Hydration and rotational diffusion of levoglucosan in aqueous solutions.

Hydration and rotational diffusion of levoglucosan in aqueous solutions S. Corezzi, P. Sassi, M. Paolantoni, L. Comez, A. Morresi, and D. Fioretto Citation: The Journal of Chemical Physics 140, 184505 (2014); doi: 10.1063/1.4873575 View online: http://dx.doi.org/10.1063/1.4873575 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Destruction of hydrogen bonds of poly(N-isopropylacrylamide) aqueous solution by trimethylamine N-oxide J. Chem. Phys. 136, 234904 (2012); 10.1063/1.4729156 Intermolecular momentum transfer in poly(perfluorosulfonic acid) membrane hydrated by aqueous solution of methanol: A molecular dynamics simulation study J. Chem. Phys. 131, 224901 (2009); 10.1063/1.3271829 Nonideality in diffusion of ionic and hydrophobic solutes and pair dynamics in water-acetone mixtures of varying composition J. Chem. Phys. 127, 024503 (2007); 10.1063/1.2751192 Dynamics of ionic and hydrophobic solutes in water-methanol mixtures of varying composition J. Chem. Phys. 123, 234501 (2005); 10.1063/1.2137702 Hydration and transport properties of aqueous solutions of --trehalose J. Chem. Phys. 109, 1170 (1998); 10.1063/1.476662

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THE JOURNAL OF CHEMICAL PHYSICS 140, 184505 (2014)

Hydration and rotational diffusion of levoglucosan in aqueous solutions S. Corezzi,1 P. Sassi,2 M. Paolantoni,2 L. Comez,3 A. Morresi,2 and D. Fioretto1,4,a) 1

Dipartimento di Fisica e Geologia, Università di Perugia, Via Pascoli, I-06123 Perugia, Italy Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy 3 IOM-CNR c/o Dipartimento di Fisica e Geologia, Università di Perugia, Via Pascoli, I-06123 Perugia, Italy 4 Centro di Eccellenza sui Materiali Innovativi Nanostrutturati (CEMIN), Università di Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy 2

(Received 15 March 2014; accepted 16 April 2014; published online 9 May 2014) Extended frequency range depolarized light scattering measurements of water-levoglucosan solutions are reported at different concentrations and temperatures to assess the effect of the presence and distribution of hydroxyl groups on the dynamics of hydration water. The anhydro bridge, reducing from five to three the number of hydroxyl groups with respect to glucose, considerably affects the hydration properties of levoglucosan with respect to those of mono and disaccharides. In particular, we find that the average retardation of water dynamics is ≈3–4, that is lower than ≈5–6 previously found in glucose, fructose, trehalose, and sucrose. Conversely, the average number of retarded water molecules around levoglucosan is 24, almost double that found in water-glucose mixtures. These results suggest that the ability of sugar molecules to form H-bonds through hydroxyl groups with surrounding water, while producing a more effective retardation, it drastically reduces the spatial extent of the perturbation on the H-bond network. In addition, the analysis of the concentration dependence of the hydration number reveals the aptitude of levoglucosan to produce large aggregates in solution. The analysis of shear viscosity and rotational diffusion time suggests a very short lifetime for these aggregates, typically faster than ≈20 ps. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873575] I. INTRODUCTION

The mutual interaction of water with solute molecules is a complex problem of primary importance in many fields, especially in life science, due to the active role played by water in living matter.1 Both structure2 and dynamics3 of water surrounding a bio-macromolecule are profoundly modified with respect to the bulk,4 and this reverberates on the properties of the solute itself,5 such as the stability of its structure, its physiological function and its energetics.6 Understanding the structure and dynamics of hydration water is challenging since it participates to a wide range of environments with different spatial and temporal characteristics defined by, e.g., surface topology, hydrophobicity, and charged units that influence both H-bond network statics and dynamics. A possible route to try to give a rationale to this scenario is relating the properties of hydration water to those of the closest molecular groups. To this respect, MD simulations7 consistent with NMR results8, 9 have recently suggested that simple local factors can provide a nearly quantitative description of the hydration shell dynamics. Conversely, MD simulations of disaccharides in water have suggested that water dynamics is the delicate result of solute/solvent coupling over a range of length scales extending from individual hydrogen bonds to, at least, the second solvation shell and that one should not expect to fully understand hydration processes by means of a reductionist a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2014/140(18)/184505/9/$30.00

