Dynamics of Uncrystallized Water, Ice, and Hydrated Protein in

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article

Dynamics of Uncrystallized Water, Ice, and Hydrated Protein in Partially Crystallized Gelatin-Water Mixtures Studied by Broadband Dielectric Spectroscopy Kaito Sasaki, Anna Panagopoulou, Rio Kita, Naoki Shinyashiki, Shin Yagihara, Apostolos Kyritsis, and Polycarpos Pissis J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b04756 • Publication Date (Web): 14 Dec 2016 Downloaded from http://pubs.acs.org on December 16, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28

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

The Journal of Physical Chemistry

Dynamics of Uncrystallized Water, Ice, and Hydrated Protein in Partially Crystallized Gelatin-Water Mixtures Studied by Broadband Dielectric Spectroscopy Kaito Sasaki,†,‡ Anna Panagopoulou,¶ Rio Kita,†,‡ Naoki Shinyashiki,∗,† Shin Yagihara,† Apostolos Kyritsis,¶ and Polycarpos Pissis¶ †Department of Physics, Graduate School of Science, Tokai University, 4-1-1 Kitakaname Hiratuka-shi Kanagawa Japan ‡Micro/Nano Technology Center, Tokai University, 4-1-1 Kitakaname Hiratuka-shi Kanagawa Japan ¶Department of Physics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece E-mail: [email protected] Phone: +81 (0)463 58 1211 ext. 3706

1

ACS Paragon Plus Environment


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

Abstract The glass transition of partially crystallized gelatin-water mixtures was investigated using broadband dielectric spectroscopy (BDS) over a wide range of frequencies (10 mHz - 10 MHz), temperatures (113 - 298 K), and concentrations (10 - 45 wt%). Three dielectric relaxation processes (processes I, II, and III) were clearly observed. Processes I, II, and III originate from uncrystallized water (UCW) in the hydration shells of gelatin, ice, and hydrated gelatin, respectively. A dynamic crossover, called the Arrhenius to non-Arrhenius transition of UCW was observed at the glass transition temperature of the relaxation process of hydrated gelatin for all mixtures. The amount of UCW increases with increasing gelatin content. However, above 35 wt% of gelatin, the amount of UCW became more dependent on the gelatin concentration. This increase in UCW causes a decrease in the glass transition temperature of the cooperative motion of gelatin and UCW, which appears to result from a change in the aggregation structure of gelatin in the mixture at a gelatin concentration of approximately 35 wt%. The temperature dependence of the relaxation time of process II has nearly the same activation energy as pure ice made by slow crystallization of ice Ih. This implies that process II originates from the dynamics of slowly crystallized ice Ih.

Introduction The dynamics of molecules of aqueous protein solutions is an attractive research area because the dynamics of proteins in water are key to life. Various techniques including dielectric spectroscopy, infrared spectroscopy, neutron scattering, X-ray diffraction, nuclear magnetic resonance, and molecular dynamics simulations have been employed to understand the dynamics of proteins and water. 1 In particular, dielectric spectroscopy is an effective technique to detect the dynamics of water, proteins, and their cooperative motions because of its extremely wide time window between mega- and pico-seconds. 2–5 Studies of aqueous protein solutions using dielectric spectroscopy can be classified into

2


Page 2 of 28

Page 3 of 28

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


three areas: the study of solution properties near room temperature, 5–8 at the glass transition in uncrystallized mixtures, 4,9–12 and at the glass transition in partially crystallized mixtures. 2,3,10,13 Of these three types, only a few studies on the glass transition of partially crystallized mixtures have been reported, despite the existence of various molecular dynamics including those of uncrystallized water (UCW), ice, and the cooperative motions of water and solutes. This is because heterogeneous structures primarily due to ice crystal growth at the macroscopic scale prevent the observation of several physical properties as well as the molecular dynamics. 2,3,10,14,15 Studies of hydrated proteins, especially by quasi-elastic neutron scattering, suggest that the transition of water from non-Arrhenius to Arrhenius (nonA-A) occurs at a nonA-A temperature, T nonA−A , of approximately 225 K and that the nonA-A transition results from a water anomaly, i.e., the liquid-liquid transition from a high density liquid to a low density liquid. 16–19 However, the nonA-A transition of water in various non-crystallized aqueous mixtures, which contain alcohols, 20–23 sugars, 24,25 and polymers, 26,27 does not always occur at 225 K, but rather occurs at the glass transition temperature of the structural α process, T g,α of each of the mixtures, which are distributed over a temperature range from 160 to 280 K. Origin of the nonA-A transition has been debated by many scientists. Recently, Cerveny et al. reviewed in their review paper. 28 According to the review paper, three alternative explanations for nonA-A transition are introduced. To discuss the molecular dynamics from liquid to glass states for partially crystallized aqueous protein solutions, we have used broadband dielectric spectroscopy to study gelatin-water mixtures at 40 and 20 wt%. 2 According to the results, three relaxation processes, originating from the dynamics of UCW, ice, and hydrated gelatin were observed. The temperature dependence of the relaxation time of UCW shows a nonA-A transition, which is the same property as the relaxation process of water in various non-crystallized aqueous mixtures. 20–27,29 T nonA−A of UCW in the partially crystallized gelatin-water mixture appears at the glass transition temperature, T g , of the relaxation process of hydrated gelatin. 2,3 The relationship between the relaxation process of UCW and

