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Identifying the Origins of Two Secondary Relaxations in Polysaccharides K. Kaminski,*,† E. Kaminska,† K. L. Ngai,‡ M. Paluch,† P. Wlodarczyk,† A. Kasprzycka,§ and W. Szeja§ Institute of Physics, Silesian UniVersity, ul. Uniwersytecka 4, 40-007 Katowice, Poland, NaVal Research Laboratory, Washington, D.C. 20375-5320, and Silesian UniVersity of Technology, Department of Chemistry, DiVision of Organic, Chemistry, Biochemistry and Biotechnology, ul. Krzywoustego 4, 44-100 Gliwice, Poland ReceiVed: NoVember 5, 2008; ReVised Manuscript ReceiVed: March 13, 2009
The main goal of this paper is to identify the molecular origins of two secondary relaxations observed in mechanical as well as in dielectric spectra in polysaccharides, including cellulose, and starches, such as pullulan and dextran. This issue has been actively pursued by many research groups, but consensus has not been reached. By comparing experimental data of monosaccharides, disaccharides, and polysaccharides, we are able to make conclusions on the origins of two secondary relaxations in polysaccharides. The faster secondary relaxations of polysaccharides are similar to the faster secondary relaxations of mono-, di-, and oligosaccharides. These include comparable relaxation times and activation energies in the glassy states, and also all the faster secondary relaxations have larger dielectric strengths than the slower secondary relaxation. The similarities indicate that the faster secondary relaxations in the polysaccharides have the same origin as that in mono-, di-, and oligosaccharides. Furthermore, since the relaxation time of the faster secondary relaxation in several mono- and disaccharides was found to be insensitive to applied pressure, the faster secondary relaxations of the polysaccharides are identified as internal motions within their monomeric units. The slower secondary relaxations in polysaccharides also have similar characteristics to those of the slower secondary relaxations of the disaccharides (maltose, cellobiose, sucrose, and trehalose), which indicates the analogous motions govern the slower process in these two groups of carbohydrates. Earlier we have shown in disaccharides that the rotation of the monomeric units around the glycosidic bond is responsible for this process. The same motion can occur in polysaccharides in the form of a local chain rotation. These motions involve the whole molecule in disaccharides and a local segment in polysaccharides. It is intermolecular in nature (with relaxation time pressure dependent, as found before in a disaccharide), and hence, it is the precursor of the structural R-relaxation. These results lead us to identify the slower secondary relaxation of the polysaccharides as the Johari-Goldstein β-relaxation, which is supposedly a universal and fundamental process in all glass-forming substances. 1. Background Polysaccharides, including cellulose, starch, Curdlan, and dextran, belong to the group of polyglycanes that have the same repeating unit, namely the anhydroglucose unit. Their chemical structures differ mainly by the form of the glycosidic linkage in their polymer backbone. Cellulose has the β(1-4) linkage, starch has the R(1-4) linkage, Curdlan has the β(1-3) linkage, and dextran has the R(1-6) linkage. For each repeat unit, cellulose, starch, and Curdlan have two hydroxyl side groups and one hydroxymethyl side group, while dextran has three hydroxyl groups and no hydroxymethyl group. It is instructive to mention that the disaccharides, maltose and cellobiose, respectively, have the R(1-4) and β(1-4) glycosidic linkage of two glucose units. The chemical structures of some polysaccharides, disaccharides, and monosaccharides are shown in Table 1. The secondary relaxations in polysaccharides have been a subject of research in the past five decades.1-14 For a review and the extensive literature on this subject, see ref 13. A dominant secondary relaxation found in the dielectric spectra of all polysaccharides, called the β-relaxation by Einfeldt et al.13 †
Silesian University. Naval Research Laboratory. § Silesian University of Technology. ‡
and Meissner et al.,14 has long since occupied exclusively the attention of many researchers using dielectric spectroscopy because it has the largest dielectric strength compared to other secondary relaxations. Since not all workers use β to stand for this relaxation, we rename this the βE-relaxation, where the suffix reminds us that this is the designation by Einfeldt et al. Several interpretations of its molecular origin have been offered. For the starch pullulan, Nishinari et al.8 suggested that the relaxation originates from rotation of the methylol (or hydroxymethyl) CH2OH side group on C-5 of the glucose residue. Montes et al.10,11 showed that the βE-relaxation of cellulose, which they called the γ-relaxation, does not involve a significant entropic contribution and originates from the rotation of the methylol group in the anhydroglucose unit. Their molecular modeling suggests that the rotation of the side groups does not lead to conformational change in the rest of the chain, and it transpires without cooperativity. This interpretation by Montes et al. is in stark contrast to the identification of the βE-relaxation (the same as the γ-relaxation of Montes et al.) as a local motion of the main chain segments via the glycosidic linkages by Einfeldt et al. for celluloses and starches in general. In one publication,14 it was concluded that the local chain segment motion in cellulose involves more than two but less than five repeat units. Adding more confusion in interpreting data, the motion of methylol or hydroxyl side groups was used instead by Einfeldt et al. as the
10.1021/jp809760t CCC: $40.75 2009 American Chemical Society Published on Web 07/02/2009
Origins of Two Secondary Relaxations in Polysaccharides
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TABLE 1: Chemical Structures, Glass Transition Temperatures, and Activation Energies of the β- and γ-Relaxations in the Polysaccharides, an Oligosaccharide, the Disaccharides, and the Monosaccharides Discussed in This Papera
a The symbol “m” indicates that the datum was derived from mechanical relaxation measurement; otherwise, all data were obtained by dielectric relaxation. The notation “n.a.” indicates that the datum is unavailable.
