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Dielectric Relaxation of Ice in Gelatin–Water Mixtures Takahito Yasuda, Kaito Sasaki, Rio Kita, Naoki Shinyashiki, and Shin Yagihara J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b00149 • Publication Date (Web): 13 Mar 2017 Downloaded from http://pubs.acs.org on March 17, 2017

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The Journal of Physical Chemistry

Dielectric Relaxation of Ice in Gelatin–Water Mixtures Takahito YasudaA, Kaito SasakiA,B, Rio KitaA,B, Naoki ShinyashikiA,* and Shin YagiharaA A

Department of Physics, School of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan

B

Micro/Nano Technology Center, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan

AUTHOR INFORMATION Corresponding Author Phone: +81 (0)463 58 1211 ext. 3706 Fax: +81 (0)463 58 9543 E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Broadband dielectric spectroscopy measurements were performed on partially crystallized gelatin–water mixtures with gelatin concentrations of 1–5 wt. % for temperatures between 123–298 K in order to study the dynamics of ice. These systems contain only hexagonal ice. Four dielectric relaxation processes of ice were nevertheless observed. At temperatures below the crystallization temperature, a loss peak was observed, and it separated into four loss peaks at around 225 K. Using the temperature and concentration dependencies of these relaxation processes, we confirmed that these four processes originated from ice. For the relaxation time of ice, τice, the deviation of the temperature dependence of τice from the Arrhenius type is larger for the relaxation process at higher frequency side. For the temperature dependence of τice for the dominant process, three temperature ranges with different activation energies, Ea, were investigated. The intermediate temperature range of τice with the smallest Ea decreased as the gelatin concentration increased; therefore, τice of the dominant process changed from the relaxation process with smaller τice to that of the larger τice as the gelatin concentration increased. In addition, the relaxation process of ice with larger τice values was found to have larger values of Ea. These results suggest that a greater gel network density affects the temperature dependence of τice.


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INTRODUCTION The dynamics of water in protein–water mixtures are related to our daily lives as they take place in our bodies. Research about the dynamics of ice in partially crystallized protein–water mixtures is the basis of the use of these dynamics in various practical applications such as frozen food. The dielectric relaxation process of ice in pure water has been extensively investigated, both experimentally1–9 and theoretically.10–12 The temperature dependence of the relaxation time of ice, τice, can be classified into two types: the first type shows an Arrhenius temperature dependence across the 207–273 K temperature range;1 the second type, meanwhile, shows changes in the activation energy, Ea, at approximately 230 K2–9 and 140 K.4, 6, 7, 9 The change in Ea is considered to occur due to the change in the relaxation mechanism of water molecules in ice.4, 6, 7, 11 A generally accepted theory for this relaxation mechanism describes it using two wellknown types of orientational defects, Bjerrum’s D- and L-defects.10 A hydrogen bond consists of a hydrogen atom and a negatively charged atom; however, Bjerrum’s theory states that a hydrogen bond may also have either two hydrogens (D-defect) or no hydrogen (L-defect). Impurities in ice are thought to induce more numerous orientational defects.4, 6, 7, 11 The change in Ea at 230 K is thought to be caused by a change in the relaxation mechanism from Bjerrum’s “intrinsic orientational defects” to “impurity-produced orientational defects,” and the change at 140 K is considered to be caused by the reverse transition4, 6, 7, 11. In a previous study, we have reported that the temperature dependencies of these two types of τice can be controlled using the preparation method;9 when ice is prepared by stirring during its preparation, rapid crystallization is avoided and τice exhibits an Arrhenius temperature dependence across a temperature range of 193–273 K. However, when ice is prepared without this treatment, τice shows the aforementioned


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changes in Ea at approximately 230 and 140 K. As per our previous results,9 ice that shows an Arrhenius temperature dependence is expected to contain less “impurity-produced orientational defects” than ice that shows changes in its Ea; this is because the impurities that cause the change in the Ea of ice are expected to be excluded. Numerous studies have investigated the dielectric relaxation process of ice in partially crystallized aqueous mixtures.13–17 For partially crystallized bovine serum albumin (BSA)– water14 and gelatin–water16, 17 mixtures, three dielectric relaxation processes have been observed; those originating from uncrystallized water, from ice, and from hydrated BSA or gelatin. The temperature dependence of τice in BSA–water mixtures exhibited changes in the Ea of the ice 14, whereas for the gelatin–water mixtures, τice was found to have an Arrhenius temperature dependence across the entire range of temperatures measured.16,

