Identification of the Molecular Motions Responsible for the Slower Secondary (�)Relaxation in Sucrose

K. Kaminski,† E. Kaminska,† S. Hensel-Bielowka,*,† E. Chelmecka,†,‡ M. Paluch,† J. Ziolo,†P. Wlodarczyk,† and K. L. Ngai§

Institute of Physics, UniVersity of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland, Statistical DiVision,Department of Instrumental Analysis, Medical UniVersity of Silesia, ul. Ostrogorska 30, Sosnowiec, Poland,and NaVal Research Laboratory, Washington, D.C. 20375-5320

ReceiVed: December 6, 2007; ReVised Manuscript ReceiVed: February 27, 2008

Broad-band isothermal dielectric relaxation measurements of anhydrous sucrose were made at ambient pressurein its liquid and glassy states. We found a new secondary relaxation that is slower than the one commonlyobserved in sugars. Additionally, we carried out the dielectric measurements of the equimolar mixture ofD-glucose and D-fructose in wide ranges of temperature and frequency. Comparison of the behavior of thesetwo systems allowed us to make suggestions on the origin of the slower �-relaxation in sucrose. Computersimulations and coupling model calculations were performed to support our interpretation of the kind ofmolecular motions responsible for the slower secondary relaxation in the disaccharide considered.

Introduction

Carbohydrates form a large family of compounds whichincludes monosaccharides such as glucose, fructose, galactose,sorbose, and mannose; disaccharides such as sucrose, lactose,maltose, cellobiose, and gentiobiose; oligosaccharides such asrafinose, stochiose, and cellopentaose; and polysascharides suchas cellulose, starch, chitosan, and dextran. The existence of sucha large number and variety of sugars is due to the fact thatmonosaccharides can link together to form larger molecules orlong chains with different molecular weights. Moreover, mono-sugars also can link through different carbon atoms to form verydifferent molecular structures resulting in different physico-chemical properties. For example, maltose and trehalose bothconsist of two glucose units but they are connected throughdifferent carbon atoms (R(1-4) and R(1-1), respectively). Thisslight difference causes differences in their physical properties,place of occurrence in nature, and applications.

The various saccharides form a very important group ofcompounds. They play a key role in many processes occurringin living organisms,1–3 and have many applications in differentindustries including cosmetics, paper manufacturing, food, andpharmaceuticals. Because of their significance, these compoundsare naturally the subject of interest for many researchers.4–12

Consequently, many investigations using different experimentalmethods have been performed. The results of these studiesprovide new insight into the structure, molecular mobility,reactivity, etc. of sugars that are promising for novel applica-tions. Among these methods, broad-band dielectric spectroscopyis regarded as a one of the most effective techniques toinvestigate molecular dynamics because of the wide frequencywindow. Although a lot of research has been done on dielectricproperties of monosaccharides, little is on the disaccharides andpolysaccharides. In the majority of the earlier papers onmonosaccharides, glucose,13–15 fructose,16 maltose,17 galactose,18

and sucrose,19 two relaxation processes were found. The slower

one is the structural R-relaxation, which determines theliquid-glass transition, and the much faster one is a secondaryrelaxation process. The molecular mechanism of the secondaryrelaxation process is currently a subject of intensive researchand discussion. Many different interpretations of this processhave been offered in the literature. Gangasharan and Murthysuggested that the secondary relaxation process in glucose isrelated to the segmental rotation of the linear chain of themonosugars.18 Another point of view presented by Faivre et al.maintained that intra- and intermolecular interactions bothcontribute to secondary relaxation.20 On the other hand, Noelet al. argued that secondary relaxation in glucose (monosac-charide) and maltose (disaccharide) may be correlated withrotation of the hydroxymethyl groups attached to the sugar’sring.17 However, 13C NMR measurements carried out by vanDusschoten et al. demonstrated that this interpretation is notcorrect.21 Very recently we provided by dielectric spectroscopynew experimental facts that helped to elucidate the nature ofthe secondary relaxation in the monosaccharides. We showedin glucose, fructose, galactose, sorbose, and ribose that thereare in fact two secondary relaxation processes.22 The slower�-process (not observed before) was identified as the Johari-Goldstein (JG) �-relaxation that involves the motion of es-sentially the entire molecule and has properties mimicking theR-relaxation such as pressure dependence of the relaxationtime.22 On the other hand, the faster γ-process, commonlyobserved by others, is a local motion involving intramoleculardegrees of freedom, and its relaxation time is pressure inde-pendent. This process may originate from the hydrogen bondingscheme in the monosaccharides having a number of hydroxylgroups to form intramolecular as well as intermolecularhydrogen bonds. Therefore it is reasonable to suppose that theprerequisite of any conformational changes or motion of thesugar ring is breaking of hydrogen bonds, which is responsiblefor the presence of the secondary γ-relaxation observed in thedielectric loss spectra of the mono-, di-, and polysaccharides.

