J. Phys. Chem. B 2002, 106, 6331-6337
6331
Anisotropic Reorientation and Intermolecular Interactions of Sucrose Molecules in Aqueous Solution. A Temperature and Concentration-Dependent 13C NMR Relaxation Study Carine Baraguey,† Dirk Mertens, and Andreas Do1 lle* Institut fu¨ r Physikalische Chemie, Rheinisch-Westfa¨ lische Technische Hochschule Aachen, 52056 Aachen, Germany ReceiVed: December 31, 2001; In Final Form: March 27, 2002
The reorientational dynamics of sucrose in aqueous solutions were investigated by measurement of 13C spinlattice relaxation times for several different concentrations from 0.1 to 4.0 mol kg-1 and in a temperature range between 298 and 328 K. The relaxation data were used as input to evaluate the reorientational correlation times and rotational diffusion constants. The correlation times and rotational diffusion constants follow an Arrhenius law in the observed temperature range with activation energies from 22 to 46 kJ mol-1 at 0.1-4.0 mol kg-1, respectively. It was shown that the rotational motion of sucrose molecules in aqueous solution is anisotropic, and the anisotropy of the molecular reorientation turned out to be concentration-dependent. The concentration dependence reflects the change in the intermolecular interactions of the sucrose from mainly water-sucrose interactions to a mixture of water-sucrose and sucrose-sucrose interactions. It was thus possible to detect sugar-sugar interactions, which are of biological relevance.
Introduction Carbohydrates are an important family of compounds which are involved in many biological processes, and their interactions, with proteins mainly, lead to specific responses, such as hostparasite interactions, fertilization, immune reactions, and cellular differentiation and recognition.1 Some saccharides, such as trehalose, sucrose, and maltose, also act as cryoprotectives in cells and organisms.2,3 Finally, aqueous solutions of saccharides are interesting from a physicochemical point of view, the knowledge of their properties being a prerequisite for optimizing processes in many technical and pharmaceutical productions. The measurements of 13C spin-lattice relaxation times and nuclear Overhauser enhancement (NOE) factors provide valuable information about the structure and dynamics of molecules in liquids, and several communications concerning the reorientational motions of sugars using NMR methods were thus reported for monosaccharides and also oligo- and polysaccharides.4,5 Sucrose (β-D-fructofuranosyl R-D-glucopyranoside) is one of the most frequent sugars, occurring widely in plants, fruits, and honey. Its structure as well as the nomenclature used to number the carbon atoms in the present study are given in Figure 1. 13C relaxation times of sucrose were first reported by Allerhand et al.,6 who studied the overall motion of the molecule and concluded that both sugar rings of sucrose behave together as a single rigid entity reorienting isotropically with correlation times of about 7 × 10-11 and 3 × 10-10 s in 0.50 and 2.0 mol L-1 aqueous solutions, respectively. Recently, Kovacs et al. studied disaccharides, including sucrose, dissolved in a mixture of D2O and [2H6]DMSO at temperatures and magnetic fields also outside the extreme narrowing region and assuming * To whom correspondence should be addressed. E-mail: doelle@ rwth-aachen.de. † Present address: Instituto de Tecnologia Quı´mica e Biolo ´ gica, Universide Nova de Lisboa, Rua da Quinta Grande, 6, Apartado 127, 2780156 Oeiras, Portugal.
Figure 1. Labeling of the carbon atoms in the sucrose molecule.
isotropic reorientation7 like in studies performed in aqueous solutions by Lu¨demann et al.8,9 An anisotropic reorientational behavior was, however, suggested by McCain and Markley after having measured 13C spin-lattice relaxation times and nuclear Overhauser enhancements as a function of temperature, concentration, and magnetic field,10,11 but to our knowledge no investigation was carried out to confirm this assumption and to describe the anisotropy in a quantitative way. In the present investigation, the anisotropy of sucrose reorientation in aqueous solution was studied by evaluation of the rotational diffusion constants obtained from dipolar 13C spin-lattice relaxation times. To observe the influence of temperature and concentration on the rotational motions, the spin-lattice relaxation times were measured for concentrations ranging from 0.10 to 4.0 mol kg-1 and in a temperature range from 298 to 328 K. Results Conformation and Structure of the Sucrose Molecule. For the analysis of the reorientational dynamic behavior of molecules by application of NMR relaxation methods (see below), it is essential to know the correct molecular structure, both regarding the exact internuclear distances as well as the proper conformation. In the present study, the molecular geometry was obtained from a semiempirical geometry optimization. The structure of sucrose related to the principal axis system of inertia is represented in Figure 2, and values for C-H distances of carbons with directly bonded protons are listed in Table 1. The principal moments of inertia obtained from this structure for the axes x, y, and z are 4.07, 5.31, and 2.22 × 10-44 kg m2,
10.1021/jp014654l CCC: $22.00 © 2002 American Chemical Society Published on Web 05/25/2002
6332 J. Phys. Chem. B, Vol. 106, No. 24, 2002
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Figure 2. Optimized molecular structure of the sucrose molecule with respect to the principal axis system of inertia.