molecular mechanism of another secondary relaxation (much faster than the βE-relaxation and with smaller activation en-
thalpy) found in the polysaccharides which they called the γ-relaxation and which we shall called γE. However, at this point
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it should be noted that the relaxation process denoted by γE was visible only in mono-, di-, and oligosaccharides (glucose, cellobiose, gentiobiose) but was not seen in polysaccharides (starch, dextran, cellulose). The main reason for that is that, in the case of glucose, cellobiose, and gentiobiose, Meisner et al. performed measurements on completely crystalline samples. On the other hand, polysaccharides were only partially crystalline, and hence, they could observe reorientation of the molecules from the amorphous parts of the polysaccharides. Therefore, it makes no sense for us to compare with the data of glucose, cellobiose, and gentiobiose published by Meisner et al. Moreover, we use a new notation, the βE-relaxation, for the γ-relaxation of Montes et al., which is identical to the β-relaxation of Einfeldt et al. (renamed as the βE-relaxation here). From now on, γ-relaxation (of Montes et al.) and β-relaxation (of Einfeldt et al.) are just two different names for the same secondary relaxation of the polysaccaharides. The βErelaxation was observed in dextran. But, since the methylol group is not present due to the C-6 carbon being used in the formation of the R(1,6) glycosidic linkage, Nishinari attributed the γ- or βE-relaxation to libration of glucose residues around the R(1,6) glycosidic linkage. Scandola et al.9 argued that this interpretation is unlikely and instead proposed local chain motion for the γ- or βE-relaxation of dextran, in accord with Einfeldt et al. Boat-chair interconversion of the pyranose ring is another interpretation given by others to the γ- or βE-relaxation.5,15 The entirely different interpretation of the γ- or βE-relaxation is orientation of bound or bonded water,12,16 or confined water17 in the polysaccharides. This interpretation cannot be excluded because polysaccharides are hygroscopic, and traces of water may be present even in dry specimens. From the above, the conflict between the different interpretations of the γ- or βErelaxation of cellulose and other polysaccharides is evident. Actually, in addition to the so-called βE-relaxation, a slower secondary relaxation has long been observed by dynamic mechanical measurements performed on dried cellulose,2,4,10,11 and dried dextran,5,11 and confirmed by dielectric measurements.8,13,14,18 Montes et al. called this the β-relaxation naturally because they also observed the faster secondary γ-relaxation (or the βE-relaxation of Einfeldt et al.). The activation energy of the β-relaxation increases when the water content decreases in the cellulose and reaches 85 kJ/mol for the anhydrous sample, and simultaneously the pre-exponential time τ∞ decreases to attain a small value of the order of 10-20 s. The high activation energy and small τ∞ led Montes et al. to conclude that the β-relaxation has considerable activation entropy, and they associated it with localized motion of the main chain. Einfeldt et al. also found the same slower secondary relaxation in cellulose, but since they had already used β (βE in this paper) to denote the faster secondary relaxation, it was called the δ-relaxation.13,14 This δ-relaxation was found in various well dried polysaccharides, including many celluloses, starches, dextran, and pullulan.8,13,14 The use of δ for the name of the slowest secondary relaxation in the polysaccharides is not natural because usually secondary relaxations are named β, γ, and δ in the order of decreasing relaxation time and activation enthalpy. Einfeldt et al. stated that the molecular origin of the δ-relaxation in many well dried polysaccharides is unclear, and they speculated that it is an orientational motion of a mixed phase of polysaccharide and water. The speculation was based on the observation of a similar process in wet specimens, called the βwet-relaxation by Crofton and Pethrick.6 A slower secondary relaxation also was observed in dried dextran in addition to the dominant γ- or βE-relaxation by
Kaminski et al. dielectric spectroscopy8,18,13,14 and by dynamic mechanical spectroscopy.9,11 Montes et al. and others named the slower one β-relaxation and the faster one γ-relaxation, which are respectively the δ-relaxation and βE-relaxation in the nomenclature of Einfeldt et al. The γ-relaxation time τγ of dextran from Montes et al. has an activation energy of 32 kJ/mol and a preexponential time τ∞ of 5 × 10-15 s, respectively (comparable with 38.6 kJ/mol and 4.7 × 10-16 s of the βE-relaxation of Einfeldt et al.). Application of the analysis of the Arrhenius T-dependence of τγ according to that proposed by Starkweather19 showed that the γ-relaxation is a simpler secondary relaxation in the sense that its activation energy has a negligible entropy contribution. On the other hand, the β-relaxation time τβ of dextran has a much larger activation energy Eβ of 82 kJ mol-1 and a shorter pre-exponential time τ∞ of 3 × 10-19 s, respectively. It is a more complex secondary relaxation because its activation energy has both enthalpic and entropic contributions. These properties of the β-relaxation of Montes et al. (equivalent to the δ-relaxation of Einfeldt et al.) led Montes et al. to suggest that it originates from the motion of main chain segments. The same conclusion was made by them on the β-relaxation of cellulose, which has Eβ ) 85 kJ/mol and τ∞ ) 5 × 10-20 s.10,11 If motion of main chain segments manifests itself as a secondary relaxation in polysaccharides, then it likely is the slowest among possible secondary relaxations. From this standpoint, the assignment of local main chain motion by Montes et al. as the β-relaxation observed by them (i.e., the δ-relaxation of Einfeldt et al.) is more plausible than the same assignment as the βE-relaxation by Einfeldt et al. (i.e., the γ-relaxation of Montes et al.). 