J. Phys. Chem. B 1999, 103, 3457-3460
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Thermodynamic Study of the Glass Transition in Polyamine-Polyalcohol Mixtures: Entropy-Theoretical Interpretation of Anomalous Glass Transition Behavior Kiyoshi Takeda,* Katsuo Murata,† and Shinsuke Yamashita‡ Department of Chemistry, Naruto UniVersity of Education, Naruto, Tokushima 772-8502, Japan ReceiVed: NoVember 13, 1998; In Final Form: February 16, 1999
The glass transition temperatures of binary mixtures of polyamines and polyalcohols are investigated by differential scanning calorimetry (DSC). For all systems, the composition dependence of the glass transition temperature Tg shows clear maxima, in stark contrast to those of polyalcohol-polyalcohol mixtures reported previously. A thermodynamic analysis based on the entropy theory is carried out for (1,2-propanediamine)x(glycerol)1-x and (1,2-propanediamine)x(1,3-propanediol)1-x systems. The composition dependence of Tg predicted from the entropy theory of regular solutions (regular solution model, RSM) is not able to reproduce the anomalous behavior, and the excess configurational entropies ScE are negative and larger than 20 J K-1 mol-1 in absolute value at the minima. The origin of the large value of ScE is discussed with respect to the change of hydrogen bond network structure on mixing.
Introduction The glass transition phenomenon, which reflects the molecular-rearrangement rate in supercooled liquid, is affected by the local structure of liquids. Extensive investigations have been carried out for various associated liquids in which the hydrogen bond structure often plays an important role in molecular dynamics. We have already reported the glass transition behavior of binary mixtures analyzed in terms of entropy theory, by which the dynamic properties are related to the configurational entropy reflecting the disordered structure in supercooled liquids.1,2 In particular, we observed that the glass transition behavior of binary polyalcohols can be understood as regular mixtures despite their characteristic structures resulting from the extensive hydrogen bond (H-bond) network.3 In this paper we report the glass transition behavior of some polyamine-polyalcohol binary mixtures as studied by the differential scanning calorimeter (DSC). Amines are also one of the typical associated liquids in which N-H‚‚‚N type H-bonds are formed. When amine and alcohol are mixed, other types of H-bonds such as O-H‚‚‚N are expected to be formed. The composition dependence of Tg is analyzed within the framework of the entropy theory to estimate the excess configurational entropy ScE. We will describe the anomalous behavior of polyamine-polyalcohol systems and compare them with polyalcohol-polyalcohol systems. The relationship between structural change and the anomalous glass transition behavior is discussed on the basis of the excess configurational entropy. Experimental Section The special grade materials of ethylenediamine (ED), 1,2propanediamine (racemic, 12PDA), 1,3-propanediamine (13PDA), ethylene glycol (EG), 1,2-propanediol (racemic, 12PDO), 1,3* To whom correspondence should be addressed. E-mail:takeda@ naruto-u.ac.jp. † E-mail address:
[email protected]. ‡ Present address: Department of Natural Science, Hyogo University of Teacher Education, Yashiro-cho, Kato-gun, Hyogo 643-1415 Japan.
propanediol (13PDO), and glycerol (Gly) were purchased from Wako Pure Chemical Industry, Ltd. and used as they were. Binary mixtures were prepared as follows. Pure components were poured into an Erlenmeyer flask in a dried nitrogen atmosphere, weighing each component independently. Weighing was done by stopping the flask at the tip to avoid contamination with a hygroscope. The concentration of the mixture was determined from the ratio of masses of components, which can be determined with precision within 0.1%. The mixture was homogenized by stirring over a water bath, with the tip tightly stopped, for more than 5 h, keeping the temperature around 50 °C because some of the present materials are so viscous at room temperature that homogeneous solutions cannot be obtained readily. The homogeneity of the mixture was checked by the observation of a single, clear glass transition for every sample. Prepared mixtures were all kept free from the hygroscope. The glass transition temperature was measured by the differential scanning calorimeter (DSC10, Seiko Instruments Industry Co. Ltd.) in the temperature range from 120 K to room temperature. A few drops of sample (20-30 mg) was loaded into the sample container and was readily set inside the DSC apparatus with flowing dried nitrogen. Samples were cooled at about -5 K min-1 to liquid-N2 temperature (78 K), and then the DSC experiment was performed at a heating rate of 2 K min-1. The glass transition temperature, Tg, was determined by the usual method of tangent intersection, i.e., the temperature at which the extrapolated tangent at the point where the slope is largest during the baseline shift crossed the baseline in the glassy state. The values of Tg were obtained within (0.5 K for each sample in this method. All pure amines, EG, and 13PDO crystallized easily at a cooling rate of -5 K min-1. A rapid cooling method was applied in which the sample was dropped into a sample container that was cooled to liquid-N2 temperature in advance. The cooling rate with this method was about -200 K min-1, which is 40 times faster than the usual method. However, EG and pure amines except 12PDA were not able to be vitrified even with this rapid cooling method.
