J. Phys. Chem. 1995,99, 12349-12354
12349
Nature of the Relaxation Processes in the Supercooled Liquid and Glassy States of Some Carbohydrates Gangasharan and S. S. N. Murthy* School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India Received: January 23, 1995; In Final Form: May 17, 1995@
Dielectric relaxation measurements are made in a number of carbohydrates in their supercooled liquid and glassy states over a frequency range 106-10-3 Hz and a temperature range 77-400 K. Differential scanning calorimetric measurements are also made. In all the samples two relaxations, which were identified as aand B-relaxations, were observed. The a-relaxation is very broad and is strictly non-Arrhenius, and it follows a critical power-law temperature dependence. The j3-process is Arrhenius, with an activation energy varying from 8.5 to 13 kcaUmo1. Also a systematic variation of the magnitude of the j3-process with the molecular structure is noted. The origin of the j3-process in these systems appears to be intramolecular in nature.
Introduction
Experimental Section
A supercooled liquid usually exhibits two relaxation processes, the major one being the so-called primary or a-process, which on lowering the temperature gets arrested at the glass transition temperature Tg, and the minor one being the so-called secondary or B-process, which continues to the sub-T, region. The latter process has subsequently created a lot of interest among both theorists and experimentalists in view of its importance in the elucidation of the structure of In most of the studies on B-relaxation, the dielectric relaxation technique is the major source of information. In this technique, the frequency and temperature dependence of real and imaginary parts of the dielectric constant (e' and e") are studied, from which one gets information about the activation energy ( E ) for the rotation of the dipole, from which one speculates about the mode of relaxation. In simple organic liquids, the activation energy for the B-process (Eg)is found to be in the range 2.56.0 kcavmol, which can conveniently be explained in terms of the intramolecular degrees of f r e e d ~ m . ~ - ~ - ' In view of the presence of the strongly polar OH groups and, hence, hydrogen (H-) bonding in biological systems, the dielectric relaxation technique has been used increasingly in the area of biology." With recent interest in the vitrification and its implications in cryobiology, a few studies are reported on the a- and B-processes in the supercooled carbohydrate^.'^-'^ However, the activation energies (Eg)for the P-process are found to be in the range 9-14 kcal/mol, which are larger as compared to the corresponding Eg values in monohydroxy systems and simple organic liquids. However no explanation has so far been offered for these high Ep values, and this, in turn, gave rise to various speculations about the structure of glass in general. The problem of B-processes in the carbohydrates seems to be more complicated, as some researchers have reported the absence of B-processes in some of the systems.I5 Also in the above report,l5 the a-process is noted to be Arrhenius in all the systems, which appears to be contradicting the generally held view that the a-process should be non-Arrhenius. To clarify the problems associated with the relaxation processes in these systems, we have studied these systems over wider frequency and temperature ranges than the earlier workers with a systematic variation in the chemical structure, the results of which we report here.
The samples investigated are D-xylose, L-arabinose (Loba. Chem., India; ExcelR grade), D-galactose (E. Merck, Germany), D-fructose (Loba. Chem., India; 0.5% impurity), D-sorbitol, D-mannitol, and dulcitol (all from CDH, India; 0.5% impurity), the chemical formulas of which are given in Figure 1. The crystalline materials were dried by desiccating them for 2 days at 333 K prior to their use. No additional purification was done. The differential scanning calorimetric (DSC) measurements are made using a DuPont TA 2000 thermal analyzer. The dielectric measurements are made using a HP 4284A Precision LCR meter in the frequency range 20 Hz to 1 MHz. The dc step response technique is also used for the measurements of dielectric loss at ultralow frequencies. For the accuracy in the measurements, the temperature controlling, and other details of the measurements the reader may consult our earlier articles,5~7Al6 The glasses are formed in the dielectric cell itself by cooling the molten liquid very quickly. Care is taken to avoid caramelization in the samples.
@
Abstract published in Advance ACS Abstracrs, July 1, 1995.
