Water Mixtures

J. Phys. Chem. B 2007, 111, 10079-10087

10079

Dynamics of Water in Partially Crystallized Polymer/Water Mixtures Studied by Dielectric Spectroscopy Naoki Shinyashiki,* Mayumi Shimomura, Takahiko Ushiyama, Takashi Miyagawa, and Shin Yagihara Department of Physics, Tokai UniVersity, Hiratsuka, Kanagawa 259-1292, Japan ReceiVed: April 19, 2007; In Final Form: June 11, 2007

The dielectric relaxation process of water was investigated for polymer/water mixtures containing poly(vinyl methyl ether), poly(ethyleneimine), poly(vinyl alcohol), and poly(vinylpyrrolidone) with a polymer concentration of up to 40 wt % at frequencies between 10 MHz and 10 GHz in subzero temperatures down to -55 °C. These polymer/water mixtures have a crystallization temperature TC of water at -10 to -2 °C. Below TC, part of the water crystallized and another part of the water, uncrystallized water (UCW), remained in a liquid state with the polymer in an uncrystallized phase. The dielectric relaxation process of UCW was observed, and reliable dielectric relaxation parameters of UCW were obtained at temperatures of -26 to -2 °C. At TC, the relaxation strength, relaxation time, and relaxation time distribution change abruptly, and their subsequent changes with decreasing temperature are larger than those above TC. The relaxation strength of UCW decreases, and the relaxation time and dynamic heterogeneity (distribution of relaxation time) increase with decreasing temperature. These large temperature dependences below TC can be explained by the increase in polymer concentration in the uncrystallized phase Cp,UCP with decreasing temperature. Cp,UCP is independent of the initial polymer concentration. In contrast to the relaxation times above TC, which vary with the chemical structure of the polymer and its concentration, the relaxation times of UCW are independent of both of them. This indicates that the factor determining whether the water forms ice crystals or stays as UCW is the mobility of the water molecules.

Introduction Various kinds of biopolymers exist in living bodies. They work under the control of water, and some of their functions control the structure and mobility of water. Such an interdependent relationship is also important for various polymer products. The classification of water into aqueous polymer systems has been attempted, and various types of water have been defined. The criteria used to evaluate the quantities and physical properties of classified water vary from method to method. If we do not consider the effects of various time- and space-scale heterogeneities among the criteria of the classification of types of water, we will be unable to understand water in aqueous systems, particularly at subzero temperatures. Differential scanning calorimetry (DSC) is the most conveniently and frequently used method for the evaluation of water in materials at subzero temperatures.1,2 DSC is commonly used as the sample cools at a scanning rate of 5-10 °C/min or is heated at approximately the same rate. Therefore, the phase behavior of the material can be obtained immediately by controlling its thermal history. For various aqueous polymer systems, the melting enthalpy of ice is smaller than that expected from its water content. The water that does not contribute to the melting peak can be considered to be a liquid state below the melting temperature. Part of the water in materials is not crystallized even below 0 °C; i.e., the water is partially crystallized. The time scale for the crystallization process in partially crystallized aqueous polymer systems seems to be larger than the experimental time scale. * To whom correspondence should be addressed. E-mail: [email protected].

Dielectric spectroscopy can directly detect the relaxation process due to the rotational motion of polar molecules. Water molecules have a dipole moment, and the rotational motion of water can be detected as dielectric relaxation processes. Most of the rotational motion of the dipole moments of water molecules contributes to the primary relaxation process of water, which shows a large loss peak at 20 GHz at 25 °C. At higher frequencies, a small secondary process also exists.3,4 When water molecules form ice crystals at subzero temperatures, the dielectric loss peak of ice appears at about 10 kHz.5-7 Then, if part of the water is crystallized and another part of the water remains in a liquid state in partially crystallized polymer/water mixtures, we can distinguish the two loss peaks as ice (crystallized water)8,9 and uncrystallized water in the liquid state.9-14 The dielectric relaxation process of water at subzero temperatures has been studied for aqueous polymer systems. In particular, a lot of attention has been paid to macroscopically homogeneous glass-forming mixtures of low water content systems. In these systems, water can be cooled without crystallization to below the mixture Tg.15-27 In such glassforming water mixtures, the relation between the glass transition phenomenon and the dynamics of water, the plasticization of structural relaxation by water, and the relations between water and secondary relaxation processes are the main topics of research. In these studies, crystallized mixtures in water-rich systems are generally out of the focus of the discussion. Various time-dependent spaces and dynamic heterogeneity make it difficult to control and discuss the partially crystallized systems. Therefore, systematic investigations of the dynamics of water molecules in partially crystallized systems are still lacking.

10.1021/jp0730489 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/03/2007

10080 J. Phys. Chem. B, Vol. 111, No. 34, 2007

Shinyashiki et al.

