Origin of the Commonly Observed Secondary Relaxation Process in

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Origin of the Commonly Observed Secondary Relaxation Process in Saccharides K. Kaminski,* P. Wlodarczyk,* K. Adrjanowicz, E. Kaminska, Z. Wojnarowska, and M. Paluch Institute of Physics, Silesian UniVersity, ul. Uniwersytecka 4, 40-007 Katowice, Poland ReceiVed: April 18, 2010; ReVised Manuscript ReceiVed: July 12, 2010

Broadband dielectric relaxation studies were performed on D-glucose and 1,6-anhydro-D-glucose. In the liquid phase of both systems, one can observe the cluster relaxation and structural relaxation. In the glassy state of D-glucose two secondary relaxations were recorded. The slower one, hardly detectable in the loss spectra, was identified as the Johari-Goldstein type (JG) relaxation. The faster one, the γ-relaxation, is visible as a well pronounced peak. For the past few years the origin of this process has been a subject of hot debate. Different authors have speculated about the source of this relaxation, but no consensus was reached. Moreover, application of more sophisticated method, such as NMR and MD simulations have not resolved this problem yet. Comparison of the dielectric loss spectra measured for D-glucose and 1,6-anhydro-D-glucose, combined with other experimental findings described in detail in this paper, enabled us to certify unquestionably, that the rotation of hydroxymethyl group is the origin of γ-relaxation in D-glucose as well as in the whole family of saccharides. Additionally, calculations of conformational changes with use of density functional theory (DFT) were performed to support our identification. Introduction Saccharides are natural compounds widespread around the world. They play various roles in living organisms. For example, they control exchanging information between the cells and metabolism and they are a main source of energy. A large variety of sugars differing in physicochemical properties made them materials that are applicable in many types of industries. Ongoing studies still reveal new potential applications of these compounds. Because of their great glass formation ability, they exhibit promising properties for the novel application in the pharmaceutical industry. In the literature we can find reports which demonstrate that application of the sugars enhances chemical stability of the proteins.1-4 It was shown that sucrose prevents proteins from aggregation very effectively. Furthermore, it is also reported that addition of the saccharide to the amorphous drug enhances its solubility. For instance, dissolution rate of the solid dispersed griseofulvin with saccharide was even 170 times higher that the pure drug.5 The other very promising feature of carbohydrates is that they can absorb significant amount of water. Consequently, carbohydrates form crystalline stoichiometric hydrates. This property is of exceptional importance in view of the use of the glassy saccharides as stabilizers of the amorphous drugs. It is worth noting that one molecule of raffinose can link five molecules of water while trehalose sequesters two water molecules. Thus, even in humid environment amorphous drug will not absorb water. Finally, it is also expected that glassy sugar matrix can form hydrogen bonds with the target molecules and in consequence suppress its tendency to crystallization. Because of the reasons given above, identification of the relaxation processes observed in the glassy state of carbohydrates seems to be crucial and important not just from a scientific point of view. Molecular dynamics of carbohydrates was very intensively investigated by dielectric,6-13 NMR14-19 spectroscopies, and computer simulations.20-22 In the liquid phase of the monosaccharide, * To whom correspondence should be addressed. E-mail: kaminski@ us.edu.pl; [email protected].

two relaxation processes can be observed by means of dielectric spectroscopy. The faster one is structural relaxation which governs liquid-glass transition, and the slower one can be assigned to the long range correlations of density fluctuations (LRCDF).23 In the glassy state of monosaccharide one can observe well resolved secondary relaxation process. This process is a characteristic feature of the whole family of saccharides.24 Interestingly, this process has almost the same characteristic dynamical properties irrespective of the molecular weight and architecture. It should be mentioned that activation energy determined from dielectric or mechanical data lies within the range Ea ) 42-60 kJ/mol, and dielectric strength of this process decreases rapidly with lowering temperature. Moreover, this relaxation process can not be described satisfactorily by the Cole-Cole function, because of its asymmetric shape. For almost 20 years different authors speculated about the origin of this relaxation. Murthy and Gangasharan ascribed this process to the segmental rotation of the linear chain of the monosugar.25 However, in light of the latest research, this interpretation can not be valid. It was shown, that even a trace of acyclic form can not be found in glucose solutions.26 Another explanation was provided by Faivre, she maintained that intra- and intermolecular motions contribute to the well resolved secondary relaxation.12 Noel et al argued that this relaxation may originate from the rotational motions of the hydroxymethyl groups attached to the monosugar ring.11 Another very interesting point of view was presented by De Gusseme et al. They postulated that this process in trehalose has an intermolecular origin.27 On the other hand molecular dynamics simulation carried out by Molinero et al. indicated that there is a bending movement of the D-glucose coupled to the diffusion of water in the glassy matrix.20 This type of movement cannot be precisely identified because a coarse grain model was adapted for D-glucose in the cited paper. To gain more detailed information about the molecular origin of the γ-relaxation in saccharides data obtained from NMR spectroscopy were compared directly to that collected from the dielectric measurements.19 Unfortunately, there was large discrepancy in magnitudes and temperature dependences of the correlation times determined from NMR and dielectric