3



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

that of hydrated gelatin mimics the relationship between the local motion of ordinary glass formers, called the Johari-Goldstein(JG)-β, and cooperative motion, the structural α process. In our previous paper in 2014, we only discussed the origins of relaxation processes and these basic properties. 2 However, detailed discussions of the relaxation processes of partially crystallized gelatin-water mixtures are insufficient in terms of a) the relationship between the nonA- A transition of UCW and the hydrated gelatin dynamics at temperatures near T g , b) the relationship between the amount of UCW and the dynamics of hydrated gelatin, and c) the origin of the relaxation process of ice and its relaxation mechanism. The reason why understanding of partially crystallized aqueous system does not progress in the fields of physical chemistry and also bio physics is lack of the systematic measurements which is due to the fundamental difficulty on its measurements caused by partial crystallization. To understand relationship between the dynamics of protein and water, the changing of some external conditions of protein (temperature, pressure and concentration) must be examined. To discuss the above topics, in this paper, we present detailed studies of these three relaxation processes and the relationship between the nonA-A transition of UCW and the glass transition of the cooperative motion of gelatin and UCW for partially crystallized gelatin-water mixtures with various gelatin concentration. The dynamics of UCW, ice, and hydrated gelatin were investigated by two dielectric techniques, broadband dielectric spectroscopy (BDS) and thermally stimulated depolarization current (TSDC) over a wide gelatin concentration range (10 - 45 wt%) and temperature range (113 - 298 K).

Experimental Sample preparation The protein used in this study was a gelatin obtained from porcine skin purchased from MP Biomedicals. The gelatin was deionized to reduce the ionic interferences, which create direct current (dc) conductivity and electrode polarization (ep) in the dielectric spectra. Details of 4


Page 4 of 28

Page 5 of 28

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


the deionizing procedure are given in our previous paper. 2 Appropriate amounts of distilled and deionized water (Milli-Q water, Milli-Q Lab., Simplicity UV) with an electrical resistivity of approximately 18.2 MΩ·cm were added to the gelatin to obtain 45, 40, 35, 30, 25, 20, 15, and 10 wt% gelatin-water mixtures. The mixtures were heated to 313 K until the undissolved gelatin completely dissolved.

Broadband dielectric relaxation spectroscopy measurements Dielectric measurements were performed in a frequency range of 10 mHz - 10 MHz and at temperatures between 113 and 298 K. We used an Alpha A analyzer (Novocontrol) equipped with a coaxial capacitor with 24 and 19 mm outer and inner diameters, respectively. The temperature was controlled with a Quatro cryosystem (Novocontrol). Measurements for the 10 to 45 wt% gelatin-water mixtures were carried out at temperatures from 113 to 253 K at 10 K intervals, from 253 to 273 K at 1 K intervals, and from 273 to 298 K at 5 K intervals. The mixtures, especially with high gelatin concentrations, gelatin-water solution immediately shows gelation when the mixture is poured into measurement cell. To reduce the heterogeneity of gel structure of the mixture, just before the series of measurements, the temperature of the mixture in the electrode was raised to 323 K and held constant for approximately 30 min. Then, the temperature was lowered from 323 to 113 K for 2 h and held constant at 113 K for 30 min before the dielectric measurement at 113 K. The temperature was then raised to the next measurement temperature over 10 min and was maintained at that value for 30 min before to the following measurement. This procedure was repeated for each of the measurements. In general, the dynamics of water during cooling are difficult to describe because supercooled water crystallizes spontaneously during cooling, and the crystallization temperature is sensitive to the thermal history. Therefore, we can only discuss the results obtained during the heating process.

5



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

Thermally stimulated depolarization current TSDC is a dielectric technique in the temperature domain, which corresponds to measuring the dielectric loss as a function of temperature at a fixed low frequency range, i.e., 10−4 -10−2 Hz (equivalent frequency). 30 In this technique, the sample is inserted between the parallel plates of a capacitor and polarized by the application of an electric field, Ep , at a temperature, Tp , for a time, tp , which is large compared to the relaxation time of the dielectric relaxation under investigation. While applying the electric field, the sample is cooled to a temperature, T0 , which is sufficiently low to prevent thermal depolarization, and then the sample is shortcircuited and reheated at a constant rate. The discharge current generated during heating is measured as a function of temperature using a sensitive electrometer. The technique is characterized by high sensitivity and high resolving power. TSDC measurements were carried out in the temperature range from 113 to 273 K using a Keithley 617 electrometer in combination with a Novocontrol sample cell. Typical experimental conditions were Tp = 253 K, Ep = 2 kV/cm, tp = 5 min, a cooling rate of 10 K/min to T0 = 113 K, and a heating rate of 3 K/min.

Results BDS measurements Figure 1 shows typical dielectric relaxation spectra of the real and imaginary parts of the complex permittivity plotted as a function of the frequency for the 30 wt% gelatin-water mixture from 123 to 263 K at every 10 K. There are three main relaxation processes. The fastest relaxation process, process Ia, is located at 10 Hz at a temperature of 143 K. The middle relaxation process, process IIa, is located at 1 Hz at a temperature of 173 K. The slowest process, process IIIa, is located at 1 Hz at a temperature of 243 K. The loss peak of process IIIa is hidden by the dc-conductivity, except at 263 K. All processes are shifted to