To understand the dynamics of uncrystallized water in partially crystallized aqueous polymer systems, we investigated the dielectric relaxation process of uncrystallized water in polymer/water mixtures. Four types of water-soluble randomly coiled polymers were used. Dielectric measurements were performed at frequencies between 10 MHz and 10 GHz at subzero temperatures down to -55 °C. The relaxation time and the dynamic heterogeneity of the uncrystallized water are discussed on the basis of the temperature-dependent polymer concentration in the uncrystallized phase. Even if the thermal history of the sample does not coincide between the dielectric and DSC measurements, the experimental results are worth discussing. Experimental Section Poly(ethyleneimine) (PEI; Mw (weight average molecular weight) ) 50000, 50 wt % solution in water), poly(vinyl methyl ether) (PVME; Mw ) 90000, 50 wt % solution in water), and poly(vinyl alcohol) (PVA; Mw ) 30000-70000) were obtained from Aldrich Chemical, Scientific Polymer Products, and Sigma Chemical Co. Ltd., respectively. These polymers were used without further purification. Deionized and distilled water was added to the PEI and PVME solutions to adjust the concentration, and the solutions were kept at room temperature for 24 h before the measurements. PVA was immersed in distilled and deionized water for one week to allow water to penetrate into the PVA. PVA/water mixtures were heated and stirred at 70 °C for 1 h, 24 h before the measurement. Mixtures of 10, 30, and 45 wt % PEI/water, 10 and 30 wt % PVME/water, and 10, 20, and 30 wt % PVA/water were prepared. Poly(vinylpyrrolidone) (PVP; Mw ) 10000)/water mixtures of 20 and 40 wt % PVP have already been reported,10 and the results were taken from the literature. DSC measurements were performed with a DSC7 instrument (Perkin-Elmer). The sample was put in an aluminum pan and placed into a sample holder in a nitrogen atmosphere. The sample was cooled at 10 °C/min from +25 to -55 °C and then kept for 10 min at this temperature. Then the measurement was carried out at a heating scan of 5 °C/min from -55 °C to +25 °C. In contrast to the measurements during the heating process of DSC, dielectric measurements were made during the cooling process. For the DSC measurement, measurements during the cooling process are possible, but less information is obtained than for measurement during the heating process, because the first cooling rate induces the supercooling of water. For the high polymer concentration, the water in the mixture sometimes crystallized after the cooling scan or during the heating scan. Dielectric measurements of the polymer/water mixtures at temperatures between +25 and -55 °C in the frequency range from 10 MHz to 10 GHz were performed by time domain reflectometry (TDR) (Hewlett-Packard 54124T). A flat-ended coaxial semirigid cable (outside diameter of the outer conductor of 2.2 mm with a thickness of 0.52 mm and inner conductor diameter of 0.51 mm) with an electric length of 0.15 mm was used for the measurements of frequencies above 100 MHz. A coaxial cylindrical cell-type electrode with an outer conductor with an inner diameter of 3.5 mm and inner conductors with various sizes between the largest (diameter of 2.0 mm, length of 1.5 mm, electric length of 3.1 mm) and the smallest (diameter of 1.0 mm, length of 0.3 mm, electric length of 1.0 mm) were employed for the measurements below 2 GHz. The appropriate cell size depends not only on the frequency but also on the dielectric constant of the materials. Therefore, judgments of the

Figure 1. DSC curves of polymer/water mixtures with (a) PVP, (b) PEI, (c) PVME, and (d) PVA. The numbers indicate the polymer concentration Cp (wt %) of the mixtures.

appropriate cell and frequencies to use were based on the measured data of samples with known dielectric functions. The details of the procedures for TDR measurements have already been reported.28 When we tried to perform dielectric measurements during the heating process, after the measurements upon heating from -55 to +25 °C, the sample in the electrode sometimes contained bubbles. These were due to the decrease in volume of the sample by the melting of ice upon heating. To avoid the contamination of the melting process by the bubbles, we performed dielectric measurements during cooling. Below 0 °C (the melting temperature of pure ice), the sample was cooled every 2 °C at a cooling rate slower than 10 °C/min. When the temperature reached the objective temperature, this temperature was then maintained for 1 h. If the reflected step voltage pulse, which is the reflection of the pulse applied for dielectric measurement, from the sample remained the same for 1 h, we started dielectric measurement, which took 15 min. After the measurement, we confirmed that the signal had not changed from that before the measurement. We then started to change the temperature for the next measurement. The criterion for the stable condition of our dielectric measurements is that there is no change in the dielectric function for 80 min. Results DSC. Figure 1 shows DSC curves obtained for polymer/water mixtures. For all the mixtures, an endothermic peak due to the melting of ice appears. Except for the PEI/water mixtures, the step of the heat flow due to the glass transition2 is recognized below the melting peak. A similar step is commonly observed for various polymer solutions, and this step has been considered to be due to the glass transition in the uncrystallized phase in partially crystallized polymer/water mixtures. For the 40 wt % PVP/water and 30 wt % PEI/water mixtures, the crystallization upon heating can be recognized at about -20 °C. From the area of the melting peak, we obtained the heat of fusion ∆H of the melting of ice in the mixtures. The glass transition temperature Tg was defined as the temperature at the midpoint of the step. ∆H, Tg, and the melting temperature Tm are listed in Table 1. ∆H decreases with polymer concentration and varies with polymer structure. Tg is independent of the polymer concentration and varies with the polymer structure. The height of the step depends on the polymer structure and is largest for PVME/water mixtures. For the PVME/water and