approach.10 Moreover, THz absorption experiments suggest a size dependent dynamical perturbation, which involves two hydration layers for the disaccharides trehalose and lactose and a single layer for the monosaccharide glucose.11 In this context, extended frequency range depolarized light scattering (EDLS) experiments12 performed on carbohydrates, peptides, amino acids, and proteins, have recently shown that a significant increase of the dynamical retardation and extension of the perturbation occurs when increasing the chemical complexity of the solute. EDLS spectra provide a considerable amount of information, which is quite unique in giving a complete picture of the mutual influence of water and solute, and to unveil the very reach phenomenology of the structure and dynamics of hydration water. Mono and disaccharides that have been studied up to now by EDLS have shown a relatively small effect upon surrounding water, as about 3.3 water molecules per hydroxyl group are retarded in their translational diffusion with respect to bulk water, with a retardation factor ξ ranging from 5 to 6.13–17 A considerable change in water perturbation has been found when passing from carbohydrates to peptides, aminoacids, and protein, where retardation factors up to ξ = 8 extending up to three or more water shells have been found by EDLS.12 Noticeably, the molecular weight of peptides and aminoacids is comparable or even smaller than that of monosaccharides, so that a greater perturbation cannot be trivially attributed to a larger volume. From a different perspective, one could argue that the mono and disaccharides studied up to now are “anomalous” in inducing a so small perturbation

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FIG. 1. 1,6-Anhydro-β-D-glucopyranose (left) and D-glucose (right).

to surrounding water, possibly due to the “mimetic” ability of hydroxyl groups within the water H-bond network. In fact, these molecules, intensively studied as models of hydrophilic hydration and for their cryoprotective attitude,9, 10, 18–22 can be considered as peculiar solutes due to the almost uniform distribution of hydroxyl groups on their surface, suggesting that each molecule can easily settle down into the H-bond network so that the perturbation of surrounding water is limited to the nearest neighbors. On the other hand, recent MD simulations have suggested that energetic interactions between solute and water molecules, like H-bonds, are the most effective source of perturbation of water dynamics, and the absence of such specific sites of interaction should give a negligible dynamic perturbation of interfacial water.23 From this perspective, conventional sugar molecules, like glucose, sucrose, etc., with their abundance of hydroxyl groups, should be the ideal candidate for the strongest dynamic perturbation of hydration water. Water-levoglucosan (1,6-Anhydro-β-D-glucopyranose) (LG) solutions are here investigated to assess the effect of the presence and distribution of hydroxyl groups on the dynamics of hydration water. In fact, LG structure is different from that of glucose in that the hydroxymethyl group is blocked, forming an anhydro bridge between 1 and 6 carbon atoms (Fig. 1). This small structural change reduces from five to three the number of hydroxyl groups, and this should be reflected in a drastic reduction in the ability to participate in the H-bond network. The main purpose of this work is to critically test whether the reduction of hydroxyl groups in contact with surrounding water is responsible for a reduction of dynamic perturbation of water, or the alternation between hydrophilic and hydrophobic areas, mimicking the complexity of peptides and amino acids, gives rise to an increase of the perturbation of surrounding water.12 Moreover, understanding the mutual interaction of levoglucosan with water is per se interesting due to its potential as preserving agent. In fact, it has been shown that the long term stability of protein embedded in sugarglasses strongly correlates with the depression or slowing down of high frequency secondary relaxations,24 since these motions couple to the conformational flexibility of proteins and to the transport of small-molecules, such as oxygen and water. Given that the fast (γ )-relaxation process in carbohydrates is due to the rotation of the hydroxymethyl group,25 which is completely suppressed in LG, this sugar is actually an optimal candidate to improve food protection and to stabilize amorphous drugs. EDLS measurements in water-LG solutions are here reported at different concentrations and temperatures, allowing us to analyze the dynamics of the solution at different time scales, ranging from that of the rotational diffusion of solute (few GHz) to that of the translational dynamics of hydration