10.1021/jp9844260 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/09/1999
3458 J. Phys. Chem. B, Vol. 103, No. 17, 1999
Takeda et al. reported previously.3 For (ED)x(Gly)1-x, only a slight concentration dependence is observed in the range 0 < x < 0.5, and the glass transition was not observed for x > 0.8 because of the crystallization. It is not plausible that the hypothetical Tg of pure ED is far higher than that of 12PDA (Tg ) 144.6 K), which has an extra methyl group at the molecular end. Thus, the composition dependence of Tg for (ED)x(Gly)1-x is expected to decrease rapidly in the region 0.8 < x < 1 if it could vitrified. Analysis in Terms of RSM. The configurational entropy has been recognized as an important parameter to understand the glass dynamics since the appearance of entropy theory developed by Gibbs et al.1,2 Gordon et al.9 applied it to regular solutions to reproduce the composition dependence of Tg (regular solution model, RSM). For the functional form of the composition dependence of Tg, they employed
Figure 1. DSC curves of Gly, 13PDO, and 12PDA.
Tg(x) )
xTg,1 + K(1 - x)Tg,2 x + K(1 - x)
(1)
where Tg,1, Tg,2, and K are the glass transition temperatures of the first and second components and the fitting parameter. It was also assumed that eq 1 can be applied with the common value of K to the Kauzmann temperature10 TK(x) by replacing Tg, Tg,1, and Tg,2 with TK, TK,1, and TK,2, respectively. However, we employed another type of function in the present study because eq 1 is not capable of reproducing the composition dependence of Tg with an extremum. One of the most general functions that traces the glass transition temperature of pure components is given by
Tg(x) ) xTg,1 + (1 - x)Tg,2 + x(1 - x)f(x)
(2)
where f(x) is any function. In the present analysis, we used the second-order polynomial for f(x): Figure 2. Glass transition temperatures of polyamine-polyalcohol mixtures plotted against the mole fraction of amines: (b) (12PDA)x(Gly)1-x; (2) (13PDA)x(Gly)1-x; (4) (12PDA)x(12PDO)1-x; (O) (12PDA)x(13PDO)1-x;(0)(13PDA)x(13PDO)1-x;(9)(13PDA)x(12PDO)1-x; (3) (ED)x(Gly)1-x.