17

For the gelatin–water

mixtures, ice crystal formation was considered to have been hindered by the gel network, and the growth rate of ice in these mixtures was expected to be slower than in pure water.17 Moreover, it has been suggested that a slow growth rate of ice induces low concentrations of “impurityproduced orientational defects.” 17 As a result, the temperature dependence of τice in gelatin– water mixtures was not found to show any change in the Ea of ice. Furthermore, a relaxation process that had a similar relaxation time to that of ice in gelatin–water mixtures16,

17

was

observed for partially crystallized glycerol–water mixtures;13 however, this relaxation process was thought to have originated from interfacial water, which is assumed to exist between ice particles and the mesoscopic glycerol–water domain.13 The relaxation processes of interfacial water13 and ice16, 17 were observed in a close-frequency range; however, it is difficult to know if the relaxation processes originated from the ice in the gelatin–water mixtures. A similar relaxation process, which was interpreted as being that of interfacial water, was observed in


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partially crystallized PVP–water mixtures.18 As such, the origin of the relaxation process of ice in gelatin–water mixtures should be defined more clearly. If we investigate this process in gelatin–water mixtures that contain lower concentrations of gelatin, then the temperature dependence of τice will likely show a change in its Ea, and the origin of the relaxation process will become clearer. In this study, we carried out broadband dielectric spectroscopy measurements between 123–298 K for gelatin–water mixtures that had gelatin concentrations of 1–5 wt. %; we did this in order to investigate the change in the temperature dependence of τice from the Arrhenius temperature dependence which found in gelatin–water mixtures with 10 wt. % or more high gelatin content to the temperature dependence of the relaxation time of pure ice.


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EXPERIMENTAL METHODS A. Sample Preparation The gelatin used in this study was obtained from porcine skin, which had been purchased from MP Biomedicals. The gelatin was deionized in order to reduce the influence of ionic contributions; for dielectric spectra, these are direct current (DC) conductivity and electrode polarization (EP). To deionize the gelatin, we formed 5 mm cubes of approximately 10 wt. % aqueous gelatin gel and placed approximately 100 g of these cubes in 2 L of ultrapure distilled and deionized water (Milli-Q water, Milli-Q Lab.); the water had an electrical resistivity of approximately 18.2 MΩcm.16 The ions in the gelatin gel diffused into the water due to the ion concentration gradient. On the first day of the deionization, the water was changed five times. After that, the water was replaced daily for four days. The cubes of the deionized aqueous gelatin gel were then removed from the water and freeze-dried in order to obtain dehydrated gelatin. Appropriate amounts of Milli-Q water were then added to the dried gelatin so as to obtain gelatin–water mixtures that had gelatin concentrations between 1–5 wt. %. The mixtures were then heated to 313 K until the gelatin had completely dissolved; this process took approximately 5 h. B. Broadband Dielectric Relaxation Spectroscopy Measurements

Dielectric measurements were performed on the gelatin–water mixtures between 10 mHz and 10 MHz at temperatures between 123–298 K. An alpha-A analyzer (Novocontrol 10 mHz–10 MHz) with a coaxial capacitor was used, and it had outer and inner diameters of 24 and 19 mm, respectively. The temperature was controlled by a Quarto cryosystem (Novocontrol).


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Measurements were conducted between 123–298 K, at intervals of 5 K. The temperature was changed to the next measurement temperature over the course of 10 min and was then maintained at this temperature for 30 min before the next measurement. A dielectric measurement was performed for approximately 25 min at each temperature. Cooling measurements were also conducted in a similar manner preceding the measurements on heating process; however, only the results obtained during the heating process are discussed in this study.


