Experimental (FTIR, BDS) and theoretical analysis of mutarotation kinetics of D-fructose mixed with different alcohols in the supercooled region

Abstract

The mutarotation kinetics of pure molten D-fructose and its binary mixture with alcohols (i.e., sorbitol and maltitol) have been reported using Fourier Transform Infrared (FTIR), Broadband Dielectric Spectroscopy (BDS) and Density Functional Theory (DFT) calculations. The time evolution of the integrated intensity and structural relaxation time acts as a suitable dynamical observable to monitor the progress of the reaction in FTIR and BDS, respectively, leading to the construction of kinetic curves for the process. The bands at 776 cm⁻¹ (ν_β) and 990 cm⁻¹ (ν_α) indicate the respective vibrations originating from the β and α-isomers of D-fructose. The rate constants estimated from FTIR, (k_IR) are shorter than those obtained from BDS, (k_BDS) studies and the activation energies determined from both spectroscopies differ by more than 30 kJ mol⁻¹. This is interpreted in the context of specific reaction pathways that contribute to the rate constants and drive mutarotation. Additionally, it is found that the rate of mutarotation depends on the system studied i.e., in binary mixtures consisting of sorbitol and D-fructose it becomes faster, while in solid dispersion with maltitol it gets slower. This fact can be explained by taking into account the viscosity of the system. In addition, natural bond orbital (NBO) calculations and an electrostatic potential surface (EPS) analysis were carried out to gain insight into the atomic charge distribution and description of the possible interactions between D-fructose and alcohol molecules. We note that there are some differences between both systems under examination in the strength of H-bonds. However, the impact of these interactions on the progress on mutarotation is not as significant as viscosity.

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Introduction

Mutarotation is one of the most fundamental bio-chemical reactions in the reduction of saccharides. It was first witnessed by Dubrunfaut in 1846.¹ Saccharides comprise a unique class of organic compounds that offer potential applications in the fields of pharmaceuticals and food industries.² Dissolved or melted crystalline saccharides can attain different configurations i.e., α,β-furanose, -pyranose and linear forms. The reversible inter-conversion of rings is translated into a systematic temporal evolution of macroscopic dipole moments, dielectric relaxation times, conductivity, viscosity and specific optical rotations in the system until thermodynamic equilibrium is reached. Moreover, the analysis of these dynamical observables provides a quantitative description of the reaction. In addition, the reaction kinetics and the populations of the tautomers are governed by external thermodynamically intensive parameters (temperature, pressure) and the nature of the solvent.³ Furthermore, the mechanism of this reaction has also been discussed as an acid- or base-mediated process.⁴ In the linear structure, there is a carbonyl group that is converted into the hydroxyl substituent when the ring is formed. The carbon atom from the carbonyl group becomes chiral when the ring is closing and it is called an anomeric center. The mutarotation mechanism is connected to the proton transfer (intra- and intermolecular) between the hydroxyl group attached to the anomeric carbon and the oxygen from the ring.⁵ Nevertheless, the fundamental mechanism of this specific chemical conversion in the supercooled state is a matter of attention and debate. Thus, a combination of experimental and theoretical work is anticipated to provide a possible resolution of the mutarotation mechanism in a supercooled state. The study of mutarotation in pure saccharides offers a unique opportunity to gain a deeper understanding of the intrinsic reaction mechanism because it excludes the role of solvent. Moreover, studying the aspects of mutarotation in binary mixtures of saccharides with alcohols will also deliver a suitable potential connection between reaction rate, viscosity and H-bond networks.

This reaction has mainly been investigated in aqueous,⁶ methanol,⁷ ethanol,⁸ benzamidine,⁹ benzene solutions¹⁰ etc. Due to the characteristic variation in specific optical rotation,¹¹ polarimetry has been considered the most important tool with which to probe this process.¹² Nevertheless, several other techniques, such as nuclear magnetic resonance¹³ and liquid chromatography,^14,15 have been applied to study kinetics as well as changes in the populations of a given isomer in different solutions and temperatures.

Again, aside from the examination of this process for saccharides in solution, only a few efforts have been made to study solid state mutarotation.¹⁶ It is important to note that the crystal lattice is the major barrier effectively preventing carbohydrates from mutarotation. Recently, Tombari et al. showed that even during annealing much below melting temperature, crystalline D-fructose undergoes liquefaction.¹⁷ This was explained in the context of mutarotation. Thus, at high temperatures, the energy of the molecules located close to the vacancies triggers the process. Ultimately, more vacancies are formed and propagate through the entire sample. To initiate mutarotation in pure saccharides, the crystalline lattice must be destroyed. Hence, for this purpose different methods such as milling, melting, spraying, and freeze drying can be applied^18,19 and in each case samples with different populations of various isomers are produced.

However, recent experimental and theoretical studies carried out by Wlodarczyk et al. on a series of supercooled saccharides undergoing mutarotation delivered a new set of data that could be useful to understanding the mechanism underlying mutarotation using the BDS technique.^20–23 It is worth noting that the activation barrier for mutarotation differs significantly with respect to the solution. Moreover, the estimated activation energies are low compared to the theoretical computation for the gaseous carbohydrates. Other interesting observations were reported by Dujardin et al.¹⁶ on mutarotation in supercooled and glassy glucose using Raman spectroscopy. They showed an anomaly in thermal evolution of the characteristic time of mutarotation at the calorimetric glass transition temperature. The activation barrier for the mutarotation in the glassy phase was three times higher than in the reaction carried out in the supercooled regime. This indicates that the mechanism for this specific reaction must be different in the supercooled, glassy state and in the solutions. To address this problem, Wlodarczyk et al. proposed a new model involving double proton exchange between two neighboring carbohydrates as an underlying mechanism for mutarotation in the molten supercooled saccharides.⁵ They found very good correspondence between the E_a determined from DFT calculations and the activation barrier estimated from the experimental data. On the other hand, due to the mobility restriction below T_g, internal proton transfer from the hydroxyl group to the oxygen atom in the ring was proposed as an explanation for mutarotation in the glassy state.