Results and Discussion DSC Measurement and the Glass Transition Temperature. The DSC results of some pure components for which the glass transition was observed are shown in Figure 1. For glycerol, only a clear glass transition was observed over the measured temperature range. For 13PDO and 12PDA, a glass transition and some large exothermic anomalies due to crystallization and stabilization were observed. The glass transition phenomenon of 12PDA was rather smeared compared to those of the other two substances shown in Figure 1, and the overshooting usually observed associated with a baseline shift at Tg was not observed. This is because 12PDA was vitrified by the rapid cooling method. The exothermic enthalpy relaxation, however, commonly observed for glasses vitrified at an extremely high cooling rate4-8 was not observed. This could be because of the insufficient sensitivity of the apparatus. For EG and all other amines except for 12PDA, the glassy state was not obtained even with the rapid cooling method. Thus, only an endothermic peak due to fusion was observed for these pure samples. In Figure 2, the Tg’s of polyamine-polyalcohol systems were plotted against mole fraction x. It is observed that the composition dependence of Tg shows a clear maximum for every system. This behavior is in clear contrast to that of alcohol-alcohol for which the composition dependence of Tg is monotonic as
f(x) ) A + Bx + Cx2
(3)
The reason we used it is that it was the lowest order polynomial function that reproduces the experimental values satisfactorily. It is assumed again that TK(x) is also reproduced by eqs 2 and 3 with common values of parameters A, B, and C, replacing Tg, Tg,1, and Tg,2 by TK, TK,1, and TK,2, respectively. Therefore, we employed the functional form of the composition dependence of Tg and TK,
Tg(x) ) xTg,1 + (1 - x)Tg,2 + x(1 - x)(A + Bx + Cx2) (4) and
TK(x) ) xTK,1 + (1 - x)TK,2 + x(1 - x)(A + Bx + Cx2) (5) respectively. Method of analysis is the same as described in ref 3. Figure 3 shows the results of the analysis in terms of RSM carried out for (12PDA)x(Gly)1-x and (12PDA)x(13PDO)1-x for which thermodynamic quantities of pure components have already been obtained.11-13 Thermodynamic quantities used in this analysis are compiled in Table 1. In Figure 3, the composition dependence of Tg of several polyalcohol-polyalcohol systems predicted by RSM is also shown for comparison. As reported previously,3 the RSM prediction was quite successful for them. It is obvious that RSM does not work for polyamine-polyalcohol systems although it does for polyalcohol-polyalcohol systems. It is proved (see Appendix) that the composition dependence of the Kauzmann temperature shows no maximum for any regular solution systems. Thus, it is impossible to reproduce the composition dependence of Tg in terms of RSM for systems that exhibit a maximum in Tg.
Polyamine-Polyalcohol Mixtures
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Figure 3. Glass transition temeperatures of (12PDA)x(Gly)1-x (b) and (12PDA)x(13PDO)1-x (2). Solid and chain lines indicate predictions from RSM and best fit curves to a power polynomial described in the text, respectively. Dotted lines are those predicted from RSM for several alcohol-alcohol mixtures. A: (Gly)x(EG)1-x. B: (13PDO)x(Gly)1-x. C: (13PDO)x(EG)1-x.
TABLE 1: Thermodynamic Quantities Used in the Analysis. substance
Tg K
Tfus K
glycerol 186.6 290.95 1,3-propanediol 147.6 248.16 1,2-propanediamine 144.6 236.53
∆fusSm J K-1mol-1
TK K
ref of Cp
62.84 52.16 77.83
139.4 108.7 117.0
11 12 13
Figure 4. Excess configurational entropies for (12PDA)x(13PDO)1-x (solid line) and (12PDA)x(Gly)1-x (broken line) evaluated from the deviation of observed Tg from prediction by RSM.
