Inhibition of Recrystallization of Ice Grains by Adsorption of Poly(Vinyl Alcohol) onto Ice Surfaces Takaaki
Inada*,†
and Shu-Shen
Lu‡
Institute for Energy Utilization, National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki, 305-8564, Japan, and School of Chemistry and Chemical Engineering, Sun Yat-Sen University, Guangzhou 510275, China Received February 24, 2003;
CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 5 747-752
Revised Manuscript Received July 1, 2003
ABSTRACT: The effect of poly(vinyl alcohol) (PVA) on recrystallization of ice was studied by comparison with the effect of antifreeze protein (AFP) type I. Polycrystalline ice wafers consisting of numerous ice grains, whose initial size was less than 130 µm (i.e., less than the thickness of the ice wafer) were made from solutions containing PVA or AFP type I at various concentrations. The ice wafers were annealed between -2.3 and -2.0 °C for 5 h, and then the size of the ice grains was measured using digital microscopy. Even at a PVA concentration as low as about 5 × 10-7 mol/L, the size of the annealed ice grains made from the PVA solution did not change significantly from the initial size, indicating that PVA is as effective as AFP type I in inhibiting ice recrystallization. The effectiveness of PVA increased (i.e., the grain size decreased) with increasing molar concentration, molecular weight, or degree of hydrolysis of PVA. The function of PVA molecules in the inhibition of recrystallization was analyzed by using the Langmuir adsorption equation. Introduction During the past 30 years, several different antifreeze proteins (AFPs) and antifreeze glycoproteins (AFGPs) have been discovered in fish, insects, and plants living in cold regions.1 One important effect of AFPs and AFGPs is noncolligative and nonequilibrium lowering of the freezing temperature at which ice crystals can grow in AFP or AFGP solutions. The difference between this nonequilibrium freezing temperature and the equilibrium melting temperature is called thermal hysteresis. Another effect is inhibiting or retarding the recrystallization of ice when solutions of AFP or AFGP exist between ice grains. These two effects are thought to be caused by the adsorption of the antifreeze molecules onto ice surfaces and thus by the subsequent Kelvin effect.2 The adsorption of the antifreeze molecules produces curvature of the ice surface by pinning the crystal growth. This surface curvature causes a depression in the local freezing temperature at the growth front, and the freezing temperature depression is inversely proportional to the radius of curvature. Therefore, crystal growth slows and sometimes stops as the growth front expands. The adsorption mechanism is still in dispute, however.3 Knight et al.4 experimentally showed that molecules of AFP type I from the winter flounder are adsorbed onto {202 h 1} planes. They hypothesized that this adsorption is caused by hydrogen bonding between repeated hydrophilic amino acids and ice crystal lattice. On the other hand, Chao et al.,5 Haymet et al.,6 and Zhang and Laursen7 replaced hydrophilic amino acids with other amino acids in AFP type I and showed that hydrogen bonding is not necessary for antifreeze effects. These results suggest that van der Waals and hydro* To whom correspondence should be addressed. E-mail: t-inada@ aist.go.jp. † National Institute of Advanced Industrial Science and Technology (AIST). ‡ Sun Yat-Sen University.
phobic interactions are the main cause for the adsorption and that the complementary fit between ice-binding surface of AFP molecules and ice surfaces is required for adsorption.3 In engineering applications, AFPs are useful in inhibiting agglomeration of ice particles. Grandum et al.8 showed that adding AFP type I to ice slurries, even at an AFP concentration as low as 5 mg/mL, inhibits agglomeration of ice particles and that ice slurries containing AFP type I can flow in a pipe with a pressure drop only three times larger than that for liquid water. This relatively similar flow to that of liquid water significantly advances the application of ice slurries as cold-energy transport media. However, AFPs are currently too expensive and unstable to use in practical applications. Therefore, cheap, stable substitutes for AFPs that inhibit agglomeration of ice particles are needed. Several other additives exhibit effects upon crystal growth of ice similar to effects by AFPs and therefore are expected to inhibit agglomeration of ice particles in ice slurries at low concentrations of additive. For example, observations of ice surfaces by using scanning tunneling microscopy showed that adding silane coupling agents at 5 mg/mL or poly(vinyl alcohol) (PVA) at 10 mg/mL influence the morphology of ice surfaces.9,10 These results suggest that adsorption of the molecules of these additives onto ice surfaces is similar to the adsorption of AFPs and thus inhibit further crystal growth between the adsorption sites by the Kelvin effect. A silane coupling agent was actually used as an additive to ice slurries made from water-oil mixtures, and positive effects in dispersion of fine ice particles in the ice slurries were clearly evident.11,12 Observation of recrystallization of ice grains in a thin polycrystalline ice wafer made from a PVA solution showed that PVA is effective also in inhibiting ice recrystallization.13 In this observation, liquid between ice grains was maintained by adding sodium chloride
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Table 1. Poly(Vinyl Alcohol) Additives (a)c
PVA PVA (b)d PVA (c)d PVA (d)d PVA (e)d PVA (f)d c
Mw a
ηb
7200 9000-10000 13000-23000 13000-23000 31000-50000 89000-98000
0.98 0.80 0.87-0.89 0.98 0.98-0.99 >0.99
a Weight-average molecular weight. b Degree of hydrolysis. Product of Fluka. d Product of Aldrich Chemical.