Water Dynamics in Polymer/Water Mixtures

J. Phys. Chem. B, Vol. 111, No. 34, 2007 10081

TABLE 1: Temperatures of Melting Tm, Glass Transition Tg, and Crystallization TC of Polymer/Water Mixtures and the Concentration of Polymer in the Uncrystallized Phase Cp,UCP below Tm by DSC and TC by Dielectric Spectroscopy DSC

polymer PVP PEI PVME PVA

dielectric spectroscopy

Cp (wt %)

Tm (°C)

Tg (°C)

∆H (J/g)

Cp,UCP[∆H] (g of polymer/ g of solution)

20 40 10 30 10 30 10 20 30

-3.3 -7.5 -0.4 -8.0 -1.3 -4.2 -1.6 -2.6 -3.9

-27.7 -28.6

205.3 94.2 229.1 94.1 237.3 123.7 268.7 217.1 165.5

0.52 0.56 0.32 0.42 0.35 0.48 0.52 0.57 0.60

-18.4 -18.1 -39.4 -38.3 -37.6

TC (°C)

Cp,UCP[TC] (g of polymer/ g of solution)

Cp,UCP[-20 °C] (g of polymer/ g of solution)

-5 -7 -4 -6 -4 -8 -4 -6 -10

0.50 0.49 0.35 0.37 0.60 0.66 0.54 0.60 0.63

0.77 0.69a 0.48 0.50 0.99b 0.99b 0.77 0.81 0.79

a The values were obtained by extrapolation from the plots above -18 °C. b The values were obtained by extrapolation from the plots above -14 °C.

PVP/water mixtures, two steps were observed, but only the larger one is listed in Table 1. We assume that if all the water in the mixture crystallizes, the heat of fusion of all the water ∆Hall is proportional to the water content of the mixture. However, ∆H obtained by DSC for polymer/water mixtures is always smaller than ∆Hall. This means that part of the water does not contribute to the melting peak, i.e., part of the water is in a liquid state even below Tm. We call this water uncrystallized water (UCW). Such a partially crystallized polymer/water mixture is not a homogeneous system and is composed of at least two phases; one consists of ice crystals, and the other is an uncrystallized (liquid) phase. The ice phase includes water molecules only; thus, the polymer concentration in the uncrystallized phase is higher than that in the homogeneous polymer/water mixture above TC. Such an uncrystallized phase in partially crystallized materials has been called the freeze-concentrated phase.2 Thus, we can obtain the content of UCW, and we can estimate the polymer concentrations in the uncrystallized phase Cp,UCP[∆H] (g of polymer/g of solution) as

Cp,UCP[∆H] )

(

Cp 100 - Cp ∆H 1+ 100 Cp ∆Hall

)

(1)

where Cp (wt %) is the polymer concentration in the prepared mixtures and ∆Hall for a mixture with polymer concentration Cp is given by ∆Hall(Cp) ) 333[(100 - Cp)/100]. The value 333 J/g is the heat of fusion of pure water. The values of Cp,UCP[∆H] obtained by eq 1 are listed in Table 1. Dielectric Spectroscopy. Figure 2 shows the real and imaginary parts of the dielectric functions for 10 wt % PEI/ water mixtures at various temperatures. At -2 °C, a large dielectric constant and lower frequency tail of the loss peak at about 10 GHz can be observed. This process is due to the reorientational motion of water molecules. At -4 °C, the relaxation process suddenly becomes smaller and the peak shifts to lower frequencies than that at -2 °C. This change results from the crystallization of water at the crystallization temperature TC between -2 and -4 °C. For convenience, we defined TC as -4 °C, which is the crystallization temperature or the highest temperature of dielectric measurements below the genuine crystallization temperature. The values of TC determined by dielectric measurements of the polymer/water mixtures are listed in Table 1. The dielectric measurements were carried out during the cooling process so that the polymer/water mixtures were supercooled. Therefore, when we discuss the experimental results around TC and Tm, possible hysteresis of melting and

Figure 2. Real and imaginary parts of the dielectric function for 10 wt % PEI/water mixtures at various temperatures: b, -2 °C; O, -4 °C; 2, -8 °C; 4, -12 °C; 9, -16 °C; 0, -20 °C; [, -24 °C; ], -28 °C. The lines were drawn using eq 2.

crystallization must be taken into account. Below TC, the relaxation process of water remains, and this process shifts to lower frequencies and becomes weaker with decreasing temperature. Figure 3 shows the real and imaginary parts of the dielectric functions for a 30 wt % PEI/water mixture at various temperatures. Above TC, the dielectric constant is larger for lower polymer concentrations, since the amount of water is higher in the lower polymer concentration mixture. Below TC, the dielectric constant is larger for higher polymer concentrations, in contrast to that above TC. Above TC, all the water molecules in the mixture are in a liquid state and contribute to the relaxation process of water. Below TC, part of the water is crystallized, but another part of the water still remains in a liquid state and contributes to the relaxation process in the frequency range measured. The crystallization of part of the water is prevented by polymer chains. This water can be considered to be similar to the UCW suggested by the DSC results. We also call this water UCW, and the amount of UCW will be compared to that obtained from DSC results. The relaxation process due to the motion of water molecules in ice appears at frequencies of around 10 kHz5-7 and is completely different from that of liquid water. The properties mentioned above are common to the other mixtures examined. To characterize the relaxation process of UCW, we performed curve fitting to the dielectric spectra. The experimental results

