Universality of Separation Behavior of Relaxation Processes in

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Universality of Separation Behavior of Relaxation Processes in Supercooled Aqueous Solutions As Revealed by Broadband Dielectric Measurements Seiichi Sudo* Department of Physics, Tokyo City UniVersity, Tamazutsumi, Setagaya, Tokyo 158-8557, Japan

Shin Yagihara Department of Physics, Tokai UniVersity, Hiratsuka, Kanagawa 259-1292, Japan ReceiVed: February 26, 2009; ReVised Manuscript ReceiVed: July 8, 2009

We investigate the universality of the relaxation processes for high-water-content aqueous solutions in a supercooled and glassy state, to clarify the molecular dynamics of water in aqueous solutions. The appearance of the additional process at the crossover temperature is due to structured water arising, and it is a universal feature of aqueous solutions. The normalized relaxation strength of the β process plotted against reciprocal temperature obeys -3 power law that is due the arrangement region of the water molecules through the tetrahedral hydrogen bond structure. Introduction The kinetics and thermodynamics of water have been extensively studied over wide temperature and pressure ranges.1-17 Supercooled water can occur below the melting point (273 K). It is possible to supercool water to TS ) 235 K, at which point it crystallizes.1 Glassy water can be obtained below 100 K by depositing water vapor onto a cold plate2 or by cooling micrometer-sized droplets of liquid water extremely rapidly.3-5 Glassy water exhibits a glass to liquid transition around a glass transition temperature, Tg ) 136 K,6-10 and it crystallizes at 150 K.11,12 Because of this crystallization, supercooled water does not occur in the temperature range between 150 and 235 K. Water does not crystallize when it is mixed with a certain amount of polymers or small organic compounds. Various aqueous solutions including molecular liquids, polymers, and biopolymers have been intensively investigated by using dielectric spectroscopy to clarify the relaxation phenomena in the supercooled and glassy states of aqueous solutions.18-30 The R process and secondary β process are observed around Tg for some aqueous solutions in the water-rich region. The separation behavior of the β process from the R process can be monitored by the results of the temperature dependence of the dielectric relaxation times and strengths. This separation around the crossover temperature, TC, depends on the molecular structure of the solute.19-25 However, the β process is considered to be due to the motion of some of the water molecules that are restricted by the rearrangement region of the R process, and this molecular mechanism of the β process is independent of the solute. Capaccioli and co-workers suggested that the β process is a Johari-Goldstein (JG) process of water.30 However, the microscopic environment of water molecules contributing to the β process has not been clarified yet. We expect that the separation behavior of aqueous solutions in the water-rich region reflects universal dynamics of water (i.e., dynamics of water independent of the solute molecules), and the glass transition of water can be clarified by investigating this universality. In * To whom correspondence should be addressed. E-mail: sudo@ ph.ns.tcu.ac.jp.

this study, therefore, we investigated the separation behavior of aqueous solutions in the water-rich region and analyzed the molecular mechanism of the separation behavior and the microscopic environment of the water molecules contributing to the β process. Results and Discussion A. Universal Behavior of the Relaxation Strength around TC. To discuss the universality of the separation behavior of the relaxation processes, we analyzed the temperature dependence of the relaxation time and strength for the supercooled aqueous solutions. To do so, we carried out broadband dielectric measurements on various aqueous solutions by changing the water content and molecular structure of the solute molecules systematically over the temperature range of 120-300 K and tried to ascertain the molecular mechanism of the relaxation processes. These water mixtures were ethylene glycol-, glycerol-, 1-propanol-, and triethylene glycol-water mixtures with various concentrations,19-21,24,25 and 65 wt % ethylene glycol oligomer (EGO)- and polyethylene glycol (PEG)-water mixtures with various numbers of repeat units of solute molecules.22,23 We checked that the crystallization of each mixture could be avoided in the temperature range of the dielectric measurements.23 The R and β processes are observed below TC in all of these aqueous solutions in the water-rich region, and the separation behavior of the relaxation processes could be classified into three scenarios as illustrated by the example results shown in Figure 1a,b, Figure 1c,d, and Figure 1e,f, respectively. Scenario II. Figure 1, a and b, plots the relaxation time and strength against reciprocal temperature for a aqueous solution of small polyhydric alcohol solution (a 65 wt % diethyelene glycol-water). Only one relaxation process, called the a process, is observed in high-temperature range. This process continues to the R process below TC, and its temperature dependence obeys the Vogel-Fulcher (VF) law. The additional β process appears at a frequency higher than that of the R process below TC.20,22 Here, TC is defined as the temperature at which the relaxation strength of the β process, ∆εβ, is estimated to be zero. ∆εβ increases with decreasing temperature when the relaxation