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RESULTS AND DISCUSSION A. Relaxation Spectra of Ice Figures 1(a) and 1(b) show the frequency dependencies of the real, ε′(f), and imaginary, ε′′(f), parts of the dielectric permittivity of the 2 wt. % gelatin–water mixture between 123–273 K. A loss peak of a relaxation process is observed in the imaginary part, and steps in the real part of the process can be seen at approximately every 5 kHz at 263 K. This relaxation process moves to the lower-frequency side as the temperature decreases, and it disappears at temperatures above 273 K. This relaxation process is comparable with the relaxation process of ice.9,

14, 16, 17

However, as shown in Fig. 1(b), the single loss peak separates into two or more loss peaks at temperatures below 183 K. This property is different from that observed in gelatin–water mixtures that have gelatin concentration of 10 wt. % or more, as such mixtures exhibited a single loss peak over the entire range of temperatures measured.16, 17 For the 2 wt. % gelatin–water mixture, the relaxation process that originated from the hydrated gelatin was also observed at the lower-frequency side. The relaxation process of the hydrated gelatin will be discussed in a future study, as this study only focuses on the relaxation processes potentially related to ice. In addition, the relaxation process of uncrystallized water, which has previously been observed in more concentrated gelatin–water mixtures,16,

17

was not observed for the gelatin–water mixtures

investigated in this study; this is believed to be because the strength of the relaxation process of uncrystallized water decreased as the gelatin concentration decreased, and the uncrystallized water content in this study was considered to be too small to detect. To characterize the relaxation processes, we carried out a curve-fitting procedure. The dielectric constants and losses, including those of the ionic contributions of the gelatin–water mixtures at


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various temperatures, can be described by a simple sum of the relaxation processes given by the Cole–Cole equation19 and DC conductivity: ∗ = +

∆

+ . (1) 1 + ( )

Here, ω is the angular frequency, i is the imaginary unit given by = −1, ε0 is the dielectric constant in a vacuum, ε∞ is the limiting high-frequency dielectric constant, ∆ε is the relaxation strength, τ is the relaxation time, β is the symmetric broadening parameter (0 < ≤ 1), σ is the DC conductivity, and k indicates four relaxation processes of ice, defined as A, B, C, and D, EP, and the relaxation process originated from the hydrated gelatin. Figure 2 shows an example of the curve-fitting procedure; it uses the frequency dependencies of ε′′(f) that were observed for the 2 wt. % gelatin–water mixture at six selected temperatures between 133–263 K. At 133 K, a loss peak can be seen at a frequency of approximately 1 Hz; this relaxation process appears at the highest-frequency side and is labeled as process A. At approximately 10 mHz, another relaxation process, B, is observed. Processes C and D appear at 143 K and 163 K, respectively, in the lowfrequency limit of the measurement. The loss peaks approach one another as the temperature increases. At temperatures above 163 K, the loss peaks of processes A, C, and D cannot be distinguished from those of process B. As the temperature increases further still, processes A, C, and D become unnecessary for reproducing the dielectric spectra at temperatures above 188 K. The relaxation strength, ∆ε, of processes A, B, C, and D, as observed for the 2 wt. % gelatin– water mixture, is shown as a function of temperature in Fig. 3; the ∆ε of pure ice9 is also shown for comparison. The sum of ∆ε of the four processes is plotted for temperatures above 158 K, where all of the processes are in the frequency range measured. The sum of ∆ε of the four


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processes agrees well with the ∆ε of pure ice. This is one of the reasons why processes A, B, C, and D are considered to originate from ice. For the 2 wt. % gelatin–water mixture, process B was found to have the largest ∆ε at temperatures above 150 K. The relaxation process with the largest strength in each mixture will hereafter be referred to as the “dominant process.” B. Change in the Temperature Dependence of τice