2. Introduction From the brief review of research of secondary relaxations in polysaccharides in the past four decades, it is clear that different authors gave different and often contradictory interpretations to the molecular origins. Naturally, progress of research of molecular dynamics in polysaccharides is impeded without resolution of this ambiguity and controversy. Since secondary relaxations are local motions within the chains of polysaccharides, they may be related to those of oligo-, di-, and monosaccharides in molecular origins. Recent broadband dielectric measurements have found two secondary relaxations in the disaccharides and the monosaccharides.20-22,23 The slower one (β) has not been seen before and is found to shift to lower frequencies on elevating pressure20-23 and is sensitive to thermal history22 while the faster one (γ) does not. From these results, it was concluded that the γ-relaxation is intramolecular in origin and is unrelated to the structural R-relaxation responsible for the glass transition. On the other hand, the slower β-relaxation is intermolecular in nature and has properties mimicking those of the R-relaxation. In some disaccharides, the β-relaxation is accompanied by the rotation of the D-glucopyranose and D-fructofuranose rings around the glycosidic bond. Thus, the β-relaxation of disaccharides and monosaccharides belongs to the important class of secondary relaxations, called the Johari-Goldstein (JG) β-relaxation,24 that are correlated with the R-relaxation in behavior and properties.25-32 These correlations imply that the cooperative R-relaxation that is responsible for the glass transition may actually originates from the JG β-relaxation, which is supposedly a universal process present in all glassformers. It should also be present in oligosaccharides and polysaccharides if it is truly a universal and fundamental process in all glassformers. The present paper reports a combined and comparative study of the secondary relaxations in polysaccharides with those in
Origins of Two Secondary Relaxations in Polysaccharides the oligo-, di-, and monosaccharides. We compare their characteristics, including relaxation times and temperature dependences. From the comparison, we look for a possible connection between the secondary relaxations in the polysaccharides and those of the other saccharides. If they are closely related, then we can draw from our knowledge of the secondary relaxations in disaccharides and monosaccharides to identify the molecular origins of the secondary relaxations in the polysaccharides. Our study confers a bonus of resolving the controversy created by the various interpretations of the secondary relaxations of polysaccharides in the literature. 3. Comparing with the Secondary Relaxations in Monoand Disaccharides Confusion has been created by various authors in using different notations for the same secondary relaxation in polysaccharides, To avoid this confusion in this paper, we refer to the faster secondary relaxation as the γ-relaxation, which is the same as the γ-relaxation of Montes et al., and the β- or βE-relaxation of Einfeldt et al. The slower secondary relaxation is referred to as the β-relaxation, which is the same as the β-relaxation of Montes et al., and the δ-relaxation of Einfeldt et al. Before our recent broadband dielectric relaxation measurements over an extended temperature range,20-23 only one secondary relaxation was observed by others33-36 in the monosaccharides, and in the disaccharides except trehalose in the work of De Gusseme et al.37 and Noel et al.38 In addition to this well observed secondary relaxation, we found a slower secondary relaxation with significantly lower dielectric strength.20,21,23 In accordance with the convention of denoting secondary relaxations by Greek letters, i.e., β, γ, δ, ..., in order of decreasing relaxation time, the new and slower secondary relaxation is designated as β and the faster and commonly observed one by γ.20 The much weaker β-relaxation compared with the γ-relaxation in the mono- and disaccharides is perhaps the main reason why it has not been detected before by others. This is usually the case when a faster γ-relaxation with large dielectric strength is present dominating the loss spectra at frequencies higher than the R-relaxation and obscuring the slower β-relaxation. This situation in the mono- and disaccharides is common and found in many other glassformers such as the much studied dialkyl phthalates.39 The oligomeric and polymeric carbohydrates are no exception, and this confounds the identification of the relaxation processes in these more complex carbohydrates despite the amount of experimental effort. Our dielectric study of the monosaccharides fructose and ribose,20 and the disaccharide leucrose,22 with applied pressures has shown that the β-relaxation shifts to lower frequencies on elevating