6


Page 6 of 28

Page 7 of 28

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


higher frequencies with increasing temperature. To characterize all the processes, curve-fitting procedures were applied. However, it is impossible to completely fit the curve with four Havrilak-Negami functions composed of three relaxation processes (Ia, IIa, and IIIa), the electrode polarization (ep), and the dc conductivity. 2 As an example of the fitting procedure, Fig. 2 shows the curves obtained by fitting Eq. (1) and the data obtained experimentally for the complex permittivities at 243, 203, and 163 K. A small relaxation process, process Ib, located between processes I and II, can be seen in Figs. 2c and 2d. This small process appears at temperatures above 183 K. A small hump, hump IIb, is located on the lower frequency side of the real part of process II at 243 K (Fig. 2 a). Hump IIb cannot be found at temperatures above 203 K because it is obscured by relaxation process III. In addition, hump IIb cannot be identified as a relaxation process. After applying curve fitting, assuming an additional Havriliak-Negami equation was found to be necessary for describing hump IIb. However, the relaxation strength and relaxation time of the additional Havriliak-Negami equation were highly sensitive to the assumed relaxation functions of the major relaxations. Conversely, process Ib can be seen, independently, in the real part as the step in Fig. 2c. Therefore, the three major relaxation processes and process Ib are obvious and originate from molecular motion. Additional functions for process Ib and hump IIb will not be discussed because they are used in the fitting procedure to give the best fit and these were not needed at temperatures lower than 163 K. The dielectric constants and losses for the gelatin-water mixtures at various temperatures can be described by the simple sum of the relaxation processes as given by the Havriliak-Negami equations and the contribution from the dc conductivity as

ε∗ = ε∞ +

X k

∆εk (1 + (iωτk

)βk )αk

+

σ . iωε0

(1)

Here, ω is the angular frequency, i is the imaginary unit given by i 2 = −1, ε0 is the dielectric constant in vacuum, ε∞ is the limiting high-frequency dielectric constant, ∆ε is the relaxation

7



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

strength, τ is the relaxation time, β is the symmetric broadening parameter (0 < β ≤ 1), α is the asymmetric broadening parameter (0 < α ≤ 1), σ is the dc conductivity, and k = I, Ib, II, IIb, III, and ep. Figure 3 shows the temperature dependence of τI and τIII . Additionally, τI determined by peak frequency of process I are plotted together by cross symbol and these are agree with τI which are determined by curve fitting procedures. Figure 4 shows the temperature dependence of τII with literature values 31,32 of pure ice for comparison.

TSDC measurements Figure 5 shows the TSDC thermograms for the 10 and 30 wt% gelatin-water mixtures with Tp = 253 K. From the TSDC measurement, we see that the peak of the thermogram is related to Tg because the depolarization current is a discharge phenomenon resulting from the dipole moment of the unfreezing molecular motion as the temperature increases. In every thermogram, three peaks are observed, which are indicated by the arrows in Fig. 5. We assumed that the peak temperatures are the TSDC-derived glass transition temperatures, Tg,TSDC . The peaks are named peaks I, II, and III from low to high temperature. The lowest Tg,TSDC,I is located at temperatures between 113 and 143 K and does not depend on the concentration. The middle Tg,TSDC,II is located at temperatures between 140 and 160 K and is unchanged or slightly decreased with increasing concentration. The highest Tg,TSDC,III is located at temperatures between 190 and 210 K.

Glass transition temperatures The relationship between the Tg obtained by thermal analysis and that obtained by dielectric spectroscopy has already been investigated in an aqueous solution. 24 According to the previous investigation, τ for the relaxation process that induces the glass transition is 100-1000 s at Tg as determined by differential scanning calorimetry (DSC). In this study, we defined the glass transition temperature, Tg,τ , as the temperature at which the relaxation time is 100 - 1000 s by extrapolating from a relaxation time of less than 100 s for each relaxation 8


Page 8 of 28

Page 9 of 28

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


process. At temperatures just above Tg,τ of processes I and III, for the plots shown in Fig. 3 as filled symbols, the temperature dependence of τI , τII , and τIII can be described by the Arrhenius equation, τ = τ∞Arr exp

∆E RT

,

(2)

where T is the absolute temperature, τ∞Arr is the pre-exponential factor, R is the gas constant, and ∆E is the apparent molar activation energy. The filled symbols in Fig. 3 were used for fitting with the Arrhenius equation. However, Tg,τ,III for the 10 wt% gelatin-water mixture cannot be determined because the number of plots, which can be described by the Arrhenius type temperature dependence, is not sufficient because process III is covered by ep at temperatures lower than 243 K. The activation energies of processes I and II were approximately 50 kJ/mol and 43 kJ/mol, respectively. These values are almost independent from the concentration of gelatin. Additionally, in fig. 6, the temperature dependence of τI and τIII for 20 wt% gelatin-water mixture are shown. The temperature dependence of τI deviates from the Arrhenius temperature dependence at around Tg,τ,III . The gelatin concentration, Cg (wt%) and dependencies of Tg,τ of the relaxation processes I, II, and III are shown in Fig. 7 together with Tg,TSDC,I for each of the peaks as determined by the TSDC measurements. Tg,τ clearly agrees with Tg,TSDC . The T g observed for the gelatin water mixture measured by DSC 33 is also plotted in Fig. 7. Although in the thermal history of the DSC measurements is totally different from our BDS measurements, the Tg,III obtained by DSC 33 agrees well with Tg,τ and Tg,TSDCIII . These correspondences suggest that the dielectric relaxation processes observed by BDS, the peaks observed by TSDC, and the Tg,III obtained by DSC all have the same origin. Tg,τ,I and Tg,τ,II are nearly independent of Cg for the concentration range measured. Below 35 wt% gelatin, T g,τ,III is approximately 190 K and has no Cg dependence. On the other hand, above 35 wt%, T g,τ,III decreases with increasing Cg . This Cg dependence of T g,τ,III is strongly related to the amount of UCW per gelatin amount. This point will be discussed further in the discussion section. 9



