Article pubs.acs.org/JPCB
Dielectric Relaxation for Studying Molecular Dynamics of Pullulan in Water Yuki Kishikawa, Yuki Seki, Kou Shingai, Rio Kita,* Naoki Shinyashiki, and Shin Yagihara Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan ABSTRACT: We performed an experiment of broadband dielectric relaxation spectroscopy (BDS) to study the molecular dynamics of an aqueous pullulan solution as a function of pullulan concentration. The frequency range of the BDS experiment is 40 Hz to 50 GHz, and the solution temperature is set at T = 25.0 °C. Two relaxation processes originating from pullulan and water molecules are obtained in the megahertz and gigahertz regions, respectively. Additionally, the electrode polarization and the contribution of dc conductivity are also observed at lower frequencies. The relaxation process at a frequency higher than 10 GHz is associated with the primary process of water (h-process), and that at 100 MHz is attributed to the local chain motion of pullulan (m-process). Impurities in the aqueous solutions, which are practically disregarded in the analysis of polysaccharide solutions, affect the quality of the relaxation spectrum. Thus, the purification of pullulan sample is carried out by methanol precipitation from aqueous pullulan solution. This iterative purification reduces the contributions of electrode polarization and DC conductivity, which enables the clear observation of the relaxation of the m-process. It was found that the relaxation times of the m- and h-processes increase with pullulan concentration. The relaxation strength of the m-process shows increasing behavior with increasing pullulan concentration, whereas the relaxation strength of the h-process decreases with increasing pullulan concentration. It is suggested that the relaxation strength of the mprocess is mainly determined by the magnitude of the dipole moment of solvent molecules. The relaxation process of water (hprocess) is affected by the interactions of pullulan chains. The interdependence between the h- and m-processes is discussed with respect to the findings of recent dielectric relaxation studies on aqueous polymer solutions.
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INTRODUCTION Biopolymers are subjected to water, where molecular interactions among the water and biopolymers play a key role in their structural formation and biological functions. Chemical and physical studies of biopolymer solutions have been carried out extensively with respect to their static and dynamic behavior, which have provided intrinsic information clarifying the properties and biological functions of biopolymers. Broadband dielectric relaxation spectroscopy (BDS) is one of the most powerful methods used to reveal the molecular dynamics of polymers in solvents.1−3 For polymer solutions, molecular motions originating from solvent molecules and polymer chains are observed simultaneously in the dielectric relaxation spectrum at room temperature. It is revealed that the relaxation process of solvents observed at the GHz region is affected by polymer addition, which implies the relaxation parameters such as the relaxation time, the relaxation strength, and the distribution parameter of the relaxation curve provide information about interactions among polymer chains and solvent molecules.3−6 In the megahertz region, the relaxation process due to the motion of polymer chains is observed to also be affected by interactions with solvent molecules.2,3 These facts should be utilized to reveal the interdependence of solute polymers and solvent molecules. Although studies of aqueous solutions of polymers through dielectric relaxation measure© 2013 American Chemical Society