In this manuscript, we report systematic experimental work supported by theoretical calculations on mutarotation kinetics in pure molten D-fructose and its binary mixture with two different alcohols: sorbitol and maltitol. The role of viscosity and H-bond networks is considered. Finally, the discrepancy in activation energy obtained from FTIR and BDS methods is debated.

Experimental

Samples

Anhydrous D-fructose, maltitol and sorbitol of purity higher than 99% were supplied by the Aldrich Company. The binary mixtures were prepared in the weight ratio 1 : 1 by dissolving D-fructose in molten alcohol.

BDS

Isothermal time-dependent measurements of the dielectric permittivity, ε*(ω) = ε′(ω) − iε′′(ω), were carried out using a Novo-Control Alpha dielectric spectrometer (Novocontrol Technologies GmbH & Co. KG, Hundsangen, Germany), over a frequency range from 10⁻² to 10⁶ Hz at ambient pressure. Pure D-fructose and solid dispersions of D-fructose with alcohols were placed in a parallel plate cell (diameter, 20 mm; gap, 0.1 mm) immediately after preparation of the amorphous samples. Sample temperatures in the range (308–333 K) were controlled by a Quatro System using a nitrogen gas cryostat. The temperature stability was better than ±0.1 K.

FTIR

Infrared measurements were performed using an Agilent Cary 640 FTIR spectrometer equipped with a standard source and a DTGS Peltier-cooled detector. The spectra were collected using a GladiATR diamond accessory (Pike Technologies) in the 4000–400 cm⁻¹ range. All spectra were accumulated with a spectral resolution of 4 cm⁻¹ and recorded by accumulating 16 scans. The kinetic measurements at various temperatures (308 K, 313 K, 318 K, 323 K, 328 K and 333 K) were performed with temperature stabilization ±0.5 K. A baseline correction was made and water vapor and carbon dioxide were subtracted from each spectrum. Finally, a difference analysis with an A_i/A₀ procedure (A_i – infrared spectra collected at successive time points, i = 1, 2,…, A₀ – the first infrared spectrum) was applied to highlight the changes and to monitor the mutarotation process.

DFT calculations equipped with the electrostatic potential surface and natural bond orbitals analysis

The geometries of the α,β-furanose and -pyranose forms of pure D-fructose and of a binary mixture of D-fructose combined with alcohol were optimized using the B3LYP exchange–correlation functional^24–26 and 6-311++G(2d,2p) basis set.²⁷ The calculations were carried out in the gas phase using density functional theory (DFT)^28–30 and the Gaussian 09 software package.³¹ Vibrational analysis was performed at each stationary point to confirm its identity as an energy minimum. The optimized structures were used as input files to calculate the wave functions with the DIRECT self-consistent field algorithm of Gaussian 09. The molecular electron densities and molecular electrostatic potential surfaces (EPS) of various anomeric forms of pure D-fructose, pure alcohols (maltitol, sorbitol) and binary systems of furanose and pyranose forms of D-fructose with alcohol were determined using the CUBE option implemented in Gaussian 09 and visualized using GaussView 5.0. A color map of the potential surface was chosen to gain maximum contrast for a system of a given net charge. The relative locations of partial positive (blue) and negative (red) charge were found to be independent of the choice of basis set. Finally, a population analysis was performed using natural bond orbital theory at the 6-311++G(2d,2p) level of theory, using the natural bond orbital (NBO) program under the Gaussian 09 program package.^32,33

Results and discussion

The isothermal time evolution of FTIR and dielectric loss spectra of molten pure D-fructose and its binary mixtures with sorbitol and maltitol are illustrated in Fig. 1. It is observed that the recorded spectra undergo permanent change, which includes shifting of the structural process towards lower frequencies (BDS) as well as a change in the integral intensity of some bands (FTIR).

Fig. 1 Left panel: Representative time-dependent infrared spectra measured for pure D-fructose (F_e) as well as for binary systems consisting of D-fructose and maltitol (M + F_e) or sorbitol (S + F_e) obtained at T = 308 K. The blue (M_e) and green (S_e) lines indicate a pure alcohol infrared spectrum as a reference. The lower region (thinner and multicolor lines) depicts difference spectra with respect to the first spectrum. These data refer to the right y-scale. Right panel: Time-dependent dielectric loss spectra for all systems obtained at T = 308 K.

To avoid structural changes occurring during FTIR measurements, the infrared data were magnified and presented in the form of difference spectra i.e., based on the subtraction of an initial FTIR spectrum (FTIR₁ at the beginning of the process) from the next spectra measured after some time (FTIR_i, i = 2, 3, …, n) (see Fig. 1). It was found that the intensities of the bands undergo permanent change as the reactions progress. This indicates that the concentration/population of different isomers in supercooled D-fructose evolve with time. Additionally, the applied approach gives us a unique opportunity to precisely identify the wavenumber range where the changes associated with the mutarotation are most prominent. Significant changes were observed in the low wavenumber range from 700 to 1200 cm⁻¹, where bands originating from furanose and pyranose ring vibrations can be detected.