Excess Configurational Entropy. The result that the composition of Tg cannot be reproducible with RSM implies the irregular nature of these systems. We evaluated the excess configurational entropy ScE in the same way as described before.3,14 The quantity ScE is the configurational part of the excess configurational entropy ∆mixSE, the change in the degree of structural variation on mixing. The evaluated ScE values for (12PDA)x(Gly)1-x and (12PDA)x(13PDO)1-x were shown in Figure 4. It is observed that ScE values for both polyaminepolyalcohol systems were negative with extremely large absolute values exceeding 20 J K-1 mol-1. The excess configurational entropies for some polyalochol-polyalcohol systems has been previously reported3 to be around 0.5 J K-1 mol-1 even at the maxima, which is comparable to the evaluation error of ScE. This clear contrast of the polyamine-polyalcohol systems
compared to polyalcohol-polyalcohol systems implies an essential difference in the change of structure upon mixing. With the decrease of the configurational entropy upon mixing, we have to conclude that extensive structure formation occurs in polyamine-polyalcohol systems, whereas such a structural change does not occur in polyalcohol-polyalcohol systems. For some amine-alcohol systems, it has been observed that the excess entropy of mixing (e.g., -23.2 J K-1 mol-1 for the system of ethylenediamine and ethylene glycol16) is about the same as the present one. The entropy change in this system is suggested to be mainly caused by the change in hydrogen bond structure. It is expected that the same discussion can be made for the present systems and that comparable values of the excess entropy of mixing ∆mixSE can be obtained for the present system. If we obtained a similar value for ∆mixSE, it would be a strong test for the Adam-Gibbs theory because it would be possible to compare the results of quite independent experiments. Hydrogen Bond Structure of Amine-Alcohol Mixtures. The structural change that causes a large value of the excess configurational entropy involved with mixing polyamine and polyalcohol is considered in this section. It is reported15 that each hydroxyl group in liquid alcohol interacts with 1.8 other hydroxyl groups around room temperature. It is plausible that this interaction would mainly be caused by the H-bond between the hydroxyl groups. This means that nearly 90% of hydrogen bonds were formed because an -OH group is expected to interact with two other -OH groups if H-bonds formed completely, and it is expected that most of the -OH groups should get involved at a lower temperature around Tg. In such a situation, we point out two effects of mixing concerned with the structural formation of amines and alcohols. One is that the hydrogen bond is formed between different kind of groups, -NH2 and -OH, although only the H-bond between the same group can be formed in pure components. The hydrogen bond O-H‚‚‚N is stronger than O-H‚‚‚O and/ or N-H‚‚‚N because of the stronger tendency of electron pair donation of the nitrogen atom and electronegativity of the oxygen atom. It is observed that the hydrogen bond structure would be more developed by introducing stronger types of hydrogen bond at finite temperature. This picture is an analogue of the discussion that has been sometimes suggested for the interpretation of the thermodynamic properties of mixing of alcohol-alcohol mixtures.17 Another effect is that the number of lone pairs and H atoms that can participate in H-bonds increases by introducing the second component. There are two lone pairs and one hydrogen atom in the -OH group and one lone pair and two hydrogen atoms in -NH2. If hydrogen bonds are formed between a lone pair and a hydrogen atom completely, the lone pairs in pure alcohols and hydrogen atoms in pure amines have to remain free. On the other hand, mixing the two substances makes it possible to form excess hydrogen bonds between species that remain free. This idea is effective even when the H-bonds are completely formed in the pure components and in this sense at 0 K. Actually, however, the above two effects cannot be separated from each other. The former effect seems useful for understanding the change in H-bond character with temperature, i.e., the temperature dependence of distribution in the population of H-bond type, such as O-H‚‚‚O, N-H‚‚‚O, etc. On the other hand, the latter would be suitable for explaining the static structural change on mixing, since this effect is most emphasized when the H-bond formed completely, i.e., at 0 K. In the present results, both pictures are capable of explaining the increase of