10082 J. Phys. Chem. B, Vol. 111, No. 34, 2007

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Figure 3. Real and imaginary parts of the dielectric function for 30 wt % PEI/water mixtures at various temperatures: b, -2 °C; O, -6 °C (liquid); 2, -6 °C (partially crystallized); 4, -10 °C; 9, -14 °C; 0, -18 °C; [, -22 °C; ], -26 °C; 1, -30 °C. The lines were drawn using eq 2.

of all the polymer/water mixtures for all the concentrations and temperatures can be reproduced by a simple summation of the Cole-Cole equation29 for the relaxation process of UCW and dc conductivity as

*(ω) ) ∞ +

∆ σ -j 0ω 1 + (jωτ)β

Figure 4. Dielectric relaxation strength ∆ against temperature T (°C) for the polymer/water mixtures with (orange squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellowgreen circles) 30 wt % PVA. The vertical lines were drawn at TC. The other lines were drawn by the least-squares method for the plots above TC and those below TC, separately. The inset shows the plots of ∆ against polymer concentration, Cp (wt %), at 0 °C. The double circle represents ∆ for pure water at 0.2 °C taken from ref 4. The straight line was drawn by the least-squares method.

(2)

Here, ω is the angular frequency, j is the imaginary unit given by j2 ) -1, 0 is the dielectric constant in a vacuum, ∞ is the high-frequency limit dielectric constant, ∆ is the relaxation strength, τ is the relaxation time, β is a symmetric shape parameter (0 < β e 1), and σ is the dc conductivity. A smaller value of β represents a broader symmetric loss peak. The lines shown in Figures 1 and 2 were obtained from eq 2. For the PEI/water mixtures, the relaxation strength is the largest among the mixtures measured. At temperatures below -26 °C, the loss-peak frequency cannot be evaluated, since the loss peak is close to the low-frequency limit of the measurements. The relaxation process is too small to evaluate the relaxation parameters below -20 °C (10 and 20 wt % PVA) and -22 °C (30 wt % PVA) for PVA/water mixtures and below -14 °C for 10 and 30 wt % PVME/water mixtures. According to the verification of the data for PVP/water mixtures, the relaxation parameters are valid down to -20 °C for 20 wt % PVP/water and -18 °C for 40 wt % PVP/water mixtures. Below these temperatures, the strength of UCW is small and the estimation of the strength and relaxation time is affected by the low-frequency contribution, e.g., dc conductivity, the highfrequency tail of the relaxation process of ice, and interfacial polarization. Therefore, we refrain from estimating the relaxation parameters. To obtain the correct relaxation parameters of UCW at lower temperatures, measurements at frequencies lower than 10 MHz are necessary. However, the relaxation process of UCW can be evaluated sufficiently accurately for our purpose in this paper using frequencies down to 10 MHz and valid temperatures. The temperature dependences of the relaxation strength ∆ are shown in Figure 4 for all the polymer/water mixtures measured. For all the mixtures, ∆ shows large values above TC, since all the water in the mixture can contribute to the relaxation process of water. The crystallization of part of the

Figure 5. Relaxation time τ against temperature T for the polymer/ water mixtures with (orangle squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellow-green circles) 30 wt % PVA. The “×” symbols are τ for pure water taken from ref 4. The lines were drawn down to TC by the least-squares method for the plots above TC. The inset shows the plots of τ against temperature T for (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME/water mixtures at around TC. The vertical lines were drawn at TC, and the other lines were drawn by the least-squares method.

water at TC induces the sudden decrease in ∆. The difference in ∆ above and below TC is larger for the mixtures with lower polymer concentrations, since a larger amount of water crystallized in the mixtures with lower polymer concentrations. Even for the same polymer concentration, the difference in ∆ below TC depends on the chemical structure of the polymer. Figures 5 and 6 show the temperature dependences of the relaxation time τ and the symmetric distribution parameter β, respectively. The plots above TC are connected by lines. The temperature dependences of τ and β below TC are larger than those above TC for all the mixtures. The inset of Figure 5 shows, as an example, the plots of τ at around TC. At TC, a discontinuity in the temperature dependence can be recognized. In contrast



Figure 6. Symmetric shape parameter β against temperature T for the polymer/water mixtures with (orange squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellow-green circles) 30 wt % PVA. The lines were drawn down to TC by the leastsquares method for the plots above TC.

to the variation of τ for the polymer structure and the concentration above TC, plots of τ almost form a single trace below TC.

Figure 7. Dielectric relaxation strength ∆ against temperature T for 10, 30, and 45 wt % PEI/water mixtures. The straight solid lines were drawn by the least-squares method assuming a linear dependence of ∆ on T above -2 and -6 °C for 10 and 30 wt % PEI/water mixtures, respectively, and over the whole temperature range for the 45 wt % PEI/water mixture. The solid curves for 10 and 30 wt % PEI/water mixtures below TC were drawn by the least-squares method. The vertical lines were drawn at TC for 10 and 30 wt % PEI/water mixtures.

