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Microwave Dielectric Study of an Oligomeric Electrolyte Gelator by Time Domain Reflectometry Shyamal Kumar Kundu,† Shin Yagihara,‡ Masaru Yoshida,§ and Mitsuhiro Shibayama*,† Institute for Solid State Physics, The UniVersity of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan, Department of Physics, School of Science, Tokai UniVersity, 1117 Kitakanane, Hiratsuka, Kanagawa 259-1292, Japan, and Nanotechnology Research Institute, National Institute of AdVanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan ReceiVed: February 4, 2009; ReVised Manuscript ReceiVed: June 11, 2009
The dynamics of water molecules in aqueous solutions of an oligomeric electrolyte gelator, poly[pyridinium1,4-diyliminocarbonyl-1,4-phenylene-methylene chloride] (1-Cl) was characterized by microwave dielectric measurements using the time domain reflectometry method. The dielectric dispersion and absorption curves related to the orientational motion of water molecules were described by the Cole-Cole equation. Discontinuities were observed in the concentration dependence of the dielectric relaxation strength, ∆εh, as well as in the Cole-Cole parameter, βh. These discontinuities were observed between the samples with concentrations of 6 and 7 g/L 1-Cl/water, which correspond to a change in the transparency. Such a discontinuity corresponds to the observation of the critical concentration of gelation. The interaction between water and 1-Cl molecules was discussed from the τh-βh diagram. As 1-Cl carries an amide group, it could be expected that 1-Cl may interact hydrophilically with water, but the present result suggests that 1-Cl interact hydrophobically with water. Introduction It is well-known that the physical properties of water molecules near surfaces of biopolymers, synthetic polymers, amphiphilic systems, etc. differ measurably from those of bulk water molecules. The water molecules surrounding biopolymers are directly bound to the polymer by hydrogen bonding. The bound water molecules form an intermolecular network structure as found by cryogenic X-ray crystal structure analysis.1 The relaxation process due to bound water was observed by dielectric measurements on DNA,2,3 globular proteins,4-7 moist collagen,8 etc. The relaxation time of bound water has been reported to be about 1 ns at 25 °C, which is about 100 times slower than that of bulk water. These relaxation processes are also correlated with ions and polymer chain dynamics.9-11 Free water is usually observed in moist materials, e.g., water/polymer mixtures,12 aqueous gels,13 skin,14 etc. The relaxation process of free water is generally expressed by the Cole-Cole equation where the relaxation curve is broader than that of the Debye type. Note that the principal dielectric relaxation peak of bulk water exhibits the Debye-type relaxation curve. The relaxation parameters are strongly dependent on the solute concentration.12,13 Shinyashiki et al.12 reported the relationship between the polymer structure and the dynamic feature of the water in several polymer-water mixtures. They observed that all the relaxation curves were symmetric and described by the Cole-Cole equation.15 The symmetrical broadening of the dielectric spectrum was phenomenologically interpreted by the variation of the local structure of water.12 Ryabov et al.16 reported that plots of relaxation time against Cole-Cole parameter were classified into two groups of polymer structures, hydrophobic and hydro* To whom correspondence should be addressed. E-mail: sibayama@ issp.u-tokai.ac.jp. † The University of Tokyo. ‡ Tokai University. § National Institute of Advanced Industrial Science and Technology.