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Figure 1. Temperature dependence of the relaxation time and strength for a (a,b) 65 wt % diethylene glycol-water mixture; (c,d) 65 wt % pentaethylene glycol-water mixture, and (e,f) 80 wt % 1-propanol-water mixture.36

strength of the R process, ∆εR decreases, and ∆εβ decreases with decreasing temperature when ∆εR increases. This scenario is similar to what occurs in many glass-forming polymers, such as polycarbonate, polyvinyl chloride, polychloroprene, and poly(ethylene terephthalate).31,32 Scenario I. Figure 1, c and d, plots the relaxation time and strength against reciprocal temperature for a water-rich solution of polymer (a 65 wt % pentaethylene glycol-water mixture). In this case, the a process above TC continuous to the β process below TC, and it is the R process that appears to be the additional process below TC. In this plot, TC is defined as the temperature at which ∆εR is estimated to zero. The temperature dependence of the relaxation time of the R process obeys the VF law. ∆εR increases and ∆εβ decreases with decreasing temperature. Phenomena like this also occur in poly(n-alkyl methacrylate)s and polyepoxy compounds.31-33 Scenario III. Figure 1, e and f, illustrates water-rich solutions of monohydric alcohol (an 80 wt % 1-propanol (POH)-water mixture). A Debye-type primary a process is observed in the high-temperature range above TC. There are two small relaxation processes in the high-frequency wing of the a process. These processes are similar to processes II and III of pure POH,34 and their molecular mechanism relates to the motion of POH molecules. They are beyond the scope of our discussion in this paper. Below TC, the additional β process appears at a frequency lower than that of the a process, and this additional β process is due to the motion of water molecules.24,30 Here, TC is defined as the temperature at which the relaxation strength of the additional β process is estimated to be zero. The relaxation strength of the β process slightly increases with decreasing

temperature when the relaxation strength of the a process steeply increases, and it steeply increases with decreasing temperature when the relaxation strength of the a process slightly increases. The separation behavior of scenario III is similar to that of ethanol-water mixtures.35 The similar features of the relaxation processes in each scenario indicate a universality to the separation behavior of the relaxation processes for aqueous solutions. Figure 2 plots the relaxation strength of the additional relaxation process for each separation scenario against reciprocal temperature. The relaxation strengths of the additional R process in scenario I (the closed symbols in the plot) linearly increase with reciprocal temperature. The relaxation strengths of the additional β process in scenario II (the open symbols) linearly increase with increasing reciprocal temperature, but the strength for 65% diethylene glycol (marked as 4) begins to rapidly decrease for temperatures below 180 K. The relaxation strengths of the additional β process in scenario III (the superimposed open and closed symbols) increase with increasing reciprocal temperature but the rise is not as sharp in the low-temperature region. TC for each aqueous solution is 210 ( 10 K, and this temperature is slightly lower than TS.1 The slopes of the plots are very similar in the corresponding temperature range of TC < T < 180 K. It is reported that the additional R process for the aqueous solutions conforming to scenario I has the VF-type temperature dependence, and this process is due to the cooperative motion of water and solute molecules.20,22,23,25 On the other hand, the additional β process for the aqueous solutions conforming to scenarios II and III shows an Arrhenius-type temperature dependence around Tg, and this process is due to the motion of water molecules.19-25

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Figure 2. Relaxation strength versus reciprocal temperature of the additional relaxation process for various aqueous solutions. Open symbols: scenario II (the β process for 60% glycerol, O; 70% glycerol, 0; and 65% diethylene glycol, 4). Closed symbols: scenario I (the R process for 65% triethylene glycol, b; 65% triethylene glycol, 9; 65% pentaethylene glycol, [; 65% hexaethylene glycol, 2, and 65 wt % polyethyelene glycol 400, 1). Superimposed symbols: scenario III (the β process for 80% 1-propanol, superimposed circles, and 90% 1-propanol, superimposed squares).