to the PVA solution in advance. Therefore, the suppression of recrystallization occurs because PVA molecules move freely in the liquid and then induce the Kelvin effect by being adsorbed onto the grain surfaces. A similar observation showed that block copolymers based on a poly(ethylene oxide) block and a poly[2-(2-hydroxyethyl)ethylene] block are also effective in inhibiting ice recrystallization.14 Because these two additives have the same effects upon ice recrystallization as do AFPs, these additives are also expected to inhibit agglomeration of ice particles in ice slurries at low concentrations. Certain surfactant additives, such as poly(oxyethylene) sorbitan monooleate, poly(oxyethylene) sorbitan dioleate, diacylmannosylerythritol, and a mixture of cetyl dimethyl betaine and sodium oleic acid, have recently been shown effective in dispersing ice particles in ice slurries at low concentrations.15,16 It is not known, however, if their mechanisms are the same as those of AFPs. In this study, to find effective additives for inhibiting agglomeration of ice particles, the effect of several additives on recrystallization of ice was determined and then compared with the effect of AFP type I. We further examined the effectiveness of one type of additives, PVA, by varying the concentration, molecular weight, and degree of hydrolysis because we found PVA particularly effective as AFP type I in inhibiting ice recrystallization. Finally, we analyzed the adsorption of PVA onto ice surfaces by using the Langmuir adsorption equation, in relation to the ability of PVA to inhibit the recrystallization of ice. Experimental Section Additives. A total of 13 additives were used; six types of PVA (Aldrich Chemical and Fluka); AFP type I from the winter flounder (A/F Protein; molecular weight M of 3300); two types of poly(oxyethylene) sorbitan monooleate (Sigma Chemical, Tween 80, and Tween 81; M: 1308), hereafter called Tween 80 and Tween 81; poly(oxyethylene) sorbitan trioleate (Sigma Chemical, Tween 85; M: 1612), called Tween 85; vinyl triethoxy silane (Shin-Etsu Chemical; M: 190), called VTES; poly(ethylene glycol) (Aldrich Chemical, number-average molecular weight Mn of 10 000), called PEG; and poly(acrylic acid) (Aldrich Chemical, weight-average molecular weight Mw of 2000), called PAA. Table 1 lists the six types of PVA with different Mw and different degrees of hydrolysis, η. Because PVA is generally made by alkali hydrolysis of poly(vinyl acetate), η represents the hydroxyl content. VTES is a silane coupling agent, which is expected to be an effective substitute for AFPs.9 Although the molecular weight of VTES is only 190, VTES molecules generate long-chain molecules in water by dehydration and therefore behave as a polymer when in water. Tween is a trademark name of surfactants, some of which are known to be effective in dispersing ice particles in ice slurries.15,16 Preparation of Solutions. Polycrystalline ice wafers were made from separate solutions of the 13 additives at various
Figure 1. Procedure to evaluate recrystallization inhibition. (a) Making an ice wafer by splat cooling. (b) Annealing of ice grains. (c) Observation and measurement of ice grains. concentrations between 5 × 10-5 and 5 mg/mL. Deionized water (Millipore, Milli-Q Jr.) was used as solvent. In addition to these additives, calcium chloride was added to all solutions at a concentration of 0.5 mg/mL to maintain the liquid between the ice grains. Because the eutectic point of a calcium chloride solution is about -55 °C, which is lower than the annealing temperature used in this study, the liquid solution still remains between ice grains even after the polycrystalline ice wafer has been formed from the solutions. For a control, an ice wafer was also made from a solution of calcium chloride (0.5 mg/mL) without any other additive. Evaluation of Recrystallization of Ice Grains. Figure 1 shows the experimental procedures used in this study; first, preparation of the polycrystalline ice wafers (Figure 1a), then, annealing of the ice grains (Figure 1b), and finally, the measurement of the size of the ice grains (Figure 1c). All the apparatus were installed in a thermostatic cold room. Figure 1a shows the splat cooling method described by Knight