TABLE 1: 13C-1H Bond Lengths rC-H, 13C Spin-Lattice Relaxation Times (nHT1)i, and Correlation Times τci for the Protonated Carbons i of Sucrose in 0.10 mol kg-1 Aqueous Solution at 328 K carbon atom
rC-H/pm
(nHT1)i/s
τci/ps
1g 2g 3g 4g 5g 6g 1f 3f 4f 5f 6f
112.6 112.7 112.7 112.5 112.6 112.3 112.3 112.6 112.5 112.5 112.3
1.13 1.16 1.20 1.20 1.18 1.44 1.35 1.12 1.14 1.07 1.61
50 49 47 47 48 39 41 51 49 53 35
respectively. The anisotropies F, which result from taking the reciprocal value of the square roots of the moments of inertia divided by the z value, are for x and y 0.74 and 0.65, respectively. Thus, a slight anisotropy has already to be expected for rotational motion in the gas phase. 13C Relaxation Data. The 13C spin-lattice relaxation times T1 for the eleven protonated carbons were measured from 298 to 328 K for aqueous solutions with the concentrations 0.10, 0.50, 1.0, 2.0, 3.0, and 4.0 mol kg-1. As an explicit example for the observed relaxation times, the nHT1 values for the 0.10 mol kg-1 sucrose solution at 328 K are presented in Table 1. The number of directly bonded protons nH in the above product takes into account that a 13C nucleus interacting with two protons relaxes faster by a factor of 2, because the contributions from several interacting protons to relaxation are additive. It is known that aliphatic 13C nuclei with directly bonded protons such as in sucrose relax exclusively via the dipolar relaxation mechanism. Contributions from CSA relaxation are only becoming important for relaxation of, e.g., aromatic 13C nuclei or 13C nuclei in carbonyl groups. The SR mechanism is only effective for small molecules or highly mobile molecular segments such as methyl groups at low viscosities (that means low concentrations in the present case) and/or high temperatures. Measurements of the NOEs at lower temperatures and higher concentrations deliver values that are less than the maximum value, and it is then impossible to decide if this is a result of competing relaxation mechanisms or just of leaving the extreme narrowing regime with relaxation fully via the dipolar pathway. Thus, the only way to prove if other relaxation mechanisms are competing to a considerable extent with the dipolar one is to measure NOEs in the extreme narrowing regime, i.e., at low concentration and high temperature. Therefore, the NOE factors were determined especially at high temperatures and dilute
Figure 3. Average 13C relaxation rates 〈1/T1〉CH of the sucrose ring carbon atoms as a function of reciprocal temperature 1/T.
sucrose solutions. They showed the expected maximum value for 13C nuclei with directly bonded protons. For them, all measured relaxation rates 1/T1 were taken to be equal to the dipolar spin-lattice relaxation rates 1/T1DD. That means that in the case of sucrose the 13C nuclei with directly bonded protons relax fully via the dipolar relaxation pathway. Data Reduction. A set of 385 relaxation rates (1/T1DD) was obtained for the different 13C nuclei with directly bonded protons, temperatures, and solutions. To present the data in a closed form and to be able to deduce some general statements about them, it was necessary to perform a data reduction that was achieved in the following way: First, since all relaxation rates of 13C nuclei i with one directly bonded proton at a given concentration cm and temperature Tn were quite similar, they were averaged over the nCH different 13C nuclei.