0022-365419512099-12349$09.0010
Results Prior to the dielectric measurements, all the samples are tested using the DSC instrument for the ability of glass formation. Sucrose (Cl2H22011)is found to form glass easily with Tg = 334 K, with the DSC base line showing a small steplike change around 207.5 K, similar to the case of D-glUCOSe reported earlier.8 Our subsequent studies show that the latter is probably due to the caramelization. In view of this, we have not studied sucrose further using dielectric spectroscopy, as it is found to be very difficult to avoid caramelization. In the case of D-glucose, we could avoid caramelization to a greater extent by quickly cooling the melt, but it could not be avoided completely. We have also tested the glass-forming ability in three of the 10 isomers of the linear hexitol (CH20H(CHOH)&HzOH), viz., D-sorbitol (D-glucitol), D-mannitol, and dulcitol. Very high cooling rates on the order of 100"Imin are required to form glasses in D - r " i t 0 1 (Tg= 269 K) and dulcitol (Tg = 283.8 K), whereas D-sorbitol forms glass very easily even at ordinary cooling rates. Both D-rnannitOl and dulcitol are not studied further in our dielectric studies since such high cooling rates are not possible in our dielectric setup. The chemical formulas of the samples studied are shown in Figure 1. The samples D-XylOSe and L-arabinose are isomers 0 1995 American Chemical Society
12350 J. Phys. Chem., Vol. 99,No. 32, 1995
Gangasharan and Murthy the form of normalized Cole-Cole diagrams. There is a significant contribution to the total polarization from the highfrequency process @-process); hence, we have subtracted the contribution of the @-process(which is approximated from the low-temperature extrapolation of the corresponding parameters) to resolve the a-process, which is then described by the Havriliak-Negami e q ~ a t i o n , given ~ ~ . ~by ~
CH2OH
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where EO is the static dielectric constant, E , is the high-frequency limit of the dielectric constant for the process under consideration (which, in the absence of any other process on the higher a H N and frequency side, is approximately equal to 1.051~~); j 3 are ~ the ~ symmetric and asymmetric distribution parameters, respectively, and fo is the relaxation frequency. The peak loss frequency fm is obtained from the formula f , = fo tan(n/ 2(1+j3")). In Figure 4, we have given the temperature variation of the total dielectric strength ( E O - 1 . 0 5 n ~ of ~ )the samples above T,. (We have measured the nD value for the supercooled liquid glucose from room temperature to 348 K using Abbe's refractometer, and we have noticed that the nD value varies from 1.5340 to 1.5239 in this temperature range. However, we have abandoned the measurement of nD in the supercooled state of other materials due to experimental difficulties arising out of the high viscosity of the liquids. The nD value for D-sorbitol obtained on extrapolation of the aqueous solution data at room temperature listed in ref 17 is found to be approximately 1.5280, which is not too different from that of glucose. Hence, a value of 1.53 is assumed for n~ for all other materials. Since EO values are very large for these supercooled liquids, the error present due to this approximation ~ be negligible.) We in the measurement of EO - 1 . 0 5 n ~will have observed a systematic variation of PHNwith the number of OH sites per molecule (as in our earlier reference"), which is shown in Figure 5 for the present cases. We show the general dielectric behavior of the samples below T, in Figure 6 , in the form of Cole-Cole diagrams, where the B-process can be seen as a very broad process, which can be described by the Cole-
1
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C
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I CHIOH
lbl D Fructose
-
-
IC1
D Sorbitol Figure 1. Chemical structures of the samples used in the study.