On the other hand, shifting of the maximum of the structural relaxation towards lower frequencies registered by the BDS method is closely related to the change in viscosity due to the equilibration between different isomers. Since this change is quite significant, it is evident that the glass transition temperatures of the furanose and pyranose moieties are different. Similar observations have been reported recently for other monosaccharides and pharmaceuticals.^21,23,34,35 In addition, we found that the shift in structural relaxation time (τ_α) strongly depends on the sample and type of alcohol. This can be related to the different populations of fructose isomers in binary mixtures.

Analysis of the kinetics of mutarotation with the use of FTIR

The detailed analysis of difference FTIR spectra makes it possible to detect bands of growing (776, 863, 960, 1052, 1080 cm⁻¹) and lowering intensity (832, 930, 990, 1017 cm⁻¹) involved in mutarotation (see Fig. 1). A similar type of analysis was previously performed by Kossack et al. for L-fucose.³⁶ However, it is worth noting that, in contrast to D-fructose, they did not detect any vibrations for which integral intensity decreases, probably due to the high overlap of bands in L-fucose.

To shed more light onto the kinetics or specific pathways of mutarotation in D-fructose and in binary mixtures, DFT calculations were carried out to assign the vibrations of a given isomer to the bands observed in the experimental infrared spectrum. Recently, Kossack et al. have shown that this kind of analysis can be exceptionally important for a better understanding of mutarotation in pure molten saccharide.³⁶ The authors were able to identify two bands in the FTIR spectrum originating from symmetric stretching vibrations occurring within the pyranose ring ∼813 cm⁻¹ (ν_α – alpha form) and ∼860 cm⁻¹ (ν_β – beta form). Following those considerations, the theoretical FTIR spectra computed for each D-fructose isomer are presented together with the experimental ones in Fig. 2. Direct comparisons of those data have enabled precise and proper assignments of the vibrations in D-fructose (see Table 1). Unfortunately, closer analysis of the spectra presented in Fig. 2 has not allowed us to find a single band originating solely from the furanose or pyranose moiety. Almost every band is assigned to the combined vibrations occurring within different isomers. However, despite this we were still able to identify two bands at ∼776 cm⁻¹ (ν_β) and ∼990 cm⁻¹ (ν_α) whose nature can be easily assigned to the symmetric stretching vibrations originating from β and α-isomers of D-fructose, respectively. Interestingly, those two bands do not overlap with those of uncertain assignment. Moreover, their position and intensity in the FTIR spectrum are not affected by the vibrations coming from maltitol or sorbitol. Consequently, by monitoring the changes in ν_β and ν_α band integral intensity we have the opportunity to obtain genuine information about the progress of mutarotation in D-fructose and binary mixtures. It should also be mentioned that an additional very weak intense band at 1740 cm⁻¹, which is assigned to the stretching vibration of the carbonyl moiety of ν(C=O) from the open-chain form of the carbohydrate, has been identified in the FTIR spectrum. The amplitude of this band varied significantly, indicating different populations of the linear form in the studied systems.

Fig. 2 Comparison of experimental FTIR spectrum of supercooled D-fructose in the 1250–700 cm⁻¹ region (black, solid) measured at ambient temperature with theoretical data calculated for α,β-furanose and α,β-pyranose isomers of fructose obtained at DFT/B3LYP/6-311++(d,p) levels of theory.

Table 1 Constant rates (k) of the mutarotation occurring in pure saccharide as well as in binary mixtures with sorbitol and maltitol determined from BDS and FTIR investigations

	Pure D-fructose, k (10^−4 s^−1)	D-Fructose + sorbitol, k (10^−4 s^−1)	D-Fructose + maltitol, k (10^−4 s^−1)
308 K
να	0.79 ± 0.03	0.72 ± 0.04	0.34 ± 0.01
νβ	0.83 ± 0.01	1.25 ± 0.02	0.45 ± 0.01
νlinear	0.94 ± 0.06	1.10 ± 0.07	—
BDS	0.21 ± 0.01	0.57 ± 0.02	0.27 ± 0.01
313 K
να	0.91 ± 0.04	2.59 ± 0.13	0.63 ± 0.03
νβ	1.13 ± 0.03	2.47 ± 0.13	0.87 ± 0.03
νlinear	1.08 ± 0.12	1.91 ± 0.29	—
BDS	0.46 ± 0.09	0.94 ± 0.31	0.64 ± 0.60
318 K
να	1.12 ± 0.20	3.31 ± 0.21	1.14 ± 0.02
νβ	1.68 ± 0.03	3.07 ± 0.13	1.27 ± 0.04
νlinear	1.96 ± 0.16	5.18 ± 0.78	—
BDS	1.12 ± 0.10	1.71 ± 0.45	1.06 ± 0.20
323 K
να	3.93 ± 0.19	6.87 ± 0.37	1.22 ± 0.05
νβ	4.01 ± 0.12	5.85 ± 0.35	1.43 ± 0.03
νlinear	3.35 ± 0.19	5.37 ± 0.98	—
BDS	2.10 ± 0.31	2.57 ± 0.08	1.53 ± 0.11
328 K
να	4.49 ± 0.07	12.80 ± 1.03	3.21 ± 0.13
νβ	4.03 ± 0.04	8.12 ± 0.49	2.62 ± 0.06
νlinear	5.05 ± 0.08	10.40 ± 1.03	—
BDS	2.66 ± 0.46	5.45 ± 0.54	2.43 ± 0.43
333 K
να	8.21 ± 0.44	14.70 ± 0.28	4.75 ± 0.19
νβ	7.73 ± 0.17	13.70 ± 0.62	3.93 ± 0.10
νlinear	6.24 ± 0.49	19.60 ± 2.68	—
BDS	5.72 ± 0.23	8.62 ± 0.24	3.23 ± 0.51