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and bulk water (tens and hundreds of GHz), up to the characteristic stretching and bending vibrational modes of H-bonds (some THz). The results will be compared with those previously obtained by the same technique on mono and disaccharides, in order to investigate the effect of the reduction of hydroxyl groups on the number of perturbed water molecules and on their relaxation time. II. EXPERIMENT

EDLS experiments were carried out on water-LG mixtures, by varying the concentration of sugar, up to 300 mg of solute per ml of solvent (300 mgLG /mlH2O ), and by varying the temperature in the range 15–55 ◦ C at the fixed concentration of 100 mgLG /mlH2O . LG was purchased by SigmaAldrich with purity 99% and dissolved without further purification into doubly distilled deionized water. Freshly prepared solutions were directly filtered, through filters with a 0.2 μm pore size, into the optical quartz cell. Depolarized (IVH ) light scattering spectra were acquired in the range between 0.3 GHz and 30 THz by means of two different spectrometers: a Sandercock-type (3 + 3)-pass tandem Fabry– Perot interferometer26 in the range 0.3–200 GHz, and an ISA Jobin–Yvon model U1000 double monochromator in the range 3 GHz–30 THz. More details on the experimental setup can be found in Ref. 27. The imaginary part of the susceptibility spectrum χ (ν) was calculated as the ratio between IV H (ν) and [n(ν) + 1], where n(ν) = exp[(hν/kB T ) − 1]−1 is the Bose–Einstein occupation number. III. RESULTS AND DISCUSSION

The susceptibility spectra of our samples at different solute concentrations are reported in Fig. 2(a) and those at different temperatures in Fig. 2(b). The depolarized spectrum of pure water is characterized by three resonant peaks, assigned to intermolecular Raman modes, namely, H-bond bending mode (O · · · O · · · O unit) at about 1.5 THz and Hbond stretching mode (O · · · O unit) at about 5.1 THz,28 and to a large librational feature in the 10–30 THz region. In addition, the low frequency shoulder of the spectrum has been assigned to the structural relaxation of water.29 It has been shown30 that the major contribution to the scattering in this region comes from dipole-induced dipole (DID) effects, indicating that the dynamics of water polarizability is dominated by the translational dynamics, which is known to be strongly affected by the relaxation of the H-bond network.30, 31 This has been also confirmed upon mixing water with carbohydrates.14 Fig. 2 shows that both addition of LG and change of temperature are responsible for considerable variations of the spectrum, especially in the low frequency side. To better emphasize this effect, we also report the solvent-free (SF) spectra, obtained by subtraction of the pure water signal normalized at the librational band. In fact, two features clearly emerge, similar to those previously observed in different carbohydrates: one around 10 GHz, which can be assigned to the rotation of LG molecules,32, 33 and another one around 100 GHz, attributed to water molecules whose translational motion is retarded with respect to bulk water.34 The amplitude


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FIG. 2. Depolarized light scattering susceptibility (solid circles) of waterLG solutions at different concentrations (a) and temperatures (b). The solid lines represent solvent-free spectra, obtained by subtraction of the pure water signal. The region around 10 GHz has been intentionally cut away from the depolarized spectra since it contains a spurious contribution arising from longitudinal phonons, whose strong polarized signal is not completely extinguished by the analyzer.

of both features increases with increasing LG concentration, though the one related to hydration water grows more slowly than that related to LG rotation (Fig. 2(a)), suggesting that the number of retarded water molecules for each solute molecule decreases at increasing concentration. SF spectra are also reported at two different temperatures, namely, T = 25 and 35 ◦ C, in Fig. 2(b). Also in this case, SF spectra clearly show a strong low frequency contribution arising from both rotation of LG molecules and retarded hydration water. The ratio of the amplitudes does not appreciably change with temperature, suggesting an almost T-independent hydration number, similar to that already observed in different solutions.15 Concerning the resonant modes in the THz region of the spectrum, Figs. 2(a) and 2(b) show that the bending mode is almost not affected by both sugar concentration and temperature. Previous low frequency Raman investigation on pure supercooled water35 had, indeed, shown that the bending mode is almost insensitive to changes in temperature. This is the reason why this peak is frequently used as a reference to nor-