of aldopentose; D-fructose is a ketohexose; samples D-glucose and D-galactose are isomers of aldohexose. All these samples exhibit a ring chain tautomerism in the liquid state; that is, in the liquid state both the (open-ended) chains and ring structures are present in e q u i 1 i b r i ~ m . IIf ~ ~a~small ~ amount of aldehyde conformation (chain) is removed from the liquid by a chemical reaction, a fresh amount forms to restore equilibrium. However, in the crystalline structure the preference is for the ring structure. D-Sorbitol exists in chain conformation only as the ring formation is not possible in this molecule. We have studied the samples shown in Figure 1 by quenching the melt of the sample in the dielectric cell itself to ensure that there is no crystallization. The samples are then equilibrated at 77 K before starting the measurements. At each temperature the sample is kept isothermally for about 15 min before taking the measurements over the entire frequency range. To get firsthand information about the various relaxation processes, we have plotted tan 6 (=E"/€') at 1 KHz test frequency as a function of temperature in Figure 2, which shows very clear a- and p-processes in all the samples. The shape of the relaxation spectrum above Tg for all the samples is shown in Figure 3 in
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Relaxation Processes of Some Carbohydrates
J. Phys. Chem., Vol. 99, No. 32, 1995 12351
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Figure 4. Variation of the total dielectric strength (EO - 1 . 0 % ~ ~with ) temperature (normalized to the corresponding T,’s)above T, for (0) D-xylose, (0)L-arabinose, (0) D-glucose, (A) D-galactose, ( x ) D-
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0.5-
o-fructose; and (f) D-sorbitol. The thick line corresponds to the Havriliak-Negami equation (1) for the resolved a-process with the parameters shown in the figure. Note the presence of the ,!?-process on the high-frequency side. Also note that in (f) the &process is dissolved into the a-process, and correspondingly there is a large change in the shape of the Cole-Cole diagram; hence, the thick line shown in the figure corresponds to the a j3 process.
0.4 -
+
Cole depressed arc equationI9 (which results from (1) by putting = 1):
BHN
where &c is the symmetric distribution parameter. At temperatures near 77 K we have not found any considerable dispersion in the e’ values. However, we noticed a significant difference between d and 1 . 0 5 n ~ *(where n D is the refractive index), which indicates the existence of other processes at much higher frequencies at 77 K. The variation of the strength of the /?-process and the distribution parameter aC with temperature is shown in Figures 7 and 8, respectively. In Figure 9 we have given the Arrhenius plot showing the variation offmcorresponding to all the processes. Thef, values corresponding to the resolved a-process are found to follow the power-law e q u a t i ~ n : ~ ~ ~ . * , ’ ~
(3) where Tgl is the limiting temperature, and the fm values corresponding to the /3-process are found to follow the Arrhenius
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Figure 5. Variation of the asymmetric distribution parameter flm with the number of OH groups present on the molecules. The vertical
double-headed arrows indicate the variation of the parameter BHNin the temperature range studied. The unnamed points correspond to 2-phenylethanol (one OH group); 1,3-butanediol, propyleneglycol (two OH groups); glycerol, 1,2,6-hexanetriol (three OH groups) (for more details on this the reader may consult ref 11).
equation:
fm,p =fo,p exp(-EpJRT)
(4)
The details of the above two fits are given in Table 1.
Discussion a-Process. One striking feature of the a-process in these carbohydrates is that the dielectric relaxation spectrum is very broad with large a H N and 1 - BHNvalues (see Figure 3). In addition to that, the asymmetric parameter BHNis found to increase almost linearly with the number of OH sites per molecule (Figure 5). We believe this is an indication of increase in the “coupling” of dielectric modes to the structural modes via the H-bonding. (Here the term dielectric mode is used in a
Gangasharan and Murthy
12352 J. Phys. Chem., Vol. 99, No. 32, 1995
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Figure 7. Variation of the dielectric strength (EO - E,) (where 6- is the extrapolated high-frequency limit of the dielectric constant for the process under consideration) with temperature (normalized to T,)for the &process in the samples studied. The symbols correspond to ( x ) Pxylose, (A) L-arabinose, (0) D-glucose, (*) D-galactose, (0) Dfructose, and (+) D-sorbitol.
e‘ Figure 6. Cole-Cole diagrams corresponding to the low temperatures in L-arabinose.