〈
1 T1(cm,Tn)
〉
1
)
nCH
∑i
nCH
CH
(
1
)
T1(cm,Tn)
(1)
i
The result of this averaging is plotted in Figure 3, in which the mean relaxation rates are given as a function of reciprocal temperature and concentration. In a next step, the relaxation rates of each nucleus i (also those with two directly bonded protons) at a given concentration cm and temperature Tn were divided by the number of directly bonded protons nH. The ratios of the latter values and the former average values obtained from eq 1 at that concentration and temperature were calculated. Finally, these ratios were averaged over the nT temperatures Tn for a given concentration.
〈 〉 1
T1(cm)i
) T
1
nT
∑n
nT
〈T1(cm,Tn)〉CH nHT1(cm,Tn)i
(2)
These relative average relaxation rates being a function of position i of the 13C nucleus in the sucrose molecule and concentration cm are shown in Figure 4. Reorientational Correlation Times. When the relaxation times are measured under 1H decoupling conditions, the cross relaxation term vanishes12 and the intramolecular dipolar longitudinal relaxation rate (1/T1DD)i for relaxation of 13C nucleus i by proton j is connected to the molecular reorientations by12
( ) 1
) T1DD ij 1 (2πDij)2[Ji(ωC - ωH) + 3Ji(ωC) + 6Ji(ωC + ωH)] (3) 20
Sucrose Molecules in Aqueous Solution
J. Phys. Chem. B, Vol. 106, No. 24, 2002 6333 TABLE 2: Fit Parameters Preexponential Factor τ0i, Activation Energy EAi, and Generalized Order Parameter Si2 for the 13C Relaxation Rates of Aqueous Sucrose at a Concentration of 4.0 mol kg-1 carbon atom
τ0i/10-2 fs
EAi/kJ mol-1
Si2
1g 2g 3g 4g 5g 6g 1f 3f 4f 5f 6f
4(2 2(1 2(1 2(1 1.7 ( 0.9 (3 ( 4) × 101 (5 ( 6) × 101 1.4 ( 0.7 1.5 ( 0.8 2(1 (1 ( 1) × 102
44 ( 2 46 ( 1 46 ( 1 46 ( 1 46 ( 1 37 ( 3 36 ( 3 47 ( 1 47 ( 1 46 ( 1 32 ( 3
0.900 ( 0.007 0.872 ( 0.006 0.857 ( 0.006 0.853 ( 0.006 0.868 ( 0.006 0.77 ( 0.04 0.82 ( 0.04 0.856 ( 0.005 0.847 ( 0.006 0.870 ( 0.005 0.79 ( 0.05
Figure 4. Average relative 13C relaxation rates 〈1/T1〉T of the sucrose carbon atoms as a function of concentration m.
with the dipolar coupling constant
Dij )
TABLE 3: Fit Parameters Preexponential Factor τ0, Activation Energy EA, and Generalized Order Parameter S2 for the Average 13C Relaxation Rates 1/(nH〈T1〉C) of Aqueous Sucrose
µ0 p -3 γ γ r 4π C H2π ij
where µ0 is the magnetic permeability of the vacuum, γC and γH are the magnetogyric ratios of the 13C and 1H nuclei, respectively, p ) h/2π with the Planck constant h, and rij is the length of the internuclear vector between 13C nucleus i and proton j. The Ji(ω) are the spectral densities of nucleus i with the resonance frequencies of the 13C and 1H nuclei, ωC and ωH, respectively. To interpret the relaxation data, the “model-free” approach for the spectral density by Lipari and Szabo13 was applied. In the case of isotropic overall motion the spectral density is described by the correlation time of overall molecular motion τc and the generalized order parameter S2.
Ji(ω) )
2Si2τci 1 + (ωτci)2
(5)
As is shown by the maximum NOE factors η, the observed relaxation rates at the most dilute solution and highest temperature (0.10 mol kg-1 and 328 K, respectively) were in the extreme narrowing regime and eq 5 holds. Thus, the correlation time values τci for each of the protonated carbons of sucrose can be calculated when assuming that Si2 is equal to unity, and they are listed in Table 1. Rotational diffusion is a thermally activated process and an Arrhenius equation can be used to describe the temperature dependence of the correlation times
τci ) τ0i exp(EAi/RT)
τ0/10-2 fs
0.1 0.5 1.0 2.0 3.0 4.0 4.0
(1.3 ( 0.2) × (2.7 ( 0.4) × 103 (2.4 ( 0.4) × 102 33 ( 6 6(2 2(1 2(1
a
103
EA/kJ mol-1
S2a
22.7 ( 0.3 21.6 ( 0.3 28.7 ( 0.4 35.4 ( 0.5 41.6 ( 0.8 45 ( 1 46 ( 1
a a a a a a 0.865 ( 0.006
A value for the generalized order parameter S2 of 0.87 was assumed.