The temperature dependencies of τice for processes A, B, C, and D in the gelatin–water mixtures are shown in Fig. 4. Processes A, B, and C were observed for gelatin–water mixtures that had gelatin concentration of 5 wt. % and lower, whereas process D was only observed for concentrations below 3 wt. %. Process D seems to be hidden by process C in the mixtures with gelatin concentrations higher than 3 wt. %. As shown in Figs. 4 (a)–4(d), the dominant process for the 1 wt. % gelatin–water mixture is process A. However, for the 2 and 3 wt. % mixtures, processes B and C are the dominant processes, respectively. The relaxation time of ice observed for gelatin–water mixtures with gelatin concentrations of 10 wt. % and higher has previously been reported,17 and they are given by the gray solid line in all of the panels in Fig. 4. The location of the relaxation times of process D agrees well with that of the gray line. These indicate that the dominant process changes from the relaxation process at the higher-frequency side to that at the lower-frequency side by the increase of gelatin concentration. Figure 5 shows the concentration dependence of ∆ε for processes A, B, C, and D at 153 K, which was the temperature at which all of the processes were observed. The ∆ε of process A decreased as the concentration of gelatin increased. In contrast, the ∆ε of process C increased as the concentration of gelatin increased. This corresponds to the change in the dominant process from processes A to C via B as the concentration of gelatin increases, as shown in Fig. 4. The gelatin


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concentration dependencies of τice and ∆ε lead us to conclude that processes A, B, C, and D originate from ice. Let us discuss the Arrhenius temperature dependence of τice in 10 wt. % gelatin and higher by comparing the dominant processes for gelatin–water mixtures with gelatin concentration of 5 wt. % and less. Figure 6 shows τice for dominant processes of 2 and 4 wt. % gelatin-water mixtures and that for pure ice as a function of temperature. As shown in Fig. 6, Ea shows changes at two temperatures, Tc1 and Tc2. We define the temperature ranges above Tc1, between Tc1 and Tc2, and below Tc2 as high, intermediate, and low temperature ranges, respectively. The intermediate temperature range decreases as the concentration of gelatin increases; therefore, the deviation from the Arrhenius temperature dependence becomes smaller as this concentration increases. Figure 7 shows the concentration dependences of Tc1 and Tc2; the melting points of the gelatin– water mixtures are also shown for the sake of comparison. As shown in Fig. 7, the intermediate temperature range disappears for the gelatin–water mixture when the gelatin concentration is approximately 9 wt. % and greater. This finding can explain why the gelatin–water mixtures with gelatin concentrations of 10 wt. % and greater that we used in our previous study showed an Arrhenius temperature dependence for τice.16, 17 C. Characteristics of the Four Relaxation Processes of Ice

The four relaxation processes of ice observed in this study may not have different ice structures. According to Dowell’s study20 on X-ray diffraction in partially crystallized gelatin–water mixtures, cubic ice is the most common form of ice in gelatin–water mixtures that have gelatin concentrations of 20 wt. % or greater. However, for 10 wt. % gelatin–water mixtures, the cubic


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ice phase is not observed and only hexagonal ice is. 20 As such, we believe that the structure of the ice in our study was hexagonal. In this study, we define T100s at which the relaxation time of ice is 100 s to characterize the relaxation processes. Furthermore, the temperature dependencies of the relaxation times of the dominant processes described above can be divided into three temperature ranges, and Ea and T100s for each temperature range were obtained in order to characterize the relaxation processes of the ice. To obtain Ea and T100s in high, low, and intermediate temperature ranges for processes A, B, C, and D, we used a least squares fit that assumes an Arrhenius temperature dependence. The Arrhenius equation of τice is given by the following equation: = exp $

∆% (. (2) &'

Here, T is the temperature, τ∞Arr is the pre-exponential factor, R is the gas constant, and Ea is the molar activation energy. To clarify the error range of Ea and T100s, the least squares fit was conducted two or three times by choosing the temperatures nearest to Tc1 and Tc2. Plots of Ea as a function of T100s for processes A, B, C, and D are shown in Fig. 8. The plots obtained for the relaxation time of pure ice1, 6, 9 are also plotted in the three temperature ranges for the sake of comparison. In this figure, all plots are located within a limited region from the lower-left-hand side to the upper-right-hand side, indicating that the relaxation processes A, B, C, and D are incorporated around the melting point of ice; this implies that the four processes are of the same origin. The plots of Ea as a function of T100s for the low temperature range can be classified into four specific regions for all four of the processes. This indicates that, even when the concentration of the gelatin in the mixture is different, all four of the processes have the same τice in each mixture. In addition, the characteristics of processes A, B, and C are quite different, but