The common feature of the molecular mechanisms of all these additional processes in scenarios I, II, and III is that water molecules contribute to them. Hence, it is expected that the appearance of these additional processes at TC relates to the hydrogen bonds of water. The hydrogen bond of water has been intensively investigated by comparing experimental results with molecular dynamics calculations.37-41 One water molecule can form hydrogen bonds with up to four surrounding water molecules, and a water molecule surrounded by four hydrogen bonds has an icelike tetrahedral arrangement. The hydrogen bond rapidly breaks but a new bond forms or the old one is restored. The probability of bond breaking depends on the thermal energy,37 and the lifetime of the hydrogen bond increases as temperature decreases. In molecular dynamics calculations, a long-lived hydrogen bond is treated as a fairly compact initial ice nucleus.38,39 The growth rate of the ice nucleus, called the nucleation rate, is very small in the high-temperature range, and the ice nucleus vanishes through hydrogen bond breaking. The nucleation rate increases with decreasing temperature, and it approaches ∼1030 m-3 s-1 around 200 K. This nucleation rate is good agreement with the experimental values obtained from supercooled water transforming into ice Ih at TS.40,41 These results on ice nucleus growth indicate that water molecule structures arise in accordance with the decrease in probability of hydrogen bonds breaking at TS, and the water molecules form the tetrahedral network structure (i.e., ice Ih). In the case of aqueous solutions, water molecules can form hydrogen bonds with surrounding water molecules and/or OH groups of the solute, and these hydrogen bonds also quickly break in the high-temperature range. At TC, the water molecules whose microscopic environment is similar to that of pure supercooled water form a structure related to the tetrahedral rearrangement region in which the molecules cooperatively reorient themselves. Accordingly, the aqueous solution stays in a supercooled state because the growth of the rearrangement region is constrained by the solute molecules. The rearrangement region leads to the appearance of the additional relaxation process of each separation scenario as follows.

Sudo and Yagihara Two rearrangement regions coexist in the high-temperature range for the aqueous solutions conforming to separation scenario II.21,40 Some of the water molecules form hydrogen bonds with surrounding solute molecules, and these water and solute molecules form the rearrangement region. Other water molecules, called excess water, cannot form hydrogen bonds with solute molecules, and these excess water molecules form other rearrangement regions by making hydrogen bonds among each other. The water molecules can switch between each rearrangement region by breaking and reforming hydrogen bonds. The motion of the rearrangement regions leads to the high-temperature a process. At TC, structured water arises, and the size of the rearrangement region including the excess water molecules begins to increase as the water molecules leave the rearrangement region including the water and solute molecules. The motion of this rearrangement region leads to the appearance of the additional β process. Other water and solute molecules contribute to the R process. For the aqueous solutions conforming to scenario I, the water molecules form hydrogen bonds with surrounding water and solute molecules in the high-temperature range. The solute molecules are too large to move cooperatively with water molecules, and thus, the solute molecules act as a constraint on the motion of the water molecules. Hence, the high-temperature a process is mainly due to the motion of the rearrangement region including water molecules restricted by the solute molecules. At TC, structured water arises, the rearrangement region including solute and part of the water molecules begins to form, and the motion of this rearrangement region leads to the additional R process. The rearrangement region including excess water only contributes to the β process. For the aqueous solutions conforming to scenario III, water molecules can move cooperatively with surrounding solute molecules because of the hydrogen bonds and/or clathrate-like hydrate aggregates.40 The motion of the rearrangement region including the water and solute molecules leads to the primary a process. At TC, structured water arises, the water molecules forming the clathrate-like hydrate aggregate with surrounding solute molecules, and a rearrangement region including only water molecules forms. The size of this rearrangement region rapidly increases with decreasing temperature, and the motion of this rearrangement region leads to the additional β process. Thus, the solute molecules contribute to the a process below T C. We can conclude from the above discussion that the additional relaxation processes for the aqueous solutions at TC are brought about by structured water rising as the probability of hydrogen bond breaking decreases. Such a structure forming around 200 K is a feature of the dynamics of water, and it does not depend on the solute. Furthermore, the similar slopes of relaxation strength against reciprocal temperature for each aqueous solution in the corresponding regions of TC > T > 180 K reflect that the probability of the hydrogen bond breaking and forming depends on only the temperature. Below 180 K, the relaxation strength of the additional process depends on the microscopic environment of the rearrangement region. B. Universal Behavior of the Relaxation Strength around Tg. The Avrami theory has been used to analyze the isothermal crystallization process of polymer.43-45 When the crystal growth arises, the volume fraction of crystalline increases and that of amorphous phase decreases. The plots of the logarithm of the normalized relaxation strength in amorphous phase against logarithm of the crystallization time is called the Avrami plot. The slope of the Avrami plot, so-called Avrami index, k, is