Discussion Polymer Concentration in the Uncrystallized Phase. According to the Kirkwood equation,30 ∆ is determined by the strength of the dipole moment, the number of molecules in a unit volume that contribute to the relaxation process, the temperature, the Kirkwood structural factor g, and the internal electric field. According to the polymer concentration dependence of ∆ for polymer/water mixtures at 0 °C, shown in the inset of Figure 4, ∆ above TC is almost proportional to the water content. The structure of UCW is expected to be somewhat different from that of water above TC, since UCW molecules exist at neighboring polymer chains in the uncrystallized phase. For a higher polymer concentration, ∆ of water is almost proportional to the water content of the polymer/water mixture at 25 °C.31 Figure 7 shows the temperature dependences of the relaxation strength for 10, 30, and 45 wt % PEI/water mixtures. The 45 wt % PEI/water mixture did not crystallize at the measurement temperatures. ∆ changes monotonically with temperature, as shown in Figure 7. If the mixture did not crystallize, the relaxation strength of all the water in the mixture ∆all was obtained by the extrapolation of the plots by assuming a linear dependence of ∆ on the temperature above TC, as shown by the dotted lines in Figure 7. We also assumed that ∆ below TC is proportional to the density of UCW. On the basis of these assumptions, we estimated the polymer concentrations in the uncrystallized phase Cp,UCP in partially crystallized mixtures using ∆ as

Cp,UCP )

Cp ∆ Cp + (100 - Cp) ∆all

(3)

where Cp is the polymer concentration of the prepared mixture. The linear dependence of ∆ on inverse temperature is plausible.30 However, the temperature dependences of ∆ are in agreement with a linear dependence of T rather than that of 1/T at temperatures up to 45 °C for PVP/water mixtures and 25 °C for other mixtures. However, the biggest difference

Figure 8. Polymer concentration in the uncrystallized phase Cp,UCP against temperature T (°C) for the polymer/water mixtures with (orange squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellow-green circles) 30 wt % PVA. The lines were drawn by connecting the plots.

between the linear dependences of T and 1/T is less than 3% for ∆all and less than 1% for Cp,UCP at -20 °C. In the partially crystallized mixture, the density of the mixture is expected to decrease by the crystal growth. If all the water in the mixture is crystallized, the density decrease is greatest at 9% for the 10 wt % polymer/water mixture. The densities of polymer/water mixtures are between 1.00 and 1.09 g/cm3 at 25 °C, and the density is larger for higher polymer concentrations. The density reduction due to ice crystallization is partly compensated by the higher density of the higher polymer concentration mixture. Thus, we treat the densities of the mixtures below TC as being 1 g/cm3, with an error of less than 9%. This means that Cp,UCP can be considered as grams of polymer per gram of solution in the uncrystallized phase. The values of Cp,UCP obtained from the dielectric relaxation strengths at TC and -20 °C are listed in Table 1. Figure 8 shows the temperature dependence of Cp,UCP. Above TC, each Cp,UCP is equal to the concentrations of the prepared mixture Cp. Below TC, the trend is different. Cp,UCP is almost the same for mixtures of the same polymer for various Cp values.

10084 J. Phys. Chem. B, Vol. 111, No. 34, 2007 Cp,UCP depends on the chemical structure of the polymers in the order PEI < PVP < PVA < PVME. This means that each polymer structure has its own capacity of UCW resulting from the interaction between the polymer chain and water molecules. Cp,UCP depends on the temperature. For all the mixtures, Cp,UCP increases with decreasing temperature, i.e., UCW decreases with decreasing temperature. Note that the capacity of each polymer chain for UCW is not a constant and is a function of temperature. At lower temperatures, even when obstructed by polymer chains, the decrease in thermal fluctuation allows UCW to gradually join to form ice crystals with decreasing temperature. We intend to use Cp,UCP, but it is also possible to discuss the results on the basis of the number of uncrystallized water molecules per repeat unit of polymer. However, below TC, UCW has a broad relaxation time distribution, i.e., a smaller β value, as shown in Figure 6. Thus, it can be interpreted that the concentration fluctuation of the polymer chain is expected to be large in the uncrystallized phase. At present, the heterogeneity of the uncrystallized phase is unclear; thus, we avoid discussing the “number of uncrystallized molecules per repeat unit of polymer”, which implies the homogeneous mixing of water and polymer. Uncrystallized Water Obtained from DSC and Dielectric Spectroscopy. Even though the low-temperature tail of the melting peak, i.e., the melting starts just above Tg, which is lower than -20 °C for PVP/water and PVA/water mixtures, the area below -20 °C is less than 1% of that of the whole area of the melting peak of DSC curve. Accordingly, for the temperature range used for the estimation, Cp,UCP[∆H] obtained by DSC is compatible with Cp,UCP[-20 °C] rather than Cp,UCP[TC]. However, Cp,UCP[∆H] obtained by DSC is larger than Cp,UCP[-20 °C] and close to Cp,UCP[TC]. To interpret the difference between Cp,UCP obtained by DSC and Cp,UCP[-20 °C] obtained by dielectric measurements, two different ideas can be considered as follows. One is that the gradual decrease in ∆ below TC is due to the change in the mobility of UCW. If part of the UCW can gradually move cooperatively with polymer chains, the relaxation time of water will be larger than that of the observed UCW. In the partially crystallized polymer/water mixtures, the relaxation time of UCW is on the order of about nanoseconds and can be expected to be different for different polymer chains. According to our dielectric measurements of PVP/water mixtures at 25 °C, the relaxation times of the PVP chain motion are about 10 and 60 ns for 20 and 40 wt % PVP/water mixtures, respectively.32 For the partially crystallized PVP/water mixtures below TC, Cp,UCP is higher than Cp,UCP[TC] for 50 wt % PVP and probably higher than Cp,UCP[-20 °C] for 70 wt % PVP. At these concentrations, the relaxation time of PVP chain motion is expected to be several microseconds at 25 °C. TC is more than 30 °C lower than 25 °C. Thus, the relaxation time of PVP chain motion at temperatures below TC should be larger than 10 µs, which is far larger than that of UCW. The UCW is expected to be confined by polymer chains and behaves similarly to the local motion of water in glass-forming water mixtures of a polymer and an oligometric solute without crystallization.22-27 In the glass-forming water mixtures of poly(ethylene glycol) and ethylene glycol oligomers longer than diethylene glycol,23,26,27 the water molecules in the mixtures do not move cooperatively with the solute molecules, and the solute molecules behave as a constraint to the motion of water molecules above -50 °C. At about -50 °C, the cooperative motion of water and solute molecules begins, and the amount of water which moves cooperatively with the solute molecules increases