philic, and all the curves were continuous as the solute molecules directly bound to the water molecules by H-bond. Nakasako1 reported the lateral and radial distributions of hydrated water molecules around the surface of the enzyme, focusing on the characteristics of hydrogen-bonded networks of the hydrated water molecules and the hydration patterns around hydrophobic residues. According to Nakasako’s report, hydrated water molecules form aggregates of various shapes and dimensions, and some of the aggregates cover hydrophobic residues by forming oligomeric arrangements. In addition, the aggregates lead to large-scale networks of hydrogen bonds. In our previous report,17 we studied an oligomeric electrolyte, poly[pyridinium-1,4-diyliminocarbonyl-1,4-phenylene-methylene chloride] (1-Cl) aqueous solutions, by rheology and discussed the gelation mechanism and the gel recovery process. We also proposed a possible assembly of the supramolecular structure of 1-Cl in water.17 Since the 1-Cl molecule carries an amide group, it is naively anticipated that intermolecular H-bonding is formed between neighboring amide groups. However, due to strong repulsive electrostatic interaction induced by the positive charges on the main chain, direct H-bonding between the amide groups of 1-Cl molecules are hardly formed. Instead, gel formation may take place by crosslinking of the amide groups via chlorine ions and with water molecules. We also studied the sol-gel transition and estimated the critical concentration for gel formation.18 However, the relationship between the structure of the gel and the dynamics of free water has not been clarified yet. It is needless to mention that microwave dielectric spectroscopy is a powerful tool to explore such properties. The objective of the present study is to investigate the dynamics of water molecules in the aqueous solution of an oligomeric electrolyte gelator (1-Cl) by microwave dielectric spectroscopy.
10.1021/jp901043h CCC: $40.75 2009 American Chemical Society Published on Web 07/02/2009
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SCHEME 1: Chemical Structure of Poly[pyridinium-1,4-diyliminocarbonyl-1,4-phenylenemethylene chloride] (1-Cl)
Experimental Section An oligomeric electrolyte, 1-Cl, was prepared in a manner similar to the previous report (Scheme 1).19 A powder of 1-Cl was immersed in distilled water, and the mixture was sonicated for 30 min. Then the dispersion was heated at around 97 °C by a heat gun to form a clear isotropic sol phase (1-Cl/water). The concentrations of 1-20 g/L 1-Cl were used for the dielectric measurements. Dielectric measurements were carried out by two subsystems: time domain reflectometry (TDR) (Agilent HP 54120B digitizing oscilloscope mainframe) having a frequency range of 100 MHz to 30 GHz and impedance analyzer (IA) (Agilent Technology HP4294A) having a frequency range of 40 Hz to 110 MHz. A coaxial cylindrical cell with the inner conductor diameter (made by platinum) of 2 mm and the outer conductor (gold-plated stainless steel) inner diameter of 3.5 mm was used for the IA system of dielectric measurements. The lengths of the inner and outer conductors were 2 and 23.7 mm, respectively, and the electric cell length was approximately 2.65 mm. A flat end coaxial probe with an outer conductor diameter of 2 mm was employed for TDR measurements. Conductors at the end of the semirigid coaxial line were plated with platinum to make it sensitive and stable. The electric cell length was approximately 0.165 ( 0.02 mm. During the dielectric measurements, the sample temperature was kept constant at 25.0 °C with an accuracy of (0.01 °C. Result and Discussion The real and imaginary parts of the complex dielectric permittivity (ε* ) ε′ - iε′′, where ε′ and ε′′ are, respectively, the real and imaginary parts of the complex dielectric permittivity) measured at 25 °C for 2 g/L 1-Cl/water are shown in Figure 1, parts a and b. The experimental data points were collected from IA (5 kHz to 100 MHz) and TDR (100 MHz to 30 GHz) measurements. It is possible to separate the relaxation processes obtained from the complex dielectric permittivity, ε*, by the following equation:
ε*(ω) ) aωA +
σdc + iωε0
2
∆ε
k ∑ 1 + (iωτ )β
k)1
k
+ ε∞
(1)
k
where a is a constant, A is the power law exponent, σdc is the dc conductivity, ε0 is the dielectric constant in vacuum, ∆εk is the dielectric relaxation strength, τk ) 1/2πυk is the relaxation time, υk is the characteristic frequency, βk is the symmetric shape parameter (β ) 1 gives the Debye function and 0 < β < 1 gives the Cole-Cole function),15 and ε∞ is the high-frequency permittivity. It is seen from Figure 1 that the low-frequency process (EP) appearing around the kilohertz region is due to electrode polarization where ε′ showed a power law behavior with exponent A ) -1.74 ( 0.02. The middle frequency process (m process) appearing around 10 MHz is due to ionization where the gelation occurs with the dissociative hydration of the
Figure 1. Frequency dependence of (a) the real, ε′, and (b) imaginary, ε′′, parts of the complex dielectric permittivity at 25.0 °C for 2 g/L 1-Cl/water. The fitting curves were drawn using eq 1. The dotted line in panel a in the lower frequency shows power law (ε′ ∼ ωs, where s is the power law exponent) with exponent s ) -1.74.