(4)
The reorientational correlation time τci is a measure of the velocity of rotational motion of the corresponding internuclear 13C-1H vectors of carbon i. The meaning of the generalized order parameter will be discussed below. For the extremenarrowing case (ωτc , 1), the following relation is valid.
Ji(ω) ) 2Si2τci
m/mol kg-1
(6)
with the gas constant R and activation energy EAi for carbon i. For the highest concentration a temperature-dependent fit to the measured relaxation rates by means of eqs 3, 4, and 6 could be performed, for which the results are given in Table 2. Using the average for Si2 over the carbon nuclei i with one directly bonded proton as a fixed parameter, giving a value of S2 ) 0.87, the average relaxation rates 〈1/T1〉CH were fitted to obtain the activation parameters of reorientational motion, which are
Figure 5. Rotational diffusion constants Rl (with 4, 0, O for l ) x, y, z) as a function of reciprocal temperature 1/T and concentration m.
contained in Table 3. Relaxation rates calculated with the fit parameters are plotted in Figure 3 as lines through the observed data points. Rotational Diffusion Constants. The rotational motion of molecules can be described by the rotational diffusion constants Rl. As usual, it was assumed that the rotational diffusion principal axis system coincides with the inertial principal axis system.14 The equations used to calculate the dipolar relaxation times as a function of the rotational diffusion constants were developed by Woessner15 and are given here in a simplified form:
( ) 1
DD
T1
i
nH
)
(2πDij)2f(Ck,Rl) ∑ j)1
with
l ) x, y, z (7)
where the Ck are geometric constants related to the orientation of the corresponding 13C-1H vector to the rotational diffusion axis system and Rl the rotational diffusion constants. The evaluated rotational diffusion constants Rl are shown in Figure 5 as a function of reciprocal temperature for all concentrations. Some of the rotational diffusion constants could not be
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calculated because of major problems in determining these values outside the extreme narrowing regime. The temperature dependence of the rotational diffusion constants was described by an Arrhenius equation
Rl ) R0l exp(-EAl/RT)
(8)
where EAl is the activation energy for rotational diffusion about axis l. The activation energies obtained by fitting the data with eq 8 were of approximately the same size as the ones obtained from the correlation times using eq 6. Discussion Conformation and Structure of the Sucrose Molecule. The most important feature of the sucrose structure for the dynamic analysis is the conformation of the glycosidic linkage: It determines the orientation of the inertial principal axis system to which the orientation of the 13C-1H bonds is related when it is assumed that the inertial and rotational diffusion axis systems coincide. Besides the correct determination of the sucrose conformation, an exact calculation of the 13C-1H bond distances is crucial for the evaluation of reorientational motion. The molecular structure of crystalline sucrose is known from X-ray16 and neutron diffraction17 studies. However, the conformation in aqueous solution was the subject of numerous investigations, sometimes leading to controversial results. Two important problems arise for the present investigation concerning the structure in solution: Is the solution structure more or less rigid regarding the interresidue conformation, and when it is, what is its preferred conformation? For the present investigation it is important that the Woessner equations can only then be employed to evaluate the anisotropy of rotational motion when the solution structure is not flexible. In their study Poppe and van Halbeek claimed explicitly that the solution structure was not rigid,18 while in other experimental studies it was stated that in solution the interresidue conformation differed from the crystalline structure (13C-1H19,20 and 13C13C coupling constants20) or that the data could not be explained by the assumption of a single conformation in solution (FTIR spectroscopy,21,22 Raman,22 X-ray,23 optical rotation,24,25 NOESY,25-27 and 1H steady-state NOEs and 13C-1H coupling constants26). Several different conformers, i.e., minima on the energy surface, were also found in computational studies (molecular mechanics,25-32 ab initio on a sucrose analogue,30 molecular mechanics/ab initio hybrid,33 and molecular dynamics (MD) simulation27,31). However, in most studies it was found that the crystalline structure conformer fell into the region of the computed absolute minimum on the energy map and was similar to the predominant conformer with lowest energy.24,25,27-32 In contrast to the latter investigations, Bock and Lemieux34 concluded from NMR data and molecular modeling studies that the sucrose molecule was not conformationally flexible about the glycosidic bond in solution and that its conformation was close to the one in the crystalline state and stabilized by an intramolecular O2g‚‚‚H-O1f hydrogen bond. McCain and Markley10 as well as Effemey et al.35 agreed in their experimental study with the major conclusions by Bock and Lemieux. Karger and Lu¨demann8 and Girlich and Lu¨demann9 also did not find flexibility about the glycosidic bond. In a very recent structure determination of sucrose in dilute aqueous solution by multidimensional NMR methods from the group of Griesinger36 a structure was found which is in excellent agreement with the crystalline structure.
