolute values of the negative DH mix for mixtures of monoalcohols and monoamines decrease with the carbon number in the backbones of either alcohols or amines, and also decrease with the enhanced steric hindrance due to the introduction of branched chains [26][27][28]40 . Approximately, the DH mix maximum for the mixtures of 2E1H vs. 2EHA is evaluated to be ,22200 J/mol. The values of DH mix and DT g /T g (5.6% 39 ) for the 2E1H -2EHA mixtures appear to coincide well with the correlation shown in Fig. 6.
The mixing systems of positive DH mix are much less available. The system of 1-butanol vs. 1-bromobutane is reported to have a quite large and positive DH mix with the maximum reaching 1044 J/mol at 298 K 41 . The composition dependence of the kinetic glass transition temperature, T g-kin , defined by the temperature where the a-relaxation time approaches 100 s 39,42 , can be obtained based on the studies of the dielectric relaxation dynamics for the pure components and the mixtures investigated by Goresy et al 43 and by Murthy et al 44 . When combining the data from the two groups, a negative T g deviation with the maximum of DT g /T g to be 23.2% is yielded. The result is comparable with the predicted one by the correlation in Fig. 6.
For ideally mixing systems with DH mix 5 0, a common observation is the negative T g deviation from the ideal mixing rule, as shown in Figs. 5 and 6 for the MMT vs. MOT mixtures. This is the typical feature driven by mixing entropy 29,45 . According to the Adam-Gibbs' configurational entropy (S c ) theory 46 , t(T) 5 t 0 exp(DmC AG / TS c ), where t 0 is the pre-exponent having the phonon time, Dm is potential barrier hindering molecular rearrangement, and C AG is a constant [47][48][49] , if the intermolecular interaction keeps unchanged (DH mix 5 0), the variation in Dm is negligible, and the increase in S c during mixing at a fixed temperature would correspond to a decrease in t(T), which makes the relaxation time curves move toward low temperature regions in activation plots (log t(T) vs. 1/T), and finally leads to a decrease in T g-kin (or T t 5 100 s ). Furthermore, for the small and comparably-valued DH mix of opposite sign, the case with positive DH mix (for example, the o-vs. m-MMB system in the inset of Fig. 6) would correspond to relatively larger T g shift (negative) than the shift (positive) in the case with negative DH mix (for example, the ovs. m-DBB system).
In addition to the correlation between DH mix and the T g shifts in glass forming mixtures, recent studies explored the liquid fragility in various mixtures with varying DH mix , which defines how rapidly the liquid dynamic properties (viscosity or relaxation time) change with temperature at T g , and found a general trend of negative deviations from the ideal mixing rule 25 , somehow regardless of the enthalpy of mixing. Combining the impacts of DH mix on T g and fragility in mixtures, it is evident that large and negative enthalpy of mixing would correspond to the high viscosity within supercooled liquid regions 50 , which further favors kinetically glass formation. This rationalizes the empirical criterion that the large and negative enthalpy of mixing is a crucial consideration in order to prepare multicomponent bulk metallic glasses 51,52 .
Finally, the present results of the quantitative correlation between DH mix and the composition dependence of T g in mixtures can provide a guidance to estimating the T g for materials which are extremely difficult to be vitrified, such as benzene. For the mixtures containing benzene, although a complete dataset of both mixing thermodynamics and glass transition are not available, considering the fact that for most mixtures the composition dependences of T g generally show a similar trend as the composition dependence of viscosity 29,53 , the latter can consequently be used to roughly estimate the former. DH mix and viscosity for benzene vs. decane mixtures have been reported, showing a positive DH mix 54 but negative deviation in the composition dependence of viscosity 55 , which could imply the negative deviation in the composition dependence of T g . This agrees with the observation in the present work for the correlation between the mixing thermodynamics and glass transitions in various mixtures. It is therefore speculated that, provided that the enthalpy of mixing is given for the glass forming miscible mixtures containing benzene, the reliable extrapolation towards the T g of pure benzene can be ensured based on the accessible T g values of the mixtures. Such endeavor will be conducted in further study.

Methods
Chemicals. o-and m-isomeric systems of methoxymethylbenzene (MMB) and dibromobenzene (DBB) were selected in this study with the former system having small and positive DH mix and the latter system small and negative DH mix 22 . The system of 1, 2-propanediamine (12PDA) vs. propylene glycol (PG) was selected for the considerably large and negative DH mix generated during mixing 23  Thermodynamic measurements. A Perkin-Elmer differential scanning calorimeter (Diamond DSC) was used for the calorimetric determination of the heat capacity curves, and the glass transition temperatures, T g . A sapphire sample (31.4 mg) was used for the C p standard. The sample was initially quenched to low temperatures at the accessible highest cooling rate in the calorimeter to guarantee the complete vitrification, and a subsequent heating-cooling-reheating cycle was performed around the glass transition at a fixed rate of 20 K/min. The calorimetric quantities for the systems are determined from the reheating C p curves. The sapphire and baseline heat curves were obtained following the same procedure. The DSC was calibrated using indium and cyclohexane prior to the measurements 56 .