TABLE 1: Details of a-and fi-Processes in Eqs 3 and 4a a-process T,’ r 260 16.04 260 13.72 258 16.61 280 15.54 292 10.99
6-process no. sample Tg log& Eg(kcal/mol) logf08 1 D-xylose 274.7 15.25 9.34 15.02 2 L-arabinose 270.2 13.85 8.62 13.58 3 D-fructose 277.2 14.30 11.49 14.82 4 D-galaCtOSe 295.9 15.73 10.79 14.60 5 D-glucoseb 309.0 13.10 8.5017.49 12.40 15.99 6 D-sorbitol 267.8 253 14.29 16.16 13.22 14.98 All temperatures are in Kelvin. We believe that the large uncertainity in the parameters of the B-process is due to unavoidable caramelization in this sample. (I
more general sense as the mechanism by which the dipole involved in a particular relaxation process rotates to contribute to polarization without any bias toward any particular mechanism. Similarly, one can define the structural mode as the mechanism by which the structure of the liquid adjusts itself, if, for example, there is a change in the temperaturesz0 Since the rotation of the dipole requires a displacement or adjustment of the surrounding matrix (our test dipole is part of it), dielectric relaxation cannot proceed without the structural adjustment.20 The extent to which this cooperation is required is termed the “coupling” in the present study. In a simple van der Waals liquid, the dielectric mode corresponding to the a-process may be identified with the cooperative rotation of the dipolar molecule as a whole and the structural mode may be identified mainly with the translational movement of the molecule. In the case of hydrogen-bonded liquids, there is still some controversy regarding the cause of the large dielectric polarization. The simplest case of this group of liquids is a monohydroxy alcohol, where there is only one hydrogen-bonding site per molecule. If one accepts the “OH flipping” between make and break of the hydrogen-bonded network as the cause of the main polarization,20the dielectric mode may be identified with
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Figure 8. Variation of the Cole-Cole distribution parameter with temperature (normalized to Tg)in the samples studied. The symbols correspond to ( x ) o-xylose, (A) L-arabinose, (0) D-glucose, (*) D-galactose, (0)D-fructose, and (+) D-sorbitol.
“OH flipping” because the dipole which is mainly situated in the OH group cannot rotate unless the hydrogen-bonded network is broken. Here, the make and breaks of the hydrogen-bonded network constitutes the structural mode. Since several makes and breaks are required for the neighboring hydrogen-bonding site to accept the OH group (this is the “flipping” process), the dielectric relaxation time is several times larger than the corresponding structural relaxation time. In this particular case, one can see that the dielectric mode is not directly “coupled” to the structural mode. However, with increase in the number of OH groups per molecule, the dielectric mode gets increasingly “coupled” to the structural mode, because for the dielectric relaxation to occur, there must be large intermolecular as well as intramolecular cooperation through the make and break of the hydrogen bonding. Thus, we see that the word “coupling” has nothing to do with the “mode-coupling” of the recent mode-
Relaxation Processes of Some Carbohydrates
J. Phys. Chem., Vol. 99, No. 32, 1995 12353
7.751
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Figure 9. Arrhenius plot for the samples studied normalized to their respective Tg’s.The point given by the symbol (0)corresponds to the structural relaxation corresponding to the DSC (Tg).Only the data for four of the six samples is given to avoid crowding of the points. The symbols correspond to ( x ) D-xylose, (A) L-arabinose, (*) D-galactose, and (0) D-fructose.
coupling theory4 of liquids.) Large a H N values are essentially foundz2in the case of high molecular weight polymers, where different modes involving segmental rotation is believed to be the cause of the large a H N . In simple glass-forming van der waals liquids that we studied re~ently,~.’-~ only slight deviation of a H N from 0 is noticed. The value of a H N is not too different from 0 even in linear multiple-H-bonded liquids such as glycerol and hexantriol.” (There are three H-bonding sites per molecule in these cases.) In the case of D-sorbitol, which is a linear molecule, we could not resolve the a-process as there is a very large contribution from the j3-process to the polarization (see Figures 3f and 7). The fit shown in Figure 3f is for the combined a @ process, and at present we believe that the large a H N value in D-sorbitol is probably due to the presence of the ,&process. In view of the above discussion, we believe that the large value of a H N is a result of the existence of molecules in both ring and chain conformations and is also due to a probability of chair-boat or chair-chair transformations, which would increase the modes of relaxation and hence would result in a distribution of relaxation times. (A symmetric Cole-Cole diagram (i&c f 0 in (2)) is generally taken as evidence of distribution of relaxation times, whereas the asymmetric ColeDavidson type of plot @HNf 1) is generally taken as an indication of a cooperative p r o c e ~ s . ~ ) One may also notice from Figure 3 that in those cases where there is a large contribution from the /?-process the shape of the Cole-Cole diagrams varies with temperature, thus invalidating the frequency-temperature-superpositionprinciple. Such an observations was made earlier by us in.the case of simple glassforming The other interesting aspect of the a-process is that it is strictly non-Arrhenius down to Tg,obeying the power-law equation, and freezes at the Tg (as seen in the DSC experiments), indicating that both the dielectric and structural modes are strongly coupled, unlike the case of monohydroxy alcohols (which show a Debye behavior).” We believe that the large PHNvalue in these carbohydrates is a result of this strong coupling between dielectric and structural modes via the very high degree of H-bonding present in these systems.