10.1021/jp1034773  2010 American Chemical Society Published on Web 08/09/2010

Secondary Relaxation Process in Saccharides

Figure 1. Haworth projection and 3d view of structures of D-glucose and 1,6-anhydro-D-glucose. Two dihedral angles, which describe reorientation of hydroxymethyl group are defined. By changing the Ψ angle, we have simulated rotation of hydroxymethyl unit. Change of Ξ angle is connected with the rotation of hydrogen attached to the hydroxymethyl unit.

investigations for the secondary relaxation. Consequently, the origin of the γ-relaxation process in saccharides has been still puzzling over past few years. Significant progress toward understanding the molecular origin of this relaxation mode has been made by systematic isobaric and isothermal broadband dielectric studies carried out by our group. We showed that there are in fact two secondary relaxation processes in the glassy state of monosaccharides.28 Our high pressure measurements revealed that the new mode (β) is sensitive to pressure, whereas that commonly observed (γ) by the others is not. This fact implies that β relaxation originates from the intermolecular interactions, the faster one is surely related to the conformational reorientation. In our previous paper, we were not able to explain what molecular motions are responsible for the γ-relaxation process. We only speculated that probably some kind of deformation of the sugar ring, like chair to boat interconversion, or motions of hydroxymethyl group are responsible for the faster secondary relaxation process in saccharides. In this paper, we will reveal the origin of the γ-relaxation process, which is an inherent feature of the molecular dynamics of the whole family of saccharides. Since there is discussion on the molecular origin underlying secondary relaxation processes in polysaccharides, we are sure that our data will resolve this problem. Moreover, it is important to note that we will show how to suppress molecular mobility of glassy state saccharides. This information can be very helpful for researchers using saccharides as stabilizers of proteins, amorphous drugs, etc. This paper is divided into two parts. In the first part, we will characterize molecular dynamics of D-glucose and 1,6-anhydroD-glucose. In the second part, we will focus on the identification of what kind of motion is responsible for the faster secondary relaxation in D-glucose and in the whole family of the saccharides. For this purpose, dielectric measurements as well as QM calculations were performed on both saccharides. Experimental and Computational D-Glucose and 1,6-anhydro-D-glucose were supplied from Sigma-Aldrich. The chemical structures of both compounds are presented in Figure 1. Isobaric dielectric measurements at ambient pressure were carried out using a Novo-Control GMBH Alpha dielectric spectrometer (10-2-107 Hz). The sample was placed between two stainless steel flat electrodes of the capacitor

J. Phys. Chem. B, Vol. 114, No. 34, 2010 11273 with a gap of 0.1 mm. Temperature was controlled by the NovoControl Quattro system, with the use of a nitrogen-gas cryostat. Temperature stability of the samples was better than 0.1 K. Quantum mechanical calculations were performed on both structures, i.e., D-glucose and 1,6-anhydro-D-glucose. We have calculated energy barriers for different conformational motions at the B3LYP/6-311+g(d,p) level. For the D-glucose chair to boat transition as well as rotations of hydroxymethyl group were checked. In the case of 1,6-anhydro-D-glucose, the hydroxymethyl group is blocked; thus, deformations of the ring were only checked. At the beginning we have optimized the geometry of D-glucose and 1,6-anhydro-D-glucose. The crystalline form of D-glucose in the Sigma Aldrich sample is β-glucopyranose. In the supercooled liquid state, this tautomer can be transformed into R-glucopyranose during mutarotation phenomenon.29 Contrary to D-glucose, 1,6-anhydro-D-glucose cannot undergo a mutarotation process, because of the anhydro bridge between 1 and 6 carbon atoms. Calculations were performed for only one D-glucose tautomer, i.e., for β-D-glucopyranose. The most stable pyranoses have possibly the largest amount of hydroxyl groups in equatorial positions. In the case of β-glucopyranose, all five hydroxyl substituents can exist in equatorial positions. In the second step geometry scans for two interconversions of D-glucose (ring deformation and hydroxymethyl group rotation) and one interconversion (ring deformation) for 1,6-anhydro-D-glucose at the 6-311++G(d,p)/B3LYP level were performed. Transition states were optimized by use of eigenvector following method at the same level of theory. For minima and transition states vibrational frequencies were calculated to check their validity. Energy barriers were obtained by subtraction of all nonthermal energy (sum of electronic and zero-point vibrational energy) of the transition state from the nonthermal energy of minimum state. Finally, dipole moment analysis was performed. Changes of the dipole moment direction as well as dipole moment values were noted. All calculations were conducted with use of Orca package.30 Results and Discussion Part A. In Figure 2, dielectric loss spectra measured for (upper panel) and 1,6-anhydro-D-glucose (lower panel) are presented. Above the glass transition temperature of both carbohydrates, structural relaxation and DC-conductivity moving toward lower frequencies with lowering temperature are visible. Below Tg, secondary relaxations become detectable in the experimental window. In case of glucose, there are two secondary relaxations (β and γ) visible, whereas in the glassy state of 1,6anhydro-D-glucose, the only one β mode was observed. In fact, the β-relaxation process can be seen in loss spectra only as an excess wing on the high frequency side of the structural relaxation in both investigated herein carbohydrates. However, direct prove that there is a true relaxation process under the excess wing comes from the loss spectra measured for galactose and sorbose. In these two monosaccharides, being homologues of the glucose, the excess wing is transformed into a well separated β-relaxation peak.28 Recently, the nature of this secondary process was revealed. We showed that it is related to the intermolecular interactions. Thus, it was classified as a true JG relaxation process.31 On the other hand, we were not able to certify what kind of motion is responsible for the γ-process. Moreover, despite a great number of papers devoted to the examination of the molecular dynamics of the simple monosaccharide such as glucose any explanation of the origin of this process seemed to be commonly acceptable. In case of 1,6anhydro-D-glucose, we did not detect the γ-relaxation process. It became completely suppressed by forming a bridge between the D-glucose