ments have gained the interest of researchers, there are still a limited number of publications on biopolymers in water. Properties of biopolymers are strongly affected by various factors, such as temperature, pH, ionic strength, concentration, and so on. Although BDS is a powerful technique characterizing the molecular dynamics of polymers, experiments and analyses have been hindered by ionic ingredients (impurities) in the sample. For example, the DC conductivity and electrode polarization increase owing to the existence of impurities. Even in the case of that in neutral biopolymers such as polyglucans, impurities give rise to a higher DC conductivity in comparison with synthetic polymer systems. Although there are a limited number of publications on dielectric relaxation measurements for polysaccharide solutions due to the difficulty of BDS measurements previously mentioned, dielectric relaxation studies have been reported for glucans in water.7−11 We selected pullulan as a neutral biopolymer to clarify its molecular dynamics in water-rich concentrations. Pullulan is produced by a fungus and is treated with a pullulan-hydrolyzing enzyme to prepare pullulan samples with different molecular weights. The solution properties of Received: April 12, 2013 Revised: June 22, 2013 Published: July 9, 2013 9034
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pullulan have been well-characterized by various methods,12−18 and pullulan is considered to be a polymer standard for watersoluble polymers. In our preliminary experiments, the procedure used to purify a pullulan sample was found to extensively reduce the DC conductivity. Pullulan is a linear polysaccharide composed of α−(1 → 6) linked maltotriose as the repeating unit, while maltotriose is composed of α−(1 → 4) linked glucose. Although the dielectric relaxation of monosaccharides, oligosaccharides, and polysaccharides in water has been reported,7,19−29 systematic studies to clarify the relaxation processes of both water and polysaccharides have not been reported for a broad concentration range of pullulan in water at room temperature. We report the experimental results of broadband dielectric relaxation in the frequency range of 40 Hz to 50 GHz for a pullulan−water mixture at the temperature T = 25.0 °C. The purification of pullulan by methanol precipitation from an aqueous solution is repeatedly performed. Increasing the number of purifications enables us to study the relaxation process associated with pullulan (m-process). This finding leads us to reveal the interdependence of the molecular dynamics of water (h-process) and pullulan (m-process). Furthermore, the h-process is analyzed using the fractal concept with utilizing the Cole−Cole distribution parameter β, which characterizes the broadness of the relaxation curve.30,31 The m-process is discussed by analogy to the Onsager and Frölich concepts for the relaxation behavior of the dipole moment on polymer chains interacting with the dielectric relaxation of solvent molecules.32
precision impedance analyzer and were calibrated by a similar procedure with the VNA.
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RESULTS AND DISCUSSION Effect of Pullulan Purification on Dielectric Relaxation Spectra. Figure 1 shows dielectric relaxation spectra; the real
Figure 1. Dielectric dispersion and absorption curves for 20 wt % pullulan in water at T = 25.0 °C. As a reference, dielectric relaxation spectrum of water (0 wt % pullulan) is also plotted (blue ○). Symbols refer to the number of purifications for pullulan samples: without purification (purple ●), single purification (red ◇), double purification (orange ▲), and triple purification (green ■).
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EXPERIMENTAL SECTION Materials. Pullulan was obtained from Hayashibara. Deionized water with an electric conductivity lower than 18.3 MΩcm was obtained from an ultrapure water product (Millipore, Milli-Q Lab.). The molecular weight of pullulan was measured in water by static light scattering to be Mw = 440 kg/mol. For dielectric relaxation experiments, pullulan was purified by methanol precipitation from aqueous pullulan solution. The solution (50 mL) of pullulan in water (7.5 wt %) was pored dropwise to 2.0 L of methanol while stirring. The precipitated pullulan was again dissolved in water and freezedried to recover the pullulan as powder. This operation was considered as a single purification, which was repeated for further purification. To examine the effect of purification, we carried out BDS measurements for solutions of pullulan in water (20 wt %) using singly, doubly, and triply purified pullulan samples and an unpurified pullulan sample. To investigate concentration dependence of the relaxation processes, we used triply purified pullulan sample in the concentration range between 0 and 50 wt %. Methods. Dielectric relaxation measurements were performed in the frequency range from 40 to 50 GHz using a vector network analyzer (VNA) (Agilent Technologies N5230C, 10 MHz−50 GHz), an impedance/material analyzer (Hewlett-Packard 4291A, 1 MHz−1.8 GHz), and a precision impedance analyzer (Agilent Technologies 4294A, 40 Hz−110 MHz) at a solution temperature of 25.0 °C. Coaxial-line reflection measurements were carried out with the VNA combined with probes (Agilent 85070E-050, 0.5−50 GHz). The VNA was calibrated using air, mercury, and water or dimethyl sulfoxide as a standard. Coaxial cylindrical cells with a geometrical capacitance of 0.15 pF were used for the measurement using the impedance/material analyzer and the