et al.13 to make the polycrystalline ice wafers. A 120 mm diameter aluminum disk was cooled to -80 ( 5 °C by using liquid nitrogen. From a height of 1400 mm, a 10 µL droplet of additive solution was released from a micropipet and dropped through an acrylic hollow cylinder, which was used as a windshield, onto the aluminum disk. Immediately upon hitting the disk, the droplet transformed into a 10 mm diameter polycrystalline ice wafer roughly about 130 µm thick (based on the droplet volume and wafer diameter) and then spontaneously separated from the disk. During this procedure, the temperature in the cold room was kept at about -8 °C to retard the recrystallization of ice. For annealing, the ice wafer was then placed on a slide glass, covered with a cover glass, then covered with a lid, and finally sealed with grease (Figure 1b). The lid with a grease seal was used to avoid sublimation of the ice wafer. The temperature in the cold room was then increased, and the temperature inside the lid was kept at between -2.3 and -2.0 °C for 5 h. Figure 2 shows the temperature change in the lid after the temperature in the cold room was increased. After 5 h annealing, the temperature in the cold room was again cooled to about -8 °C. For evaluating the recrystallization of the ice grains, the lid was removed, and the remaining sandwiched unit (i.e., slide glass, ice wafer, and cover glass) was placed between two crossed polarizing plates, and then the sizes of the ice grains in the ice wafer were measured by using a digital microscope
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Figure 4. Photographs of annealed ice grains made from (a) 0.5 mg/mL solution of poly(vinyl alcohol), Mw: 89 000-98 000 and (b) 5 mg/mL solution of poly(acrylic acid). Annealing was done between -2.3 and -2.0 °C for 5 h. Figure 2. Time variation of annealing temperature.
Figure 3. Photographs of recrystallization process of ice grains made from a control solution (i.e., 0.5 mg/mL calcium chloride solution). Elapsed time is based on the time at which the temperature in the cold room was increased from about -8 °C. (Intel, Intel Play QX3) (Figure 1c). Here, we define the representative length of the ice grains as follows. First, we measured the length of each ice grain along the x axis (see Figure 3) within the field view of the microscope (3.0 × 2.3 mm) and then picked out the largest value. This largest value was defined as the representative length. Determining a representative length larger than 130 µm from the twodimensional microscope image is possible because the thickness of the ice wafer was about 130 µm. Although strictly speaking determining a representative length smaller than 130 µm is difficult, we show the apparent representative length in the following experimental results. The representative length of ice grains was obtained from the averaged value of four trials for each experimental condition for the PVA and AFP type I additives and from that of two trials for the other additives. The results were highly reproducible, so that even two trials were sufficient to obtain the representative length.
Results Figure 3 shows photographs of the recrystallization process of ice grains made from a control solution (i.e., a 0.5 mg/mL solution of calcium chloride without any other additives). The elapsed time in the figure is based on the time at which the temperature in the cold room was increased from about -8 °C as shown in Figure 2. Just after an ice wafer was formed, the representative length of ice grains was smaller than 130 µm (Figure
3a). Even if additives were in the control solution, this initial representative length was always smaller than 130 µm. Ice grains recrystallized with elapsed time (Figure 3b-d) even before the annealing temperature was reached. This indicates that both the annealing temperature as well as the reproducibility of the temperature change before reaching the annealing temperature are important in evaluating the recrystallization process quantitatively. Figure 3 shows the fastest recrystallization process because a control solution was used. When a control solution was used, recrystallization was almost completed by 50 min of annealing. When PVA or AFP solutions were used, however, recrystallization