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εS(ε∞ + 2)2 µ2Ng ∆ε ) 9(2εS + ε∞) kBTV

Figure 3. (a) Normalized relaxation strength of the β process versus 1/T - 1/TC for various aqueous solutions conforming to scenario I (], 65% pentaethylene glycol; 4, 65% polyethyelene glycol 400; O, 65 wt % polyethyelene glycol 600) and scenario II (2, 65% diethylene glycol). The inset is plots of relaxation strength against 1/T for a 65% polyethylene glycol 600-water mixture. (b) Normalized relaxation strength versus 1/T - 1/TC for various aqueous solutions conforming to scenario III (O, 80% 1-propanol; ], 90% 1-propanol). The inset is plots of relaxation strength against 1/T for an 80% 1-propanol-water mixture.

related to the nature of nucleation and geometry of the growing crystals. Generally, 100% crystallinity cannot be obtained in metastable equilibrium for semicrystalline polymers, and the maximum degree of crystallinity depends on temperature. Thus, the Avrami theory has been extended to deal with the temperature-dependent crystallinity of semicrystalline polymers,46-48 and the Avrami index can be used to characterize the microscopic environment of the polymer molecules in the crystalline region. We considered that the Avrami theory can be applied to the temperature dependence of the relaxation strength of the β process in high-water-content aqueous solutions, because the dynamics of the rearrangement region of the R process can be treated as the freeze in the observation time around Tg and the water contributing to the β process is in metastable equilibrium. Figure 3, a and b, shows the normalized relaxation strengths of the β process for each separation scenarios versus 1/T 1/TC. Here, the normalized relaxation strength is defined as

∆εnorm )

∆ε - ∆εf ∆εi - ∆εf

(1)

where ∆εi is the relaxation strength at TC and ∆εf is the lowtemperature limiting value. For the aqueous solutions conforming to scenarios I and III, the slope of logarithm of ∆εnorm against the logarithm of the reciprocal temperature approaches k ) -3 below 1/T - 1/TC = 1. Here, this temperature in scenario I agrees with its glass transition temperature. ∆εnorm for the aqueous solutions conforming to scenario II seems to be close to those of scenario I, as shown in Figure 3a. However, it is difficult to obtain an accurate value of ∆εf for the aqueous solutions conforming to scenario II, because the β process moves outside of the observation window at the temperature in which the relaxation strength reaches ∆εf. Therefore, the normalized relaxation strength showing a power law is a universal behavior of the β process for aqueous solutions in the water-rich region. The temperature dependence of the dielectric relaxation strength can be expressed by the Kirkwood and Fro¨hlich equation as49,50

(2)

where εS is the limiting low-frequency permittivity, ε∞ is the limiting high-frequency permittivity, µ is the dipole moment, N is the total number of dipolar units, V is the volume, and kBT is Boltzmann’s factor. g is called the Kirkwood correlation factor and describes the static arrangement of the dipoles. For many glass-formers, the relaxation strength of the β process decreases with decreasing temperature, and this temperature dependence can be understood as a decrease in the number of moving dipoles with temperature.32 We assumed that the g value for the relaxation strength of the β process is independent of temperature, because these water molecules in the rearrangement region form the tetrahedral arrangement caused by hydrogen bonding, and this molecular arrangement is independent of temperature. Accordingly, the descriptions of water contributing to the β process become clear. Change of ∆εnorm is brought about by the change in the number of the water molecules in the rearrangement region of the β process, i.e., by the change in the size of the rearrangement region of the β process. ∆εf reflects the limit size of the rearrangement region of β process. The number of water molecules included in the volume change of the rearrangement region is proportional to 1/T2, and the normalized relaxation strength is proportional to 1/T3. For the aqueous solutions conforming to scenarios I and II, the water molecules in the rearrangement region of the β process are gradually absorbed into the rearrangement region of the slow R process, and the rearrangement region of the β process shrinks with decreasing temperature around Tg. On the other hand, for the aqueous solutions conforming to scenario III, the water molecules in the rearrangement region of the a process are gradually absorbed into the rearrangement region of the slow β process, and the rearrangement region of the β process grows with decreasing temperature. Therefore, the amount of excess water molecules, which cannot move cooperatively with the solute, strongly depends on the temperature. The original criteria of the Johari-Goldstein (JG) process is identified with the secondary process of noncooperative intramolecular motion of single molecules.51-53 It has not been reported that the JG process is due to the motion of the molecules (or moving units of polymers) forming a local structure, such as the rearrangement region or cluster. Capaccioli and co-workers considered that the β process in high-watercontent aqueous solutions is the JG process of water.30 However, our results indicate that this β process is brought about the excess water molecules forming the rearrangement region. Thus, according to the original criteria, such a β process cannot be a JG process. We think that the criteria of the JG process should be revised to account for the molecular environment of its process. Hence, for the glass formers with the reported secondary processes, the microscopic environment of molecules contributing to the secondary process has to be reexamined in light of the normalized relaxation strength of the secondary process. Conclusion We investigated the universality of the relaxation processes reflecting the dynamics of water by results of the broadband dielectric measurements on high-water-content aqueous solutions. The ways in which the primary and secondary processes at TC distinguish themselves depend on the solute and can be classified into three scenarios. Structured water arises around 200 K, because the probability of hydrogen bonds breaking