pressure, mimicking the behavior of the R-relaxation. In contrast, the γ-relaxation is unchanged by applied pressure. For trehalose, De Gusseme et al.37 were able to probe the R-relaxation of trehalose close to Tg by means of specific heat spectroscopy (TMDSC) and obtained an estimate of 0.30 for the stretch exponent, 1 - n, of the Kohlrausch-Williams-Watts correlation function, φ(t) ) exp[-(t/τR)1-n], of the R-relaxation. With this value of the stretch exponent, they calculated the primitive relaxation time τ0(Tg) at Tg of the Coupling Model,24-26,29 by the relation τ0(T) ) (tc)n[τR(T)]1-n and tc ≈ 2 ps for molecular glassformers such as the saccharides. Furthermore, from the analogy of the primitive relaxation of the Coupling Model to the Johari-Goldstein (JG) β-relaxation, their relaxation times should be comparable, and hence, τ0(T) ≈ τβ(T). De Gusseme et al. found order of magnitude agreement between the calculated τ0(T) and the observed β-relaxation time τβ(T) at T
J. Phys. Chem. B, Vol. 113, No. 30, 2009 10091 ) Tg obtained by extrapolating the Arrhenius T-dependence of τβ measured below Tg. The relation τβ(Tg) ≈ τ0(Tg) if obeyed is one of the established criteria for identifying a secondary relaxation as the JG β-relaxation.25 Hence, De Gusseme found the JG β-relaxation in trehalose. In the cases of the monosaccharides D-ribose and D-deoxyribose,40 the location of the β-relaxation in the dielectric spectrum is also in agreement with that predicted by the Coupling Model. The pressure dependence of τβ and the relation τβ(Tg) ≈ τ0(Tg), if obeyed, are two criteria that we can use to identify the β-relaxation in the mono- and disaccharides as the universal JG β-relaxation, like that found in many glass-formers with diverse chemical structures.24-26,28-30 We have shown before by theoretical modeling computations of the disaccharide sucrose21 that the β-relaxation originates from motion of the entire molecule involving rotation of the two monosaccharide rings around the glycosidic bond. This characteristic of the β-relaxation in sucrose satisfies another criterion24 that it is the JG β-relaxation. The activation energies determined for the JG β-relaxations in seven disaccharides are within the range 73-96 kJ/mol,23 and similar values are found for the JG β-relaxations of the monosaccharides sorbose and galactose.20 These are close to the values of the β-relaxation of two polysaccharides, which are 85 kJ/mol (τ∞ ) 5 × 10-20 s) for anhydrous cellulose11 and 82 kJ/mol (τ∞ ) 10-20 s) for anhydrous dextran.18 The faster γ-relaxation in the mono- and disaccharides is of intramolecular nature, as inferred from the insensitivity of its relaxation time τγ to applied pressure and thermodynamic history.22 We have also seen before that the activation energies determined for the γ-relaxations of seven disaccharides studied23 are within the range Ea ) 44-52 kJ/mol, and they are close to Ea ) 42 kJ/mol determined for the γ-relaxations in some monosaccharides.20 These are comparable to the range of the activation energies of β-relaxation of several kinds of polysaccharides: 36-50 kJ/mol from Montes et al. and Einfeldt et al., 40.8 kJ/mol for cellulose from Schartel et al.,12 and 45-48 kJ/ mol for various other types of cellulose from Einfeldt et al. The glass transition temperatures and the activation energies of the γ- and β-relaxations of several polysaccharides from the literature are reproduced in Table 1 to compare with those of some disaccharides and monosaccharides. In Figure 1 we present as a function of reciprocal temperature the relaxation times of the β- and γ-relaxations in the polysaccharides, cellulose, dextran, and pullulan obtained by others2,10,11,13,7,8 and the monosaccharides and disaccharides obtained ourselves.20,22 The β-relaxation times τβ (equivalent to τδ of Einfeldt et al.) of cellulose from different sources are in rough agreement with each other. Data represented by open black circles are τβ from ref 11, closed black circles are τδ from ref 13, and the lone open black diamond is from ref 2. The τβ of the trimer and tetramer of cellulose are close to that of cellulose41 and therefore not shown in Figure 1. The τβ of dextran, the closed blue squares from ref 11, and the lone open square from refs 7 and 8 are also close by. Remarkably, the τβ values of these two polysaccharides nearly overlap the JG β-relaxation time τJG of leucrose (open green squares), maltose (magenta short dashed line), and cellobiose (brown long dashed line). The other two lines with higher activation energy are τJG of trehalose (green dashed-dotted line) and of sucrose (red short dashed-long dashed line). The magenta inverted triangles lying in between the last two lines are the τJG values of the monosaccharide galactose. As can be seen by inspection of Figure 1, there is good correspondence in the magnitude and