Shinyashiki et al. with decreasing temperature. Even if the water molecules which move cooperatively with the polymer chains can exist in a partially crystallized mixture, this water should appear below the cooperativity onset temperature of about -50 °C. Therefore, the idea that the gradual decrease in ∆ below TC is caused by an increase in water that moves cooperatively with the polymer chain is unacceptable. Thus, another theory that the gradual decrease in ∆ below TC is due to the gradual crystallization of UCW is plausible. Upon cooling of the polymer/water mixtures during our dielectric measurements, after the temperature of the sample reaches the temperature for measurement, sometimes the change in the dielectric signal continues for 1 h. This means that the crystallization continues for 1 h. Even though the sample size of DSC measurements is smaller than that of dielectric measurements, the crystallization process during DSC measurements should not be completed because of the faster scanning rate and the short length of time for DSC measurements. The water that crystallized at TC during dielectric measurement is similar to pure water. This water does not require a long time for crystallization, and the crystallization can be detected by DSC. On the other hand, the crystallization of water between TC and -20 °C occurs in a highly concentrated polymer solution. In this case, the rearrangement of water molecules reflecting the growth of ice crystals takes a longer time than in low polymer concentration solutions. The rearrangement of the polymer chain accompanied by the rearrangement of water molecules should also be the cause of the growth of ice crystals taking a much longer time than the experimental time scale. Thus, during the DSC measurements, the crystallization of this water should not proceed if compared to that of the dielectric measurements, and Cp,UCP[∆H] obtained by DSC is close to Cp,UCP[TC] rather than Cp,UCP[-20 °C]. It is well-known that, for foods stored in a refrigerator at -20 °C, the change in its quality continues for several months or longer. The UCW in subzero temperatures is in a nonequilibrium state, and the growth of crystals, i.e., the decrease in UCW, proceeds at the various rearrangement time scales of mobile molecules in the partially crystallized material. To perform a more rigorous comparison between DSC results and the amount of UCW and its dynamics, measurements based on the same thermal history are important. Relaxation Time and Relaxation Time Distribution. The two most pronounced features of the relaxation time of water in the partially crystallized phase are (1) τ values below TC appear on a single trace and (2) τ suddenly increases at TC, and the dependence of τ on temperature below TC is much stronger than that above TC. The former means that the relaxation time below TC is independent not only of the polymer concentration but also of the chemical structure of the polymer. Of course, a different chemical structure of polymer provides a different environment for water in the mixtures, since the relaxation time of water observed above TC depends on the chemical structure of the polymer.33, 34 The independence of τ on the polymer structure can be interpreted as whether the water molecules form ice crystals or stay in the liquid state below TC is determined by the relaxation time (mobility) of water. For the dynamically heterogeneous water in the polymer/water mixture,32 the water molecules with high mobility are expected to be far from the polymer chains, and their dynamic and thermal properties are similar to those of pure water. In contrast, the water molecules with low mobility are expected to be close to the polymer chains, and their dynamic and thermal properties are different from those


Figure 9. Relaxation time τ against the polymer concentration in the uncrystallized phase Cp,UCP for the polymer/water mixtures with (orange squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellow-green circles) 30 wt % PVA. The large symbols are at temperatures immediately above TC. The “×” symbol is the τ for pure water at 0.2 °C taken from ref 4. The lines were drawn as a guide to the eyes for 10 wt % PEI/water, PVME/water, and PVA/water mixtures and the 20 wt % PVP/water mixture.