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ε*(ω) ) ε +

Figure 2. Dielectric spectra of D-glucose and 1,6-anhydro-D-glucose. The slowest process (slow mode) may originate from cluster relaxations. The β-relaxation is manifested as an excess wing on the high frequency shoulder of structural relaxation (see ref 28). The γ-process in anhydroD-glucose is suppressed.

first and sixth carbon atoms. This finding indicates that probably deformation of the monosugar ring or motions of the exocyclic hydroxymethyl group are a source of the γ-relaxation process. In the second part of this paper, this issue will be investigated in more detail. In the loss spectra of the D-glucose presented in Figure 2, one can also detect another relaxation process which is much slower than the structural relaxation. Although in loss spectra this process is covered by the DC-conductivity, it can be identified in the real part of the complex permittivity. In our very recent papers we have demonstrated that this process may originate from the LRCDF commonly called Fischer clusters.23 Since 1,6-anhydro-D-glucose has almost the same chemical structure as D-glucose, it is very interesting to check if a similar phenomenon can be also found in this carbohydrate. In the inset to Figure 3, one can see that the cluster relaxation can be also detected in the dispersion spectra of 1,6-anhydro-D-glucose. Unfortunately, the relaxation peak connected with LRCDF is visible rather in a very narrow range of temperatures. This is closely related to the fact that the low frequency part of the dispersion spectra of 1,6-anhydro-D-glucose is affected by the huge contribution from polarization of the electrodes. Therefore, there is no chance to extract any information about dynamics of this process at temperatures lower than T ) 298 K. In Figure 3 dependences of the dielectric strength (panel a) and shape parameters describing asymmetry (R parameter) and broadening (β parameter; panel b) of the ultraslow relaxation mode versus temperature are presented. All parameters were determined

∆ε [1 + (iωτHN)R]β

(1)

where R and β are shape parameters, ∆ε is the dielectric strength, and τHN is the Havriliak-Negami characteristic relaxation time. It can be noted that with increasing temperature the dielectric strength of the slow mode decreases significantly. The same behavior was reported in D-glucose (panel c). It is interesting that in both cases this relaxation process does not vanish, although dielectric strength of the slow mode is very small at very high temperatures. This finding is in opposite to the commonly observed rule. It should be stressed that LRCDF can be detected in the limited range of temperatures. It is usually Tg + 100 K.32 However, both D-glucose and 1,6-anhydro-D-glucose are rather specific systems at which hydrogen bonds play an important role. Thus, one can imagine that even at very high temperatures there are small clusters consisting of a few molecules in the investigated samples. In this context, it is worth mentioning ibuprofen. In this pharmaceutical it was shown that it is possible to observe dynamics of the dimers in loss spectra.33 The lower panel in Figure 3 clearly shows that, in both cases (for D-glucose and 1,6-anhydro-D-glucose), R and β shape parameters are very close to the unity in the whole range of investigated temperatures. This means that ultraslow mode can be described by the exponential response function. Such a finding is the next indication that the ultraslow mode observed in 1,6-anhydroD-glucose is of the same origin as that found in D-glucose. In Figure 4 we have presented dielectric loss spectra measured for D-glucose and 1,6-anhydro-D-glucose. We have chosen the loss spectra with almost the same structural relaxation time. As can be seen, the distribution of relaxation times is the same for both samples. It is not surprising, since both investigated saccharides have almost the same chemical structure. However, there is something which needs a comment. We have found that the shape of the structural relaxation of glucose and 1,6anhydro-D-glucose does not change with temperature. On the other hand, one can expect that the population of hydrogen bonds in both saccharides should increase with lowering temperature. Consequently, we should observe broadening of the structural relaxation process, as it happens in the case of various H-bonded glass-forming liquids.34,35 Another experimental observation is the lack of the γ-relaxation process in the presented spectrum of 1,6-anhydro-D-glucose, whereas in D-glucose this relaxation mode is well visible as a separated relaxation peak. In Figure 5 a relaxation map of both examined carbohydrates is presented. Structural and slow mode relaxation times were fitted to the Vogel-Fulcher-Tammann equation.