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malize Raman spectra,27 especially in those cases where the librational mode is strongly perturbed by the Raman-active modes of the solute. Conversely, it can be seen that the addition of sugar and change of temperature are responsible for remarkable changes in the spectral region of the H-bond stretching. This mode can be regarded as collective in nature, involving small groups of tetra-coordinated water molecules whose motion is mutually correlated.35 Following this idea, the reduction of intensity when increasing either temperature or sugar concentration can be explained as a decrease of tetrahedral coordination of the H-bond network of water. This destructuring effect induced by LG on water network is in line with other molecular dynamics and experimental results obtained in different water-sugar solutions (see, e.g., Refs. 19, 27, and 36–38). It is also worth noting that a further Raman peak was identified at about 7 THz by previous depolarized Raman measurements of liquid and supercooled water.35 This feature is not visible in our spectra since its intensity is negligible above room temperature, but it increases by almost an order of magnitude as temperature decreases from 40 to −20 ◦ C. A comparison between our results and recent Optical Kerr Effect (OKE) measurements of supercooled water39 is due. In that work, the mode at about 5.1 THz was attributed to low density (LD) water characterized by a tetrahedral network of four-coordinated molecules, similar to the low density amorphous structure of water, and the mode at about 7 THz to high density (HD) water characterized by closely packed aggregates with lower coordination and high network distortions, similar to high density amorphous water. A modecoupling analysis of OKE spectra suggested the HD water to be coupled to the structural relaxation, while the LD water to form small aggregates, negligibly coupled to the structural relaxation. In this frame, the destructuring effect of levoglucosan documented by our spectra, i.e., the marked minimum in the SF spectra of Figs. 2(a) and 2(b), may correspond to a decrease of LD small aggregates in the region of interfacial water. To gain a more quantitative insight into the dynamic properties of hydration water and of the solute molecules, the susceptibility spectra have been fitted by the addition of five components, namely, a Debye function for the rotational diffusion of LG, two Cole Davidson (CD) functions for hydration and bulk water, and two damped harmonic oscillators (DHO) for the bending and stretching modes χ (ω) = I m −

slow − 1 + iωτ [1 + iωτslow ]βslow

b ωb2 f ast + [1 + iωτf ast ]βf ast ω2 − ωb2 − iω b s ωs2 , + 2 ω − ωs2 − iω s −

(1)

where , τ , slow , τ slow , β slow and fast , τ fast , β fast are the amplitudes, characteristic times, and shape parameters of the sugar relaxation term and of the two relaxation processes of water, respectively. ωb , b , ωs , and s are the frequencies


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cal point of view, a slightly stretched relaxation modeled by, e.g., a Cole-Cole function would improve the quality of the fit, without significantly changing the characteristic relaxation time. We thus prefer to use the simplest Debye model for this rotational diffusion contribution, which can be more straightforwardly interpreted in terms of the Debye-Stokes-Einstein diffusion model. The results of the fitting procedure are reported in Table I and discussed in the following, focusing on the dynamics of hydration and bulk water and on the rotational diffusion of LG.

A. Hydration and bulk water

The Arrhenius plot in Figure 4(a) shows the temperature dependence of the average relaxation time of bulk and hydration water, obtained from the CD relaxation parameters by the relation τ = βτ . A very good agreement can be noticed between the relaxation time of bulk water (τ fast ) and that of pure water, which substantiates the adopted analysis and the proposed dynamical scenario in terms of two water components. The relaxation time of hydration water (τ slow ) is well discriminated from that of bulk water in the whole temperature range, and the Arrhenius fit of the two series of data gives an activation energy of 15.8 ± 1.5 kJ/mol for bulk water, and 16 ± 3 kJ/mol for hydration water. The relaxation time of the solute, reported in the same figure for comparison, can be also modeled by an Arrhenius behavior with an apparent activation energy of 17.7 ± 0.5 kJ/mol. This suggests a reasonable correlation of the rotational diffusion of LG with the viscosity of water that will be discussed below in more details. The values here reported for the activation energy of both bulk and hydration water are very close to those obtained for the fast density fluctuations, associated with the H-bond rearrangements of the water network.27, 42, 43 This supports the idea that the polarizability fluctuations here revealed are dominated by density fluctuations. The obtained similar activation energies for hydration and bulk water are synonymous of a retardation ratio ξ = τ slow /τ fast that is quite constant in temperature, as reported