proceeded more slowly; therefore, it took about 5 h to evaluate the recrystallization-inhibition ability. Figure 4 shows two typical photographs of ice grains, annealed between -2.3 and -2.0 °C for 5 h. The representative length of ice grains made from a 0.5 mg/ mL solution of PVA (f) was similar before and after annealing (Figure 4a), indicating the ability of PVA (f) to inhibit recrystallization. In contrast, the representative length of ice grains made from a 5 mg/mL solution of PAA increased to as much as 280 µm after annealing (Figure 4b), indicating a much lower ability to inhibit recrystallization as compared with PVA (f). Figure 5 shows the representative length of ice grains after annealing for various additives at a concentration of 5 mg/mL. The dashed line represents the representative length of ice grains (250 µm) made from the control solution after annealing. If the representative length of ice grains made from the solutions with additives equals or exceeds this value, then the additive is not effective in inhibiting recrystallization. The representative lengths of ice grains made from PVA solutions were smaller than those of others, including the control solution, indicating that PVA is more effective in inhibiting the recrystallization of ice than the other additives at the same mass concentration. Also, at the same molar concentration, PVA should be more effective in inhibiting recrystallization than the other additives because the molecular weight of PVA used in this study is larger than or approximately equal to those of the Tweens, VTES, PEG, and PAA. Tween 85 was also effective in inhibiting recrystallization of ice, although less effective than PVA, whereas the other additives (Tween 80, Tween 81, VTES, PEG, and PAA) had almost no effect on ice recrystallization. Figure 6 shows the representative length of ice grains made from solutions of the six types of PVA (Table 1) after annealing. For reference, the results of AFP type
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hydroxyl group of PVA molecules or to a conformation change in PVA molecules by exchange of -OH and -OCOCH3. The effectiveness of PVA (f) in inhibiting recrystallization was similar to that of AFP type I at the same molar concentration (Figure 6), even at a PVA concentration as low as about 5 × 10-7 mol/L. However, at the same mass concentration, the AFP type I was still more effective than PVA (f) because the molecular weight of PVA (f) is about 30× larger than that of AFP type I. Discussion
Figure 5. Representative length of ice grains made from various solutions with different additives (5 mg/mL) after 5 h annealing between -2.3 and -2.0 °C. Dashed line represents the data for a control solution (i.e., 0.5 mg/mL calcium chloride). VTES: vinyl triethoxy silane, PEG: poly(ethylene glycol), PAA: poly(acrylic acid).
The measured effectiveness of PVA in inhibiting the recrystallization of ice (Figure 6) was discussed by analyzing the adsorption of PVA molecules in the solution onto ice surfaces assuming dynamic equilibrium. In this analysis as follows, first, the Langmuir equation is rearranged, and then the surface coverage of PVA is derived as a function of the molar concentration of PVA in the solution, the molecular weight of PVA, and the degree of hydrolysis of PVA molecules. The rate of adsorption, Rads, is expressed as
( )
Eads ) RT
Rads ) F(1 - θ) exp -
(
NAcv(1 - θ) exp -
)
Eads (1) RT
where F is the rate of arrival of PVA molecules at the surface, θ is the surface coverage of PVA molecules, Eads is the activation energy for adsorption, R is the gas constant, T is the temperature, NA is Avogadro’s number, c is the molar concentration, and v is the average velocity of PVA molecules. Assuming that v is proportional to the square root of the self-diffusion coefficient of PVA and that the self-diffusion coefficient in a dilute solution of PVA is inversely proportional to the square root of the molecular weight of PVA,17 then eq 1 can be rewritten as
Figure 6. Representative length of ice grains made from PVA and AFP solutions after 5 h annealing between -2.3 and -2.0 °C, as a function of molar concentration. Dashed line represents the data for a control solution (i.e., 0.5 mg/mL calcium chloride).