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Next, we applied a deconvolution procedure to separate various bands in the infrared difference spectra for all analyzed systems. The Gaussian–Lorentz fitting function was applied in order to find the integrated absorbance (A), width (FWHM) and spectral position for each band. We note that only the first parameter changed while the others two quantities remained constant, as mutarotation progressed in each studied system. The only exception is the band at ∼1007 cm⁻¹ which moved slightly as the reaction proceeded, just as in the binary mixture consisting of D-fructose with maltitol. Therefore, it is concluded that there is no special impact of alcohol on the vibrations of individual structural subunits occurring within the carbohydrate. Our data have also proved that the main bands previously assigned to α,β-forms of D-fructose derived from an unchanged vibrational energy.

The integral intensities of bands observed at ∼776 cm⁻¹ (ν_β), ∼990 cm⁻¹ (ν_α) and ∼1740 cm⁻¹ (ν_linear) were analyzed to describe the change in population as well as to follow the formation or consumption rate of the corresponding isomers during mutarotation. Herein, we assume that the oscillator strength of individual bands is independent of concentration, local structure and measurement time.

The time-dependences of the integral intensities (I) of the abovementioned infrared bands have been plotted in Fig. 3a. As can be noted, the amplitudes of bands related to the vibrations occurring within the β-form of fructose grow in an exponential manner, and those for α and open-chain forms of fructose decrease in an exponential manner. This simple analysis unambiguously indicated the direction of the mutarotation that seems to rely on the formation of β-forms of fructo-furanose and -pyranose at the expense of α and linear moieties in each investigated sample.

Fig. 3 (a) The kinetic curves obtained after renormalization of the data presented in the insets, showing time evolution of the integral intensities of bands associated with ν_β-ring, ν_α-ring (pure D-fructose, D-fructose + sorbitol, D-fructose + maltitol) and ν_linear (pure D-fructose, D-fructose + sorbitol). Panel (b) summarizes the time evolution of the structural relaxation times (τ_α) measured for each analyzed system. BDS and FTIR data were rescaled according to eqn (1). Red solid lines refer to an exponential fit according to eqn (2) (Table 1).

Furthermore, taking into account the results of fitting infrared data measured upon mutarotation, we were able to elucidate the relative change in the integrated absorbance of analyzed bands. Note that this parameter was defined as A_∞/A₀, using the definition provided by Kossack et al.³⁶ Generally, it was found that A_∞/A₀ determined for vibration related to β-moiety (I_β) increases with temperature by more than several dozen percentage points (it oscillates within the range 30–60%) with the exception of the dispersions consisting of sorbitol and D-fructose where the opposite trend is observed. A similar kind of analysis was also carried out to follow the change in the relative intensity of the band assigned to α-forms as a function of temperature. We observed a decreasing ratio of A_∞/A₀ with temperature for pure D-fructose and the binary system consisting of carbohydrate and alcohols. Interestingly, A_∞/A₀ varied within the range 14–32%. Finally, FTIR spectra allowed us to estimate the relative intensity of the band assigned to vibration of the open-chain form to be around (25 ± 1)% and (6 ± 1)%, respectively, for the pure fructose and the binary mixture composed of sorbitol and carbohydrate at low temperatures. The ratio A_∞/A₀ increased slightly with temperature in both systems. It is important to note that we were not able to follow real absorbance changes of the band detected around 1700 cm⁻¹ in the D-fructose + maltitol solid dispersion due to its very low amplitude. In addition, the results of our analysis differ slightly from the data published previously by Kossack et al. for L-fucose.³⁶ However, this discrepancy can be assigned to a specificity of the mutarotation in the considered systems. Therefore, the change in population of a given isomer due to mutarotation can be quite different, depending on the type of saccharide.

As discussed above, there is a significant change in the A_∞/A₀ ratio for the analyzed band, indicating that the change in population of a given isomer is substantial as composition and temperature are changed. However, it must be stressed that calculations of the real concentration from the analysis of I_α and I_β are hardly possible, since integral intensities are not linearly correlated with the real concentration of the D-fructose isomer due to the explanation provided by Kossack et al.³⁶

The next point of this paper is devoted to an analysis of the kinetic curves presented in Fig. 3a. However, we note that due to different timescales and variation in the integral intensities of the analyzed bands it was impossible to present the whole set of data in one graph. To overcome this problem, eqn (1) has been used to renormalize kinetic data:

where I_p is the initial integral intensity, I_k is the final integral intensity in the equilibrium state. The parameter α can be treated as a degree of reaction conversion.

As mentioned before, the constructed kinetic curves have an exponential character, which means that the consumption or formation of given isomer can be well described by the use of the first-order kinetics. Therefore, all data presented in the upper panels of Fig. 3a has been fitted by eqn (2):

I_x − I = exp(−kt) (2)

It is noted that exponential fits describe experimental data very well, enabling determination of the constant rates (k_{IR,α/β/linear}) for the formation or consumption of a given isomer of D-fructose in pure saccharide and in binary mixtures. We found that for pure carbohydrate the k_IR,β rate is slightly faster than k_IR,α. Interestingly, the difference between both types of k becomes more important with increasing temperature. Here, Kossack et al. illustrated the opposite trend in the rate of formation and consumption of β and α isomers, showing that k_IR,β is much slower than k_IR,α.³⁶ In addition, our data indicated that rates of formation of the β-isomer and consumption of the open-chain form are very close to each other. A similar trend was detected in the binary mixture with maltitol while for sorbitol the constant rate behavior was quite different. In this case, the rate of β-form production at T = 308 K is almost twice (∼1.7) as fast as the consumption of the α-form. As the temperature increases, both k tend to be comparable. Finally, it was also found that the rates determined for β- and linear forms were similar at lower temperature while at higher temperature the difference between them becomes more notable.