FIG. 3. Susceptibility of the 100 mgLG /mlH2O water-LG solution at 35 ◦ C. The total fit curve (red line) is shown, together with the single components: rotational diffusion of LG (orange), relaxation of hydration (blue) and bulk water (cyan), bending and stretching resonant modes of water (full lines).

and the widths of the intermolecular bending and stretching modes of water, respectively. It is worth noting that the use of a stretched exponential (a CD in the frequency domain) for the relaxation of anisotropy fluctuations of water is well documented in the literature.29, 39, 40 Here, to reduce the number of free fitting parameters, β slow and β fast are fixed to 0.6, the value obtained in pure water.16, 27 Concerning the stretching mode, we use a single DHO function since the mode at 7 THz cannot be disentangled from that at 5 THz at the relatively high temperatures and with the signal to noise ratio of our experiments. The fitting curve obtained by this procedure in a single representative spectrum is reported in Fig. 3, together with the five distinct contributions. The residuals, also reported in Fig. 3, show a very small extra contribution in the sub-GHz region of the spectrum. This phenomenon may be attributed to a distribution in the size of solute particles, possibly induced by aggregation phenomena, as discussed in the following. From a phenomenologi-

TABLE I. Relaxation parameters obtained by fitting Eq. (1) to the experimental spectra of Fig. 2(a) and of Fig. 2(b). (a) mgLG /mlH2O 50 100 200 300 T (◦ C) 15 25 35 45 55

Molar ratio, f

τ (ps)

slow

τ slow (ns)

fast

τ fast (ns)

0.00556 0.01111 0.02223 0.03334

0.029 ± 0.001 0.065 ± 0.001 0.104 ± 0.001 0.144 ± 0.001

19.4 ± 0.6 19.9 ± 0.4 21.9 ± 0.3 23.1 ± 0.3

0.033 ± 0.004 0.071 ± 0.008 0.088 ± 0.005 0.101 ± 0.005

3.2 ± 0.5 2.9 ± 0.3 3.6 ± 0.2 3.6 ± 0.2

0.220 ± 0.004 0.219 ± 0.007 0.195 ± 0.004 0.177 ± 0.004

0.80 ± 0.02 0.80 ± 0.04 0.85 ± 0.03 0.89 ± 0.04

0.073 ± 0.002 0.073 ± 0.001 0.065 ± 0.001 0.0664 ± 0.0008 0.0627 ± 0.0008

τ (ps) 32 ± 1 25.6 ± 0.5 19.9 ± 0.4 15.8 ± 0.2 13.3 ± 0.2

τ slow (ns) 4±1 3.3 ± 0.3 2.9 ± 0.3 2.3 ± 0.2 1.9 ± 0.2

fast 0.19 ± 0.02 0.221 ± 0.007 0.219 ± 0.007 0.213 ± 0.006 0.205 ± 0.007

τ fast (ns) 1.3 ± 0.1 0.94 ± 0.04 0.80 ± 0.04 0.66 ± 0.03 0.53 ± 0.03

(b) slow 0.06 ± 0.02 0.070 ± 0.009 0.071 ± 0.008 0.067 ± 0.009 0.068 ± 0.009


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FIG. 4. Average relaxation time of bulk (τ fast ) and hydration (τ slow ) water and of LG rotation obtained by fitting Eq. (1) to the spectra of Fig. 2(a) at different temperatures at 100 mgLG /mlH2O (a) and to the spectra of Fig. 2(b) at different LG concentrations at T = 35 ◦ C (b). Solid lines represent Arrhenius fit curves. In panel (b), the solid line represents the Arrhenius behavior, where the logarithm of the relaxation time is proportional to the solute molar fraction;41 68% confidence bands are indicated with dashed lines.