+
process. The most important observation that is made here is that the /?-process is smaller in magnitude in aldopentoses and is larger in hexoses. Note that only D-sorbitol exists completely in a linear form and the rest of the systems exist in both ring and chain conformations. In addition, aldopentoses have H atoms in the place of CH2OH in the R3 group position, as shown in Figure 1, hexoses have a CH2OH group in the place of the H atom in aldopentoses, and in D-sorbitol there are two CH20H groups at the chain ends. The above observations imply that it is perhaps the chain segments (along with the end group CH20H) which are dominating the j3-process. The activation energy measured for the j3-process (Table 1) accounts for the rotation of chain segments consisting of approximately two to three carbon atoms. If one looks at the ring structure for a possibility of the /?-process, rotation of parts of the ring about the C-C or C-0 bonds along the ring are not possible. However, the OH groups or CHzOH groups attached to the rings (as side groups) may give rise to some amount of polarization. But, the corresponding activation energies are generally smaller; for example, OH group rotation requires about 2.5 kcdmol and CH20H requires about 4 kcdmol, which follows from our recent ~ t u d y Apart . ~ ~ ~ ~ ~ ~ ~ from the difficulty in explaining the large EDvalues, one cannot explain the systematic variation of the magnitude of the @-processdescribed in the previous paragraph, if the side groups are responsible for the j3-process. We are also aware that the pentoses and hexoses studied here can have two ring conformations, viz., the boat and chair conformations, which are separated by a potential energy barrier.’* This barrier energy is found23 to be 10 kcal/mol in cyclohexyl chloride and cyclohexyl bromide and may be larger in the present cases. Apart from this one cannot explain the /?-process in D-sorbitol on the basis of this explanation. Thus, in view of the above discussion we believe that the j3-process in the present samples is due to segmental rotation in the linear chain structure of the molecules. Note that in the samples studied here (other than D-sorbitol) only half the molecules exist as linear chains, and the corresponding j3-process is smaller in these systems as compared to D-sorbitol. In Johari’s model of glassz4 the @-relaxation arises from a few molecules existing in lower density (liquid-like) regions in the otherwise rigid matrix. If this was the case, one cannot explain the dependence of the magnitude of the @-process on the molecular structure, and also there is some amount of difficulty in explaining the larger i&c values, as the “liquidlike” region is supposed to have a smaller acCvalue. (However the difference in the number of CH20H or OH groups results in a change in the intermolecular energy and the distribution of the hydrogen bonds, which cause the difference in the density distribution and hence may cause the j3-process in the glass. Moreover, the local density in the glass is not uniform but variously distributed due to the fluctuations in the liquid just above Tg,and hence the largeness of i&ccannot alone be argued as evidence for the intramolecular process.) In Williams’ model of glass,z4/?-relaxation arises due to a small angle rotation of the molecule as a whole, and it is very difficult to explain the systematic dependence of the j3-process on molecular structure on the basis of this model. Also the activation energy for a molecule of the size of the hexose is expected to be much larger, which follows from our previous s t ~ d i e s . ~ - ~ , ~(Perhaps, ,’~*” Williams’ model is valid for the rotation of small molecules in a glass formed of its mixture with other liquids.25) The temperature variation of A q (Figure 7) is similar to that seen in other organic liquids and appears to be somewhat related to the thermal expansion. With increase in temperature more and more “free volume” is available for the small segments,
12354 J. Phys. Chem., Vol. 99, No. 32, 1995
which might now be able to rotate easily and contribute more to the polarization. At T,, the free volume starts increasing more steeply, and hence, this can be realized as a much faster AEB variation above Tg(see Figure 7) (The steeper variation of AEB above T, may not be due to a large change in the number of molecules participating in the /3-process, as speculated previ0us1y.~) Also one may notice in Figure 8 that the qcvalue falls with increase in temperature, which may be due to a reduction in the distribution of relaxation times with thermal expansion, which we wish to pursue at a later stage.