Analysis of the kinetics of mutarotation with the use of dielectric spectroscopy

Among several techniques, BDS has emerged successfully as a suitable probe to examine mutarotation kinetics and to explore the step growth polymerization of amino epoxy systems.^37–40 A quantitative description of the progress of a chemical reaction or polymerization can be given by dynamical observables such as segmental relaxation time, dielectric constant, dc conductivity or dielectric permittivity measured in the high-frequency range.³⁸ There are studies that show a very good correlation between dielectric and FTIR or calorimetric kinetic data. Recent studies by Wlodarczyk et al. have shown that, in the case of mutarotation, analysis of the dynamical property of the system expressed by structural relaxation time seems to be the appropriate measure of the progress of this chemical conversion.^21–23 This method was also applied to a study of the tautomerism phenomenon in supercooled drugs.³⁶

In order to apply eqn (1) to dielectric response, the time integral intensity was replaced by the structural relaxation time, τ_α. Dielectric measurements provide information related to the changes in the structural relaxation characteristic time during a reaction. Perturbation in structural relaxation time is associated with change in viscosity. The constructed kinetic curves are shown in the lower panels of Fig. 3b. It can be seen that, except for the lowest temperatures in pure fructose, where the clearly sigmoidal character of the kinetic curves can be noted, data collected for the other systems follow a rather exponential dependence which is consistent with the results obtained from FTIR studies.

However, mainly due to the sigmoidal shape of the kinetic curves constructed for the mutarotation carried out at low temperature in pure D-fructose, an Avrami model⁴¹ has been used, as shown by eqn (3):

α = 1 − exp(−ktⁿ) (3)

where α, k and n denote the dielectric progress of the reaction, k is a constant rate, while n denotes character of the crystallization or chemical reaction. To justify this choice, one can add that this model is quite often used to describe both crystallization and chemical reactions occurring in the solid state.^42,43 The other advantage of the Avrami equation is that it describes sigmoidal kinetic curves. On the other hand, eqn (2) was applied to other samples studied herein. As can be seen in the lower panels in Fig. 3b, both models describe the experimental data very well, enabling calculation of the constant rates which are plotted against reciprocal temperature in Fig. 4a–c.

Fig. 4 Left panels present the log(k) outcomes determined from BDS and FTIR data plotted vs. inverse temperature (a–c). Filled symbols refer to BDS data, open symbols depict FTIR constant rates obtained for various anomeric forms – yellow circles: linear form (1740 cm⁻¹), red triangular: α-fructopyranose (α-form; 990 cm⁻¹), green rectangular: β-fructopyranose (β-form; 776 cm⁻¹). Right panels show temperature dependence of constant rates determined from BDS (d) and FTIR (e) studies. In panel (f) log(k)_IR was plotted vs. log(τ)_BDS. All solid lines represent Arrhenius fits.

Fig. 4d and e depict the constant rates of production or consumption of the α,β-fructopyranose, fructofuranose forms as well as the linear isomer determined from FTIR studies together with those estimated from dielectric considerations for pure fructose and binary mixtures. It is well observed that the rates determined from dielectric studies k_BDS are much slower than k_IR determined for pure carbohydrate (see also Table 1). A similar situation is also observed for the binary mixtures; although the difference in k_BDS and k_IR is not so significant and gets much smaller. The other observation is that the rates evaluated from dielectric and FTIR measurements are very different at low temperatures and tend to be similar in the higher temperature region. This means that the activation barrier for the mutarotation estimated from dielectric and infrared measurements is very different in each sample studied herein. To quantify this observation and to calculate E_a eqn (4) has been used:

where k₀ is a pre-exponential factor, E_a is the activation barrier and R is the gas constant.

As can be seen in Fig. 4 and Table 1, the activation barrier calculated from dielectric measurements is in fact 20–30 kJ mol⁻¹ higher than that determined from FTIR studies. Interestingly, similar results were recently reported by Kossack et al.³⁶ They explain that, while FTIR spectroscopy enables one to monitor different pathways of mutarotation selectively, the shifting of the structural process recorded by BDS is closely related to the equilibration at a mesoscopic length scale due to (i) fluctuation in the concentration of fructose isomers and (ii) equilibration in the hydrogen-bonding pattern and supramolecular structures in the carbohydrate. Consequently, constant rates and activation barriers estimated from dielectric measurements for the mutarotation process can be slightly under- or overestimated. In this context, it is also worth reminding ourselves of numerous studies on step growth polymerization, where a shift in the segmental relaxation process is also observed due to the increasing length scale of the polymer. In this case, τ_α can be also used as an indicator of the progress of the reaction.⁴⁴ However, analysis of this variable may provide slightly faster or slower constant rates than calorimetric or FTIR studies.^39,41

The other very interesting information which one can obtain from Fig. 4 is that the rates and activation barrier estimated for the production or consumption of the α,β fructofuranose, fructopyranose or open-chain isomer are almost the same in pure fructose and binary mixtures (see panel in Fig. 4a–c). Again, the activation barrier for the mutarotation estimated from dielectric and infrared measurements, although different, varies only slightly (within experimental uncertainty) in pure fructose and in binary mixtures. Hence, the addition of sorbitol or maltitol does not change the barrier for the production or consumption of a given isomer.