In this paper we present a dielectric study of moleculardynamics of the disaccharide sucrose in its liquid and glassystates. Sucrose is composed by the two monosugars D-glucose

† University of Silesia.‡ Medical University of Silesia.§ Naval Research Laboratory.

J. Phys. Chem. B 2008, 112, 7662–76687662

10.1021/jp711502a CCC: $40.75 2008 American Chemical SocietyPublished on Web 05/31/2008

and D-fructose linked by the glycosidic bond �(1-2), where 1denotes the first carbon atom of the D-glucose and 2 is thesecond carbon atom of the D-fructose The chemical structuresof glucose, fructose, and sucrose are presented in Figure 1. Sofar, only one secondary relaxation process in sucrose has beenreported in the literature.19 However, these measurements carriedout by Champion et al.19 were made over relatively narrowfrequency and temperature ranges. Thus, it would be difficultfor these authors to detect any additional relaxation process ifpresent in sucrose. For this reason, we carried out dielectricmeasurements of sucrose over a much broader range offrequencies from 10-2 to 106 Hz and temperatures from -145to 126 °C covering both the liquid and the glassy states. Indeed,our detailed study revealed the presence of an additional weakersecondary �-relaxation process that is slower than the previouslyobserved secondary γ-relaxation. After discovering the second-ary �-relaxation, the remaining task is to identify the molecularmechanism responsible for this new process. Toward this goal,we performed computer simulations, and we compared the datawith equimolar mixture of D-glucose and D-fructose as well aswith the coupling model prediction.

Experimental Section

Dielectric Spectroscopy. The anhydrous samples of glucose(98% of purity), fructose (98%), and sucrose (99.6%) werepurchased from Aldrich Chemicals. Measurements were startedimmediately after receiving the saccharides. The melting processof the sugars was performed very quickly and carefully to avoidcaramelization, because it is well-known that at higher temper-atures sugars undergo the caramelization process. For somesaccharides, the temperature of caramelization is very close tothe melting temperature. Thus, melting of the sugars has to beperformed very quickly in order to limit the time of keepingthe sugars at high temperatures.

Isothermal dielectric measurements at ambient pressure werecarried out using a Novo-Control GMBH Alpha dielectricspectrometer (10-2-106 Hz). The temperature was controlledby the Quatro system, employing a nitrogen gas cryostat, andthe temperature stability of the sample was maintained at betterthan 0.1 K.

Computational Method. The initial geometry of sucrose wasoptimized using the MM+ molecular modeling method imple-mented in HYPERCHEM 5.0 software. In the next step the DFT

calculations were performed with the Gaussian 03 softwarepackage.23 For the rings of both glucose and fructose, we haveused the recommended symbols and nomenclature as suggestedby IUPAC. Oxygen atoms have the same number as carbonatoms that they are linked to, except for the oxygen atombetween the glucose and fructose rings, which is denoted simplyby “O”.

The optimized structure of the isolated sucrose molecule wascalculated by the density functional three-parameter hybridmethod (DFT/B3LYP) using the 6-31G basis set. The stationarypoint was identified by frequency analysis at the same level oftheory.

Results

Dielectric Measurements. We measured the dielectricrelaxation of sucrose and the glucose-fructose mixture atambient pressure over a broad range of frequencies (10-2-106

Hz). The frequency-dependent spectra were collected startingat temperatures well above the glass transition temperature, Tg,down to temperatures deep into the glassy state. As can be seenin Figure 2, the relaxation dynamics of sucrose consists of threerelaxation processes: the structural R-relaxation and two second-ary processes. For clarity and ease of identification, the entireset of collected dielectric loss data is presented in three separateparts for different temperature ranges. Figure 2a shows exclu-sively the R-loss peak and the loss from ionic conductivity inthe temperature range from 126 °C down to 74 °C. Figure 2bshows data at temperatures from 72 °C down to 12 °C that arecontributed by the faster and more intense γ-relaxation and theemergence of the new, slower and weaker �-relaxation at lowertemperatures within this range. The data in the lowest temper-ature range from 6 °C down to -145 °C (Figure 2c) emphasizethe evolution of the γ-relaxation. On decreasing temperature,

Figure 1. Chemical structures of (a) glucose, (b) fructose, and (c)sucrose.