part ε′ and imaginary part ε″ of the complex permittivity ε* (= ε′ − jε″) are shown as functions of frequency for the solution of 20 wt % pullulan in water at T = 25.0 °C. Symbols indicate the number of purifications for pullulan: without purification (purple ●), single purification (red ◇), double purification (orange ▲), and triple purification (green ■). The spectrum of water is also shown (0 wt % pullulan, blue ○). A relaxation process at a frequency of ∼10 GHz is observed in all samples, and this relaxation process is named the h-process. The intensity of the h-process decreases and the peak position of the imaginary part shifts to a lower frequency with the addition of pullulan to water. In the frequency range of 1 to 100 MHz, a relaxation process at a middle frequency (m-process) is observed in the real part, while no relaxation process is observed at the same frequency for water. Additionally, a large relaxation process at a lower frequency (l-process) is observed.33−36 Insets show the spectra on a double-logarithmic scale where the l-process is realized. It is clearly observed that the l-process shifts to the lower frequency side or the intensity of the l-process decreases with increasing number of purifications. In the imaginary part, the contribution of DC conductivity is significant for the unpurified pullulan sample. The contribution of DC conductivity decreases with increasing number of purifications. These results mean that the amount of impurities in the pullulan samples is reduced by repeated purification, which enables us to analyze the relaxation curve of the m-process with high precision. To characterize the relaxation curve in detail, curve fittings were carried out to obtain dielectric relaxation parameters. The dielectric spectrum of pullulan in water can be described by 9035
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Δε h βh
+ Δεm
∫0
Article ∞⎛
1 + (jωτh) Δε l σ −j exp( −jωt ) dt + βl ε 0ω 1 + (jωτl) β ⎡ ⎛ KWW ⎤ t ⎞ ⎥ ⎟⎟ ,Φm = exp⎢ −⎜⎜ ⎢ ⎝ τm,K ⎠ ⎥ ⎣ ⎦
dΦ ⎞ ⎜− m ⎟ ⎝ dt ⎠
Figure 3 shows the effects of the number of purifications on the relaxation times of the h- (blue ○), m- (red ○), and l- (○)
(1)
Here ω is the angular frequency, t is the time, j is the imaginary unit given by j2 = −1, ε0 is the dielectric constant in vacuum, ε∞ is the limiting high-frequency dielectric constant, Δε is the relaxation strength, τ is the relaxation time, β is the symmetric broadening parameter (0 < β ≤ 1) of the Cole−Cole function,37 βKWW is the asymmetric broadening parameter (0 < βKWW ≤ 1) of the Kohlrausch−Williams−Watts (KWW) function,38 and σ is the DC conductivity. The subscripts h, m, and l refer to the h-, m-, and l- processes, respectively. Figure 2 shows the typical result of the curve fitting for 20 wt % pullulan in water (green ●) using the triply purified sample.
Figure 3. Effect of purifications for pullulan. The relaxation times of the l-process τl (○), m-process τm (red ○), and h-process τh (blue ○) of 20 wt % pullulan in water pullulan at T = 25.0 °C are plotted as a function of number of purifications. Curves are drawn to guide eyes.
processes. The relaxation time τ of the l-process increases with the number of purifications, whereas the relaxation times of the h- and m-processes show no significant change. The apparent effectiveness of repeated purification is investigated in terms of the DC conductivity σ, as shown in Figure 4. The DC
Figure 4. DC conductivity σ obtained by fitting using eq 1 for 20 wt % pullulan in water (○) at T = 25.0 °C plotted against the number of purifications of pullulan. DC conductivity σ of pure water (blue ○) is also plotted for comparison. The curve is drawn to guide eyes.