Finally, the data presented in Fig. 4e and f revealed that addition of sorbitol and maltitol affects the kinetics of the mutarotation in completely different ways. The latter and former alcohol slow down and speed up the pace of the particular interconversion, respectively, at a given temperature. To provide an explanation for this observation, one should remember that the glass transition temperatures of sorbitol (T_g = 263 K)⁴⁵ and maltitol (T_g = 321 K)⁴⁶ differ by almost 60 K. Hence by mixing D-fructose with both alcohols we obtained solid dispersions with completely different viscosities at the same temperature. In fact, the molecular dynamics studies (not shown) showed that the relaxation times of a D-fructose + maltitol binary mixture are significantly slower than those of the pure carbohydrate and a solid dispersion consisting of sorbitol. That simply means that at a given temperature the system composed of D-fructose and maltitol is much more viscous than the others. Here it should be remembered that τ_α can be used as some kind of approximation of viscosity, since these variables are interrelated via the Maxwell relation. To probe the role of viscosity on the progress of mutarotation in the investigated samples, constant rates determined from FTIR spectroscopy are plotted versus log τ_α in Fig. 4f. From the presented dependence it can be easily found that the constant rates start to collapse into one curve. Such a finding is clear evidence that besides temperature viscosity also plays an important role in controlling the mutarotation of D-fructose.

Theoretical calculation: natural bond orbital, electrostatic potential maps analysis

As a final point in our investigations, the impact of alcohol on the mutarotation kinetics of D-fructose through a role in possible intermolecular interactions was considered. For this purpose, the natural bond orbital (NBO) approach was used to determine the atomic distribution charge and stabilization energy, E⁽²⁾, of the binary system (see Fig. 5), whereas the molecular electrostatic surface potential (EPS) was determined to analyze pure compounds (maltitol, sorbitol, furanose, pyranose isomers as a reference) and a system of furanose/pyranose with maltitol/sorbitol (see Fig. 6).

Fig. 5 NBO charge distribution calculated for α,β-furanose and -pyranose isomers of D-fructose as well as for maltitol and sorbitol. Electron donor and acceptor charge values for OH moieties and O-ring within carbohydrate ring are marked on the figure. The NBO data were calculated using DFT/B3LYP/6-311++G(2d,2p) and visualized in GaussView 5.0. In addition, the geometric structures of each molecules are labeled.

Fig. 6 The electrostatic surface potential calculated using DFT/B3LYP/6-311++G(2d,2p) for: single compounds and for binary system consisting of alcohol (maltitol, sorbitol) and furanose or pyranose isomers of pure D-fructose. As an inset, the part associated with the H-bond formation between OH (from alcohol) and a lone pair of oxygen from the carbohydrate ring is magnified. Red refers to a negative charge concentrated on the lone pair of oxygen while blue denotes a positive charge on the hydrogen. The red arrows indicate the CH₂OH group which is a quite effective steric hindrance preventing the formation of a strong H-bond between oxygen in the saccharide ring and alcohol. GaussView 5.0 software was used to visualize the data.

A charge distribution analysis over the atoms was performed to understand the formation of donor and acceptor pairs, especially those involving inter- or intramolecular charge transfer as well as processes of electronegativity equalization.^47,48 Thus, the NBO approach showed that all hydrogen atoms in single D-fructose isomers exhibit positive charge while the oxygen atoms have negative charge. Oxygen in hydroxyl groups has a maximum negative charge value ranging between −0.727 and −0.787 while in an O-ring the negative charge is a little bit lower, with values equal to ∼0.632 in alpha forms and ∼0.633 in beta isomers (see Fig. 5). The maximum positive atomic charge for maltitol is for hydrogen (0.465–0.486) located in OH groups, whereas oxygen with lone electron pairs exhibiting in the hydroxyl moieties has the strongest negative charge, with values from −0.727 to −0.765. Interestingly, the maximum magnitude of charge for sorbitol molecules is localized on hydrogen atoms in the OH groups and is close to 0.467 and 0.483. All the oxygen atoms among the hydroxyl groups exhibit a negative charge from −0.740 to −0.769 at an applied level of theory (see Fig. 5). In consequence, O-ring oxygen and oxygen in OH units play a role as electron acceptors due to presence of lone pairs, while hydrogen from hydroxyl groups might be considered as a electron donors. Moreover, the presence of a large negative charge on an oxygen atom and a net positive charge on hydrogen within the OH groups promotes the development of intermolecular interactions in form of a hydrogen-bonding network (CO–H⋯O–CH) between one of the D-fructose isomers and alcohol.

Hence, to accurately analyze the charge distribution within the investigated binary systems, an electrostatic potential was calculated simply using Coulomb's law. The calculation allowed us to obtain the electrostatic potential at a points (x, y, z) of a molecule which was given by the electrostatic potential energy between an imaginary positively charged (+1) ion located at (x, y, z) and the molecule. Thus, the potential becomes negative when the ion is attracted to the molecule (electron-rich regions) while a positive potential has been observed in case of the ion being repelled by the molecule (electron-deficient regions). Furthermore, calculations of the electrostatic potential at selected points of the iso-density surface allowed us to create color maps of the surface where individual colors refer to different potentials. Hence, red has been assigned to the negative potential and blue to the positive.