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The values of ξ here obtained in water-LG mixtures are significantly lower than those previously found in watermono and di-saccharides solutions,12 typically ranging between 5 and 6, and closer to those obtained by EDLS and Brillouin spectroscopy in solutions of small hydrophobic molecules,12, 44, 45 which typically range between 2 and 5. In our opinion, this is due to the reduction of hydroxyl groups of LG with respect to glucose. We must recall that our technique gives the sum of all the contributions to anisotropic polarizability coming from the whole scattering volume. It is thus reasonable to infer that the CD function used to model the slow relaxation component is receiving the contributions from water molecules facing both sides of the LG solute, i.e., the one closer to the hydroxyl groups and the other one closer to the anhydro bridge. This suggests that water around the anhydro bridge is faster than that around hydroxyl groups, with a relaxation time close to that obtained around small hydrophobic molecules. The reduced value for the retardation ratio is not the only difference between LG and glucose aqueous solutions. A noticeable increase of the hydration number is also found, possibly related to the reduction in the number of hydroxyl groups. In fact, starting from the amplitudes (slow and fast ) of the water relaxation functions, we calculated the number of perturbed water molecules and found that it is much higher than that obtained in water-glucose mixtures. According to the procedure discussed in previous papers,34 the average number of water molecules dynamically perturbed by a single LG molecule is evaluated by the relationship −1 −1 Nh = slow slow + f ast f where f is the mole ratio of LG. The values of Nh obtained by this procedure are reported in Figs. 6(a) and 6(b), showing a temperature

in Figure 5. In the same figure, the values of the retardation ratio obtained at different solute concentrations are also reported showing, again, an almost constant behavior. The average value for the retardation factor is ξ = 3.7±0.3.

FIG. 5. Retardation ratio of hydration to bulk water, as a function of temperature at 100 mgLG /mlH2O (solid symbols) and as a function of solute mole ratio at T = 35 ◦ C (open symbols).

FIG. 6. Average number of retarded water molecules for each LG molecule, Nh , as a function of molar ratio at T = 35 ◦ C (a) and as a function of temperature at 100 mgLG /mlH2O (b). In panel (a), the analytical (solid line) and the numerical (dashed line) predictions from the water-sharing model for noninteracting molecules44 are also reported.


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independent behavior and an appreciable decrease with increasing LG concentration. The adopted procedure to estimate Nh relies upon the assumption that the cross-section of hydration water is not significantly different from that of bulk water. In support of this hypothesis, we note that the sum of the values of slow and fast in Table I remains constant within the experimental error, in the whole investigated concentration range. A remarkable result of the present work is the relatively high hydration number obtained for very diluted solutions, namely, Nh0 ≈ 24. From this result, it is quite evident that the scaling law we found in mono and disaccharides,13 corresponding to an average value of 3.3 perturbed water molecules for each hydroxyl group, does not apply to LG. In fact, despite the lower number of hydroxyl groups, LG perturbs more water molecules than glucose (16) and fructose (15), the hydration number being closer to that found in trehalose (25), and sucrose (27).12 In the ideal case of absence of aggregation between solute molecules, the moderate reduction of Nh for increasing solute molar ratio can be understood, at least for the two lowest concentrations, in terms of water-sharing between solute molecules, i.e., of a finite probability of overlapping of the hydration shells of close-to-contact molecules.46 In the simplest case each solute can be modeled as a sphere of radius c, and the hydration water within a spherical shell of external radius a corresponds to a maximum hydration number Nh0 = 4/3π (a 3 − c3 )ρH , where ρ H is the number density of water. In diluted solutions, under the simple assumption of dominant two-body effects, the overlapping of hydration shells gives rise to a reduction of the average hydration number Nh according to the relationship Nh (f ) = Nh0 −

f , 1 + nf

(2)

where = 8/9ρH2 π 2 (a 6 − 8a 3 c3 + 9a 2 c4 − 2c6 ), and n = 4/3π ρ H c3 . The radius of the solute can be estimated from, e.g., the rotational relaxation time obtained from the low frequency part of our EDLS spectra, as explained in the next paragraph, or from the van der Waals volume. Moreover, the radius a can be deduced from Nh0 = 24, i.e., from the extrapolation at f → 0 of Nh (f). Accordingly, the LG molecule has been modeled as a sphere of radius c = 2.97 Å, with a hydration shell of radius a = 5.82 Å. All the parameters entering in Eq. (2) are thus fixed, and the corresponding dependence on mole ratio of the average hydration number is reported in Fig. 6(a) as a continuous line. It is interesting to notice that the curve in Fig. 6(a) is consistent only with the experimental data obtained at the two lowest concentrations. By increasing the solute concentration, a steeper decrease of the experimental values of Nh with respect to those expected from the simple water-sharing model occurs. This deviation from the ideal behavior plays in favor of an aggregation process occurring in the solution. Our data cannot reveal the details of the aggregation process, and a structural characterization by means of scattering