Figure 2. Typical result of curve fitting for complex permittivity of triply purified pullulan in water (20 wt %) (green ■) at T = 25.0°. The plots were obtained experimentally and curves are fitting results using eq 1. The line color refers to the l-process (orange ), m-process (red ), h-process (blue ), contribution dc conductivity (purple ), and summation of these relaxation processes (yellow ).
conductivity σ of pure water (blue ○) is also plotted in Figure 4 for comparison; σ for pure water lies on the x axis and shows good agreement with the literature value within the experimental uncertainty.39 The DC conductivity σ of aqueous pullulan solution without purification has a magnitude three decades larger than that of pure water. The DC conductivity σ decreases with increasing number of purifications. This result shows that the effects of impurities or ionic ingredients in the sample are effectively reduced by purification with methanol precipitation. This is also observed in Figure 1, where the electrode polarization (l-process) shifts to a lower frequency or the intensity of the l-process decreases. Figure 5 shows the relaxation strength Δε and the broadening parameters for the h- and m-processes βh (blue ○) and m-process βKWW (red ○), respectively as a function of the number of purifications. The relaxation parameters βh and Δεh for the h-process show no change with pullulan purification. The relaxation strength Δεm decreases slightly and the broadening parameter βKWW increases and tends to saturate with purification. The increase in βKWW indicates that the dielectric relaxation curve of the m-process tends to gradually become narrow and symmetric, which implies that the obtained values of the m-process depend on the amount of impurities. For higher pullulan concentrations, the amount of impurities increases, which enhances the l-
The bold curve (yellow ) is obtained using eq 1, which shows good agreement with the data points. The Cole−Cole equation is used for the h-process (blue ), and the KWW equation gives the best fit for the m-process (red ). Note that the intensity of the l-process is much higher than those of the hand m-processes. The mechanism of electrode polarization (lprocess) is still controversial, and the fitting of the entire relaxation curve of the l-process is indeed difficult. Therefore, the fitting for the l-process is tentatively carried out with the Cole−Cole equation using the high-frequency tail of the lprocess. The relaxation time τ in the Cole−Cole equation agrees with that obtained from the peak position in the imaginary part. The relaxation time of the KWW function could not be simply identified using τm,K in eq 1. This is because the relaxation time in the empirical equation has no physical meaning and the method of estimating the relaxation time is still controversial. Therefore, we use the relaxation time τm derived from the loss peak frequency of the m-process, f mp, using the relation τm = 1/(2πf mp); here τm is independent of the model and the most probable relaxation time. 9036
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Figure 5. Relaxation strengths and broadening parameters of the mprocess (red ○) and h-process (blue ○) obtained by fitting using eq 1 for 20 wt % pullulan in water (○) at T = 25.0 °C plotted against the number of purifications of pullulan. Curves are drawn to guide eyes.
Figure 6. Dielectric dispersion and absorption curves for pullulan in water at T = 25.0 °C. The symbols indicate the pullulan concentrations as 0 wt % (blue ○), 10 wt % (red ◇), 20 wt % (green ■), 30 wt % (purple ●), 40 wt % (orange ◆), and 50 wt % (□). Here pullulan is the triply purified sample.
process. Thus, the relaxation curve of the l-process masks the relaxation curve of the m-process. Reducing the amount of impurities is important for fitting of aqueous polymer solutions because the small magnitude of the m-process associated with the dynamics of polymer chains can be distinguished. The impurities in the pullulan sample may have arisen from the biological resources and preparation schemes of pullulan. We use the triply purified pullulan sample for further experiment according to the results of the DC conductivity σ (Figure 4) and the parameter βKWW with considering the sample loss caused by the purification procedure, where the sample loss is marked in a limited amount of pullulan sample. The dielectric relaxation behavior of the h-process has no correlation with the amount of impurities under this experimental condition, which could be due to the much smaller characteristic decay time of water motion compared with the relaxation of the l-process. Concentration Dependence of h- and m-Processes. Figure 6 shows the dielectric relaxation spectra for pullulan (after triple purification) in water measured at T = 25.0 °C. The pullulan concentrations used are 0 wt % (blue ○), 10 wt % (red ◇), 20 wt % (green ■), 30 wt % (purple ●), 40 wt % (orange ◆), and 50 wt % (□). The spectra of the pullulan solutions indicate the h-, m-, and l-processes, whereas those of 0 wt % (blue ●) solution indicate the h- and l-processes. The peak position of the h-process shifts to a lower frequency, and the intensity of the h-process decreases with increasing pullulan concentration. The broadening of the relaxation curve of the hprocess also occurs with increasing pullulan concentration. In contrast, the intensity of the m-process, which can be observed in the real part in the megahertz region, increases with pullulan concentration. To derive the relaxation parameters of the hand m-processes, we carried out curve fittings using eq 1; the typical result of fitting has already been shown for 20 wt % pullulan in water (Figure 2). The obtained parameters for the triply purified pullulan sample in water are shown in Figure 7 as a function of pullulan concentration. As shown in Figure 7, the relaxation times of the h- and mprocesses τh (blue ○) and of m-process τm (red ○), respectively, increase with increasing pullulan concentration.