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

Discussion Relationship between Tg,τ,I of process III and the amount of uncrystallized water Figure 8 shows the temperature dependence of τIII , the inverse temperature derivative of τIII , d(logτIII )/d(103 /T ), and ∆εI for the 10 and 30 wt% gelatin-water mixtures. The relaxation process I is at a frequency higher than our measurement in this temperature range. Therefore, τI and βI cannot be estimated. On the other hand, ∆εI can be estimated by the fitting procedure using Eq. 1 assuming that ε∞ is independent of the temperature. For the 10 wt% gelatin-water mixture, ∆εI increases from 263 K to higher temperatures due to the melting of ice. τIII also decreased steeply with an increase in temperature at the same temperatures. d(logτIII )/d(103 /T ) also increases with increasing temperature. The temperature dependence of τIII is affected by two factors. One is the decrease in τIII by a simple activation effect, and the other is the plasticization effect from the increase in the amount of UCW with melting ice. This means that, for the temperature at which ice is melting, the effect of the later is added to the former and the temperature dependence of τIII is expected to be larger. According to the relationship between the temperature dependences of τIII , d(logτIII )/d(103 /T ), and ∆εI , for the 10 wt% gelatin-water mixture, the decrease in the gelatin concentration in the uncrystallized phase, Cg,UCP , i. e., the increase in the amount of UCW from the melting of ice can be monitored by the increase in ∆εI with increasing temperature above 263 K, and then, hydrated gelatin, the source of process III, is plasticized and this gives rise to a steeper decrease in τIII . On the other hand, the temperature dependence of ∆εI for the 30 wt% gelatin-water mixture shows a peak at 263 K. At temperatures from 259 to 263 K, ∆εI increases with temperature due to the melting of ice. Between 263 and 265 K, ∆εI decreases with increasing temperature, due to the cold crystallization of UCW. The cold crystallization of gelatin-water mixtures were also reported by Nishinari et al. with DSC measurements. 33 Above 265 K, ∆εI 10


Page 10 of 28

Page 11 of 28

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


increases drastically with increasing temperature due to ice melting. This cold crystallization may highly depend on thermal history of the mixture. Recently, dynamics of UCW during ice formation on heating in glycerol-water mixtures is discussed by Popov et al. 34 Also Cerveny et al. discuss dynamics of water in poly(vinyl pyrrolidone)-water mixture before and after isothermal crystallization. 35 Contrastingly, the temperature dependence of τIII changes at 265 K which is the same temperature as the temperature dependence of the ∆εI change. For the 30 wt% gelatin-water mixture, d(logτIII )/d(103 /T ) is almost constant at temperatures between 253 and 259 K. In this temperature range, Cg,UCP does not change because ∆εI is almost constant. Increasing the temperature from 259 to 266 K, d(logτIII )/d(103/T ) yields a peak. Above 266 K, d(logτIII )/d(103/T ) and ∆εI increase with increasing temperature. This correlation between d(logτIII )/d(103 /T ) and ∆εI indicates that the decrease in τIII is the result of an increase in the amount of UCW. Therefore, the change in the temperature dependence of τIII is strongly affected by the plasticization of gelatin due to increasing UCW. Figure 9 shows the gelatin concentration, Cg , and the dependence of ∆εI at 163 K. Near 163 K, ∆εI is nearly temperature independent for all concentrations of the gelatinwater mixtures and a value of ∆εI at 163 K can be used to discuss Cg,UCP . Above 35 wt% gelatin, ∆εI increases drastically with increasing gelatin concentration. The increase in ∆εI implies an increased amount of UCW. The slope of the concentration dependence of ∆εI corresponds to the amount of UCW per unit amount of gelatin. The steeper slope of the mixtures above a concentration of 35 wt% gelatin implies the presence of a large amount of UCW per gelatin. The values of the slopes are approximately 0.24 wt%−1 below 35 wt% gelatin and approximately 1.4 wt%−1 above 35 wt% gelatin. The estimation of the absolute amount of UCW per unit weight of gelatin is impossible because we do not know the ∆ε of pure water at 163 K. However, the ratio 1.3/0.24 is 5.4, which means that the ratio of the increase in UCW per unit weight of gelatin above 35 wt% is 5 times larger than that below 35 wt% gelatin. In general, the solute in the mixture is plasticized by the solvent, and the T g of the solute decreases with increasing solvent concentration. In this system,

11



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

plasticization of the gelatin seems to occur by UCW in the uncrystallized phase because the growth of ice crystals on cooling excludes the gelatin molecules, and gelatin is condensed in the uncrystallized phase with UCW. UCW acts as a plasticizer for the gelatin molecules in the uncrystallized phase and an increase in UCW lowers T g,III above 35 wt% gelatin as shown in Fig. 7. The origin of the larger amount of UCW per unit weight of gelatin above 35 wt% gelatin is still unclear. A possible explanation is the difference in the gel structure of gelatin above and below 35 wt% gelatin.

Non-Arrhenius-to-Arrhenius transition of uncrystallized water In general, glass forming materials have two distinct relaxation processes that are called structural α relaxation and local β relaxation. The relaxation time of the β relaxation has an Arrhenius temperature dependence at temperatures below T g of the α relaxation. The Arrhenius temperature dependence of the relaxation time of the β-relaxation, τJGβ , does not continue to temperatures above T g and changes to the Vogel-Fulcher (VF) temperature dependence, τ = τVF exp[A/(T − T0 )]. 36,37 The dynamics of a rigid molecule from the liquid state to the glass state was investigated in the 1970s by Johari and Goldstein. 38,39 They discovered the universality of the existence of the secondary JG-β relaxation in glass-forming materials. Recently, it was discovered that JG-β relaxation is related to α relaxation and the relationship between them can be described by the coupling model presented by Ngai. 40 For aqueous solutions, a number of studies have demonstrated that the relaxation process of water in a mixture has the same temperature dependence as the JG-β relaxation. 29,41 Our previous study also demonstrated that the relationship between the α relaxation of hydrated gelatin and the relaxation of water mimic that between α and JG-β relaxations in glassy materials only for 20 and 40 wt% gelatin-water mixtures. 2 According to our results for all gelatin-water mixture concentrations, the temperature dependence of τI deviates from the Arrhenius type temperature dependence in the same temperature range at T g,III which is shown by the gray area in Fig. 3. As shown in fig. 12