(

τR ) τVFT exp

DTT0 T - T0

)

(2)

Temperature dependence of the secondary relaxation times was described by the Arrhenius power law.

( )

τγ ) τ0 exp

Ea RT

(3)

All fitting parameters were collected in Table 1. From the VFT fits glass transition and freezing temperatures respectively

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Figure 3. Spectra parameters. Temperature dependencies of shape parameters as well as dielectric strength.

Figure 5. Relaxation map for D-glucose and 1,6-anhydro-D-glucose. Figure 4. Comparison of D-glucose and 1,6-anhydro-D-glucose spectra. For the latter, there is no sign of γ-relaxation.

for the structural and slow mode relaxation of both carbohydrates were estimated. Tg and Tf were defined as temperatures at which structural and slow mode relaxation times were equaled to 100 s. We have obtained Tg ) 308 and 245 K for the D-glucose and 1,6-anhydro-D-glucose, respectively, whereas freezing temperatures were equal to Tf ) 316 (D-glucose) and 284 K (1,6anhydro-D-glucose). It can be seen that the insertion of the

oxygen bridge into glucose ring reduce the glass transition temperature very significantly. There is more than 60 K difference in Tg between glucose and 1,6-anhydro-D-glucose. Moreover, we can also observe that time scale separation between slow mode and structural relaxation is quite different in D-glucose and 1,6-anhydro-D-glucose. In the latter system there is more than 6 decades difference in time scale of the slow mode and structural relaxation in the vicinity of the glass transition temperature. The opposite scenario is found in

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TABLE 1: VFT Parameters (log[τVFT], D, and T0) for Structural and Slow Mode (Probably Clusters) Relaxation Processes for Both Saccharidesa D-glucose

log[τVFT] (s) -19.15 -9.92

D

T0 (K)

1,6-anhydro-D-glucose m

Tf (K)

log[τVFT] (s)

D

T0 (K)

m

Tf (K)

Structural Relaxation 15.7 232 96 308 -12.42 5.59 210 102 245 Cluster Relaxation 8.9 239 50 316 -6.62

3.1

246

66 284

a Characteristic temperatures Tg and Tf (glass transition temperature and freezing temperature of clusters dynamics, respectively) and fragility indexes (m) are also presented.

D-glucose,

where both modes tend to merge around Tg. Using VFT fits it was also possible to calculate steepness index, which is a measure of fragility of the investigated systems, based on the following formula:

m)

d(logτR,cluster) d(Tg,f /T)

|

(4) (Tg,f/T))1

As a result, we have obtained m ) 92 and 50 for the structural and slow mode relaxation of the glucose, whereas for 1,6anhydro-D-glucose, we have found m ) 105 and 66 for the primary and slow mode relaxation, respectively. Again we can see that both investigated carbohydrates differ. It looks like greater rigidity of the 1,6-anhydro-D-glucose makes this system more fragile. It is worth noting that there is significant difference in fragility between structural and ultraslow mode which seems to be a rule. One can try to link the difference in the fragility of the structural and slow mode relaxation processes by taking into account the difference in the size of relaxing objects. From the literature, one can find information that cooperatively rearranging regions involved in structural relaxation have around 3 nm, whereas the correlation length estimated for LRCDF reaches even 300 nm. Summarizing this part of the paper, we have found that the insertion of the oxygen bridge into the carbohydrate ring has great impact on the molecular mobility. We have shown that the glass transition temperature of the 1,6-anhydro-D-glucose has changed dramatically with respect to the D-glucose, although the distribution of structural relaxation times is the same. We also have shown that the fragility of the more rigid saccharide (1,6-anhydro-D-glucose) is greater than that of the D-glucose. Additionally, just as in the case of D-glucose, we were able to follow the dynamics of the slow mode in 1,6-anhydro-D-glucose. However time scale separation of the structural and slow mode relaxation in both carbohydrates is completely different. In 1,6anhydro-D-glucose this separation is equal to more than 6 decades in the vicinity of the Tg, whereas in D-glucose both relaxation modes tend to merge. Finally we demonstrated that in 1,6-anhydro-D-glucose there is no γ-relaxation process. Part B. In this part we will focus on identification of the origin of the secondary relaxation commonly observed in mono-, di-, oligo-, and polysaccharides. As it can be seen in Figures 2 and 4, there is no trace of the γ-relaxation in 1,6-anhydro-Dglucose. This is a clear indication that some kind of motion responsible for the considered relaxation mode has been blocked. Hence, from that the question arises about the real mechanism of the γ-relaxation mode. In order to answer this question, two scenarios have to be considered. In the first one, the γ-relaxation