In most of the above cited20-29,31-34 and other37-41 references the relevance of hydrogen bonding for stabilizing the sucrose structure in solution was discussed as well. Considering these results, the conformation of sucrose in the crystalline state was taken as a starting point to optimize the structure of the sugar molecule in the present investigation. The conformation obtained by means of the semiempirical method AM1 (Φ ) 112° and Ψ ) -46°) was quite similar to the crystalline structure (Φ ) 108° and Ψ ) -45°)17 and exhibited a stabilizing hydrogen bond between O5g and H-O6f being also present in the crystalline state.17 Furthermore, it was assumed that the sucrose structure in aqueous solution is rigid on the time scale of reorientational motion. A justification of the latter assumption will be given below and discussed in the light of the results of the present study. 13C Relaxation Data. The spin-lattice relaxation rates 1/T 1 of the methylene carbons C6g, C1f, and C6f were approximately double of the values for the methine nuclei, since two protons are involved in the dipolar relaxation rather than only one in the latter case. The relaxation times multiplied by the number of directly bonded protons nHT1 in Table 1 for a concentration of 0.10 mol kg-1 and a temperature of 328 K were in the extreme narrowing region as already stated in the Results section. The nHT1 values are directly related to the reorientational mobility of the corresponding 13C-1H vectors. While the nHT1 values for the ring carbon atoms were quite similar to each other, the values for C6g, C1f, and C6f in the hydroxymethyl groups were significantly higher, a result of faster internal dynamics of these molecular segments. However, even the ring carbons showed pronounced differences, which are an indication of an anisotropic overall rotational motion of the sucrose molecule and which cannot be explained by differing 13C-1H distances. The logarithmic plot of the average relaxation rates 1/〈T1〉CH as a function of the reciprocal temperature and concentration in Figure 3 shows a linear dependence for the concentrations 0.10 and 0.50, and 1.0 mol kg-1. This behavior is characteristic for relaxation in the extreme narrowing regime. In the case of the more concentrated solutions a clear deviation from the linear dependence was observed, because at these concentrations the extreme narrowing condition was not fulfilled anymore. Under these conditions, eq 3 does not hold, and for the determination of the rotational diffusion constants this fact had to be taken into account in eq 7. When considering the relative relaxation rates averaged over the temperatures 1/〈T1〉T (Figure 4), two important features of the concentration dependence become obvious: The 1/〈T1〉T values of the glucose ring increased, whereas those of the furanose ring decreased with increasing concentration. This behavior is in contrast to the findings by McCain and Markley10,11 and gives a clear indication of a change in the reorientational behavior of the sucrose molecule with changing concentration. Furthermore, the corresponding values of the hydroxymethyl were much lower, again showing the effect of internal motion of these molecular segments. The ordering of the relaxation rates was C6f < C6g < C1f. Reorientational Correlation Times. As can be seen from the results given in Table 1, the carbons of the two rings exhibited quite similar correlation times ranging from 47 to 53 ps. Thus, it can be concluded that they belong to the rigid part of the molecule and can be considered as being representative for the rotational motion of the overall molecule. However, the differences in the values for the different 13C nuclei were significant and were again an indication of an anisotropic reorientational motion of the sucrose molecule. The correlation