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those of processes C and D are similar. The values of Ea and T100s in the intermediate temperature range increased as the gelatin concentrations increased. As for the plots of Ea against T100s in the high temperature range, these were found to have no concentration dependences, and all of these plots are located within the narrow region in the upper right-hand side. In Fig. 8, the plots obtained for the relaxation time of pure ice6 at the high, intermediate, and low temperature ranges are located in the upper right-hand side, the lower left-hand side, and the area in-between them, respectively. As mentioned earlier, the impurities in ice are thought to change the relaxation mechanism of water in ice at Tc1 from being “intrinsic orientational defects” to “impurity-produced orientational defects.” 4, 6, 7, 11 Therefore, the plots located in the lower lefthand side imply that the relaxation processes of the ice described this area are strongly affected by the impurities; however, the plots located in the upper right-hand side imply that the relaxation processes of the ice in this area were not affected much by the impurities. This result suggests that the order in which the processes were affected by the impurities at the low temperature range was A, B, C, and D. In addition, the relaxation process of ice in the intermediate temperature range observed for lower concentrations of gelatin–water mixtures seems to have been more affected by the impurities. Greater concentrations of gelatin can be considered to hinder the formation of ice crystals in the mixture; therefore, the growth rate of ice is expected to be slower in more highly concentrated mixtures. This slower growth rate likely induces lower concentrations of “impurity-produced orientational defects.”17 Therefore, the width of the intermediate temperature range also probably depends on the concentration of “impurity-produced orientational defects” in ice. Two theories explaining the change in Ea at Tc1 have been discussed in previous studies.4, 6, 7, 11, 12, 21

Johari et al., 4, 6, 7, 11 proposed that the change in Ea at Tc1 is due to the change in the


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relaxation mechanism of ice from Bjerrum’s D- and L-defects to “impurity-produced orientational defects.” However, Bilgram and Gränicher21 proposed that the change in Ea at Tc1 is due to the change in the relaxation mechanism of ice from Bjerrum’s D- and L-defects to H3O+ and OH− states, respectively; this is known as “proton hopping.” However, the concentration dependence of the relaxation process of ice in the present study does not show any direct evidence for either of these two theories.


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CONCLUSION In this study, the dielectric properties of partially crystallized gelatin–water mixtures with gelatin concentrations between 1–5 wt. % were studied at frequencies from 10 mHz to 10 MHz and between 123–298 K. In our previous study on gelatin–water mixtures,17, 18 a relaxation process of ice with a relaxation time close to that of pure ice1 was observed. However, the temperature dependence of this relaxation process was an Arrhenius type and was completely different from the well-known temperature dependence of pure ice.4 By increasing the concentration of gelatin, we found that the temperature dependence of the relaxation time of pure ice changed to that of the Arrhenius type.1 In addition, four relaxation processes with heterogeneous dynamics were found to originate from ice.

ACKNOWLEDGEMENT This work was partly supported by JSPS KAKENHI Grant Numbers 16K05522, 15K13554, and 24350122 and MEXT-Supported Program for the Strategic Research Foundation at Private Universities, 2014-2018.


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REFERENCES (1) Auty, R. P.; Cole, R. H. Dielectric Properties of Ice and Solid D2O. J. Chem. Phys. 1952, 20, 1309–1314. (2) Worz, O.; Cole, R. H. Dielectric Properties of Ice I. J. Chem. Phys. 1969, 51, 1546–1551. (3) Gough, S. R.; Davidson, D. W. Dielectric Behavior of Cubic and Hexagonal Ice at Low Temperature. J. Chem. Phys. 1970, 52, 5442–5449. (4) Johari, G. P.; Jones, S. T. Dielectric Properties of Polycrystalline D2O Ice Ih (hexagonal). Proc. R. Soc. London, Ser. A 1976, 349, 467–495. (5) Kawada, S. Dielectric Anisotropy in Ice Ih. J. Phys. Soc. Jpn. 1978, 44, 1881–1886. (6) Johari, G. P.; Jones, S. J. The Orientation Polarization in Hexagonal Ice Parallel and Perpendicular to the c-axis. J. Glaciol. 1978, 21, 259–276. (7) Johari, G. P.; Whalley, E. The Dielectric Properties of Ice Ih in the Range 272–133 K. J. Chem. Phys. 1981, 75, 1333–1304. (8) Murthy, S. S. N. Slow Relaxation in Ice and Ice Clathrates and its Connection to the LowTemperature Phase Transition Induced by Dopants. Phase Transitions. 2002, 75, 487–504. (9) Sasaki, K.; Kita, R.; Shinyashiki, N.; Yagihara, S. Dielectric Relaxation Time of Ice-Ih with Different Preparation. J. Phys. Chem. B. 2016, 120, 3950–3953. (10) Bjerrum, N. Structure and Properties of Ice. Science. 1952, 115, 385–390.