The EPS map allowed us to visualize the charged regions of molecules and to determine their molecular properties as well.^49,50 EPS analysis also gives us an opportunity to gain insight into interactions between molecules as well as the changes in an activity within the binary system.^51–53 In this way, the studies of four different combinations of molecular systems consisting of each D-fructose isomer and alcohol could shed more light on the mutarotation process taking place in the supercooled liquid phase of the carbohydrate. Based on the abovementioned scheme, the positive (blue) and negative (red) charges have been found close to hydrogen (donor) and oxygen (acceptor), respectively, similar to the outcome of NBO analysis. It can be seen that due to the linear character and presence of six OH groups attached to the open-chain, sorbitol has quite a good ability to form effective intra- and intermolecular H-bonds. A similar situation is found for maltitol, but due to the presence of linear and saccharide pyranose ring there are 9 × OH groups which provide even greater possibilities for H-bond formation than sorbitol.

Interesting observations were noted when we consider a binary system consisting of a D-fructose isomer and alcohol. Based on these theoretical calculations, in the case of a solid dispersion constructed as a mixture of pyranose isomer with alcohol it was found that the formation of a strong H-bond between an OH group from the alcohol and an oxygen in the saccharide-ring (O-ring) varied from 1.88 Å at a dihedral angle of 168.8⁰ (maltitol) to 1.89 Å at 171.9⁰ (sorbitol) (see Fig. 6). As a consequence, the primarily negative charge concentrated on the carbohydrate O-ring is neutralized by a positive charge coming from an OH group. A completely opposite situation is observed for the furanose moiety. This form is characterized by the presence of two CH₂OH groups located close to the O-ring, preventing the possibility of strong hydrogen-bond formation. In that situation, a moderate H-bond forms from 2.00 Å (160.5⁰) for sorbitol to 2.05 Å (163.0⁰) for maltitol (see Fig. 6). Again, the negative charge located on the O-ring is only partially compensated by the positive charge from a hydrogen atom, and the whole connection is not electrically neutral as it is in the pyranose system. In addition, it is noteworthy that a moderate H-bond does not stabilize furanose isomers as much. Therefore, the inter-conversion pathway from furanose to pyranose during the mutarotation seems to be favored.

Moreover, the NBO approach has been used to consider the possible molecular bonding as well as to estimate stabilization energy (E⁽²⁾) between D-fructose isomer molecules in the presence of alcohol using second-order perturbation theory.⁵⁴ The E⁽²⁾ energy associated with delocalization i → j for each donor (i) and acceptor (j) is defined by eqn (5):

where q_i is the donor orbital occupancy, e_i, e_j are diagonal elements (orbital energies) and F_i,j is the off-diagonal NBO Fock matrix element.

It is worth noting that the large E⁽²⁾ value implies more intensive interaction between electron donors, originating from the greater extent of the whole system conjugation. Thus, the strongest molecular interactions in the systems considered are formed by the orbital overlap between lone pairs on oxygen in OH groups: from the fructose isomer and alcohol (see Table 2 and Fig. 5). At the same time, the presence of lone electrons on the O-ring inside the carbohydrate ring promote hydrogen-bond formation with hydrogen atoms in OH units. The highest values of E⁽²⁾ energies of donor (hydrogen) → acceptor (oxygen) interactions are presented in Table 2. In all systems one can see that the strongest H-bonds are found between oxygen in OH groups in isomer molecules and the given alcohol. Hence, one can find that the E⁽²⁾ values varied in the range 6.7 kJ mol⁻¹ and 17.8 kJ mol⁻¹ for sorbitol whereas for maltitol it changes within the range 6.5 kJ mol⁻¹ to 20.1 kJ mol⁻¹, implying strong stabilization of the system. In addition, confirmation of high system stability found within the C⋯OH group is the maximum occupancy value ED(e) which according to Table 2 suggests the p-character of the hybrid orbitals. The same kind of interaction was calculated for the O-ring oxygen in different isomers and OH group of alcohol. Interestingly, the interaction energy within the CH⋯O unit for sorbitol shows a higher stabilization of 7.8 kJ mol⁻¹ for the pyranose + sorbitol system than for furanose + sorbitol, with an energy equal to 6.8 kJ mol⁻¹. The stabilization energy E⁽²⁾ for the furanose + maltitol system changes from 7.5 to 9.2 kJ mol⁻¹, while for pyranose it varies from 7.4 to 9.7 kJ mol⁻¹. According to Table 2, the maximum occupancy data ED(e) shows the p-character of the hybrid orbitals, similar to sorbitol, indicating high system stability within the CCO⋯HO group. The hydroxyl groups located close to the carbohydrate ring in maltitol tend to form a stronger hydrogen bond with the O-ring oxygen in the pyranose isomer. On the other hand, due to the steric hindrance introduced by the CH₂OH moieties in furanose, the E⁽²⁾ values are lower. As a result, higher system stabilization is expected for maltitol than for systems with sorbitol (see Table 2). Finally, E⁽²⁾ values are in good agreement with the EPS outcomes, indicating higher molecular potential to form stable systems.