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Figure 1. Relaxation map of relaxation times. On the top are the JG β-relaxation times of some disaacharides represented by lines (data not shown for the sake of clarity except for leucrose): sucrose (red), trehalose (green), cellobiose (brown), maltose (magenta) from Kaminski et al.,23 trehalose from De Gusseme et al. (blue).37 JG β-relaxation times of the disaccharide leucrose are shown by open green squares. The filled black circles are the relaxation time of the so-called “δ-relaxation” (equivalent to β-relaxation in this paper) of cellulose obtained by Einfeldt et al.13 The three black open circles nearby are dynamic mechanical data of cellulose by Montes et al.11 The lone open diamond is from the mechanical data of cellulose by Kubat et al.2 The blue line represents the Arrhenius fit to the relaxation times of the so-called β-process of anhydrous dextran obtained by Montes et al.18 by a combination of dielectric and mechanical relaxation data represented by filled squares near it. The data of Scandola et al.9 consistent with that of Montes et al. are not shown. On the bottom are the γ-relaxation times of monosaccharides, fructose (+), glucose (green diamonds), and galactose (magenta inverted triangles), and disaccharides, maltose (filled red circles) and cellobiose (blue triangles). The black solid and long dashed lines represent the Arrhenius temperature dependences of the relaxation times of the βE-relaxation of two kinds of cellulose, linters pulp and avicell, respectively, from Einfeldt et al. The βE-relaxation (equivalent to the γ-relaxation in this paper) times of the Merck starch are indistinguishable from that of linter pulp cellulose and are not shown. The long and short dashed red lines are the Arrhenius T-dependence of dried pullulan from Einfeldt et al.,13 and the lone filled diamond is the isochronal dielectric data of pullulan at 10 Hz from Nishinari et al.8 At the very bottom are the relaxation times of the βErelaxation (equivalent to the γ-relaxation in this paper) obtained by Einfeldt et al. and the γ-relaxation time obtained by Montes et al. of dextran and combined with data of Scandola et al.9 and Nishinari et al.8
temperature dependence of τβ (or τδ) of the polysaccharides with the τJG values of the disaccharides in Figure 1 and monosaccharides (not shown). This correspondence can be considered as evidence that the β-relaxation of the polysaccharides is also the JG β-relaxation. This suggestion is made particularly plausible when one considers cellobiose as a dimer of the polymer cellulose, with both having the β(1-4) glucose-glucose linkage. Hence, the JG β-relaxation of cellobiose coming from the rotation of the two anhydroglucose rings around the β(1-4) linkage would not be too different from the related motion of the observed β-relaxation in cellulose. The faster γ-relaxation (βE-relaxation of Einfeldt) times, τγ, of cellulose, dextran, Merck starch, and pullulan have smaller
Kaminski et al.
Figure 2. Isothermal dielectric loss spectra showing the lower frequency and so-called δ-relaxation (equivalent to the β-relaxation in this paper) and the higher frequency βE-relaxation (equivalent to the γ-relaxation in this paper) of two polysaccharides, cellulose and dextran, and the pentamer cellopentaose obtained by Meissner et al.14 Cellulose (green diamonds, at 243 K), cellulose (black circles, at 258 K), dextran (light blue squares, at 258 K), cellopentaose (red triangles, at 243 K), and cellopentaose (magenta inverted triangles, at 258 K). These data are compared with the lower frequency JG β-relaxation and the higher frequency γ-relaxation of four dissacharides obtained by Kaminski et al.,23 and all data are shown by lines. Cellobiose (magenta dashed line at 263 K), maltose (blue solid line at 261 K), sucrose (brown short dashed-long dashed line at 285 K), and at the bottom trehalose (green dotted line at 268 K, and gray dashed line at 273 K). The ε′′ values of these four disaccharides have been scaled to have the same loss at the maximum of the γ-relaxation as that of the βE-relaxation (equivalent to the γ-relaxation in this paper) of cellulose at 258 K. The actual data points of the disaccharides are not shown to avoid crowding.
activation energies, shown as lines in Figure 1. The solid and dashed lines are for Linters cellulose and Avicell cellulose from ref 13. Merck starch has almost the same τγ as Linters cellulose and cannot be seen in Figure 1. The τγ of dextran from ref 11 differs slightly from that given by ref 13. One data point of τγ for pulluan is taken from refs 7 and 8. The τγ values of several disaccharides are shown by symbols. The data of two disaccharides, maltose and cellobiose, are represented by red filled circles and blue triangles, respectively. As can be seen by inspection, the τγ values of cellulose are sandwiched between the τγ values of maltose and cellobiose. Again, this suggests that the γ-relaxation of cellulose may be related to that of cellobiose in molecular origin when cellobiose is the dimer of the polymer cellulose. The τγ data of the monosaccharides galactose and fructose are shown by the magenta inverted triangles and black plus signs, respectively. The τγ data of fructose lies too close to that of maltose and cellulose, and some of them cannot be seen. It is remarkable that even the τγ values of the monosaccharides are nearly the same as those of the disaccharides and the polysaccharides. The good correspondence between the relaxation times of two secondary relaxations in the polysaccharides and those of the disaccharides leads us to compare their isothermal dielectric spectra. In Figure 2, the isothermal dielectric loss spectra of anhydrous cellulose, dextran, and cellopentaose, the pentamer