oligomeric electrolytes into the organic cations and chlorine (Cl) anions. The high-frequency process (h process) appearing above 10 GHz is due to free water in the solution. Although the middle frequency process is strongly affected by the dc conductivity, it can be well obtained from ε′ which is shown in the inset of Figure 1a. This process can also be easily extracted from the dielectric modulus calculations, but it is not the purpose of the present study. Note that the middle frequency process appeared more than 100 times lower than that of the water relaxation process and also the effect of the dc conductivity on the water relaxation process was poor. Hence, we consider only the water relaxation process for the present discussion, which is our purpose of the present study. The microwave dielectric measurements by the TDR (100 MHz to 30 GHz) method were performed to observe the water relaxation process. The concentration dependences of the real, ε′, and imaginary, ε′′, parts of the complex dielectric permittivity measured at a fixed temperature of 25 °C for 1-Cl/water mixtures are shown in Figure 2. It is seen from this figure that, above 1 GHz, a relaxation process exists, which is due to reorientation of free water in the mixture. The relaxation processes observed below 1 GHz are already described in Figure 1. The complex dielectric permittivity for the water relaxation process is simply described by Cole-Cole function:15
ε* ) ε∞ +
∆εh 1 + (iωτh)βh
(2)
The solid curves in Figure 2 are the fitting curves using eq 2. Shinyashiki and co-workers also observed similar results in different polymer-water mixtures.12,20
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Figure 4. Photograph of the 1-Cl hydrogel with different concentrations at 25 °C.
Figure 2. Frequency dependence of the real, ε′, and imaginary, ε′′, parts of dielectric permittivity for different concentrations of 1-Cl at 25 °C. The fitting curves were drawn using eq 2.
Figure 3. Variations of (a) dielectric strength, ∆εh, and relaxation time, τh, and (b) Cole-Cole parameter, βh, with concentrations of 1-Cl at 25.0 °C. The solid curves are drawn as a guide for the eye. The vertical dotted line corresponds to the critical concentration of gelation.
Variations of the relaxation parameters (the dielectric relaxation strength, ∆εh, the relaxation time, τh, and the Cole-Cole parameter, βh) obtained from eq 2 for 1-Cl/water at different concentrations at 25 °C are shown in Figure 3, parts a and b. The relaxation time, τh, increases with increase of 1-Cl concentration. This behavior can be explained by the decreasing free volume required to reorient the water molecules, which was observed in various polymer aqueous solutions.21,22 The relaxation strength, ∆εh, decreased as water content decreased, and it approached zero at 100% of polymer.22 In the simplest case, the relaxation strength, ∆εh, is related to the number of
dipole moments in a unit volume.23 If it is assumed that the local structure of free water is the same as that of pure water, ∆εh is proportional to the amount of free water. The quantity of free water per unit volume cf (g/cm3) could be estimated from the relaxation strength ∆εh as cf ) (∆εh/∆εW)cW, where ∆εW is the relaxation strength of pure water and cW (g/cm3) is the density of pure water. The turbidity of the ionic gelator is dependent on the concentration of 1-Cl. The sample with low 1-Cl concentration is transparent, but it becomes turbid when the concentration is higher than 6 g/L, which is shown in Figure 4. It is seen from this figure that 5 g/L 1-Cl/water is a transparent solution but 7.5 g/L 1-Cl/water is a turbid gel. Qualitative differences of the transparency and turbidity were together with the variations of the dielectric parameters (∆εh and βh) with concentration of 1-Cl. Figure 3a shows that the relaxation strength, ∆εh, decreases with concentration as water content decreases and the discontinuity is observed between 6 and 7 g/L 1-Cl/water. This discontinuity corresponds to a change in the transparency. This suggests that the hydrated structure depends on the gel structure. This change in transparency corresponds to a change in solution (transparent) to the gel (turbid). Note that the critical concentration of gelation was successfully estimated to be ca. ≈6.3 g/L by dynamic light scattering technique.18 The concentrationdependent Cole-Cole parameter, βh, deviates from unity (see Figure 3b) and the discontinuity is also observed between 