of bulk water. The water molecules with high mobility are expected to crystallize at TC or a few degrees below TC. The high-mobility water molecules that crystallize at TC have sufficient mobility to undergo rearrangement to an appropriate conformation for joining themselves to the neighboring ice crystals within the time of the experiment. On the other hand, the low-mobility water molecules are surrounded by polymer chains and cannot form a stable structure of ice crystals. To reach a location where they can join a crystal, these water molecules must move accompanied by the rearrangements of the polymer chain, which have a larger relaxation time than that of water. In this experiment, this water does not have sufficient time to join ice crystals. For the PEI/water mixture, the PEI chain can reduce the mobility of a large number of water molecules compared with other polymers. According to a dielectric study on polymer/water mixtures,33 the relaxation time and relaxation time distribution of the PEI/water mixture are the largest among the polymer/water mixtures studied in the present paper. The polymer chain, which has a relatively strong effect on water molecules (it changes the free energy surface in the phase space of water molecules), can keep a larger amount of water immobile and prevents the water molecules from forming an ice structure. Thus, the PEI chain has a large capacity of UCW. τ seems to be the criterion determining whether the water forms ice crystals or remains as UCW. Therefore, the criterion results in a polymer-structure-independent relaxation time below TC. The characteristics in the second point, the sudden increase in τ at TC and the strong temperature dependence of τ, are caused by not only by a change in temperature but also an increase in polymer concentration in the uncrystallized phase. The gap at TC is larger for lower polymer concentrations, the same as that of ∆. Plots of τ against Cp,UCP are shown in Figure 9. The values of Cp,UCP above TC are the concentrations of the prepared mixtures; thus, we plotted the results at temperatures just above TC and lower than TC. Just below TC, Cp,UCP changes abruptly from the concentration of the prepared mixture above TC to a high concentration below TC. The extrapolation of τ from temperatures below TC shows a smooth connection to the value of τ above TC. This indicates that the gap of τ at TC and also the large temperature dependence of τ below TC are due to the


Figure 10. Symmetric shape parameter β against the polymer concentration in the uncrystallized phase Cp,UCP for the polymer/water mixtures with (orange squares) 20 and (red squares) 40 wt % PVP, (aqua triangles) 10 and (blue triangles) 30 wt % PEI, (bright green tilted squares) 10 and (dark green tilted squares) 30 wt % PVME, and (yellow circles) 10, (gold circles) 20, and (yellow-green circles) 30 wt % PVA. The large symbols are at temperatures just above TC. The “×” symbol is β for pure water at 0.2 °C taken from ref 4. The lines were drawn as a guide to the eyes for 10 wt % PEI/water, PVME/ water, and PVA/water mixtures and the 20 wt % PVP/water mixture.

abrupt change in Cp,UCP at TC and the gradual increase in Cp,UCP. The temperature dependence of the relaxation time of UCW is also affected by the change in the polymer concentration because of the crystallization with decreasing temperature below TC. Therefore, conventional treatments of the apparent activation energy cannot be valid for the relaxation process of UCW, and we do not intend to discuss the apparent activation energies for the relaxation of UCW in the present paper. The sudden and subsequent decrease in β can also be considered to be due to an increase in polymer concentration, the same as for the case of τ. Figure 10 shows the plots of β against Cp,UCP. Even though changes in β in this figure are affected by a change in temperature, β changes smoothly with Cp,UCP. The trace showing smaller β for PEI/water mixtures implies the strongest influence of PEI chains on the dynamics of water molecules. In the partially crystallized polymer/water mixtures, there must be boundaries between the uncrystallized and ice phases. The effect of the ice at the boundaries on the dynamics of UCW can be expected to be different from that of the polymer chain. The effect of the boundaries on the dynamics of molecules in the uncrystallized phase depends on the size of the region of the uncrystallized phase. We could not determine the effect of such boundaries. We suppose that the large sizes of the uncrystallized phase result in a relatively small boundary area and that the effect of the boundaries can be neglected. The ice and uncrystallized phases can sometimes be distinguished by microscope;1 i.e., the sizes of the ice and uncrystallized phases are larger than 1 µm. However, this point is still unclear. The partially crystallized system obtained at various cooling rates that produces various morphologies of uncrystallized and ice phases seems interesting. The comparison between the partially crystallized mixture and the noncrystallized concentrated polymer/ water mixture should also provide some interesting information. Tg and Uncrystallized Water. For the DSC measurements of PVP/water, PVME/water, and PVA/water mixtures, the glass transition occurs at temperatures between -40 and -20 °C. Tg varies with the solute molecular structure but is independent of the concentration of the mixture. For the material to be glass without crystallization, the relaxation time of the molecular