Figure 7. Relaxation parameters τ, Δε, and β for h-process and mprocess obtained using eq 1 for pullulan (triple purification) in water at T = 25.0 °C. The curve of τ on m-process was obtained by fitting using eq 2, and the extrapolated value to zero concentration τm0 is indicated by cross (red ×). The curves for the other parameters are drawn to guide eyes.
Although the m-process is not observed at zero concentration, the extrapolated relaxation time of the m-process is shown by a cross as τm0 in the top graph. The extrapolation was carried out 9037
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using the equation proposed for polymers in nonpolar solvents, given as40 log τm = log τm0 +
BC C∞ − C
increases with increasing pullulan concentration. The relaxation strength associated with the pullulan chains (m-process) is larger than the expected value from their dipole moment. The hydroxyl groups on the pullulan chains have the ability to form hydrogen bondings with water molecules, which may form the solvation structure of water around the pullulan chains, although the solvation structure of water has not been clearly observed under these experimental conditions. To discuss the dielectric relaxation behavior of the local chain motion of polymers, we calculated the magnitude of the effective dipole moment for a repeat unit of pullulan with the Onsager equation
(2)
Here τ is the relaxation time, C is the polymer concentration, τm0 is the relaxation time at the infinite dilution of pullulan, C∞ is the polymer concentration at which the relaxation time tends to infinity, and B is a parameter indicating the degree of the concentration dependence of relaxation time. τm0 is the relaxation time of an isolated pullulan at infinite dilution. The values obtained by fitting are τm0 = 8.56 × 10−9 s, B = 0.67, and C∞ = 90.4 wt %. The increase in the relaxation time of the mprocess, τm, with increasing pullulan concentration is larger than that of the h-process, τh. This result indicates that the moving unit of the m-process is larger than that of the hprocess. The relaxation strength of the h-process Δεh decreases with increasing pullulan concentration (Figure 7). The m-process is not observed in pure water, and Δεm increases linearly with increasing pullulan concentration, which is also shown in the inset of Figure 7. These results confirm that the molecular origins of the h- and m-processes are related to the rotational motion of the dipole moments of water and pullulan, respectively. The decrease in the relaxation strength Δεh is mainly the result of the decreasing number of water molecules with increasing pullulan concentration. The shape parameter βh for the relaxation curve of the h-process decreases with increasing pullulan concentration, which indicates that the dynamics of water is affected by the addition of pullulan. Similar behavior has been observed for polymer−water mixtures at room temperature.3,4,30 For example, the broadening parameter βh of the Cole−Cole equation for the h-process has been reported to be βh = 1.00 (0 wt %)−0.94 (20 wt %) for PNiPAM in water and βh = 1.00 (0 wt %)−0.67 (60 wt %) for PVP in water. Also, for a protein−water mixture, a decrease in βh has been observed.31 It is considered that the magnitude of βh is system-dependent; nevertheless, the broadening of the relaxation curve and the increase in the relaxation time of the hprocess are induced by the interactions between water and solute molecules via hydrogen bondings. The behavior of water molecules is called “slow dynamics”.31 In the case of pullulan, the slow dynamics of water molecules occurs similarly to those in other systems. Ryabov et al. reported a theoretical treatment performed to analyze the slow dynamics of water by utilizing the fractal concept with respect to the Cole−Cole parameter βh and relaxation time τh. This context of slow dynamics for the hprocess is discussed in the next section. In contrast with the h-process, the m-process of pullulan in water can be fitted using the asymmetric KWW function. For polymer−water mixture, the relaxation process associated with the polymer motion (m-process) is generally masked by the large contributions of the electrode polarization and DC conductivity to the dielectric relaxation spectra, despite the water-soluble polymers in polar solvents or weakly polar solvents being studied at room temperature,2,3,6 where the relaxation process associated with the polymer chain is described by KWW function or Havriliark−Negami (HN) functions. The origin of the m-process is interpreted to be the local chain motion of polymers in solvents. The relaxation time of the local chain motion for an isolated chain τm0 is dominated by the viscosity of the solvent for systems in hydrogen-bonding solvents2,6 and in nonpolar solvents.41 The magnitude of Δεm