Figure 2. Dielectric spectra of sucrose in labeled temperature range.Each panel shows a relaxation process: (a) R; (b) �; (c) γ.

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it is commonly found in sugars and polyalcohols that the lossfrom ionic conductivity moves toward lower frequenciessignificantly slower than the R-relaxation, and eventually itobscures the R-peak (Figure 2a). Recently this additionalcontribution to conductivity was attributed to movements ofprotons in H-bonds.22 Because of this effect due to theconductivity, the R-relaxation peak cannot be observed inthe vicinity of the glass transition temperature. That is why thefrequency dispersion and the parameters characterizing it suchas the Kohlrausch-William-Watts exponent, �KWW, or theCole-Davidson exponent, �CD, as well as the relaxation timeτR and dielectric strength ∆εR characterizing the R-processcannot be determined in the vicinity of Tg. Consequently, thecharacteristics of the R-process are not known from dielectricexperiment and its relation to the secondary relaxations cannotbe obtained directly. Nevertheless, the derivative of the real partof the dielectric constant ε′ can be analyzed to extract therelaxation times in the vicinity of the glass transition (accordingto the Kramers-Kronig relation). The analysis gave the valueof the glass transition temperature equal to 340.5 K, which iswithin the limits of Tg reported for dry sucrose established bycalorimetric measurements.11,19

Herein we will focus our attention on the two secondaryrelaxations. The γ-relaxation (Figure 2c) can be observed abovethe glass transition temperature, it is well separated from theR-peak, and its intensity is comparable to that of the R-relaxationjust as in the case of glucose, galactose, fructose, and sorbose.22

To analyze this peak, we used the Havriliak-Negami (HN)function. However, to reproduce correctly the spectra obtainedin temperatures below Tg, we had to use also one Cole-Cole(CC) function for the lower intensity �-relaxation that appearsas a resolved peak in the glassy state, and situated between theR- and γ-peaks (Figure 2b). To fit the entire spectrum, we usethe function having the following form:

ε′′ (ω) ) σε0ω

n+ ∑

j

Im( ∆εj

(1 + (iωτ)aj)bj)j(1)

where j stands for R-, �-, and γ-relaxations, aj and bj are thesymmetric and asymmetric broadening, and ∆εj is the relaxationstrength of the j-relaxation peak.

To discuss the origin of the secondary relaxations in sucrose,we made additional experiments with a 50 wt % mixture ofglucose and fructose. The measurements of this mixture werecarried out at the same frequency and temperature ranges aswe did for sucrose. The glass transition temperature of thismixture, Tg ) 297 K, lies between the values obtained forglucose, Tg ) 307 K, and fructose, Tg ) 288 K, and is in perfectagreement with the Gordon-Taylor equation:

Tgmixt )

w1Tg1 + kw2Tg2

w1 + kw2(2)

where Tgmixt is the glass transition temperature for the mixture

of two components, 1 and 2, with glass transition temperatures,Tg1 and Tg2, and weight fractions, w1 and w2, respectively, andk is a constant24 equal to unity.

Some examples of the measured spectra are depicted inFigure 3. Only one secondary relaxation can be seen. To fitthe dielectric loss of the mixture, we use the same expressionas for sucrose (eq 1). The R-, �-, and γ-relaxation times ofsucrose, and theR- andγ-relaxation timesof theglucose-fructosemixture and of pure glucose and fructose are presented inFigure 4.

In each case the R-relaxation times were well described usingthe Vogel-Fulcher-Tamman-Hesse (VFTH) expression:

τ ) τ0 exp( DTT0

T - T0) (3)

whereas the relaxation time of all secondary relaxations followsthe Arrhenius law:

τ ) τ0 exp(Ea/kBT) (4)

For the �-relaxation of sucrose we obtained log(τ0/s) ) -18.41,and Ea ) 96.4 kJ/mol. The fit parameters for the γ-relaxationof the other sugars are collected in Table 1.