6 and 7 g/L 1-Cl/water. It also corroborates the change in the transparency as well as the change of solution to gel structure. A similar behavior was observed only on ovalbumin gels22 where the turbidity depended on the protein concentration. The sample with low protein concentration was transparent, but it became white when the concentration was higher than 20 wt % (1 wt % ≈ 10 g/L). Note that the transparent gels, in general, do not show such discontinuities. As for example, gelatin forms transparent gels even when the protein concentration is high,22 but the concentration dependences of ∆εh, τh, and βh were continuous. It is well-known that the Cole-Cole equation was originally introduced empirically to describe the dielectric relaxation. It has a poor theoretical background concerned with the molecular aspect. A Monte Carlo simulation was analytically performed on the basis of random walks in the structure of fractal dimensions.24 A random walk of a particle in a geometrical constraint in the space of the fractal structure shows a relaxation of the Cole-Cole type. The local variation of the fractal structure leads to the distribution of relaxation times. This model is applicable to the dielectric relaxation of water in the polymer-water mixtures, because the polymer chain is too large to move cooperatively with water molecules and the chain behaves as the geometrical constraint to the motion of water molecules. Therefore, local variation of the conformation of random coiled polymer induces the variation of the water structure in analogy with the Monte Carlo simulation.24
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Figure 5. Cole-Cole parameter, βh, vs relaxation time, τh, for PVP, PEG, PVME, PVA, PEI, PAA, PAlA, moist collagen, gelatin, ovalbumin, and 1-Cl. The solid and dashed curves are drawn as a guide for the eye. The experimental error of βh was less than (0.01, and that of τh was less than (5%.
It is seen from Figure 3 that the order (amount of change) of log τh is different from that of βh. This difference should be brought from the structure of the hydrated water. Plots of βh against log τh of the different kinds of water-polymer mixtures are shown in Figure 5. The plots can be divided roughly into two groups of mixtures. One group contains the mixtures of poly(vinylpyrrolidone) (PVP), poly(ethylene glycol) (PEG), poly(vinyl methyl ether) (PVME), and moist collagen and another group contains the mixtures of poly(acrylic acid) (PAA), poly(ethylenimine) (PEI), poly(allylamine) (PAlA), poly(vinyl alcohol) (PVA), and gelatin.12,13 The polymers in the former group (group I) are nonelectrolyte polymers, and those in the latter group (group II) are electrolyte polymers and PVA. The relaxation time distribution of the group II is broader than that of the group I, from the comparison of those groups with the same relaxation time. This implies that the water structures in the mixtures belonging to the group I are more uniform than those in the mixtures belonging to the group II. Therefore, depending on the structure of the hydrated water, group I and group II are classified into hydrophobic (typically, nonelectrolyte polymers) and hydrophilic (typically, electrolyte polymers) groups of polymers.12 Though PVA is one of the nonelectrolyte polymers, it was classified into the same group of electrolyte polymers12 due to the strong interaction between hydroxyl groups of PVA and water molecules. In the case of ovalbumin, (Figure 5) the plot of βh against τh indicates the same feature as that of the group of hydrophilic polymers. On the other hand, 1-Cl forms an electrolyte polymer chain and it carries an amide group so that water molecules can bind to the amide part of 1-Cl molecules via a H-bond, and we naively expected that the τh-βh curve could follow the electrolyte polymers. However, Figure 5 shows that 1-Cl hydrogel exhibits the same feature as that for the group of hydrophobic polymers13,16 and shows discontinuity. This discontinuity appeared when the transparency changed. Figure 6 shows the dependence of the Cole-Cole parameter, β, with relaxation time, τ, for 1-Cl/water. It is seen from this figure that the solution (open circles) and gel (closed circles) are well separated. Ryabov et al.16 proposed the relationship between the Cole-Cole parameter, β, with relaxation time, τ, which is given by
β)
dG ln(τωs) 2 ln(τ/τ0)
(3)
Figure 6. Cole-Cole parameter, βh, vs relaxation time, τh. The solid curves are fitted with eq 3.