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(11) Johari, G. P.; Whalley, E. The Dielectric relaxation Time of Ice V, its Partial AntiFerroelectric Ordering and the Role of Bjerrum Defects. J. Chem. Phys. 2001, 115, 3274– 3280. (12) Popov, I.; Puzenko, A.; Khamzin, A.; Feldman, Y. The Dynamics Crossover in Dielectric Relaxation Behavior of Ice Ih. Phys. Chem. Chem. Phys. 2015, 17, 1489–1497. (13) Hayashi, Y.; Puzenko, A.; Feldman, Y. Slow and Fast Dynamics in Glycerol-Water Mixtures. J. Non-Cryst. Solids. 2006, 352, 4696–4703. (14) Shinyashiki, N.; Yamamoto, W.; Yokoyama, A.; Yoshinari, T.; Yagihara, S.; Kita, R.; Ngai, K. L.; Capaccioli, S. Glass Transition in Aqueous Solutions of Protein (Bovine Serum Albumin). J. Phys. Chem. B. 2009, 113, 14448–14456. (15) Panagopoulou, A.; Kyritsis, A.; Shinyashiki, N.; Pissis, P. Protein and Water Dynamics in Bovine Serum Albumin-Water Mixtures over Wide Ranges of Composition. J. Phys. Chem. B. 2012, 116, 4593–4602. (16) Sasaki, K.; Kita, R.; Shinyashiki, N.; Yagihara, S. Glass Transition of Partially Crystallized Gelatin-Water Mixtures Studied by Broadband Dielectric Spectroscopy. J. Chem. Phys. 2014, 140, 124506–1−7. (17) Sasaki, K.; Kita, R.; Shinyashiki, N.; Yagihara, S. Dynamics of Uncrystallized Water, Ice, and Hydrated Protain in Partially Crystallized Gelatin-Water Mixtures Studied by Broadband Dielectric Spectroscopy. J. Phys. Chem. B. 2016, 121, 265–272.


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(18) Cerveny, S.; Ouchiar, S.; Schwartz, G. A.; Alegria, A; Colmenero, J. Water Dynamics in Poly (vinyl pyrrolidone)-Water Solution Before and After Isothermal Crystallization. J. Non-Cryst. Solids. 2010, 356, 3037–3041. (19) Cole, K. S.; Cole, R. H. Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics. J. Chem. Phys. 1941, 9, 341–351. (20) Dowell, L. G.; Moline, S. W.; Rinfret, A. P. A Low-Temperature X-Ray Diffraction Study of Ice Structures Formed in Aqueous Gelatin Gels. Biochim. Biophys. Acta. 1961, 59, 158– 167. (21) Bilgram, J. H.; Gränicher, H. Defect Equilibriums and Conduction Mechanisms in Ice. J. Phys. Cond. Matter. 1974, 18, 275–291.


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FIGURES

125

(a)

ε'

100

273 K

75 50 25 0

263 K

123 K 183 K 183 K

40

263 K

(b)

ε ''

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20 123 K 273 K

0 −2

0

2

4

6

log[ f (Hz)] Figure 1. Frequency dependencies of the (a) real and (b) imaginary parts of the dielectric functions for 2 wt. % of gelatin–water mixtures at various temperatures between 10 mHz and 10 MHz. The dielectric functions are shown at temperatures from 123–173 K in steps of 10 K, from 183–263 K in steps of 20 K, and at 273 K.