process originates from rotation of hydroxymethyl group. Consequently, the lack γ-relaxation in 1,6-anhydro-D-glucose is caused by blocking hydroxymethyl CH2OH by forming a 1,6anhydro bridge. In the second scenario, deformation of the ring, such as chair to boat conversion, might be responsible for the γ-process. One can imagine that the 1,6-anhydro bridge present in 1,6-anhydro-D-glucose could make the structure more rigid. As a result, changes in ring conformation are not possible. To check which thesis is true, further measurements were carried out. In Figure 6 (left panel) dielectric loss spectra of three monosacchrides (D-glucose, D-fructose, and D-ribose) as well as for disaccharides (sucrose and trehalose) are presented. All measurements were performed at the same capacitor of welldefined gap. Moreover, all samples were quenched to the desired temperature with the same rate of cooling to guarantee the same measurement conditions. It can be noted that the dielectric strength of the γ-relaxation process is characteristic for all of the studied samples. What is more, there is a correlation between tthe number of hydroxymethyl groups and the amplitude of the γ-relaxation process; that is, the smaller amplitude of the γ-process was recorded in D-ribose (five carbon monosaccharide). It is worth mentioning that D-ribose exists as a β-pyranose tautomeric form in the crystalline state. In such a form, this saccharide does not possess any hydroxymethyl group. Consequently, we should not observe the γ-relaxation process in loss spectra of this carbohydrate. However, D-ribose undergoes mutarotation after melting, which is a chemical reaction of ring transformation occurring in carbohydrates. It is well-known and described in literature. Mutarotation was extensively studied for many years in diluted solutions (mainly in water), but recently we have shown that mutarotation occurs also in supercooled carbohydrates.29,36 There are also reports about mutarotation in the glassy state.37 This issue will be described more carefully in another part of this work. Now, it is important to understand that, as a consequence of that phenomenon, two different fivemembered rings (known as R and β furanoses) appear in the measured sample, although their population is small.38 Both furanose forms (R and β) of the D-ribose have one hydroxymethyl group. Therefore, one can link small amplitude of the γ-relaxation peak with the small amount of the furanose forms of the D-ribose in the investigated sample. On the other hand, sucrose has the greatest amplitude of γ-process of all saccharides presented herein. This disaccharide consists of glucopyranose and fructofuranose units connected via the β (1-2) glycosidic linkage. Sucrose molecule has three hydroxymethyl groups which can rotate independently. Therefore, increase of hydroxymethyl groups in this saccharide is reflected by the greater amplitude of the γ-relaxation process. In Figure 6 (right panel), we have shown dielectric loss spectra obtained in the glassy state for five representative disaccharides. All spectra were chosen to have almost the same τγ (the same position of maximum of γ-process). It is evident that amplitudes of the γ-peaks are different for various disaccharides. However, there is also a correlation between the number of hydroxymethyl groups and the dielectric strength of the considered mode. Lactulose and sucrose have three and trehalose and cellobiose have only two hydroxymethyl groups. It is interesting that amplitudes of γ-relaxation peaks in sucrose and lactulose are quite different despite the fact that both carbohydrates have the same number of hydroxymethyl groups. Anyway, the same situation can be observed in trehalose, lactose, and cellobiose. However, the change of the dipole moment during reorientation of hydroxymethyl group for every

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Figure 6. Comparison of γ-relaxation strength in different mono- and disaccharides.

Figure 7. Comparison of NMR derived relaxation times with dielectric spectroscopy derived ones. NMR relaxation times are signed by dotted vertical lines.

saccharide is individual. This is the reason of differences in dielectric strength between saccharides with the same number of hydroxymethyl groups. Except of the number of -CH2OH groups, mobility of this unit seems to be a very important parameter. Mobility changes are related to the energy activation differences. As was stated earlier, saccharides can form very effective internal as well as external hydrogen bonds. One can suppose that these specific interactions may influence movements of hydroxymethyl group making this unit more or less flexible. Our dielectric data indicate that γ-relaxation process in mono-, di-, and polysaccharides is closely connected to the motion of the exocyclic -CH2OH side group rather than deformation of the sugar ring. Our interpretation will be verified by comparing dielectric data with NMR results taken from ref 39. In Figure 7 dielectric loss spectra obtained for D-glucose (upper panel) and sucrose (lower panel) at room temperature are presented. In addition, position of the correlation time of the rotation of the -CH2OH group estimated from NMR measurements, were