Computer Simulations. In our study of sucrose we haveinvestigated the dependence of the energetics of the moleculeon the two torsion angles �1 and �2, where �1 ) O(5)-C(1)-O-C′(2) and �2 ) C(1)-O-C′(2)-O′(5). For the optimized

Figure 3. Representative dielectric loss spectra obtained for the 1:1glucose-fructose mixture in the temperature range 373-138 K.

Figure 4. Temperature dependence of R-, �-, and γ-relaxation timesfor sucrose, glucose, fructose, and the 1:1 mixture of the two lattersugars.

TABLE 1: Parameters of the Arrhenius Equation (Eq 4) forγ-Relaxation for the Investigated Saccharides

name log τ0 activation energy, Ea [kJ/mol]

glucose -14.63 42.23fructose -14.33 42.12glucose-fructose, 1:1 -13.79 44.20sucrose -15 52.25

7664 J. Phys. Chem. B, Vol. 112, No. 25, 2008 Kaminski et al.

structure of sucrose the torsion angles �1 and �2 are 91.6° and-135.7°, respectively. Starting from the structure optimized atthe 6-31G level,23 the dihedral angle was changed continuouslyby 10° in the whole range of 360°. At the frozen value of thatangle the rest of the molecule was optimized and the energycorresponding to the optimized structure was calculated. Theobtained results are shown in Figure 5. The rotational surfacefor �1 consists of three minima. The energy difference betweenconformers I and II is about 27 kJ/mol and between conformersII and III is about 9 kJ/mol. The barrier height in this case is76.7 kJ/mol. As concerns the torsion angle �2, the rotationalsurface consists of five minima and the corresponding energydifferences between them are in the range 7-20 kJ/mol. Theestimation of the barrier height gives in this case the lower valueof about 55.2 kJ/mol. Additionally, the dependence of energyon angle C(1)-O-C′(2) was regarded. C(1)-O-C′(2) anglewas changed by 5° in the range of (15° around the 122.9° angle,which corresponds to the value obtained for the optimizedstructure (Figure 6). In this case the energy barrier is about 30kJ/mol.

Discussion

γ-Relaxation. As a start, we discuss the origin of theγ-relaxation (Figure 2c). Comparing the γ-relaxation of sucrosewith that of glucose, fructose, and their equimolar mixture inthe relaxation map (Figure 4), we see that they are very similar,

particularly those of sucrose and the mixture. This result impliesthat the γ-relaxation in all these materials has the same originthat may come from some internal motion in the monosaccharideunit. It is interesting that this relaxation is also visible inpolysaccharides such as cellulose and starch.25 Note that theauthors of ref 25 called this secondary relaxation the �-process(which we call the γ-relaxation). They interpret this relaxationas originating from local chain motion. However, the similarvalues of the activation energy obtained for their �-process (forexample, cellulose 43.5 kJ/mol, dextran 38.5 kJ/mol, and starch51.9 kJ/mol)25 to our γ-relaxation clearly indicates that their�-relaxation and our γ-relaxation have the same origin. It alsois worthwhile to point out that in the mentioned article25 theauthors did not observe this kind of secondary relaxation inglucose. However, this is probably caused by the problemintroduced by crystallization of glucose. Moreover, in very lowtemperatures in mono- and disaccharides they observed onemore relaxation, faster than all processes discussed in this paper.This relaxation has a small activation energy; thus the authorsascribe it to the motion of a side group in the glucose unit(methylol substituent). Interestingly, this type of relaxation isnot observed for the longer chains.25 Based on these data wetentatively conclude that the process we called γ-relaxation isprobably the backbone rotation of the monosaccharide unit.Another possible explanation is that this motion may be relatedto the boat-chair interconversion that should have an activationenergy around 56 kJ/mol.26 It may be recalled from the studywith the application of pressure22 that the relaxation time ofthe γ-relaxation of fructose did not change with pressure. Thisis perhaps the best evidence27 for the local intramolecular natureof the γ-relaxation in monosaccharides, disaccharides, andpossibly also polysaccharides.