Page 12 of 28

Page 13 of 28

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


6, T nonA−A can be determined as intersection of Arrhenius type and Vogel-Fulcher type temperature dependences of τI and it agrees well with T g,III . 2 In Fig. 7, T nonA−A is plotted with T g,I , T g,II , and T g,III . For T nonA−A in Fig. 7, error bars are given by 11 K according to our previous study. 2 T nonA−A clearly agrees with T g,III for all gelatin concentrations. These findings indicate that the relationships between relaxation processes I and III are similar to that between the α and JG-β relaxations. As mentioned in the introduction, sometimes the nonA-A transition of the relaxation time of water is understood to result from a liquid to liquid transition of water at a fixed temperature of approximately 225 K. However, our result suggests that the nonA-A transition of the relaxation time of process I, i.e., that of UCW in partially crystallized gelatin-water mixture, occurs at T g,III . T g,III is in the range of 164 - 196 K, which is lower than 225K. It should be noted that, according to the last section and the previous study on gelatin-water mixtures, 2 nonA-A transition of the process I does not related to ice melt. It is because that ∆εI does not change at T g,III . Therefore, for the partially crystallized gelatin-water mixture, the nonA-A transition of the process I is not related to the liquid to liquid transition of water.

Relaxation process of ice The temperature dependences of the relaxation times of pure ice and ice in the gelatin-water mixtures are shown in Fig. 4. The temperature dependence of the relaxation time of pure ice can be divided into two types. One shows an Arrhenius type temperature dependence across the entire temperature range. The other shows a change in the apparent activation energy at approximately 230 K. The former was reported by Auty et al. 32 and the latter has been reported by multiple researchers. 31,42–45 Johari and Whalley suggested that the change in the temperature dependence of the relaxation time of pure ice at 230 K is caused by the change in the relaxation mechanism from an intrinsically generated defect to impurity generated defect. 31,46 Alternatively, it is sometime discussed that the change of the temperature dependence of the relaxation time of pure ice is caused by the change in the relaxation 13



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

mechanism from intrinsically generated defect to ionic defects. 47 Recently, we succeeded in reproducing both ices with different preparation methods. 48 According to our study of the temperature dependence of τ of pure ice, the relaxation time of ice is influenced by the ice crystal growth process. Slow crystallization growth induces a relaxation time of ice with a constant activation energy, as found by Auty et al. in 1952. 32 This can be interpreted as impurities being coaxed out of ice crystals by slow crystallization, reducing the concentration of the impurities generated defects in ice. In the relaxation times of process II, τII is placed between those of the two types of pure ice. 31,32 However, the temperature dependence of τII indicates no change in the apparent activation energy. Here, the concentration of intrinsic defects is so high that the τII value is smaller than those of the relaxation times of pure ice. 31,32 These defects dictate the relaxation mechanism of ice in the entire temperature range and makes the activation energy of process II constant. In the gelatin-water mixtures, ice crystal formation is hindered by the gel network and the growth rates of the ice in the mixtures appear to be slow. Slow growth rates probably induce low concentrations of impurity generated defect in ice. The Cg dependence of the relaxation strength of process II, ∆εII at 163 K is shown in Fig. 9. The relaxation strengths of pure ice measured by Johari 31 and us, are also plotted in Fig. 9, which shows that ∆εII decreases linearly with increasing Cg . The extrapolated ∆εII to zero gelatin concentration is placed between the relaxation strengths of pure ice measured by Johari 31 and us. This disagreement among ∆εII of pure ice and extrapolated to zero gelatin concentration value is caused by our measurement setup and fundamental difficulty on controlling density of defects in ice. Because of them, 10 % of ∆εII error for our measurements of pure ice and gelatin-water mixtures are inevitable. These results suggest that ∆εII reflects the amount of ice in the mixture. The lowest uncrystallizable concentration can be obtained from Fig. 9 by extrapolating to the zero magnitude of ∆εII , which is at approximately 65 wt% of gelatin. Therefore, we strongly suggest that process II originates from ice. However, the change of slope in the concentration dependence of ∆εII such as

14


Page 14 of 28

Page 15 of 28

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


that of ∆εI can not be observed. Notwithstanding, ∆εII shows reasonable concentration dependence.

Conclusions In this paper, we reported the dielectric properties of partially crystallized gelatin-water mixtures with various concentrations. The dielectric measurements allowed to observe the relaxation processes of UCW, ice, and hydrated gelatins. We conclude the following. (1)The nonA-A transition of the relaxation process of water in the gelatin-water mixtures is not related to the liquid to liquid transition between high and low density liquids but is related to the glass transition. It indicates that the relationship between process III and I mimics that of the α and JG-β process. (2)The relaxation strength of process II decreases with increasing gelatin concentration. The relaxation time of process II is found to be between those of two types of pure ice and the relaxation time of process II shows no change of the temperature dependence. These findings implies that process II originates from intrinsically generated defect in the ice crystal. (3)Ice in partially crystallized gelatin-water mixtures has the same characteristic properties as those of Auty’s ice in terms of the constant apparent activation energy and its value. This suggests that ice crystal formation in the gelatin-water mixture is hindered by the gel network and therefore the growth rates of the ice in the mixtures appear to be low. (4)The concentration dependence of the amount of UCW in the mixture becomes stronger above 35 wt% gelatin. The larger amount of UCW per unit weight of gelatin above 35 wt% gives rise to the plasticization of hydrated gelatin and the reduces the relaxation time of process III and the glass transition temperature of process III (5)The remarkable relationships of the temperature dependences between the amount of UCW and the relaxation time of process III demonstrates the plasticization of the solute by the melting of ice i.e., the increase in UCW. This implies that the origin of process III is a

15



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 16 of 28

structural relaxation of hydrated gelatin.