denoted as a vertical arrows. In the case of D-glucose, the relaxation time of the γ-process differs significantly than the correlation time estimated from NMR measurements for movements of the hydroxymethyl group.39 However, there may be few reasons of this discrepancy. First, NMR measurements were performed on the D-allose which is homologue of D-glucose. Moreover, authors did not say anything about content of water in investigated sample. This information seems to be of exceptional importance. It is a well-known fact that water has a major influence on dynamics of the γ-relaxation peak in carbohydrates. One can mention that the activation energy of the γ-relaxation process changes from 42 kJ/mol (dry sample), up to 59 kJ/mol for the sample containing 10% of water.13 In the lower panel, the vertical arrow denotes the position of the correlation time estimated for the rotation of the -CH2OH group in an aqueous solution of sucrose (5% of water). It can be seen that in this case agreement between relaxation time of the γ-relaxation process and NMR correlation time estimated for the hydroxymethyl unit is much better. Moreover, after taking into account the experimental finding that the addition of water increases the activation energy of the γ-process and moves the maximum of this mode toward lower frequencies, one can expect even better agreement between the relaxation time of the γ-process and the correlation time determined for the rotation of the -CH2OH group. The problem of flexibility of the monosaccharides, with special emphasis on the chair-chair (chair to chair transition runs through the boat intermediate state) conformational flexibility, pseudorotation or motion of the exocyclic CH2OH group, was very intensively investigated by Kaatze.38 He performed acoustical absorption measurements on aqueous solutions of different monosaccharides such as arabinose, fructose glucose, etc. It was shown that there are five different relaxation processes in the studied samples. The slowest one was assigned to the chair-chair inversion, the next two were related to the pseudorotation, -CH2OH rotation, and the fastest one was postulated to originate from the association of the carbohydrate molecules. Moreover, authors also estimated volume change associated with the motions of the -CH2OH (∆V ) 2 mL/mol) and with the chair-chair interconversion (∆ V ) 0.9 mL/mol) in glucose. It is interesting that they found out that volume change caused

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by the rotation of the hydroxymethyl group is greater than that of the chair-chair transition. Now, we can compare these results to those obtained from dielectric measurements. Activation volume can be determined directly from the following formula:

(

∆V ) -RT

∂ ln τγ ∂p

)

T

(5)

In order to determine activation volume of the secondary relaxations seen in mono and disaccharides high pressure measurements (p ) 0.1-500 MPa) were carried out on fructose, ribose, leucrose, and maltose. We found out that slower secondary relaxation (β) in mono- and disaccharides is sensitive to pressure, whereas the faster one is not. ∆V determined for the β-relaxation in disaccharides leucrose and maltose was equal to 2140 and 15.6 mL/mol,41 respectively. It should be stressed that this process in the whole family of disaccharides was assigned to the rotation of the monosaccharides units around the glycosidic linkage.41-43 Unfortunately, we did not evaluate the activation volume for the β-relaxation in glucose, ribose, and fructose, because considered mode was hidden under structural relaxation peak in these carbohydrates. On the other hand, the activation volume of the γ-relaxation process in both mono and disaccharides was estimated to be 3-5 mL/mol, dependent on the sample. Hence, ∆V estimated for the γ-relaxation process is almost the same as the change in volume associated with the rotation of the exocyclic -CH2OH group as it was calculated from the acoustic measurements on the glucose. There is also one more intriguing problem which should be considered herein. On the basis of dielectric data taken on different carbohydrates, we can certify that in each case the γ-loss peak is asymmetric. It is a remarkable finding in view of the current research. It should be pointed out that usually secondary relaxation processes are symmetric and can be described by the Cole-Cole function. Of course sugars are not the only group where such a peculiar phenomenon is observed. One can mention polypropylene glycols, where a similar finding was reported.44,45 Surprisingly, we can find that both saccharides and polypropylene glycols are glass formers with a strong tendency to form effective hydrogen bonds, and in these compounds clusters form exactly via the hydrogen bonds. Therefore, it seems to be reasonable to suppose that such specific interactions may influence dielectric loss spectra and make the γ-loss peak asymmetric. Another experimental finding which should be taken into account to explain asymmetric shape of the γ-loss peak in saccharides is the presence of different conformation of the hydroxymethyl group. In monosaccharides there are three rotamers of the -CH2OH with diverse values of the dihedral angles Ψ between O6-C6-C5-C4 atoms (see Figure 1 to check atom numbers). These different arrangements of the hydroxymethyl group with respect to the carbohydrate ring are called gauche-gauche (gg, Ψ ≈ 300°), gauche-trans (gt, Ψ ≈ 60°), and trans-gauche (tg, Ψ ≈ 180°).46 The authors of ref 46 pointed out that only the gg (60%) and gt (40%) rotamers are stable at room temperature in the water solution of the D-glucose. On the other hand, it was also found that the solvent influences the stability of the given conformers in this saccharide. Therefore, we can not exclude that in the anhydrous sample there are in fact three arrangements of the hydroxymethyl group. These different space arrangements of the hydroxymethyl group are presented in Figure 10. It is worth noting that the stability of each conformer is not the same, which may lead to different

lifetimes and mobilities of the gg, gt and tg rotamers. Thus gg, gt, and tg conformers of the hydroxymethyl unit relax with different time. Moreover, change in the dipole moment associated with the rotation of the -CH2OH can be different for the gg, gt, and tg conformers. Thus, all three relaxors can contribute to the γ-relaxation process on a different scale and this is a probable explanation why we observe an asymmetric γ-loss peak in D-glucose and in the whole family of saccharides as well. We have concluded that the exocylic group reorientation is the origin of γ-relaxation. In order to show the impact of the hydrogen bond network on the γ-relaxation parameters, we have studied the mutarotation phenomenon in a few monosaccharides. Mutarotation is a chemical reaction that is specific to carbohydrates. It can be defined as tautomeric change of cyclic structure of monosaccharide. Mutarotation is very complex. Each monosaccharide can exist in four cyclic forms (two possible furanoses, five membered rings, and two possible pyranoses, six membered rings). Moreover, there is an open chain stadium during the single transformation of one cyclic form to another. Therefore mutaroration is in fact a group of parallel and subsequent reactions, which can be described by several rate constants. Creation of equilibrium at the melting point can be described by the following scheme:

However, in most cases we observe only one chain of reactions, because of differences in all cyclic form populations. As was already stated, mutarotation occurs in the supercooled liquid state. We have studied this phenomenon in supercooled D-fructose and D-ribose. Detailed kinetic analysis can be found in our earlier articles.29,36 In this work, we will focus on the γ-relaxation behavior during this phenomenon. In Figure 8, we depicted loss spectra of D-fructose and D-ribose measured in the glassy state at T ) 245 and 175 K, respectively, after different time of annealing the samples above theirs glass transition temperatures. Amplitude of γ-relaxation process of D-fructose is significantly larger after the equilibration time, while its relaxation time is almost the same. On the opposite side is the result for D-ribose, where the amplitude of γ-process is the same after the equilibration, whereas the relaxation time is shifted toward faster relaxation times. In Figure 9, we present main reactions which can be related to these changes in both monosaccharides. As one can see, both products of reactions in D-fructose have hydroxymethyl groups, whereas the product of reaction in D-ribose does not have free hydroxymethyl group. These hydroxymethyl groups are engaged in forming external hydrogen bonded network. In R-D-fructofuranose one of the -CH2OH units can be engaged in forming an internal hydrogen bond and one hydroxymethyl group can be used for the creation of an external hydrogen bond. Products of reactions, i.e., β-Dfructofuranose and β-D-fructopyranose, have sufficient number of hydroxymethyl groups to maintain the same pattern of hydrogen bond network. Contrary to this situation, the product of D-ribose transformation does not have a hydroxymethyl unit. Therefore, it can be related to the weakening of the hydrogen bond network. As a consequence, the activation energy of the γ-process is lower, which implies the shift of relaxation time and the process becomes faster. As stated in the part devoted to calculations, the major part of the γ-relaxation activation

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J. Phys. Chem. B, Vol. 114, No. 34, 2010 11279 TABLE 2: Theoretical Calculations for D-glucose and 1,6-anhydro-D-glucosea type of motion

Ea (kJ/mol) Ea corr. (kJ/mol) ∆µ (D) Φ (deg) D-Glucose

tg f gt(+) tg f gg(+) gg(-) f gg(+) gt(-) f gg(-) gt(-) f gt(+) chair f boat

13.2 14.0 16.0 24.3 14.8 50.7

11.1 13.2 13.2 23.1 11.9 48.6

chair f boat

1,6-Anhydro-D-glucose 26.3 23.4

+0.689 +0.908 +0.337 -0.198 -0.639 -0.692

23 139 38 150 28 26

+0.188

17

a

Energy was evaluated on the B3LYP/6-311++G(2d,2p) level. Ea corr. was corrected by the zero-point energy obtained on the B3LYP/6-31+G* level. We have also presented changes of dipole moment direction (Φ) and value (∆µ) as the difference between transition state and minimum.

Figure 8. Comparison of γ-relaxation before and after equilibration in D-fructose and D-ribose.

Figure 9. Probable reactions during the mutarotation phenomenon which have impact on γ-relaxation. the activation energy of the γ-process is related to the strength of the hydrogen bond network. Although the hydroxymethyl groups are mainly involved in creation of external hydrogen bonds, their amount is positively related to the hydrogen bond network strength.

energy is the energy of the hydrogen bond OH · · · H. Therefore, the activation energy of the γ-process can indicate the strength of the hydrogen bond network. The increase in dielectric strength in the case of D-fructose can be related to different dipole moment fluctuations during the same hydroxymethyl reorientation in newly formed tautomers.

All experimental findings presented above indicated that the γ-relaxation process in carbohydrates is related to the motions of the hydroxymethyl group. Moreover, mutarotation impact on the γ-process can be explained within the framework of the presented thesis. However, to rule out the possibility that the γ-relaxation process can be associated with the deformation of the carbohydrate ring, we have performed calculations of conformation interconversions within the framework of density functional theory (DFT). First, we have performed calculations of interconversion pathways in D-glucose of the chair to boat transition as well as transitions between different rotamers (tg f gt and tg f gg f gt), which can be interpreted as rotation of hydroxymethyl group and between rotamers of the same type [gg(-) f gg(+) and gt(-) f gt(+)] which can be interpreted as hydrogen from the hydroxymethyl group rotation. In the next step we have performed calculations for 1,6-anhydro-D-glucose. In this carbohydrate only the chair to boat transition is possible as the hydroxymethyl group is transformed into a 1,6-anhydro bridge. In Table 2 we have collected energy barriers as well as fluctuations of dipole moments during interconversions. Dielectric spectroscopy probes change in polarization which is directly connected with the reorientation of the permanent dipole moment of the molecules. As one can see, change in dipole moment direction and value is significant for the -CH2OH movements. On the other hand these parameters vary only slightly during the chair to boat transition in D-glucose and 1,6-anhydro-D-glucose. Therefore, the change of the dipole moment direction can be treated as the main argument, that the γ-relaxation in D-glucose and in other saccharides is closely connected to the rotation of the exocyclic -CH2OH group. Although, we have identified the γ-process origin by performing dipole moment analysis, there is a large disagreement between activation energy determined for the γ-relaxation process from dielectric data and that estimated from the DFT calculations for the rotation of the hydroxymethyl unit. The calculated energy of hydroxymethyl group reorientation is approximately equal to only 15 kJ/mol, whereas for the chair to boat transition, the activation energy is equal to 49 kJ/mol (similar to experimental value) for D-glucose and 24 kJ/mol for 1,6-anhydro-D-glucose. One of the explanations of such behavior is that DFT calculations were performed on the isolated molecules and the fact of ignoring the specific interactions with the surroundings is the most probable source of such disagreement. As was stated earlier, D-glucose as well as every other saccharide is a very specific system which is able to form very effective hydrogen bonds. This tendency is reflected by formation of the hydrogen bonded networks or clusters.23 Moreover, the OH · · · H hydrogen