Conclusions The a-processes found in carbohydrates are strictly nonArrhenius, thus contradicting Noel et al.,I5 and also the a-process is very broad, with large a H N and 1 - / ~ H Nvalues. The former is perhaps indicative of a larger number of relaxational modes present in the liquid as a result of the ringchain tautomerism, and the large value of 1 - / ~ H Nis indicative of stronger coupling between dielectric and structural modes, via the larger number of OH sites per molecule available for H-bonding. The P-process in these systems appears to be arising from the segmental rotation of the chain conformation and is not due to intermolecular degrees of freedom.
Acknowledgment. One of the authors (S.S.N.M.) wishes to thank the Department of Science and Technology, India; for financial assistance. References and Notes (1) Johari, G.P.; Goldstein, H. J . Chem. Phys. 1970, 53, 2372. (2) Williams, G. In Dielectric and Related Molecular Processes; Special Periodical Report; The Chemical Society: London, 1975; Vol. 2, p 151.
Gangasharan and Murthy (3) For details of B-relaxation, see: J . Non-Cryst. Solids 1991, 13133, especially the discussion section, p 378. (4) Gotze, W.; Sjogren, L. J . Non-Cryst. Solid 1991, 131-133, 161. (5) Murthy, S. S. N.; Sobhanadri, J.; Gangasharan J . Chem. Phys. 1994, 100, 4601. (6) Kiebel, M.; Bartch, E.; Debus, 0.;Fujara, F.; Petry, W.; Sillescu, H. Phys. Rev. E 1992, 45, 10301. (7) Nayak, S. K.; Murthy, S. S. N. J. Chem. Phys. 1993, 99, 1607. (8) Gangasharan; Murthy, S. S. N. J . Chem. Phys. 1993, 99, 9865. (9) Meir, G.; Gerharz, B.; Boese, D.; Fisher, E. W. J . Chem. Phys. 1991, 94, 3050. (10) Murthy, S. S. N.; Nayak, S. K. J. Chem. Phys. 1993, 99, 5362. (11) Murthy, S. S. N. Submitted. (12) Pethig, R. Dielectric and Electronic Properties of Biological Materials; John Wiley and Sons: Chichester, 1979. (13) Chan, R. K.; Pathmanathan, K.; Johari, G. P. J . Phys. Chem. 1975, 79, 278. (14) Naoki, M.; Katahira, S. J . Phys. Chem. 1991, 95, 431. (15) Noel, T. R.; Ring, S. G.; Wittam, M. A. J . Phys. Chem. 1992, 96, 5662. (16) Murthy, S. S. N.; Gangasharan; Nayak, S. K. J . Chem. SOC., Faraday Trans. 2 1993, 89, 509. (17) Monick, J. A. Alcohols, Their Chemistry Properties and Manufacture; Leinhold Book Co.: New York, 1968. (18) Nesmeyanov, A. N.; Nesmeyanov, N. A. Fundamentals oforganic Chemistry, 3rd ed.; M/R Publ.: Moscow, 1986; Vol. 2. (19) Hedvig, P. Dielectric Spectroscopy of Polymers; Adam Hilger Ltd.: Bristol, 1977. (20) Litovitz, T. A.; Davies, C. M. Physical Acoustics; Mason, W. P., Ed.; Academic Press: New York, 1969; Vol. IIA, p 281. (21) Hassion, F. X.; Cole, R. H. J . Chem. Phys. 1955, 23, 1756. (22) Havriliak, S.; Negami, S. J. Poly. Sci. C 1966, 14, 99. (23) Davies, H.; Swain, J. Trans. Faraday SOC. 1971, 67, 1637. (24) Johari, G. P. Ann. N. Y. Acad. Sci. 1976, 276, 117. (25) Murthy, S. S. N.; Paikaray, A.; Arya, N. J . Chem. Phys. 1995,102, 8213.
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