Origins of Two Secondary Relaxations in Polysaccharides composed of five glucopyranose rings, are compared with those of four chosen disaccharides, cellobiose, maltose, sucrose, and trehalose. We have scaled the loss data of the disaccharides to have the same maximum loss of the faster γ-relaxation as that of cellulose at 258 K. The temperatures of the spectra are not exactly the same, but they are also not too far from each other. It can be seen by inspection of Figure 2 that the two polysaccharides, the pentamer, and the disaccharides all have two secondary relaxations, and their spectral properties are similar. The same can be said for the trimer, cellotribiose, and the tetramers, cellotetrabiose and maltotetraose, had their loss data41,42 been included here. One can see that although all the saccharides considered have β- and γ-loss peaks at approximately the same frequencies, the temperatures of all the isothermal loss spectra shown differ by about 30 K. The loss spectra of the disaccharides trehalose, sucrose, maltose, and cellobiose were measured at somewhat higher temperatures (T ) 261-273 K) than those obtained for the oligomer cellopentaose and the polymers cellulose and dextran (T ) 243-258 K). This change of the secondary relaxation times with increasing molecular weight of the saccharides is similar to that found in the dimers, trimers, oligomers, and polymers of propylene glycol, where the γ-relaxation shifts to the higher frequencies with increasing number of repeat units.43 Despite this trend, the relaxation times of the β- and γ-relaxations, τβ and τγ, of the oligo- and polysaccharides are not far from the corresponding relaxation times of the disaccharides, as already demonstrated in Figure 1. The faster γ-relaxation of the polysaccaharides has a larger intensity than that of the slower β-relaxation: the same as found in the disaccharides. It can be seen from Figure 2 that the ratios of their intensities for the polysaccharides are similar in magnitude as those for cellobiose and maltose. In particular, the ratio of cellulose (green diamonds, at 243 K, and black circles, at 258 K) is nearly the same as that of the disaccharide cellobiose (magenta dashed line), and these two saccharides have the β(1-4) glucose-glucose linkage, as mentioned before. The ratio is smaller for sucrose and much smaller for trehalose and may be due to the R(1-2) glucose-fructose linkage in sucrose and the R(1-1) glucose-glucose linkage it has that are different from the β(1-4) glucose-glucose linkage in cellobiose as well as in cellulose and the R(1-4) linkage in maltose. The higher temperature for sucrose compared with all others in Figure 2 is related to the much higher activation energy of its β-relaxation, 96 kJ/mol, than those of the other disaccharides and the polysaccharides. The ratio for cellopentaose is at an intermediate level. The separation between the two loss peaks is about the same for all the saccharides in Figure 2. 4. Discussion and Conclusion The β- and γ-relaxations in cellulose (or respectively the δand βE-relaxations in the nomenclature of Einfeldt et al.) are similar to the corresponding ones in disaccharides, particularly cellobiose, which has a related chemical structure. The similarities include relaxation time, activation energy, frequency dispersion of the β- and γ-relaxations, suggesting that the molecular origins of the β- and γ-relaxations in cellulose are the same as the correspondents in disaccharides. Since the βrelaxations in disaccharides have been shown to satisfy some criteria for them to be identified as the JG β-relaxation, thus we can conclude that the β-relaxation of cellulose is also the JG β-relaxation. It involves local rotation of the repeat anhydroglucoseunitsonthemainchainabouttheβ(1-4)glucose-glucose linkage. The involvement of the local motion of the main chain
J. Phys. Chem. B, Vol. 113, No. 30, 2009 10093 suggests that it is necessarily related to the R-relaxation because the latter is the product of cooperative motions of these local ones due to intermolecular interaction. The situation in cellulose is similar to that of polymers such as polybutadiene44-48 or polyisoprene,49 where its JG β-relaxation has been found, and that necessarily originates from the local conformation transition of the main chain. Thus, we have established the presence and identified the JG β-relaxation in polysaccharides, the primary goal of this study. Consequently, the relaxation times of the β-relaxation of Montes et al. or equivalently the δ-relaxation of Einfeldt et al. can be identified as the JG relaxation time, τJG, of the polysaccharides. Another confirmation that β-relaxation of the disaccharides and β-relaxation of the cellulose and dextran (Montes et al.) or the δ-relaxation of Einfeldt et al. have the same molecular origin comes from its response to the presence of water. In the beginning section we have mentioned that the activation energy of the β-relaxation of cellulose decreases with increasing content of water. The same situation is found by Ermolina et al. in disaccharides.50 Our interpretation of the β-relaxation of polysaccharides as the JG β-relaxation is consistent with the molecular motion involving rotations of a group of glycosidic bonds proposed by Montes et al.,10 the localized movement of the backbone by Jafarpour et al.51 (observed in cellulose by the thermally stimulated currents technique), and local main chain motion by Bidault et al. (observed by dielectric relaxation in amorphous ethyl cellulose)52 This is because the β-relaxation in their specific interpretations is the precursor of the structural relaxation of the polysaccharides, satisfying the criterion that distinguishes JG β-relaxation from other secondary relaxations.24 The computer simulations