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Figure 10. Studied interconversions between different rotamers. Symbols + or - denote the orientation of hydroxen attached to the O6 oxygen atom. The rotamer is designated as + if the orientation of the hydrogen is in agreement with the rest of the hydroxyl groups.

bonds are very strong (the mean value of such hydrogen bond energy is equal to about 20 kJ/mol). Therefore, activation energies of the considered molecular motions determined from the DFT calculations are strongly underestimated and should be regarded as orientational. One can mention that in ref 41 we have also calculated energy barrier for the glycosidic units rotation in the disaccharide: maltose. The calculated activation energy was smaller by about 20 kJ/mol than that estimated for the β-process in the studied disaccharide. Therefore, agreement between activation energy calculated from the computations for the chair to boat conversion and that estimated from dielectric data is nothing else as coincidence. Interestingly the rotation of hydroxymethyl unit has different parameters in case of transition between different rotamers (tg, gg, and gt). We have found five stable rotamers for the most stable glucopyranose ring i.e., in the 4C1 conformation (all hydroxyl substituents are in equatorial positions), whereas hydroxyl groups are orientated anticlockwise. These conformers are presented in Figure 10 and are described by the two dihedral angles defined in Figure 1. We have studied five different interconversions between rotamers. By changing the Ψ angle, we have obtained interconversion between different types of rotamers (for instance gt to gg). By changing the Ξ angle, we have monitored rotation of hydrogen in hydroxymethyl group (interconversion between the same main types of rotamers). Conformational changes between given rotamers are characterized by different energy barriers and the change of dipole moment (see Table 2). Certain changes between different types of rotamers (-CH2OH rotation) are connected with enormous fluctuation of dipole moment direction. We have not found such fluctuation in the case of the hydrogen rotation within the same type of rotamer [gg(-) f gg(+) and gt(-) f gt(+)]. This information confirm in some way our earlier supposition that the asymmetric shape of the γ-loss peak is connected to the presence of three different types of rotamers and consequently with the distribution of relaxation times. At this point it should also be stated that, because of different space arrangement of the gg, tg, and gt rotamers, the -CH2OH unit may form hydrogen bonds of different effectiveness. Therefore, the difference between the calculated energy barrier for the given motions can be even greater after taking into account intermolecular interactions.

Conclusions In this paper we have focused on molecular dynamics of D-glucose and 1,6-anhydro-D-glucose. We have shown, that there

is about 60 K difference in the glass transition temperature between them and that D-glucose is less fragile than 1,6-anhydroD-glucose. In both studied saccharides, we were able to follow the dynamics of the slow mode, and we found that in the glassy state of the 1,6-anhydro-D-glucose there is no sign of the γ-relaxation process. This finding enabled us to gain better insight into the molecular mechanism of this relaxation process. We showed that there is a correlation between the amplitude of this mode and the number of hydroxymethyl groups. Moreover, we have also found other experimental evidence indicating that the γ-relaxation process in carbohydrates is closely related to the rotation of the -CH2OH unit. To make our interpretation more distinct, additional DFT calculations for D-glucose as well as for 1,6-anhydro-D-glucose were performed. Computations confirmed our interpretation and certified that the asymmetric shape of the γ-relaxation process is closely related to the presence of three different conformers of the hydroxymenthyl unit which have different energy barriers. Consequently each -CH2OH has its own relaxation time and contributes to the γ-relaxation on a different scale. Also, we have concluded that blocking of the hydroxymethyl unit in carbohydrates suppresses the molecular mobility in the glassy state, and they become more rigid. We hope that our studies will be very useful for even better use of the carbohydrates as a food protectants and stabilizers of the amorphous drugs. Acknowledgment. The authors (P.W., K.K., K.A., Z.W., and M.P.) are deeply thankful for the financial support of their research 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. P.W. thanks the Foundation for Polish Science for awarding grants within the framework of the START Programme (2010).

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