19


60

30

20

10

10

0 60

0 60

143 K

50

30

20

20

10

10

0 60 −2

0

2

4

D

40

B

C

263 K B

50

ε"

30

A

C D

0 60

6

153 K

50 40

183 K

B

50

ε"

C

30

A

D

40

A

B

C

30

20

40

B

40

A

B

163 K

50

ε"

ε"

40

ε"

60

133 K

50

ε"

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 27

A

30

20

20

10

10

dc

0

0 −2

0

2

log [ f (Hz)]

4

6

−2

0

2

4

6

log [ f (Hz)]

Figure 2. The imaginary parts of dielectric functions for 2 wt. % gelatin–water mixtures at various temperatures. The plots were obtained experimentally. The red, orange, green, light blue, and gray solid lines represent processes A, B, C, D, and the DC conductivity, respectively. The black solid lines are the sum of all the processes in each plot. The arrows in each figure specify the relaxation processes described.


20

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T(K) 250

200

4

5

150

125 100

∆ε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


75 50 25 0

6

7

8

−1

1000/T(K ) Figure 3. Temperature dependence of the dielectric relaxation strength of 2 wt. % gelatin–water mixtures for process A (red), B (orange), C (green), and D (light blue). Open circles indicate that their loss peaks are not definitely observed. The black asterisks denote the sum of the relaxation strengths of processes A, B, C, and D, while the black crosses denote the relaxation strength of the pure ice that we obtained in earlier study.9


21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

log [ (s)]


Figure 4. The temperature dependence of the dielectric relaxation times of (a) 1, (b) 2, (c) 3, and (d) 4 wt. % gelatin–water mixtures for processes A (red), B (orange), C (light green), and D (light blue). The plots with black circles denote the dominant process of ice in each gelatin–water mixture. The filled circles indicate loss peaks that were definitely observed, whereas the open circles indicate loss peaks that were not definitely observed. The black pluses and crosses in all of the panels denote the relaxation time of pure ice that we obtained in a previous study.9 The gray lines in all of the panels denote the location of the relaxation times of ice observed for the 10 wt. % gelatin–water mixture.17


22

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140 120 100 80

∆ε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60 40 20 0 0

1

2

3

4

5

Cgelatin(wt %) Figure 5. Concentration dependence of the relaxation strength of processes A (red), B (orange), C (light green), and D (light blue) at the low-temperature range at 153 K. The black open diamonds with plus symbols indicate the sum of the relaxation strengths of process A, B, C, and D. The red and light green curves were drawn by eye. The black dashed line was drawn using a least squares fit for the black open diamonds with plus symbols.


23

Page 24 of 27

0 Tc2 −2 Tc1

−4

(a) pure ice

log[τ(s)]

4

5

6

7

8

0

−2 Tc2 −4

log[τ(s)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

log[τ(s)]


Tc1

(b) 2 wt %

0

−2 Tc2

−4

(c) 4 wt %

Tc1

4

5

6

7

8

−1

1000/T(K ) Figure 6. The temperature dependence of the relaxation time of the dominant process of ice for (a) pure ice,9 (b) 2, and (c) 4 wt. % gelatin–water mixtures. The red and blue vertical dashed lines in each figure indicate Tc1 and Tc2, respectively.


24

Page 25 of 27

liquid state

280 260

Tc1, Tc2 (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


high temperature range

240 220 intermediate temperature 200 range 180

low temperture range

160 140 0

1

2

3

4

5

6

7

8

9 10

Cgelatin(wt %) Figure 7. Concentration dependence of Tc1 and Tc2. The black, red, and blue plots indicate the melting point, Tc1, and Tc2 for each concentration, respectively.


25


70 60

Ea (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 27

50 40 30

low temperature range

high temperature range

20 10 0

intermediate temperature range

80 100 120 140 160 180

T100s (K) Figure 8. Plots of Ea against T100s for processes A (red), B (orange), C (light green), and D (light blue). The triangles, right-pointing triangles, inverted triangles, left-pointing triangles, diamonds, and squares indicate the 1, 2, 3, 4, 5, and 10 wt. % gelatin–water mixtures, respectively. The solid, double, and open plots indicate the low, intermediate, and high temperature ranges, respectively. The plots of pure ice obtained by Auty and Cole1, Johari and Jones6, and our group,9 are represented by the brown, black, and gray circles, respectively.


26

Page 27 of 27

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243x152mm (120 x 120 DPI)


Dielectric Relaxation of Ice in GelatinâWater Mixtures - American

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