Table 2 Second-order perturbation theory analysis of the Fock matrix in NBO basis in binary mixtures of furanose or pyranose forms of D-fructose with sorbitol or maltitol based on the intermolecular H-bonding interaction pattern. The data are presented for the example of the O-ring oxygen (red) as well as the strongest hydrogen-bond interactions (black). LP means a lone pair, BD* is an anti-bonding orbital NBOs in the natural Lewis structure, while ED(e) is ascribed to orbital occupancy (number of electrons). E⁽²⁾ is a stabilization energy, E(j) − E(i) is an energy difference between donor (i) and acceptor (j) NBO orbitals, while F(i,j) stands for the Fock matrix element between i and j NBO

	Donor NBO (i)	Type	ED(e)	Acceptor NBO (j)	Type	ED(e)	E^(2), kJ mol^−1	E(j) − E(i) [a.u.]	F(i,j) [a.u.]
Sorbitol + furanose	O	LP	1.99975	H 96–O 95	BD*	0.03167	6.8	1.08	0.082
	O 15	LP	1.99984	H 91–O 90	BD*	0.02263	6.7	1.01	0.074
	O 15	LP	1.99984	H 87–O 86	BD*	0.04226	11.3	0.9	0.09
Sorbitol + pyranose	O	LP	1.97387	H 83–O 82	BD*	0.03967	7.8	1.05	0.07
	O 21	LP	1.97228	H 72–O 71	BD*	0.04912	17.8	1.01	0.12
Maltitol + furanose	O	LP	1.95207	H 61–O 60	BD*	0.02391	7.5	1.1	0.082
	O	LP	1.96071	H 38–O 37	BD*	0.03936	9.2	0.75	0.037
	O 12	LP	1.95761	H 55–O 54	BD*	0.04438	9.3	0.81	0.078
	O 15	LP	1.96234	H 57–O 56	BD*	0.02525	6.5	1.12	0.076
	O 21	LP	1.9651	H 70–O 69	BD*	0.03917	11.3	0.86	0.089
Maltitol + pyranose	O	LP	1.99974	H 65–O 64	BD*	0.02634	7.4	1.06	0.08
	O	LP	1.95085	H 25–O 24	BD*	0.04098	9.7	0.81	0.08
	O 12	LP	1.96682	H 70–O 69	BD*	0.04871	17.2	0.91	0.112
	O 15	LP	1.96974	H 65–O 64	BD*	0.05573	20.1	0.93	0.123
	O 21	LP	1.97212	H 61–O 60	BD*	0.03597	10.2	0.86	0.084

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Small discrepancies in H-bond strength between the systems with maltitol and sorbitol and similar stabilization energies determined for both binary systems do not allow us to discuss the role of intermolecular interaction on the progress of mutarotation in the systems considered. However, it should be noted that there is another important aspect that cannot be considered by a theoretical approach and this is related to the dynamics of H-bond formation between alcohol and saccharide. One can suppose that the relatively small sorbitol is much more mobile than maltitol; therefore it can more easily form stronger H-bonds with the active center of mutarotation. Consequently, a new direct route for proton transfer to the oxygen in the saccharide ring can be established. On the other hand, maltitol is a larger molecule and its transfer to the O-ring might be much more difficult due to (i) steric hindrance caused by the exocyclic hydroxyl methylene units attached to the saccharide ring and (ii) higher viscosity of the binary mixture consisting of this alcohol at a given temperature. Consequently, besides the viscosity that seems to play a dominant role in controlling the kinetics of mutarotation, the proton transfer triggering this chemical reaction might be reduced, which in turn may lead to further slowing down of this specific chemical reaction.

Conclusion

The kinetics of the mutarotation in pure fructose and its binary mixtures with alcohols has been studied by FTIR, BDS and DFT calculations. The combination of DFT and FTIR approaches enabled us to identify bands related to the vibration of characteristic units in α,β-isomers of D-fructose, and the vibrations of ν(C=O) which are assigned to the presence of linear forms of fructose enables us to monitor the rate of production of α,β-furanose or -pyranose and open-chain ones. Unfortunately, it was impossible to follow the rate of formation or consumption of furanose and pyranose isomers alone. But the alcohols affected the speed of the mutarotation in completely different ways. Our data indicated unambiguously that viscosity seems to play a dominant role in controlling the kinetics of mutarotation. In a less viscous system, reaction proceeds faster. Additionally, NBO outcomes and EPS theoretical considerations have shown that stable molecular systems connected by H-bonds between the D-fructose isomer and both alcohols are formed. However, the theoretical approach showed only a slight difference in strength of interaction between alcohol and active centers of mutarotation located at the oxygen in the saccharide ring. On the other hand, taking into account variation in viscosity, size, mobility and geometry of sorbitol and maltitol, one can suppose that the dynamics of H-bond formation between carbohydrate and alcohol can be quite different for the same thermodynamic conditions. Consequently, proton transfer, which underlies the mechanism of this classical chemical reaction, can be affected in different ways, contributing to the slowing and speeding up of mutarotation.

It is also essential to note that the FTIR technique estimates the rate constant that represents the specific pathways of reaction and examines the local origin. In contrast, the BDS technique/polarimetry determines the rate constant by taking into account all specific paths of reaction, which is an average quantity, and quantifies the global feature. Both methods represent kinetics reaction quantitatively by monitoring explicitly the same dynamical quantity i.e., dipole moment. In the present study, to advance our understanding, the specific and average pathways for the mutarotation reaction have been well compared. The other intriguing but still unresolved question concerns the sigmoidal shape of the kinetic curve constructed from the dielectric data. We expected that it might be due to different timescales of transformation of one isomer into another. However, as revealed by FTIR measurements, the timescales of the various pathways of mutarotation reflected by the constant rate are too close to each other. Therefore, the sigmoidal shape of the kinetic curves presented in Fig. 3 observed by BDS might be related to simultaneous probing equilibration of isomer concentration, together with reorganization of the internal structure and H-bond network. On the other hand, the contribution of some very fast steps, including opening the saccharide ring, cannot be ruled out.

Acknowledgements

K. K. is thankful for the financial support within Sonata Bis project founded by Polish National Science Centre (decision no. DEC-2015/18/E/ST4/00320). A. C. is grateful for the financial support within the Opus program (decision no. DEC-2012/05/B/ST3/02837). This research was supported in part by PL-Grid Infrastructure.

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