Sucrose Molecules in Aqueous Solution times for the carbons of the hydroxymethyl moieties were smaller than for the latter in the order C6f < C6g < C1f, suggesting that the internal rotation is hindered most at C1f and least at C6f. In contrast to fast internal motions, such as, for example, in the case of rotating methyl groups, for which the correlation times can be smaller by 1 order of magnitude,42 the internal motion of the hydroxymethyl groups seems to be severely hindered. The latter findings are in accordance with the studies by McCain and Markley10 and Girlich and Lu¨demann9 on qualitative reasoning and another study by McCain and Markley,43 who observed the same relative order for their experimental values of the generalized order parameter S2 by application of the “model-free” spectral density of Lipari and Szabo.13 Effemey et al.35 found in their investigation of the reorientational dynamics of sucrose the same order in the correlation times of internal motion. The different behavior of the hydroxymethyl groups was discussed by Bock and Lemieux34 in the light of an intramolecular hydrogen bond between O1f and O2g. MD simulation studies showed that this intramolecular hydrogen bond did not persist, but that a bridging water molecule O1f‚‚‚Ow‚‚‚O2g became important in determining the structure of sucrose in solution.27,31,40,41 The fit of the model by Lipari and Szabo13 with an Arrhenius temperature dependence for the reorientational correlation times to the relaxation rates of the 4.0 mol kg-1 sucrose solution gave the same values for the preexponential factors τ0 and activation energies EAi for the ring 13C-1H vectors within the error limits (Table 2). Whether the differences in the generalized order parameters are a result of the physical reality cannot be decided. As expected, the hydroxymethyl groups showed a different behavior, reflecting the faster internal motion of these molecular segments. The same fit for the other concentrations did not give reasonable results, because the function was not well enough defined in order to fit the parameter Si2. Therefore, the mean value of S2 ) 0.87 from the previous fit for 4.0 mol kg-1 was used as a fixed parameter to fit the average relaxation rates 〈1/ T1〉CH at the other concentrations. The high quality of the fit becomes obvious in Figure 3. The preexponential factors τ0 in Table 3 decreased by 3 orders of magnitude with increasing concentration of the solutions, whereas the activation energies increased, becoming double at the concentrated solution when compared to the dilute solution. The activation energy for the latter concentrations (0.10 and 0.50 mol kg-1) was approximately the same and corresponds to the activation energy for reorientation of pure water.44 These values are in very good agreement to the values by McCain and Markley11 for the corresponding concentrations. The same authors found a generalized order parameter of 0.89 for the ring 13C-1H vectors in all aqueous solutions regardless of temperature and concentration, which justifies the use of an average order parameter for fitting the correlation times at the other concentrations in the present study. The S2 values from the MD simulation results in aqueous solution by Engelsen et al.27 were significantly lower and ranged from 0.4 to 0.6 for the fructofuranosyl and 0.7 for the glucopyranosyl ring. In the NMR relaxation study by Kowalewski and co-workers7,35 higher values between 0.84 and 0.96 were obtained for sucrose in a solvent mixture of water/ DMSO. The 13C-1H vectors of the hydroxymethyl groups showed a slight temperature dependence in the studies by Effemy et al.35 and McCain and Markley.43 Rotational Diffusion Constants. The values of the rotational diffusion constants relative to each other, i.e., the anisotropy of rotational motion can provide valuable information about the molecular nature of liquids, since these values depend on the
J. Phys. Chem. B, Vol. 106, No. 24, 2002 6335
Figure 6. Reorientational correlation times τc calculated from the reciprocal mean of the rotational diffusion constants (eq 9) and the temperature dependence of the reorientational correlation times using eqs 3, 4, and 6 (lines).