FIG. 7. Schematic model of spherical solute molecules of radius c, surrounded by hydration shells of external radius a, which aggregate by sharing hydration water only between pairs (two-body approximation).

techniques or MD simulations is required to go into the details of the molecular landscape of these solutions. Nevertheless, we can use the departure of Nh (f) from the ideal trend (Fig. 6(a)) to infer some order of magnitude of the clustering process. To this aim, first we evaluate the reduction of Nh with respect to the condition of infinite dilution, expected in the ideal case of complete “dimerization” of the solute molecules. If each solute is in-contact to another to form a pair, it loses a definite portion of its hydration shell, corresponding to a reduction in the number of hydration water molecules given by pair Nh = ρH π/3(2a 3 − 3a 2 c + c3 ). From this and from the pair values of a and c reported above, an expected Nh = 4.2 is found, which is not enough to explain the effect observed in Fig. 6(a). By focusing on the solution at f = 0.022, a value of Nh ≈ 7÷8 can be inferred from Fig. 6(a), suggesting the occurrence of large aggregates among solute molecules. The simplest model to rationalize this effect is depicted in Fig. 7, where clusters are made of n solutes with only pairwise contacts between molecules sharing hydration water, no superposition of three or more hydration shells (two-body approximation) and no closed loops. In this picture, the total number of missed hydration water molecules is the sum of those shared by each pair, giving Nh = 2 (n − 1) /n × pair Nh . Using this relationship, we deduce that the case Nh ≈ 7÷8 can be realized by clusters of n ≈ 10÷20 molecules. This value has to be considered as a rough estimate since, with increasing n, contacts of order higher than two among solute molecules become more and more important. Among others, these higher order effects allow us to escape from the unrealistic limit imposed by pair = 8.4 for the two-body approximation Nh = 2 × Nh n → ∞. To conclude this part of the analysis, we have to recognize that the most probable scenario produced by the aggregation of LG molecules is a distribution of cluster sizes, whose detail should be investigated by diffraction or numerical methods. Nevertheless, the analysis of our results gives a non-trivial suggestion: the cluster size distribution extends up to quite large values, including at least some tens of LG molecules.


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B. Solute rotation

The relaxation peak at about 10 GHz in our solutions is attributed to the rotational diffusion of LG molecules, in analogy with what we previously found in water-glucose32 and water-trehalose33 solutions. To correctly interpret EDLS spectra, we must remind that the technique reveals the collective reorientational relaxation and that only in the limit of very diluted solutions the maximum of the susceptibility gives the single particle correlation time.47 As a consequence, only in the very low concentration range, where the aggregation process is also negligible, the measured relaxation time can be described in terms of the Stokes–Einstein–Debye (SED) equation, which relates the single particle correlation time to the dimension of the solute and to the viscosity of the solution τs = Vh η/ (kB T ) ,

(3)

where Vh is the hydrodynamic volume and η is the shear viscosity of the solution. To test the validity of Eq. (3) in our system, we have measured the shear viscosity of the 100 mgLG /mlH2O solution at the same temperatures as EDLS spectra. The values of η, reported in Fig. 8(a), have been used to draw the SED plot of Fig. 8(b). The linear behavior in Fig. 8(b) proves the validity of the SED relationship [Eq. (3)] for the rotational diffusion of LG molecules in water. The slope gives an estimate of the

FIG. 8. (a) Shear viscosity η of the 100 mgLG /mlH2O water-LG solution as a function of temperature. (b) Rotational relaxation time of LG molecules in the 100 mgLG /mlH2O solution as a function of η/T. The solid line represents the best fit with Eq. (3).