by Montes et al. of amorphous cellulose show rotation of glucose rings around a single β(1-4) glycosidic linkage has an energetic barrier ∆E2 of the order of 20 kJ/mol. From the ratio of the measured activation energy of the β-relaxation (≈85 kJ/mol) to ∆E2, they estimated four glycosidic bonds are involved in the local chain motion but cautioned that the actual number can be smaller because ∆E2 was obtained without taking into account the intermolecular effect in the computer simulation. The identification of the β-relaxation in polysaccharides as the JG β-relaxation is the main thrust of this study. This is because the JG β-relaxation is supposedly universal and is the most important secondary relaxation as far as connection with the R-relaxation and glass transition are concerned. The glass transition temperature Tg of a polysaccharide is expected to be higher than that of its dimeric substance (i.e., disaccharide). For cellulose and dextran, the dimers are cellobiose and gentiobiose, respectively. Some estimates of Tg of dry polysaccharides have been given by calorimetry.53 It is 462 K for dextran and 488 K for pullulan. Trehalose has Tg ) 390 K from calorimetry,37 and supposedly its Tg is the highest among the disaccharides.54 Maltose has Tg ) 364 K.55 The dielectric Tg of disaccharides, obtained as the temperature at which the Vogel-Fulcher fit to the R-relaxation time τR(Tg) has attained either a hundred seconds, is lower than the value from calorimetry.23 It can be seen in Figure 1 that the Arrhenius T-dependence of τJG(T) of the cellulose is approximately the same as that of cellobiose, maltose, and trehalose. Therefore, the value of τJG(Tg) of cellulose obtained by extrapolation up to its Tg would be much shorter than the those of three disaccharides by virtue of the expected higher Tg of cellulose than that of even trehalose. The coupling model provides a relation between τJG(T) and τR(T) given by τJG(T) ≈
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(tc)n[τR(T)]1-n. Here n is the intermolecular coupling parameter that appears in the stretch exponent of the Kohlrausch-Williams-Watts correlation function of the R-relaxation φ(t) ) exp[-(t/τR)1-n], and tc ≈ 2 ps for molecular glassformers such as the saccharides. When specialized to T ) Tg and assuming τR(Tg) ) 100 s, this relation is reduced to log10 τJG(Tg) ) 2 13.7n. In other words, a glassformer with a shorter τJG(Tg) necessarily has a larger n. Hence, from the deduction that cellulose and dextran have shorter τJG(Tg) values than that of the disaccharides, these polysaccharides have larger intermolecular coupling parameter n than the disaccharides. This conclusion that n is larger in the polymer than the dimers is intuitively reasonable because the multiple glycosidic bonds of repeat units in the polymer should enhance the intermolecular coupling therein as compared with that in the dimer. Examples of this anticorrelation between log10 τJG(T) and n can be found in the series of the polyols, such as when considering glycerol, threitol, xylitol, and sorbitol,56 from the dimer up to the pentamer and polymer of propylene glycol,57 and the trimer of styrene as compared with polystyrene.58 Although the γ-relaxation (or the βE-relaxation of Einfeldt et al.) of polysaccharides is simpler than the β-relaxation as gauged by the activation energy and pre-exponential factor of its relaxation time,10,11,18 its molecular origin turns out to be more illusive. Backed by computer simulations of cellulose,11 Montes et al. suggested rotation of the methylol (CH2OH) unit if responsible for the γ-relaxation. If the γ-relaxations of polysaccharides and the monosaccharide, glucose, have the same molecular origin, as suggested by the similar relaxation times
Kaminski et al. and activation energies, then, this interpretation by Montes et al. is at odds with the conclusion of the NMR study of the motion of the methylol in glucose.59 The NMR study of glucose indicates the glucose ring and the methylol (CH2OH) group mobility are strongly correlated and the rotation of the methylol should not be used to explain the faster γ-relaxation process of glucose. Einfeldt et al. and Meissner et al. also rejected the motion of the methylol groups as the origin of the γ-relaxation (their βErelaxation) of polysaccharides. Instead, they proposed the local chain motion via the glycosidic linkages. However, this suggestion, also made by Scandola et al., had been used by Montes et al.10 for the β-relaxation (δ-relaxation of Einfeldt et al.) and for the JG β-relaxation by us. The use of the same molecular mechanism (i.e., local chain motion) for two different relaxations (i.e., γ and β) by different authors is remarkable. In fact, the same number of glycosidic bonds involved in the local chain motion proposed by Montes et al.10 for the β-relaxation (δ-relaxation of Meissner et al.) was adopted by Meissner et al.14 for the γ-relaxation (their βE-relaxation). The interpretation of the γ-relaxation to involve the motion of several repeat units by Einfeldt et al. and Meissner et al. should be reflected in the relaxation times by having much higher activation energy and much shorter pre-exponential than that found for the γ-relaxations. Furthermore, acceptance of this chain motion as the origin of the γ-relaxation would leave little or no room to account for the slower β-relaxation. Therefore, this is not a viable interpretation of the γ-relaxation (βE-relaxation) of polysaccharides.