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.

References (1) Ringe, D.; Petsko, G. A. The ’Glass Transition’ in Protein Dynamics: What it is, Why it Occurs, and How to Exploit it. Biophys. Chem. 2003, 105, 667–680. (2) 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. (3) Shinyashiki, N.; Yamamoto, W.; Yokoyama, A.; Yoshinari, T.; Yagihara, S.; Kita, R.; Ngai, K. L.; Capaccioli, S. Glass Transitions in Aqueous Solutions of Protein (Bovine Serum Albumin). J. Phys. Chem. B 2009, 113, 14448–14456. (4) Jansson, H.; Bergman, R.; Swenson, J. Role of Solvent for the Dynamics and the Glass Transition of Proteins. J. Phys. Chem. B 2011, 115, 4099–4109. (5) Cametti, C.; Marchetti, S.; Gambi, C. M. C.; Onori, G. Dielectric Relaxation Spectroscopy of Lysozyme Aqueous Solutions: Analysis of the δ-Dispersion and the Contribution of the Hydration Water. J. Phys. Chem. B 2011, 115, 7144–7153. (6) Wolf, M.; Gulich, R.; Lunkenheimer, P.; Loidl, A. Relaxation Dynamics of a Protein Solution Investigated by Dielectric Spectroscopy. Biochim. Biophys. Acta 2012, 1824, 723–730. 16


Page 17 of 28

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


(7) Cametti, C.; Marchetti, S.; Onori, G. Lysozyme Hydration in Concentrated Aqueous Solutions. Effect of an Equilibrium Cluster Phase. J. Phys. Chem. B 2013, 117, 104– 110. (8) Hayashi, Y.; Oshige, I.; Katsumoto, Y.; Omori, S.; Yasuda, A. Protein-Solvent Interaction in Urea-Water Systems Studied by Dielectric Spectroscopy. J. Non. Cryst. Solids. 2007, 353, 4492–4496. (9) Panagopoulou, A.; Kyritsis, A.; Aravantinou, A. M.; Nanopoulos, D.; Serra, R. S. I.; Ribelles, J. L. G.; Shinyashiki, N.; Pissis, P. Glass Transition and Dynamics in LysozymeWater Mixtures over Wide Ranges of Composition. Food Biophys. 2011, 6, 199–209. (10) 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. (11) Panagopoulou, A.; Kyritsis, A.; Vodina, M.; Pissis, P. Dynamics of Uncrystallized Water and Protein in Hydrated Elastin Studied by Thermal and Dielectric Techniques. Biochim. Biophys. Acta 2013, 1834, 977–988. (12) Jansson, H.; Swenson, J. The Protein Glass Transition as Measured by Dielectric Spectroscopy and Differential Scanning Calorimetry. Biochim. Biophys. Acta 2010, 1804, 20–26. (13) Nakanishi, M.; Sokolov, A. P. Protein Dynamics in a Broad Frequency Range: Dielectric Spectroscopy Studies. J. Non. Cryst. Solids. 2015, 407, 478–485. (14) Shinyashiki, N.; Shimomura, M.; Ushiyama, T.; Miyagawa, T.; Yagihara, S. Dynamics of Water in Partially Crystallized Polymer/Water Mixtures Studied by Dielectric Spectroscopy. J. Phys. Chem. B 2007, 111, 10079–10087.

17



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 18 of 28

(15) Hayashi, Y.; Puzenko, A.; Feldman, Y. Slow and Fast Dynamics in Glycerol-Water Mixtures. J. Non. Cryst. Solids. 2006, 352, 4696–4703. (16) Mallamace, F.; Corsaro, C.; Baglioni, P.; Fratini, E.; Chen, S. H. The Dynamical Crossover Phenomenon in Bulk Water, Confined Water and Protein Hydration Water. J. Phys. Condens. Matter 2012, 24, 064103. (17) Chen, S. H.; Zhang, Y.; Lagi, M.; Chong, S. H.; Baglioni, P.; Mallamace, F. Evidence of Dynamic Crossover Phenomena in Water and Other Glass-Forming Liquids: Experiments, MD Simulations and Theory. J. Phys. Condens. Matter 2009, 21, 504102. (18) Chen, S. H.; Lagi, M.; Chu, X. Q.; Zhang, Y.; Kim, C.; Faraone, A.; Fratini, E.; Baglioni, P. Dynamics of a Globular Protein and its Hydration Water Studied by Neutron Scattering and MD Simulations. J. Spectrosc. (Hindawi) 2010, 24, 1–24. (19) Mallamace, F.; Broccio, M.; Corsaro, C.; Faraone, A.; Wanderlingh, U.; Liu, L.; Mou, C. Y.; Chen, S. H. The Fragile-to-Strong Dynamic Crossover Transition in Confined Water: Nuclear Magnetic Resonance Results. J. Chem. Phys. 2006, 124, 161102. (20) Sudo, S.; Shimomura, M.; Saito, T.; Kashiwagi, T.; Shinyashiki, N.; Yagihara, S. Dielectric Study on α- and β-Processes in Supercooled Diethyleneglycol- and Pentaethyleneglycol-Water Mixtures. J. Non. Cryst. Solids. 2002, 305, 197–203. (21) Sudo, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. Broadband Dielectric Study of α-β Separation for Supercooled Glycerol-Water Mixtures. J. Non. Cryst. Solids. 2002, 307, 356–363. (22) Sudo, S.; Tsubotani, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. Dielectric Study of the α and β Processes in Supercooled Ethylene Glycol Oligomer-Water Mixtures. J. Chem. Phys. 2004, 121, 7332–7340.