�-Relaxation. Next, we embark on identifying the origin ofthe �-relaxation, which is more difficult than the task for theγ-relaxation. As shown in the previous paper on monosaccha-rides,22 glucose, fructose, and ribose, the �-relaxation cannotbe resolved as a well-defined loss peak in the isothermal spectraeven in the glassy state. Although some structures such as excesswing or inflection appear in the spectra to indicate its presence,its relaxation times cannot be determined without large uncer-tainties. Sorbose and galactose behave better to show thepresence of a loss peak at a few temperatures, giving clearevidence for the presence of the �-relaxation and improvedaccuracy of locating its relaxation times. As for the origin ofthe �-relaxation of sucrose, several possibilities exist. The first

Figure 5. Relative energy, ∆E , of isolated sucrose molecule as afunction of the torsion angle: (a) O(5)-C(1)-O-C′(2) (with respectto the lowest energy of structure III); (b) C(1)-O-C′(2)-O′(5) (withrespect to the lowest energy of structure IV).

Figure 6. Relative energy, ∆E , of isolated sucrose molecule as afunction of the C(1)-O-C′(2) angle.

Origin of Slower Secondary �-Relaxation in Sucrose J. Phys. Chem. B, Vol. 112, No. 25, 2008 7665

possibility is that this relaxation comes from the heterogeneousenvironments arising from fluctuations of interactions betweenthe glucose and fructose units or their packing. To check thisscenario, we measured the loss spectra of the 1:1 mixture ofglucose and fructose. Admittedly, sucrose is not the same asthe mixture of the glucose and fructose units because in thelatter the two components are not connected to each other.However, if heterogeneous environments would appear insucrose, they would be even more prevalent in the mixture, anda more prominent �-loss peak observed in the dielectric lossspectra of the mixture. This expected trend is contrary to theexperimental data. As can be seen in Figures 3 and 7, there isweaker evidence of the presence of the �-relaxation in themixture than in pure fructose and glucose. Moreover, the �-losspeak of sucrose was resolved (Figure 2). Thus, the heteroge-neous environment scenario for the origin of the �-relaxationcan be excluded.

Another natural possibility for the origin of the �-relaxationin sucrose is the internal motion within the sucrose via theglycosidic linkage. There are two different kinds of such motion:bending of this linkage and rotation of the rings with respect tothe each other. To elucidate whether any of these motions shouldbe taken into consideration, we take advantage of the resultsfrom computer simulations (Figures 5 and 6). Comparing thevalues for the barrier height obtained from computations, onecan see that only the value of 76.7 kJ/mol for the rotation ofthe two rings is comparable with the activation energy of the�-relaxation obtained from dielectric measurements. Certainly,these values are not in perfect agreement with each other.However, one has to take into account that the calculations wereperformed for isolated molecules of sucrose and not for therealistic glassy state. Therefore, on the basis of this inference,

the rotation of the two rings round each other is a possible originof the �-relaxation in sucrose.

Finally, we consider the possibility that the observed �-re-laxation in sucrose is the universal Johari-Goldstein (JG)relaxation found in many different kinds of glass-formers27–33

and also in the monosaccachides.22 To do this, we utilize theresults obtained in a paper recently published by some of us.22

In this paper, a new secondary �-relaxation process wasdiscovered in several monosaccharides. This secondary processwas found at frequencies between the slower primary R-relax-ation and the faster secondary γ-relaxation previously observedby others in the monosaccharides. The activation energy of the�-relaxation is much higher than that of the familiar secondaryγ-relaxation of carbohydrates. The �-relaxation time wassensitive to applied pressure. These properties of the �-relaxationare all indicative that it is the true JG relaxation of themonosaccharides.27 Thus, it is worthwhile to compare the�-relaxation in sucrose with the JG �-relaxation of the monosac-charides. As mentioned in a paragraph above, sorbose andgalactose are the two monosaccharides which have resolved�-relaxation, and their relaxation times τ� have been reported(see Figure 7 in ref 22). From the fit of τ� of galactose to theArrhenius equation, eq 4, the activation energy is Ea ) 96.9kJ/mol and log(τ0/s) ) -19.15. The values of these parametersfor the two monosaccharides are almost the same as those forsucrose, which are log(τ0/s) ) -18.41 and Ea ) 96.4 kJ/mol.The Tg of sucrose is higher than that of galactose. Hence, for acomparison of the relations between the primary and thesecondary relaxation times of sucrose and galactose, their R-,�-, and γ-relaxation times, τR, τ�, and τγ, are plotted againstTg/T in Figure 8. One can observe that the γ-relaxation timesτγ are somewhat longer and the activation energy slightly higherin sucrose than in galactose in the plot against 1/T in Figure 4as well as in the plot against Tg/T in Figure 8. These differencesare reasonable when we take into account that in the case ofsucrose the internal motions within the monosugar unit maynot be independent but can be coupled to the movement of theother unit. The �-relaxation time τ� of sucrose is also longerthan galactose by about 1 1/2 orders of magnitude at the sametemperature in the plot of log τ� against 1/T, as expected forthe larger sucrose molecule. In our recent works �-relaxationobserved in the monosaccharides galactose, sorbose, ribose,22