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decreases. The motion of the rearrangement region forming the structured water leads to the appearance of the additional processes characteristic of each separation scenario. On the other hand, the relaxation strength of the β process of water obeys -3 power law. This result indicates that the volue change of the rearrangement region involved in the β process is proportional to 1/T2. Acknowledgment. The authors thank Prof. M. Iwamatsu for his helpful discussions. This work was also supported by the Sumitomo Foundation. References and Notes (1) Misima, O.; Stanley, H. E. Nature 1998, 396, 329. (2) Burton, E. F.; Oliver, W. F. Proc. R. Soc. London A 1936, 153, 166. (3) Hydrogen Bond Networks; Bellissent-Funel, M. C., Dore, J. C., Eds.; Kluwer Academic: Dordrecht, The Netherlands, 1994. (4) Bruggeller, P.; Mayer, E. Nature 1980, 288, 569. (5) Dubochet, J.; McDowall, W. A. J. Microsc. 1981, 124, RP3–RP4. (6) Blackman, M.; Lisgarten, N. D. Proc. R. Soc. London A 1957, 239, 93. (7) Ito, K.; Moynihan, C. T. K.; Angell, C. A. Nature 1999, 398, 492. (8) Handa, Y. P.; King, D. D. J. Phys. Chem. 1998, 92, 3323. (9) Johari, G. P.; Hallbrucker, A.; Mayer, E. Nature 1987, 330, 552. (10) Sastry, S. Nature 1999, 398, 467. (11) Speedy, R. J.; Angell, C. A. J. Chem. Phys. 1976, 65, 851. (12) Speedy, R. J. J. Phys. Chem. 1992, 96, 2322. (13) Cerveny, S.; Schwartz, G. A.; Bergman, R.; Swenson, J. Phys. ReV. Lett. 2004, 93, 245702. (14) Giovambattista, N.; Angell, C. A.; Sciortino, F.; Stanley, H. E. Phys. ReV. E 2005, 72, 011203. (15) Giovambattista, N.; Angell, C. A.; Sciortino, F.; Stanley, H. E. Phys. ReV. Lett. 2004, 93, 047801. (16) Giovambattista, N.; Stanley, H. E.; Sciortino, F. Phys. ReV. E 2005, 72, 031510. (17) Liu, L.; Chen, S. H.; Faraone, A.; Yen, C.; Mou, C. Phys. ReV. Lett. 2005, 95, 117802. (18) Maurin, P. O. J. Chem. Phys. 1998, 109, 10936. (19) Sudo, S.; Shinyashiki, N.; Yagihara, S. J. Mol. Liq. 2001, 90, 113. (20) Sudo, S.; Shimomura, M.; Saito, T.; Kashiwagi, T.; Shinyashiki, N.; Yagihara, S. J. Non-Cryst. Solids 2002, 305, 197. (21) Sudo, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. J. NonCryst. Solids 2002, 307-310, 356. (22) Sudo, S.; Shimomura, M.; Tsubotani, S.; Shinyashiki, N.; Yagihara, S. J. Chem. Phys. 2004, 121, 7332.

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