18


Page 19 of 28

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


(23) Sudo, S.; Shimomura, M.; Kanari, K.; Shinyashiki, N.; Yagihara, S. Broadband Dielectric Study of the Glass Transition in Poly(ethyleneglycol)-Water Mixture. J. Chem. Phys. 2006, 124, 044901–044901. (24) Shinyashiki, N.; Shinohara, M.; Iwata, Y.; Goto, T.; Oyama, M.; Suzuki, S.; Yamamoto, W.; Yagihara, S.; Inoue, T.; Oyaizu, S. et al. The Glass Transition and Dielectric Secondary Relaxation of Fructose-Water Mixtures. J. Phys. Chem. B 2008, 112, 15470–15477. (25) Kwon, H. J.; Seo, J. A.; Kim, H. K.; Hwang, Y. H. A Study of Dielectric Relaxations in Galactose-Water Mixtures. J. Non. Cryst. Solids. 2010, 356, 2836–2841. (26) Cerveny, S.; Alegria, A.; Colmenero, J. Broadband Dielectric Investigation on Poly(vinyl pyrrolidone) and its Water Mixtures. J. Chem. Phys. 2008, 128, 044901. (27) Singh, L. P.; Cerveny, S.; Alegria, A.; Colmenero, J. Dynamics of Water in Supercooled Aqueous Solutions of Poly(propylene glycol) As Studied by Broadband Dielectric Spectroscopy and Low-Temperature FTIR-ATR Spectroscopy. J. Phys. Chem. B 2011, 115, 13817–13827. (28) Cerveny, S.; Mallamace, F.; Swenson, J.; Vogel, M.; Xu, L. Confined Water as Model of Supercooled Water. Chem. Rev. 2016, 116, 7608–7625, PMID: 26940794. (29) Shinyashiki, N.; Sudo, S.; Yagihara, S.; Spanoudaki, A.; Kyritsis, A.; Pissis, P. Relaxation Processes of Water in the Liquid to Glassy States of Water Mixtures Studied by Broadband Dielectric Spectroscopy. J. Phys. Condens. Matter 2007, 19, 205113. (30) Sessler, G.; Shahi, K. Electrets, Topics in Applied Physics. J. Electrochem. Soc. 1980, 127, 530C–530C. (31) Johari, G. P.; Whalley, E. The Dielectric Properties of Ice Ih in the Range 272-133 K. J. Chem. Phys. 1981, 75, 1333. 19



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 28

(32) Auty, R. P.; Cole, R. H. Dielectric Properties of Ice and Solid D2 O. J. Chem. Phys. 1952, 20, 1309–1314. (33) Nishinari, K.; Watase, M.; Hatakeyama, T. Effects of Polyols and Sugars on the Structure of Water in Concentrated Gelatin Gels as Studied by Low Temperature Differential Scanning Calorimetry. Colloid Polym. Sci. 1997, 275, 1078–1082. (34) Popov, I.; Greenbaum, A.; Sokolov, A. P.; Feldman, Y. The Puzzling First-Order Phase Transition in Water-Glycerol Mixtures. Phys. Chem. Chem. Phys. 2015, 17, 18063– 18071. (35) Cerveny, S.; Ouchiar, S.; Schwartz, G.; 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. (36) Vogel, H. The Law of the Relation Between the Viscosity of Liquids and the Temperature. Phys. Z. 1921, 22, 645–646. (37) Fulcher, G. Analysis of Recent Measurements of the Viscosity of Glasses. J. Am. Ceram. Soc. 1925, 8, 339–355. (38) Johari, G.; Goldstein, M. Viscous Liquids and the Glass Transition. II. Secondary Relaxations in Glasses of Rigid Molecules. J. Chem. Phys. 1970, 53, 2372–2388. (39) Johari, G.; Goldstein, M. Viscous Liquids and the Glass Transition. III. Secondary Relaxations in Aliphatic Alcohols and Other Nonrigid Molecules. J. Chem. Phys. 1971, 55, 4245–4252. (40) Ngai, K. L.; Paluch, M. Classification of Secondary Relaxation in Glass-Formers Based on Dynamic Properties. J. Chem. Phys. 2004, 120, 857–873. (41) Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. The Johari-Goldstein β-Relaxation of Water. J. Phys. Chem. B 2007, 111, 8197–8209. 20


Page 21 of 28

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


(42) Johari, G. P.; Jones, S. J. The Orientation Polarization in Hexagonal Ice Parallel and Perpendicular to the c-Axis. J. Glaciol. 1978, 21, 259. (43) Gough, S. R.; Davidson, D. W. Dielectric Behavior of Cubic and Hexagonal Ices at Low Temperature. J. Chem. Phys. 1970, 52, 5442. (44) Kawada, S. Dielectric Anisotropy in Ice Ih. J. Phys. Soc. Jpn. 1978, 44, 1881. (45) Wörz, O.; Cole, R. H. Dielectric Properties of Ice Ih. J. Chem. Phys. 1969, 51, 1546. (46) 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. (47) Popov, I.; Puzenko, A.; Khamzin, A.; Feldman, Y. The Dynamic Crossover in Dielectric Relaxation Behavior of Ice Ih. Phys. Chem. Chem. Phys. 2015, 17, 1489–1497. (48) 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.