and 2-deoxyribose34 was successfully identified as the JG�-relaxation.22 The identification was based on the shift of

Figure 7. (a) Dielectric spectra of the 1:1 glucose-fructose mixturein the temperature range where �-relaxation is expected. For comparisonspectra of glucose (b) and fructose (c) in the same dynamic range.

Figure 8. Comparison of the R-, �-, and γ-relaxation times for sucrose(filled symbols) and galactose (open symbols) vs Tg/T.

7666 J. Phys. Chem. B, Vol. 112, No. 25, 2008 Kaminski et al.

relaxation time τ� on applying pressure in the cases of fructoseand ribose.22 Recent dielectric relaxation studies of two othermonosaccharides, D-ribose and 2-deoxyribose,34 have shown thatthe R-loss peaks of these two monosaccharides have higherintensity and were not affected by the other processes. Thefrequency dependence of the loss peaks of both D-ribose and2-deoxyribose were well fitted34 by the one-sided Fouriertransform of the Kohlrausch-William-Watts (KWW) function

φ(t) ) exp[ - (t/τR)1-n] (5)

where n ) 0.45. The primitive relaxation time, τ0, of thecoupling model27,29–31 was calculated by the equation

τ0 ) (tc)n(τR)1-n (6)

where τR and n appear in the KWW fit, and tc) 2 ps. There isgood agreement between the observed τ� and the calculated τ0,and this is another justification for identifying the �-relaxationof D-ribose and 2-deoxyribose as the JG �-relaxation.27 Thesimilarity of the �-relaxation of sucrose to those of themonosaccharides and its relation to the R- and γ-relaxationsnaturally suggest that it is also the JG �-relaxation originatingfrom some motion of the entire sucrose molecule, possiblyinvolving the rotation of rings via the glycosidic bond in sucrosecoupled with the translational motion of the whole molecule.NMR measurements performed on the considered sugar showthat, despite the fact that sucrose is a rigid molecule, rotationof the monosugar ring around the glycosidic bond may occur.35

This conclusion was supported by molecular mechanics calcula-tions.36 Unfortunately, we could not find any other data whichcan be compared with our dielectric results, activation energies,or relaxation times.

Note that, in the plot of τ� versus Tg/T in Figure 8, the τ� ofsucrose appears to be shorter than that of galactose at the samevalue of Tg/T. This is an artifact of scaling temperature by Tg.Nevertheless, the advantage of plotting relaxation times againstTg/T is that the separation between τR and τ� of both carbohy-drates can be easily compared at the same value of Tg/T. Forexample, at Tg/T ) 1, it can be seen that the distance ofseparation, [log(τR(Tg) - log τ�(Tg)], of sucrose is about an orderof magnitude larger than that of galactose. This trend ofincreasing [log(τR(Tg) - logτ�(Tg)] with increase of the size ofthe molecule in a homologous family of glass-formers has beenseen in genuine JG �-relaxations in oligomers of propyleneglycol37,38 and the polyalcohol series of glycerol, threitol, xylitol,and sorbitol.30,39 The trend is usually accompanied by broaden-ing of the R-peak and a larger value of the exponent n in theKohlrasuch function used to fit the data.30 The increase of n inthe coupling model is interpreted as due to increase ofintermolecular coupling, and eq 6 explains the correspondingincrease in [log(τR(Tg) - log τ�(Tg)].Unfortunately, in the casesof galactose, fructose, and sucrose we cannot compare the widthsof their R-relaxation peaks near (Tg/T) ≈ 1 because of maskingby the ionic conductivity on the low-frequency side of the R-losspeak and the overlap with the secondary relaxations on the high-frequency side. Nevertheless, by analogy with the mentionedoligomers of propylene glycol and the polyalcohols, we expectthat the R-peaks of sucrose should be broader than those ofgalactose and fructose. Thus, we can rationalize the observedincrease of [log(τR(Tg) - log τ�(Tg)] in sucrose compared withgalactose and fructose. This can be viewed as indirect evidencethat the �-relaxation observed in sucrose is the JG �-relaxation.Direct evidence must come from other experimental measure-ments outside dielectric relaxation reported in this paper. Byinspection of Figure 8, ostensibly the Tg-scaled temperature