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H-bond population. And in any case, static structure formation can be understood as a result of excess H-bond formation upon mixing. Conclusion The glass transition dynamics has been extensively studied recently considering the complexity of the structure. It is important to consider structure as well as their dynamics for a deeper understanding of supercooled and glassy liquids. In the present study, it was suggested that extra H-bonds are extensively formed in the polyamine-polyalcohol systems. It is the first time that a structural change on mixing is clearly suggested from the glass transition study. At the same time, the polyaminepolyalcohol systems are important for determining which structure is controllable to some extent by means of the H-bonds in supercooled liquids. In addition, the present analysis suggests also a method for testing the entropy theory, which has been usually discussed within the framework of itself. The excess configurational entropy ScE would be comparable with the excess entropy of mixing ∆mixSE for systems with large contributions from configurational modes. We cannot check this point at the present stage because of the lack of the excess entropy of mixing for systems under discussion. If it were done, it would be a unique case for checking the entropy theory quantitatively using independent experimental research. The discussion concerning the hydrogen bond threw light on the increase of the hydrogen bond and extensive growth of network structure. The present system would be an interesting system for studying physical properties sensitive to static structures. One recent interest in the research of a supercooled liquid is the heterogeneous structure of the liquid.18 The suggestion that the hydrogen bond network develops extensively implies that the cooperatively rearranging region enlarges in the intermediate concentration range. Acknowledgment. The authors thank Prof. D. Kivelson for his useful comments about the manuscript. Appendix The composition dependence of the Kauzmann temperature for regular solution can be obtained from the thermodynamic quantities of pure components. Here, we give a brief proof that the composition dependence of the Kauzmann temperature TK has to be monotonic for a regular solution. The configurational entropy Sc for the regular solution is given by
Sc(x,T) ) xSc,1(T) + (1 - x)Sc,2(T)
(A1)
where Sc,1 and Sc,2 are the configurational entropy of the first and second components, respectively. The composition dependence of the Kauzmann temperature TK(x) at which the configurational entropy becomes zero is obtained by setting Sc(x,TK(x)) ) 0. According to eq A1, the equation
xSc,1(TK(x)) + (1 - x)Sc,2(TK(x)) ) 0
(A2)
gives the composition dependence of the Kauzmann temperature. Differentiating both sides of eq A2 with respect to x, we obtain
Sc,1(TK(x)) - Sc,2(TK(x)) + [xCc,1(TK)/TK + (1 - x)Cc,2(TK)/TK] dTK/dx ) 0 (A3) Here, Cc,1 and Cc,2 are the configurational heat capacities of the first and second components, respectively. Since the quantity inside the bracket is positive, the gradient dTK/dx is zero only when Sc,1(TK(x)) - Sc,2(TK(x)) ) 0. Together with eq A2, this yields the result Sc,1(TK(x)) ) Sc,2(TK(x)) ) 0. This means that the Kauzmann temperatures of the two components coincide and then TK(x) is independent of x. As a result, TK(x) possesses no extrema in any cases. Therefore, the composition dependence of the Kauzmann temperature is monotonic for any regular solution system. References and Notes (1) Gibbs, J. H.; Dimarzio, E. A. J. Chem. Phys. 1958, 28, 373. (2) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139. (3) Takeda, K.; Murata, K.; Yamashita, S. J. Non-Cryst. Solids 1998, 231, 273. (4) Bigot, J. Summer School on Amorphous Metals; Matyja, H., Zielin˜ski, P. G., Eds.; World Scientific: Singapore, 1986. (5) Hikawa, H.; Oguni, M.; Suga, H. J. Non-Cryst. Solids 1988, 101, 90. (6) Takeda, K.; Oguni, M.; Suga, H. J. Phys. Chem. Solids 1991, 52, 991. (7) Takeda, K.; Yamamuro, O.; Suga, H. J. Phys. Chem. 1995, 99, 1602. (8) Tsukushi, I.; Yamamuro, O.; Nishizawa, M.; Matsuo, T.; Takeda, K. ReV. Sci. Instrum. 1998, 69, 179. (9) Gordon, J. M.; Rouse, G. B.; Gibbs, J. H.; Risen, W. M., Jr. J. Chem. Phys. 1977, 66, 4971. (10) Kauzmann, W. Chem. ReV. 1948, 43, 219. (11) Gibson, G. E.; Giauque, W. F. J. Am. Chem. Soc. 1923, 45, 93. (12) Takeda, K.; Yamamuro, O.; Tsukushi, I.; Matsuo, T. J. Mol. Struct., in press. (13) Takeda, K.; Yamamuro, O.; Tsukushi, I.; Matsuo, T. To be pubished. (14) Takeda, K.; Yamamuro, O.; Suga, H. J. Therm. Anal. 1993, 38, 1847. (15) Narten, A. H.; Habenschuss, A. J. Chem. Phys. 1984, 80, 3387. (16) Gladden, J. K. J. Chem. Eng. Data 1972, 17, 468 (17) Pola´k, J.; Murakami, S.; Lam, V. T.; Pflug, H. D.; Benson, G. C. Can. J. Chem. 1970, 16, 2457. (18) Tracht, U.; Wilhelm, M.; Heuer, A.; Feng, H.; Schmidt-Rohr, K.; Spiess, H. W. Phys. ReV. Lett. 1998, 81, 2727 and references therein.