Δεm =
3εs ⎛ ε h +2 ⎞2 N ⎜ ⎟ μ2 2εs +ε h ⎝ 3 ⎠ 3ε0kBT eff
(3)
Here εh = Δεh + ε∞ and εs = Δεm + Δεh + ε∞ are the dielectric constants on the high- and low-frequency sides of the mprocess, respectively. N is the number of dipole moments on a repeat unit of pullulan per unit volume, and μeff is the magnitude of the effective dipole moment of a repeat unit of pullulan. In general, the magnitude of the effective dipole moment μeff obtained using the Onsager equation does not agree with that in vacuum. Thus, the Kirkwood−Fröhlich equation has been used to discuss the relaxation strengths of various materials. Here μeff has the form μeff = μ0g1/2, where μ0 is the magnitude of the dipole moment of a molecule in a gas and g is the Kirkwood g factor. The g factor is used to describe the effect of the neighboring dipole moments in a local anisotropic structure. Despite the usefulness of the wellestablished g factor, the g factor itself is a hypothesis. Recently, Shinyashiki et al. have reported a new concept based on the experimentally observed representations in poly(vinyl pyrrolidone) (PVP) solutions, which clearly reveals a simple relationship between the magnitude of the effective dipole moment of the repeat unit of the PVP chain and the dielectric constant on the high-frequency side, εh, in an extremely wide dielectric constant range for solvents covering εh = 5−78.32 As revealed for PVP solutions in various solvents, the magnitude of the effective dipole moment of a repeat unit of PVP obtained using the Onsager equation is scaled simply by the dielectric constant of the solvents. This result implies that the relaxation strength of the m-process is determined by the solvent dielectric constant. According to the finding on PVP systems, the parameter D, which is an indicator of the relationship between the effective dipole moment of the repeat unit of the polymer in solution and that in vacuum, is introduced, although the equation has a similar form to the Kirkwood g factor: Δεm =
3εs ⎛ ε h +2 ⎞2 N ⎜ ⎟ (μ D)2 2εs +ε h ⎝ 3 ⎠ 3ε0kBT 0
(4)
Here μ0D = μeff. Although the only solvent investigated in this study is water, we attempt to construct a tentative plot of μ0D for pullulan against the dielectric constant of the solvent εh (= εh + ε∞), as in Figure 8. Here μ0 is the dipole moment of the repeating unit of pullulan in vacuum. The effective dipole moment μ0D is calculated from the relaxation strength Δεm using eq 4 in two cases where the repeating unit of pullulan is assumed to be maltotriose (red ○) or glucose (red □) because the repeating unit of pullulan is not simply ascertained as the dipole moment of maltotriose for the dielectric relaxation behavior. From the visual representation of the chemical structure, the repeating unit of pullulan is found to be maltotriose, where maltotriose is a trisaccharide made of α− 9038
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the existence of the solvation structure of water around the pullulan chains; the new concept of D instead of the solvation context might be applicable. Further studies are desired to determine whether this analogy can be applied to other polymer solutions and to clarify the meaning of D in eq 4 for other systems. Slow Dynamics of Water Elucidated by τ−β diagram. The dielectric relaxation process of the h-process arises from the molecular motion of water. The relaxation time τh increases and the broadening parameter βh decreases with increasing polymer concentration. This behavior is called the slow dynamics of water molecules, which is utilized to study the dynamical structure of water around polymers.31 Because the slow dynamics of water is related to the interactions with solute molecules, the investigation of this behavior may give information about the interactions of water and solute molecules. The slow dynamics of water is examined using the τ−β diagram shown in Figure 9, where the data points were
Figure 8. Magnitudes of effective dipole moment μ0D plotted against εh for aqueous solution of pullulan obtained using eq 4 where the repeating unit of pullulan is assumed as maltotriose (red ○) and glucose (red □). The dipole moment μ0 in vacuum is calculated for glucose (+), maltose (green ×), melibiose (blue ×), and maltotriose (blue ∗). The dashed lines are drawn to guide eyes.