10086 J. Phys. Chem. B, Vol. 111, No. 34, 2007 motion related to the glass transition is 1000-0.1 s at Tg.35-39 According to our observations of partially crystallized polymerwater mixtures, the relaxation time of UCW is several ns at -20 °C (the vicinity of Tg). The molecular motion concerned with this relaxation process with a small relaxation time of several nanoseconds is not the cause of the glass transition at Tg. In addition, the relaxation time of UCW is independent of the chemical structure of the polymer, but Tg depends on the structure. Therefore, we claim that the molecular motion of UCW is not the direct origin of the glass transition. However, the UCW surrounding the polymer chain is indirectly related to the glass transition, as discussed below. Below TC, the major relaxation process of ice at several kilohertz, the contribution of conductivity, and the interfacial polarization prevent us from observing the relaxation process related to the glass transition of the polymer/water mixture.8 Even though poly(vinyl acetate) (PVAc)/benzene mixtures are non-hydrogen-bonding, the DSC curves of PVAc/benzene mixtures show a glass transition step preceding the melting peak of benzene that is similar to those observed for PVP/water, PVME/water, and PVA/water mixtures.40 The local chain motion of PVAc in a partially crystallized benzene mixture has been detected by dielectric measurements.14 The temperature dependence of the relaxation time of the local chain motion of PVAc in the partially crystallized mixture is extremely large because the effect of increasing concentration is also included in the temperature dependence below TC as pointed out in the preceding section. The loss peak in the megahertz range at 4 °C (Tm) shifts to the millihertz range at -16 °C (∼Tg). This means that the local chain motion of PVAc is the origin of the glass transition in the partially crystallized mixture. For the PVP/ water mixtures,32 the local chain motion of PVP was observed at frequencies in the megahertz to kilohertz range. Even in the macroscopically homogeneous polymer/water mixtures, two distinct types of molecular motion with different time scales can coexist.32 In the partially crystallized polymer/water mixtures, it is also expected that the relaxation time of the local chain motion of the polymer suddenly increases below TC. It is expected that the glass transition of the partially crystallized polymer/water mixture is due to the local chain motion of the polymer in the uncrystallized phase. In this case, the rotational motion of water molecules with a relaxation time of several nanoseconds and the local chain motion of the polymer with a relaxation time of about 100 s are expected to coexist in the uncrystallized phase at Tg. This result can be used to solve the problem of the degradation of partially crystallized frozen foods. It has been noted that the temperature dependence exhibited by chemical or biological reactions that take place in frozen foods, although greater than that observed at noncrystallizing temperatures, is generally smaller than that expected from the decrease in viscosity.2 The coexistence of two distinct types of molecular motion with different time scales can clarify this problem. The glass transition prior to the onset of ice melting in foods is related to the molecular motion of solute molecules. On the other hand, the chemical or biological reactions that take place in frozen foods are governed by the molecular motion of uncrystallized water. The temperature dependence of the time scale of the molecular motion of UCW in a partially crystallized aqueous system is larger than that observed above TC, but smaller than that of the solute molecules related to the glass transition. For PEI/water mixtures, the glass transition cannot be observed. It should be caused by the low Cp/UCP in PEI/water

Shinyashiki et al. mixtures. In this case, the PEI chains are surrounded by a larger volume of UCW, and the relaxation time of the PEI chain is small and does not reach 100 s in the temperature range measured by DSC. In contrast, PVME/water mixtures show Tg at the highest value among the polymer/water mixtures examined. It is expected that the largest Cp,UCP, i.e., the smallest volume of UCW due to the motion of the polymer chain, leads to the highest Tg. The independence of Tg on polymer concentration is consistent with that of Cp,UCP on the prepared concentration Cp. The dynamics of molecules in partially crystallized water mixtures are affected by a number of parameters of time and thermal history due to the multi-space- and multi-time-scale heterogeneities. These kinds of systems can be understood by studying a broad variety of experimental results, not the results of a few effective experiments. Needless to say, parallel investigations of the dynamics and morphologies of ice and uncrystallized phases will be effective. Conclusion The following are the experimental results of the dielectric spectroscopy of four types of polymer/water mixtures with polymer concentrations of up to 40 wt % at subzero temperatures. (1) Part of the water crystallized, and the other part of the water remained in a liquid state as UCW, and the dielectric relaxation process of UCW was observed in a frequency range of 10 MHz to 10 GHz at temperatures between 0 and -26 °C. (2) The relaxation strength of UCW decreases with decreasing temperature, since the UCW gradually crystallized with decreasing temperature. The polymer concentrations in the uncrystallized phase Cp,UCP increase with decreasing temperature. (3) The strong temperature dependences of the relaxation time and relaxation time distribution are caused by the increase in Cp,UCP. (4) The relaxation time of UCW does not depend on the prepared polymer concentrations and chemical structures of the polymer; i.e., the plots of τ against temperature form a single trace below TC. This indicates that the criterion determining whether the water joins ice crystals or stays as UCW is the mobility of the water molecules. (5) Up to now, the various properties of partially crystallized materials have been discussed without distinguishing between the types of molecular motion of the constituents. However, two distinct types of molecular motion with different time scales coexist in the uncrystallized phase. One is the molecular motion of water, and the other is that of the solute. The molecular motion of UCW is expected to govern the various timedependent behaviors of partially crystallized aqueous systems. Acknowledgment. This work was financially supported by Grant-in-Aid for Scientific Research (C) (19540429) and that on Priority Areas (18031034) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. References and Notes (1) Franks, F. Water, A ComprehensiVe Treatise; Plenum Press: New York, 1982; Vol. 7, Chapter 3. (2) Simatos, D.; Blond, G. In The Glassy State in Foods; Blanshard, J. M. V., Lillford, P. J., Eds.; Nottingham University Press: Nottingham, U.K., 1993; p 395. (3) Barthel, J.; Bachhuber, K.; Buchner, R.; Hetzenauer, H. Chem. Phys. Lett. 1990, 165, 369. (4) Buchner, R.; Barthel, J.; Stauber, J. Chem. Phys. Lett. 1999, 306, 57. (5) Auty, R. P.; Cole, R. H. J. Chem. Phys. 1952, 20, 1309.

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