intermolecular interactions that influence the motions of the molecules in the liquids. Figure 5 clearly shows that the sucrose molecules reorient anisotropically about the principal axes x, y, and z. The reorientation about the z axis was always the fastest like calculated for the gas phase, regardless of the concentration. The velocity of the rotation about the x axis was comparable to the one about the z axis in the case of the dilute solution (0.10 mol kg-1), and slowed with increasing concentration and finally became more or less equal to the one about the y axis (4.0 mol kg-1). The anisotropies F for both extremes in the concentrations were ranging from 0.98 and 0.80 to 0.79 and 0.84 for rotation about the x and y axes. Thus, the anisotropy was a bit less pronounced than expected from the values for the moments of inertia, and a change in the anisotropy was observed with increasing sucrose concentration. For the rotational diffusion constants an Arrhenius-like behavior was observed with activation energies comparable to the values given in Table 3 for the reorientational correlation times. The activation energy for rotation about the z axis appeared to be larger than for rotation about the other two axes. When calculating the number of water molecules being present for the hydration of one sucrose molecule, one notices that this number varies from approximately 500 to 12.5 water molecules per one sucrose molecule for concentrations of 0.104.0 mol kg-1, respectively. The latter number of water molecules is hardly enough to form the first hydration shell, for which 8-11 water molecules are needed to bind to the 8 hydroxy and three ether oxygens in the sucrose molecule, not to mention that there are no more water molecules left to form something like “bulk water”. Furthermore, in Figure 5, a change in the activation energies is evident when proceeding from the dilute solutions (0.1 and 0.5 mol kg-1) to the solutions with a concentration of 1.0 mol kg-1 and higher. In Figure 6, the reciprocal mean of the three rotational diffusion constants is compared to the values calculated from the parameters for the temperature dependence of the reorientational correlation times using eqs 3, 4, and 6 and the relations
τci )
1 6R h
and
R h)
1
3
∑ Rl
3 l)1
(9)
These values are in excellent agreement except for the highest concentration, which shows a deviation because of principal difficulties in the evaluation of rotational diffusion constants with the Woessner equations outside the extreme narrowing limit.
6336 J. Phys. Chem. B, Vol. 106, No. 24, 2002 The evaluation of the rotational diffusion constants using the measured relaxation data and a sucrose structure being quite similar to the crystalline structure as input gave very good results. The difference between the calculated dipolar spinlattice relaxation rates obtained in the fit with eq 7 and the experimental relaxation rates was only very small. Thus, it is concluded that the chosen model is correct, that is the structure in aqueous solution is rigid and similar to the crystalline one. Conclusions For more concentrated sugar solutions such as in the present investigation, in which the number of water molecules is hardly sufficient to form hydrogen bonds to the hydrogen-bonding sites at the sucrose molecules, hydrogen bonds between the sugar molecules themselves are becoming more and more important. This assumption is corroborated by an MD simulation study at comparable concentrations of sugar hydrogen-bonding sites by Roberts and Debenedetti,46 who found an increasing amount of hydrogen bonds between monosaccharide molecules when increasing the sugar content of the aqueous solutions. Simultaneously, small mobile clusters of water molecules within the surrounding cages of sugar molecules were formed. At a concentration comparable to the highest one in the present study, the water-water hydrogen bonds lost much importance in comparison to saccharide-water and saccharide-saccharide hydrogen-bond networks. Furthermore, Mathlouthi et al. postulated that the results from their concentration-dependent Raman,22,47,48 FTIR,22 and X-ray23 measurements of aqueous sucrose solutions could be explained by association of sucrose molecules and the resulting sugar-sugar interactions. To clarify the role of the water molecules in their interaction with sugars, it is necessary to perform more studies on the structural and dynamic properties of water in aqueous sugar solutions (ref. e. g. to Belton et al.49-51). To the authors knowledge it is shown for the first time quantitatively in the present study that the rotational motion of sucrose molecules in aqueous solutions is anisotropic. The determination of the anisotropy by 13C relaxation data measurements proved to be a valuable tool to investigate not only the