where
ωs ) 2dEG2/dGDs /R02
(4)
Here, ωs is the characteristic frequency of the self-diffusion process, dG is the space fractal dimension of the point set where relaxation units are interacting with the surrounding, dE is the Euclidean dimension of the space,16 R0 is the size of a water molecule,16 Ds is the self-diffusion coefficient, G is the geometrical coefficient,16 and τ0 is the cutoff time of the scaling in time where the scaling parameter ξ ) τ/τ0. Moreover, the solution and gel data points (Figure 6) can be described by eq 3. The fitting parameters in the sol state are dG ) 1.43 ( 0.03, ωs × 10-11 (Hz) ) 31.8 Hz, τ0 ) 0.78 ps, and in the gel state dG ) 1.1 ( 0.08, ωs × 10-11 (Hz) ) 88.1 Hz, τ0 ) 0.8 ps. These values are almost similar with the hydrophobic polymers.16 It is well-known25,26 that the macroscopic dielectric relaxation time of the bulk water (8.27 ps at 25 °C) is about 10 times higher than the microscopic relaxation time of a single water molecule, which is about one hydrogen bond lifetime27-31 (∼0.7 ps). This fact follows from the associative structure of bulk water, where the macroscopic relaxation time reflects the cooperative relaxation process related to the space scale of the cooperative region. The values of τ0 obtained from 1-Cl/water mixtures are close to microscopic relaxation time of the bulk water. It is generally acknowledged31 that for large-scale dimensions of the polymer chains, the value of dG should be either 2 (in ideal case of concentrated solution) or 5/3 (in a dilute solution in a good solvent). The values of dG obtained from 1-Cl/water mixtures (mentioned above) are close to the prescribed values of dG. Conclusion The dielectric relaxation process of water molecules in aqueous solutions of 1-Cl hydrogel was investigated by TDR. The relaxation process due to reorientation of free water molecules occurred above 10 GHz. The water relaxation strength, ∆εh, decreased with concentration as water content decreased. The sample with low 1-Cl concentration was transparent, and it became turbid when the concentration was higher than 6 g/L. The solution and gel indicated respective characteristics from the concentration dependence of the water relaxation strength, ∆εh, and the Cole-Cole parameter, βh. The qualitative differences of the transparency and turbidity were found from the discontinuous nature of ∆εh and βh. The
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discontinuities were observed between the samples with concentrations of 6 and 7 g/L 1-Cl/water. These discontinuities occur close to the estimated value of the critical concentration of gelation. As 1-Cl carries an amide group, it was expected that 1-Cl may interact hydrophilically with water, but the present result suggested that 1-Cl forms an electrolyte polymer chain network and exhibits the same feature as that for the group of polymer gels carrying hydrophobic groups. The interaction between water and 1-Cl molecules appears to be hydrophobic. The discontinuity appeared in the τ-β diagram when the transparency changed. The macroscopic dielectric relaxation time of the bulk water (8.27 ps at 25 °C) is about 10 times larger than the microscopic relaxation time of a single water molecule (∼0.7 ps). This fact follows from the associative structure of bulk water, where the macroscopic relaxation time is reflected by the cooperative relaxation process related to the space scale of the cooperative region. The cutoff time, τ0 (∼0.8 ps), obtained from 1-Cl/water mixtures was close to the microscopic relaxation time of the bulk water. Acknowledgment. This work was supported by the Ministry of Education, Science, Sports and Culture, Japan for Scientific Research on Priority Areas, 2006-2010, No. 18068004. M.Y. thanks NEDO for the Industrial Technology Research Grant Program (05A25710a). References and Notes (1) Nakasako, M. J. Mol. Biol. 1999, 289, 547. (2) Mashimo, S.; Umehara, T.; Kuwabara, S.; Yagihara, S. J. Phys. Chem. 1989, 93, 4963. (3) Umehara, T.; Kuwabara, S.; Mashimo, S.; Yagihara, S. Biopolymers 1990, 30, 649. (4) Grant, E. H. J. Mol. Biol. 1966, 19, 133. (5) Miura, N.; Hayashi, Y.; Mashimo, S. Biopolymers 1996, 39, 183. (6) Pethig, H. Dielectric and Electronic Properties of Biological Materials; John Wiley: New York, 1979. (7) Hayashi, Y.; Miura, N.; Isobe, J.; Shinyashiki, N.; Yagihara, S. Biophys. J. 2000, 79, 1023.