TABLE 2: Summary of the Molecular Origins Proposed by the Different Authors for the Secondary Relaxations Seen in Polysaccharides
author
interpretation of the origin of the slower secondary relaxation process (denoted as β or δ in this paper)
Nishinari et al. (ref 8) Montes et al. (refs 10 and 11)
Einfeldt et al. (ref 14) Scandola et al. (ref 9) Bradley at el (ref 5) Butler et al. (ref 15) Schartel et al. (ref 12) McBrierty et al. (ref 16) Cerveny et al. (ref 17) Starkweather et al. (ref 19) Jafarpour et al. (ref 51) Bidault et al. (ref 52) authors of this paper
β-relaxation has considerable activation entropy, and it is associated to localized motion of the main chain; in addition, they showed that four glycosidic bonds are involved in the local chain motion but cautioned that the actual number can be smaller because ∆E2 was obtained without taking into account the intermolecular effect in the computer simulation it is an orientational motion of a mixed phase of polysaccharide and water
interpretation of the origin of the faster secondary relaxation process (denoted as βE or γ in this paper) the relaxation originates from rotation of the methylol (or hydroxymethyl) CH2OH side group on C-5 of the glucose residue γ-relaxation does not involve a significant entropic contribution and originates from the rotation of the methylol group in the anhydroglucose unit
local motion of the main chain segments via the glycosidic bond; in this motion more than two but less than five repeat units are involved local chain motions boat-chair interconversion of the pyranose ring orientation of bound or bonded water, or confined water
more complex secondary relaxation with its activation energy has both enthalpic and entropic contributions localized movement of the backbone; precursor of the structural relaxation of the polysaccharides local main chain motion, and precursor of the structural relaxation of the polysaccharides β-relaxation process is closely connected to the motion of the monomeric units via glycosidic linkage, a kind of local main chain motion, and can be identified with the JG relaxation of the polysaccharides that has strong connection to the structural R-relaxation.
it is a simple secondary relaxation in the sense that its activation energy has negligible entropy contribution
this process has intramolecular character and is related to the motion within the monomeric unit building the polysaccharide
Origins of Two Secondary Relaxations in Polysaccharides We have seen in Figures 1 and 2 that the γ-relaxation times of some polysaccharides, disaccharides, and monosaccharides are either comparable or nearly the same. This result implies that the γ-relaxation in all these materials may have the same origin, suggesting it may come from some internal motion in the monosaccharide unit. If indeed the origin of the γ-relaxation is the same in all sugars, this is perhaps good evidence for the local intramolecular nature of the γ-relaxation in monosaccharides, disaccharides, and polysaccharides. The proposal that the γ-relaxation is associated with local motions of two side groups -CH2OH and -OH in ref 18 and supported by an additional experiment51 on cellulose is in accord with this interpretation. Another internal motion is the boat-chair interconversion of the pyranose ring, which has an activation energy of about 56 kJ/mol.5 However, Einfeldt et al.13 and Meissner et al.14 did not consider this mechanism favorable from its higher activation energy than measured and that it requires cooperative motion of several glucose units by others.5,15 The other reason given by Meissner et al. and based on not observing themselves this relaxation in glucose, the monomer, is not valid because they measured crystalline sample. This γ-relaxation in amorphous glucose was observed20 and has an activation energy of about 40 kJ/mol. The remaining interpretation of the γ-relaxation in polysaccharides is reorientation of bound water16,12 that may be present even in normally claimed to be dried samples. Cerveny et al.17 have shown that the γ-relaxation times of avicell cellulose and Merck starch are nearly indistinguishable from the relaxation time of 6 layers of confined water in vermiculite clay, although there are significant differences of the latter from the γ-relaxation times of dextran and pullulan (see Figure 1). Capaccioli et al.60 have found the water nanoconfined in molecular sieves and silica gels has similar relaxation times as that of the six layers of confined water in vermiculite clay and, hence, also as the γ-relaxation times of avicell cellulose and Merck starch. Moreover, they found the JG β-relaxation of water in various aqueous mixtures, and their relaxation times are similar in order of magnitude and have comparable activation energies as that of the γ-relaxation times of avicell cellulose and Merck starch. The coincidence may lead one to suggest that the origin of the γ-relaxation of polysaccharides, disaccharides, and monosaccharides comes from the JG β-relaxation of water or confined water. Notwithstanding, the similarities of these water-related relaxation times observed in other systems with the γ-relaxation times of polysaccharides may be accidental, and a γ-relaxation originating from some internal motion including side groups of polysaccharides, disaccharides, and monosaccharides does exist. Attempts to clarify the effect of water on the secondary relaxations in polysaccharides have been made by several experimental studies,61,62 but the final conclusion cannot be made at the present time. In closing, we summarize different interpretations of the origins of the secondary relaxations of polysaccharaides, including our own, in Table 2. Acknowledgment. The authors are deeply thankful for the financial support within the framework of the project entitled “From Study of Molecular Dynamics in Amorphous Medicines at Ambient and Elevated Pressure to Novel Applications in Pharmacy”, which is operated within the Foundation for Polish Science Team Programme, cofinanced by the EU European Regional Development Fund. At the Naval Research laboratory, K.L.N. is supported by the Office of Naval Research. K.K. and E.K. acknowledge financial assistance from FNP (2009).
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