(1 → 4) linked glucose and pullulan is composed of α−(1 → 6) linked maltotriose. The variation of glycosidic bonds and the numerous number of hydroxyl groups on the pullulan chain may lead to the various types of orientational motion of dipole moment as a response to the applied electric field. Therefore, we consider two cases using maltotriose (red ○) and glucose (red □) as the repeating units of pullulan to calculate μ0D. To construct plots of the dipole moment of the repeating unit of pullulan in vacuum, the averaged values of dipole moments of four substances, namely, glucose, α−(1 → 4) diglucopyranose (maltose), α−(1 → 6) diglucopyranose (melibiose), and maltotriose, are obtained using ChemOffice software, where geometric optimizations are carried out using energyminimization procedures.2,32 The obtained values of dipole moments in vacuum for glucose, maltose, melibiose, and maltotriose are μ0 = 2.35 ± 0.36, 4.04 ± 0.51, 1.60 ± 0.41, and 1.76 ± 0.60, respectively. Here, ± indicates a standard deviation obtained by various energy-minimization procedures. These values are plotted on the line at εh = 1. If the dielectric relaxation strength of solute molecules (m-process) is described using the Onsager equation, the values of μ0D for the repeating unit of pullulan are expected to coincide with the dipole moment of the repeating unit in vacuum (dotted lines in Figure 8). However, the observation shows an apparent slope that is indicated by dashed lines. The dipole moments of glucose, melibiose, and maltotriose in vacuum are approximately in agreement with the points extrapolated to εh = 1 from μ0D for pullulan, although the number of data points is limited. The value of dipole moment of maltose (diglucopyranose α 1 → 4) in vacuum is relatively large and deviates further from the extrapolated line from μ0D for pullulan than those of glucose, melibiose, and maltotriose, indicating that the dipole moment of maltose is not the repeating unit with respect to the dielectric relaxation behavior of pullulan chains. The recent report on PVP in various solvent systems by Shinyashiki et al. shows that μ0D for the repeating unit of PVP in various solvents lies on a single straight line passing through the calculated value for the repeating unit of PVP in vacuum, where the number of data points of PVP is considerably greater than that in this work. The experimental results for PVP solutions and the tentative result for pullulan in water indicate that μ0D obtained by the m-process is related to the dielectric constant of solvents; that is, the relaxation strength of the m-process is simply determined by the dielectric constant of solvents, not by the local anisotropic structure of the neighboring molecules in the solutions investigated. Nevertheless, it is difficult to prove
Figure 9. Relaxation time of h-process τ versus the distribution parameter of Cole−Cole equation for h-process β obtained by various polymer solutions. Symbols refer to the systems: water (blue ×), PNIPAM (red ●), PEG (orange ▲), PVME (purple ■), PVP (green ▼), PVA (blue ▽), PAIA (brown △), PEI (purple ○), BSA (○), CEWL (orange △), and OVA (red ○). The data and abbreviations are cited from refs 3, 31, 42, and 43. The values of pullulan in water are shown by a square (green □).