Kundu et al. (8) Shinyashiki, N.; Asaka, N.; Mashimo, S.; Yagihara, S.; Sasaki, N. Biopolymers 1990, 29, 1185. (9) Kita, R.; Kaku, T.; Ohashi, H.; Kurosu, T.; Iida, M.; Yagihara, S.; Dobashi, T. Physica A 2003, 319, 56. (10) Hayashi, Y.; Miura, N.; Shinyashiki, N.; Yagihara, S.; Mashimo, S. Biopolymers 2000, 54, 388. (11) Shinyashiki, N.; Imoto, D.; Yagihara, S. J. Phys. Chem. B 2007, 111, 2181. (12) Shinyashiki, N.; Yagihara, S.; Arita, I.; Mashimo, S. J. Phys. Chem. B 1998, 102, 3249. (13) Hayashi, Y.; Shinyashiki, N.; Yagihara, S. J. Non-Cryst. Solids 2002, 305, 328. (14) Naito, S.; Hoshi, M.; Yagihara, S. Biochim. Biophys. Acta 1998, 1381, 293. (15) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341. (16) Ryabov, Y. E.; Feldman, Y.; Shinyashiki, N.; Yagihara, S. J. Chem. Phys. 2002, 116, 8610. (17) Kundu, S. K.; Matsunaga, T.; Yoshida, M.; Shibayama, M. J. Phys. Chem. B 2008, 112, 11537. (18) Kundu, S. K.; Osaka, N.; Matsunaga, T.; Yoshida, M.; Shibayama, M. J. Phys. Chem. B 2008, 112, 16469. (19) Yoshida, M.; Koumura, N.; Misawa, Y.; Tamaoki, N.; Matsumoto, H.; Kawanami, H.; Kazaoui, S.; Minami, N. J. Am. Chem. Soc. 2007, 129, 11039. (20) Shinyashiki, N.; Matsumura, Y.; Miura, N.; Yagihara, S.; Mashimo, S. J. Phys. Chem. 1994, 98, 13612. (21) Miura, N.; Shinyashiki, N.; Mashimo, S. J. Chem. Phys. 1992, 97, 8722. (22) Miura, N.; Yagihara, S.; Mashimo, S. J. Food Sci. 2003, 68, 1396. (23) Fro¨hlich, H. Theory of Dielectrics; Clarendon Press: Oxford, U.K., 1958; p 30. (24) Fujiwara, S.; Yonezawa, F. Phys. ReV. E 1995, 51, 2277. (25) Hasted, J. B. In Water, A ComprehensiVe Treatise; Frank, F., Ed.; Plenum: New York, 1972; Vol. 1. (26) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371. (27) Barthel, J.; Bachhuber, K.; Buchner, R.; Hetzenauer, H. Chem. Phys. Lett. 1990, 165, 369. (28) Ronne, C.; Astrad, P.; Keiding, S. R. Phys. ReV. Lett. 1999, 82, 2888. (29) Kaatze, U. Mol. Liq. 1993, 56, 95. (30) Buchner, R.; Barthel, J.; Stauber, J. Chem. Phys. Lett. 1999, 306, 57. (31) Grosberg, A. Y.; Khokhlov, A. R. Statistical Physics of Macromolecules; Nauka: Moscow, 1989 (English translation, American Institute of Physics, New York, 1994).
JP901043H