rotational dynamics of the solute but to be also a very sensitive probe to intermolecular interactions: The change in the rotational behavior of the sucrose molecules described in this study reflects the change in the intermolecular interactions in the aqueous solutions from mainly water-sucrose interactions to a mixture of water-sucrose and sucrose-sucrose interactions. At the highest concentrations the sugar-sugar interactions are becoming quite important and result in a change of the anisotropy of rotational motion. The results of the present investigation might also be of importance for the structural studies by NMR spectroscopy, which need the information on the rotational dynamics as input. Experimental Section Samples. Sucrose and heavy water (deuteration degree > 99.8%) were purchased from Sigma-Aldrich GmbH (Steinheim, Germany) and Merck (Darmstadt, Germany), respectively. The solutions (0.10, 0.50, 1.0, 2.0, 3.0, and 4.0 mol kg-1) were measured in 10 mm NMR tubes (Wilmad, USA). NMR Measurements. The measurements of the spin-lattice relaxation times were performed on a Bruker AM 250 spectrometer operating at a magnetic flux density of 5.875 T (ν(13C) ) 62.89 MHz, ν(1H) ) 250.13 MHz, internal lock on 2H2O). The 13C signals of sucrose in 2H2O were assigned according to earlier unambiguous results.34,45 The relaxation times were
Baraguey et al. measured under 1H broadband decoupling using the inversionrecovery pulse sequence.52 The relaxation delay was about 5 times the longest relaxation time of 13C with directly bonded protons, and 20 different delays t between the 90° and 180° pulses were used in each experiment. The spin-lattice relaxation times were calculated by performing a three-parameter fit of the signal amplitudes I to the relaxation function I ) I0 [1-A exp(-t/T1)] with the parameters I0, A, and T1. The measurements were repeated five times and the mean standard deviations for the resulting T1 were better than 2%. The temperature at the sample position was controlled measuring the chemical shift of the hydroxyl group of neat methanol,53 and the estimated temperature accuracy was (1 K. Molecular Geometry of Sucrose. The internuclear distances between 13C and 1H were obtained by optimization of the molecular structure with the semiempirical method AM154 in the MOPAC program package.55 Evaluation of the Rotational Diffusion Constants. To evaluate the rotational diffusion constants of the sucrose molecules in aqueous solution, the 13C dipolar longitudinal relaxation rates obtained by eq 3 were fitted simultaneously to the experimental relaxation rates for all 13C ring nuclei with one directly attached proton at one temperature. The rotational diffusion constants Rl are the adjustable parameters, which were obtained by means of the FORTRAN77 program RELAX.56 Because of the internal mobility of the 13C-1H vectors for the methylene carbons C6g, C1f, and C6f, the relaxation times of these were excluded during the fit. Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft (Graduate Studies Program “Methods in Asymmetric Synthesis”) is gratefully acknowledged. The authors thank M. D. Zeidler and W. R. Carper for helpful discussions and M. D. Zeidler also for his support of this work. References and Notes (1) (a) Dwek, R. A. Chem. ReV. 1996, 96, 683-720. (b) Podeva, A.; Jime´nez-Barbero, J. Chem. Soc. ReV. 1998, 27, 133-143. (2) Kawai, H.; Sakurai, M.; Inoue, Y.; Chujo, R.; Kobayashi, S. Cryobiology 1992, 29, 599-606. (3) Wang, G. M.; Haymet, A. D. J. J. Phys. Chem. B 1998, 102, 53415347. (4) van Halbeek, H. Curr. Opin. Struct. Biol. 1994, 4, 697-709. (5) Brant, D. A. Pure Appl. Chem. 1997, 69, 1885-1892. (6) Allerhand, A.; Doddrell, D.; Komoroski, R. J. Chem. Phys. 1971, 55, 189-198. (7) Kovacs, H.; Bagley, S.; Kowalewski, J. J. Magn. Reson. 1989, 85, 530-541. (8) Karger, N.; Lu¨demann, H-.D. Z. Naturforsch. 1991, 46c, 313317. (9) Girlich, D.; Lu¨demann, H-.D. Z. Naturforsch. 1993, 48c, 407413. (10) McCain, D. C.; Markley, J. L. Carbohydr. Res. 1986, 152, 73-80. (11) McCain, D. C.; Markley, J. L. J. Am. Chem. Soc. 1986, 108, 42594264. (12) Lyerla, J. R.; Levy, G. C. Top. Carbon-13 NMR Spectrosc. 1972, 1, 79-148. (13) Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546-4559. (14) Do¨lle, A.; Bluhm, T. Prog. Nucl. Magn. Reson. Spectrosc. 1989, 21, 175-201. (15) Woessner, D. E. J. Chem. Phys. 1962, 37, 647-654. (16) Hanson, J. C.; Sieker, L. C.; Jensen, L. H. Acta Crystallogr. 1973, B29, 797-808. (17) Brown, G. M.; Levy, H. A. Acta Crystallogr. 1973, B29, 790797. (18) Poppe, L.; van Halbeek, H. J. Am. Chem. Soc. 1992, 114, 10921094. (19) Mulloy, B.; Frenkiel, T. A.; Davies, D. B. Carbohydr. Res. 1988, 184, 39-46. (20) Duker, J. M.; Serianni, A. S. Carbohydr. Res. 1993, 294, 281303.
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