obtained by the h-process of various aqueous polymer solutions.4,31,42,43 Ryabov et al. expressed the relationship between the Cole−Cole parameter β and the relaxation time τ with the underling concept of the fractal structure as30 β=
dG ln(τωs) 2 ln(τ /τ0)
(5)
where dG is the fractal dimension and τ0 is the cutoff time. The characteristic frequency of the self-diffusion process, ωs, is expressed as ωs =
2dEG2/ dGDs R 02
(6)
Here, dE is the Euclidean dimension, Ds is the self-diffusion coefficient, R0 is the cutoff size of the scaling in the space, and G is a geometrical coefficient that is approximately equal to unity. The data and abbreviations involved here are obtained in refs 3, 31, 42, and 43. The slow dynamics of water is roughly classified into the hydrophilic or hydrophobic system in the diagram depending on its association nature with solute molecules. For example, comparing the hydrophilic system with the hydrophobic system shows that β decreases markedly with increasing τ. Moreover, the fractal dimension dG evaluated using eq 5 provides information about the hierarchical structure of water 9039
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molecules in the aqueous mixtures. The obtained fractal dimension of the hydrophilic system is smaller than one (dG < 1), in contrast with that of hydrophobic systems (1.3 to 1.5). For the pullulan solution (green □), the slow dynamics of water molecules in pullulan is observed in the hydrophilic system in which β decreases steeply with increasing τ. Pullulan has a large number of hydroxyl groups, which enable interactions between pullulan chains and water molecules. In a solution, the hydrogen bondings of water molecules are not fixed permanently; that is, the partners of hydrogen bondings switch over time. The reorientation of the dipole moment of water has to wait until favorable conditions for reorientation to occur (wait-and-switch model).44 This model implies that the rotational motion of water molecules is initiated by the presence of an additional neighboring hydroxyl groups that offers a new site for the formation of hydrogen bondings. Hydroxyl groups on pullulan chains are able to provide the hydrogen-bonding sites for water molecules, and thus the average relaxation time of water (τh) in pullulan is not changed significantly in comparison with that of hydrophobic systems. Therefore, the fluctuation of the relaxation time of water molecules is enhanced (β decreases). The present work suggests that the hydrophilic surface of the pullulan chain induces the slow dynamics. This distinguishing feature of water dynamics in pullulan is speculated to be based on the chemical constituent of polysaccharides; that is, the numerous hydroxyl groups induce larger fluctuation of the relaxation time of water. Recently, Feldman and his colleagues proposed a phenomenological approach to study the dynamics of water; that is, the 3D trajectory of the relaxation time, the Cole−Cole parameter, and the static permittivity that gives intrinsic information regarding to the dipole−dipole interactions between water molecules and solute molecules.45,46 Because the dielectric properties of water are affected by the chemical and physical nature of added ingredients, the analyses of the dipole−dipole interactions give important information about water and solutes dynamics. It is of great interest to study the aqueous solutions of mono-, oligo-, and poly-saccharides in relating to such a novel concept of the 3D trajectory approach as the extension of this work.
dipole moment of the repeating unit of pullulan may be dominated by the magnitudes of the dipole moment of solvent.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Pullulan samples were provided by Hayashibara Co. This work is partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan (Grant-in-Aid for Scientific Research, KAKENHI).
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REFERENCES
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CONCLUSIONS By the dielectric relaxation spectroscopy of a pullulan−water mixture with a purified pullulan sample, three relaxation processes are observed at T = 25.0 °C. These processes are related to the electrode polarization (l-process), the local chain motion of pullulan (m-process), and the dielectric relaxation of water molecules (h-process). The purification procedure used inhibits the l-process and reduces the DC conductivity; thus, the relaxation process of the m-process can be analyzed with high precision. The molecular origin of the m-process is considered to be the local chain motion, and the relaxation strength of the m-process is related to the dielectric constant of solvent. Although the characteristic decay behavior of the local chain motion is slower than those of water molecules, the interdependence between the local chain motion of pullulan and the molecular motion of water is introduced by molecular interactions via hydrogen bondings. The large number of hydroxyl groups on the pullulan chains affects the dynamical structure of water molecules, where pullulan is classified into the hydrophilic systems on the τ−β diagram. The dielectric relaxation strength of the m-process and the related effective 9040
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