FIG. 9. (a) Shear viscosity η of water-LG solutions as a function of the mole ratio f, at T = 35 ◦ C. (b) Hydrodynamic volume of LG molecules obtained by using Eq. (3), as a function of f.

hydrodynamic volume Vh = 99 ± 3 Å3 . Although this is a reasonable value, we cannot exclude the presence of residual static and dynamic correlations among LG molecules in the 100 mgLG /mlH2O solution, that would slightly affect the estimate of Vh . To check this effect, the viscosity of all the solutions has been measured at T = 35 ◦ C and used to calculate the nominal value of the hydrodynamic volume at each concentration. The shear viscosity (Fig. 9(a)) is found to increase exponentially with solute concentration, as originally reported by Arrhenius for a number of different solutions.41 We recently found a similar behavior also in case of glucose and trehalose aqueous solutions.33 Here, the values of η(f) have been used to calculate, by means of Eq. (3), the nominal values of Vh reported in Fig. 9(b). We notice that the extrapolation of Vh for f → 0 gives an estimate for the hydrodynamic volume Vh = 109±3 Å3 , which is more reliable than previously obtained at 100 mgLG /mlH2O . This value compares reasonably well with the van der Waals volume of ≈120 Å3 . The trend of Vh vs. f in Fig. 9(b) is, in some way, counterintuitive, and deserves a comment. In fact, the nominal value of Vh decreases with increasing f, which seems to be in contrast with the strong tendency to aggregate previously demonstrated at the two highest concentrations (Fig. 6(a)). In order to reconcile these results, we recall that a reduction of Vh with f can be attributed to an increase of the intermolecular correlation, similar to what we found in water-glucose solutions.32 This interpretation is corroborated by the increase


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in the amplitude of the rotational relaxation – in Table I – that is not proportional to the solute concentration, consistent with the presence of a negative static orientational correlation. The aggregation of LG molecules, similarly to trehalose and fructose,48–50 is expected to be of dynamic nature, being governed by H-bonds that are continuously broken and reformed on a time scale of the order of 10 ps, i.e. faster than the rotational correlation time of single sugar molecules. Therefore, despite a strong tendency to self-associate in aqueous solution, leading to concentration-dependent clusters, one can expect that the clustering process affects the rotational diffusion mainly by increasing the inter-molecular interaction, i.e., by increasing the viscosity and by modulating the values of the correlation parameters, which can justify the observed reduction of Vh . Specific MD simulations of water-LG solutions are required to go deeper into the details of the size distribution and lifetime of these clusters. In fact, a slightly longer lifetime with respect to other carbohydrates might be responsible in the EDLS spectrum of LG solutions for the slight increase of intensity at low frequency, which can be here glimpsed in the residuals of Fig. 3 and that becomes more and more important for increasing LG concentrations.

IV. CONCLUSIONS

The presence in the structure of the anhydro bridge considerably affects the hydration properties of LG with respect to those revealed by EDLS in mono and disaccharides. In particular, the average number of retarded water molecules is 24, almost double that found in water-glucose mixtures and close to that previously found in trehalose and sucrose.12 The average retardation factor is lower than that induced by glucose, suggesting a stronger dynamical perturbation close to hydroxyl groups, where H-bonds are formed between solute and solvent, and a weaker effect where hydroxyl groups are absent.51 Concerning the main question motivating this work, i.e., whether the reduction of hydroxyl groups in contact with surrounding water is responsible for a reduction or an increase of the dynamic perturbation of water, we can say that the magnitude (ξ ≈ 3–4) is indeed reduced, but the number of perturbed water molecules is considerably increased. To this respect, it seems that the attitude of sugar molecules to form Hbonds with surrounding water through hydroxyl groups drastically reduces the spatial extent of the perturbation produced on the H-bond network. These results reinforce the notion that mono and disaccharides with a uniform distribution of hydroxyl groups on their surface induce a peculiarly small perturbation on surrounding water, thanks to a “mimetic” attitude of hydroxyl groups within the water H-bond network. On the other hand, the presence of hydrophilic and hydrophobic areas on the surface of LG molecules is not able to mimic the complexity of peptides and amino acids, where considerably higher values of dynamical retardation (ξ ≈ 7–8) and hydration numbers (50–60 and more) have been found.12 The reason for this large gap is still a challenge, claiming for a convincing basic explanation.

J. Chem. Phys. 140, 184505 (2014)

ACKNOWLEDGMENTS

S.C. acknowledges support from MIUR-PRIN (Project No. 2012J8X57P). M.P. acknowledges support from MIURPRIN 2010-2011. 1 P.

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