dependence of sucrose is about the same as that of galactose,although this is uncertain because our dielectric data of τR arelimited to shorter than 10-2 s. Even in the case where the Tg-scaled temperature dependence or “fragility” of sucrose is thesame as that of galactose, and does not correlate with the changein the nonexponentiality, one must bear in mind that the increaseof [log(τR(Tg) - log τ�(Tg)] is only one decade, and “fragility”is a complex quantity dependent not only on intermolecularcoupling (manifested by nonexponentiality) but also on ther-modynamic variables (volume and entropy). On the other hand,nonexponentiality is independent of thermodynamic variablesas shown by the invariance of the dispersion of the R-relaxationto combinations of pressure and temperature at constant τR.40

Hence, fragility does not always correlate with nonexponentialityas found in other glass-formers.

It is worthwhile to note that the slow JG �-relaxation couldhave been observed already in several polysaccharides such ascellulose and dextran.25 The observed relaxation was called theδ-relaxation by the authors of ref 25, and it resembles our JG�-relaxation of sucrose and the monosaccharides. It would bean interesting endeavor to study the polysaccharides further tosee if whether the so-called δ-relaxation is in fact the genuineJG relaxation, which is purported to be a universal propertiesof all glass-formers.27 Before closing, a comment must be madeon the accuracy of the data of τ� near Tg, determined by fittingthe spectra by eq 1 and shown in Figure 4. Although eq 1 isone of the standard methods used to extract relaxation times, ithas assumed that all processes are independent and makeadditive contributions to the loss spectrum. This is not the casefor theJG�-relaxation.Either in thecouplingmodeldescription30,31

or by NMR experimental investigation,33 the JG �-relaxationis not independent of the R-relaxation. Hence, the values of τ�obtained by applying eq 1 may not be accurate, particularly attemperatures closer to Tg where the spectrum shows no resolvedloss peak for the JG �-relaxation. The tendency is to overesti-mate τ� by using the Cole-Cole function for the JG �-relaxationto fit the data when the only feature observed in ε′′ (f) is thehigh-frequency part of the hypothetical Cole-Cole form for theJG �-relaxation.

Conclusions

We have measured the dielectric permittivity of sucrose inbroad ranges of temperatures and frequencies. In addition tothe commonly observed primary and a secondary relaxation byothers before, we found a slower secondary relaxation lyingbetween them. Naturally, this new secondary relaxation is calledthe �-relaxation and the old secondary relaxation the γ-relax-ation. By using computer simulation of the internal motions ofthe sucrose molecular and assisted by comparison of theobserved �- and γ-relaxations in monosaccharides, we havesome preliminary identification of the molecular mechanismsfor these two secondary processes in sucrose. The γ-relaxationis a result of some internal motion within the monosaccharideunit.

Previously we have established that the �-relaxations in someof the monosaccharides are Johari-Goldstein �-relaxation.These include fructose, D-ribose, and 2-deoxyribose by applyingpressure,22 and D-ribose and 2-deoxyribose by applying thecoupling model prediction of its relaxation time.34 Propertiesof the observed �-relaxation in sucrose similar to those of themonosaccharides are found as well as an expected increase inthe separation between the R- and �-relaxations in sucrose.These constitute indirect evidence that the �-relaxation insucrose is the Johari-Goldstein �-relaxation, which is supposed

Origin of Slower Secondary �-Relaxation in Sucrose J. Phys. Chem. B, Vol. 112, No. 25, 2008 7667

to be present in all glass-formers. The �-relaxation likelyinvolves rotation of both monosugar rings and is coupled withpossible translation motion of the entire molecule. Certainly,further experiments using other techniques are needed to obtaina more exact description.

Acknowledgment. The work was supported by the Ministryof Science Poland (Grant N N202 007534), and by the Officeof Naval Research for the part performed at the Naval ResearchLaboratory. K.K. acknowledges financial assistance from FNP(2008).

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