21



10

'

10 10 10 10 10 10

''

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

10 10

Page 22 of 28

5 4 3 2 1 6 4 2 0

-2

10

-2

0

2 4 log [ f (Hz)]

6

Figure 1: Frequency dependencies of the real and imaginary parts of dielectric functions for the 30 wt% gelatin-water mixture over a range of temperatures and at frequencies between 10 mHz and 10 MHz. The dielectric functions are shown at temperatures from 123 to 263 K in 10 K steps.

22


Page 23 of 28

243 K (a) 4

10

2

ε'

ε"

10

10

6

10

4

10

2

243 K (b)

0

10 4 10

10

1

10

2

ε"

10

163 K (e)

10

10

203 K (d)

2

10

0

10

2

10

1

10

0

ε"

ε'

203 K (c) 2

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


163 K (f)

1

10 -2

0

2

4

6

8

log [ f (Hz)]

-1

-2

0

2

4

6

8

log [ f (Hz)]

Figure 2: Real (a, c, e) and imaginary (b, d, f) parts of the dielectric functions for the 30 wt% gelatin-water mixture at 243 (a, b), 203 (c, d), and 163 (e, f) K. The plots were obtained experimentally. The solid blue, solid green and solid red, dashed light blue, dashed light green, dashed gray, and dashed black dashed curves denote processes Ia, IIa, IIIa, Ib, IIb, electrode polarization, and DC conductivity, respectively. The solid black curves denote the sum of all the processes.

23



Tg for 23 wt.%

J/m ol 49 k

J/m ol 51 k

J/m ol 50 k

-2

49 k

0

J/m ol

2

-4 log[ (s)]

-6

10 wt％

15 wt％

20 wt％

Tg for 34 wt.%

25 wt％ Tg for 46 wt.%

44

kJ

/m

ol

l mo kJ/ 48

l mo 51

kJ/

kJ/

0

mo

l

2 49

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 24 of 28

-2 -4 -6

30 wt％

4 5 6 7 8

35 wt％

40 wt％

4 5 6 7 8 4 5 6 7 8 -1 1000/ (K )

45 wt％

4 5 6 7 8

Figure 3: Temperature dependences of the relaxation times of processes I and III of 10, 15, 20, 25, 30, 35, 40, and 45 wt% gelatin water mixtures. The circles and triangles denote processes I and III, respectively. The crosses indicate the relaxation time for process I obtained by peak frequency. The grayed area indicates the possible glass transition temperature of process III. The filled symbols are used for fitting with the Arrhenius temperature dependence to determine the glass transition temperatures of each of the processes.Black circles indicate possible glass transition temperature range obtained by TSDC measurements. Black diamonds indicate possible glass transition temperature range obtained previous BDS measurements quoted from reference 2. Black vertical lines indicate glass transition temperature obtained previous DSC measurements quoted from reference 33.

24


Page 25 of 28

log [ (s)]

2 0 10 wt% 15 wt% 20 wt% 25 wt% 30 wt% 35 wt% 40 wt% 45 wt%

-2 -4

Auty pure ice Johari pure ice

4

5

6

7

8

-1

1000/ (K )

Figure 4: Temperature dependence of relaxation time of process II of 10, 15, 20, 25, 30, 35, 40, and 45 wt% gelatin water mixtures. For comparison, the relaxation times of pure ice 31,32 are also plotted.

-11

-6

10

10

6 5 4

-7

Current (A)

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


10

3 2

-8

10

112 116 120 124 128 132

-9

10

-10

10

10

10 wt.% 30 wt.%

-11

120

160

200 240 Temperature (K)

280

Figure 5: TSDC thermograms for the 10 and 30 wt% gelatin-water mixtures with Tp = 253 K. The inset shows thermograms at the low temperature range.

25



2

log[ (s)]

0 -2 -4 -6 -8 4

5

6

7

-1

1000/ (K )

Figure 6: Temperature dependence of the relaxation time of process III and I for 20 wt% gelatin-water mixture. The filled symbols are utilized for Arrhenius or Vogel-Fulcher fit. The grayed area indicates the possible glass transition temperature of process III. Black diamonds indicate possible glass transition temperature range obtained previous BDS measurements quoted from reference 2.

Tg, TnonA-A (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

Page 26 of 28

200 180 160 140 120 0

20 40 Cg (wt%)

60

Figure 7: Concentration dependences of T g and T nonA−A . The blue, green, and red circles indicate T g of processes I, II, and III determined by BDS measurements. The pentagons indicate peak temperature of peaks I, II, and III determined by TSDC measurements. The orange squares indicate T nonA−A of process I by BDS. The red triangles are replotted differential calorimetric glass transition temperatures obtained by Nishinari et al. 33 The curve was drawn by eye.

26


Page 27 of 28

Figure 8: Temperature dependence of (a) the relaxation time of process III, (b) inverse temperature derivative of the relaxation time of process III, and (c) the relaxation strength of process I for 10 and 30 wt% gelatin-water mixtures. The curves and dashed lines are guide to the eye.

30 140

25

ΔεΙΙ,163 Κ

120 100

20

80

15

60

10

ΔεΙ, 163 Κ

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


40 5

20 0

0 0

10

20 30 40 50 Cg (wt% of gelatin)

60

Figure 9: Concentration dependences of the relaxation strength of processes I (blue filled circle) and II (green open hexagon) at 163 K. The blue lines are guide to the eye. The green dashed line is obtained by least squares fitting. The solid and open green stars indicate the relaxation strength of pure ice obtained by Johari 31 and us, respectively.

27



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

Graphical TOC Entry

28


Page 28 of 28

Dynamics of Uncrystallized Water, Ice, and Hydrated Protein in

Recommend Documents