I are also shown. Here, the x axis is not the mass concentration, but the molar concentration, because molar concentration makes it easier to discuss the adsorption of PVA. The dashed line is the representative length of ice grains made from the control solution after annealing. With increasing molar concentration of PVA, the effectiveness in inhibiting ice recrystallization increased. Comparison of four types of PVA with similar η, that is, PVA (a) and (d-f), reveals that the effectiveness in inhibiting ice recrystallization increased with increasing Mw. Furthermore, comparison of two types of PVA with similar Mw, that is, PVA (c) and (d), reveals that the effectiveness in inhibiting ice recrystallization also increased with increasing η. Because η represents the hydroxyl content in PVA molecules, this increase might be related to the bond energy associated with the
( ) Eads RT
Rads ) C1NAcM-1/4 (1 - θ) exp -
(2)
where M is the molecular weight, and C1 is a constant. The rate of desorption, Rdes, is expressed as
Rdes ) f
( )
Edes θ exp A RT
(3)
where f is the frequency of the bond for adsorption, A is the adsorption area for an individual PVA molecule, and Edes is the activation energy for desorption. Assuming that PVA molecules are elongated rather than globular on the ice surfaces, then A is represented by A0(M/M0), where A0 is the surface area for adsorption per segment of PVA, and M0 is the molecular weight per segment of PVA; thus, eq 3 can be rewritten as
Rdes )
( )
fM0θ Edes exp A0M RT
(4)
The equilibrium state is represented by the balance between Rads and Rdes; therefore, eqs 2 and 4 can be rewritten as
Inhibition of Recrystallization of Ice Grains
θ) b)
Crystal Growth & Design, Vol. 3, No. 5, 2003 751
bc 1 + bc
(5)
(
)
C1NAA0 3/4 Edes - Eads M exp fM0 RT
(6)
Assuming that the adsorption is caused by bond energy associated with the hydroxyl group of PVA molecules, then Edes can be simplified as
Edes ) E0
M η M0
(7)
where E0 is the bond energy per hydroxyl group. Because, in general, Eads can be neglected as compared to Edes, substitution of eq 7 into eq 6 yields
b)
(
)
E0 C1NAA0 3/4 M exp Mη fM0 M0RT
(8)
Thus, from eqs 5 and 8, θ can be represented as a function of c, M, and η. To discuss the experimental results in Figure 6 based on this analysis, we assume θ , 1, so that θ is simply approximated by bc from eq 5. In Figure 6, at the same representative length of ice grains, the number of adsorbed PVA molecules per unit area, θ/A, should be equal for all types of PVA when the assumption θ , 1 is satisfied, according to the adsorption-inhibition model.2 When θ/A has a constant value, eqs 5 and 8 can be arranged as
ln(cM-1/4) ) -C2(Mη) - C3
(9)
E0 C2 ) M0RT
(10)
(
C3 ) -ln
)
f θ C1NA A
(11)
where C2 and C3 are constants unrelated to c, M, and η. Figure 7 shows the relation between Mwη and ln(cMw-1/4) for all types of PVA (used in this study) at the same representative length of ice grains, 160 µm (from Figure 6); here, c is in units of mol/m3, and Mw is in kg/mol. The value of c was obtained from linear interpolation between two datapoints in Figure 6 and then taken as the point on the regression line at which the representative length was 160 µm. If the experimental data satisfy eq 9, then the data points should be on a straight line in Figure 7. This figure shows that when Mwη is less than 20, four data points for PVA, namely, (a-d), are actually on a straight line (obtained by using the least-squares method based on the four data points), whereas the other two points for PVA, (e) and (f), deviate from the straight line. One explanation for the deviation of datapoints for PVA (e) and (f) is that Edes deviates from eq 7 as Mwη increases. The shape of a PVA molecule on the ice surface depends not only on the interaction energy between the PVA molecule and the ice surface but also on that between the PVA molecule and the liquid water and that between the segments of the PVA molecule themselves. If the interaction energy between the seg-
Figure 7. ln(cMw-1/4) vs Mwη for six types of PVA, obtained from the data at the same representative length of ice grains, 160 µm, in Figure 6. Solid line is the fit to the data of PVA (a-d), based on eq 9.
ments of the PVA molecule themselves is lower than the interaction energy of the PVA segment with the liquid water or with the ice, then the PVA molecules become globular as the molecular weight increases. The globular shape leads to a decrease in the surface area contacting the ice surface, thus causing a decrease in Edes. Two assumptions used in this analysis should be examined. The first assumption is low surface coverage. It is difficult to deduce θ directly from the analysis because v in eq 1 is unknown. To examine this assumption, we instead estimate v by specifying a certain value of θ. From the balance between Rads and Rdes, v is expressed as
v)
(
fM0 1 E0 θ exp Mη NAA0 Mc 1 - θ M0RT
)
(12)
E0 is estimated at about 29 J/mol by substituting C2 obtained from Figure 6 into eq 10, and A0 is estimated at about 1 × 10-19 m2 based on the crystalline structure of a PVA molecule.18 Other variables in eq 12 are known; f is on the order of 1013 s-1, and M0 is 0.044 kg/ mol. When θ ) 1 × 10-3, which is a sufficiently low surface coverage to satisfy the assumption, v is thus estimated between 102 and 104 m/s by substituting the values of c, M, and η for PVA (a-f) into eq 12, where M is corrected by using the regression line based on eq 9 shown in Figure 7. This large order of magnitude for v is inconsistent with the low value of the self-diffusion coefficient of PVA molecules, estimated at about 10-11 m2/s.19 Therefore, θ should be lower than 1 × 10-3, indicating the validity of the assumption of low surface coverage. The second assumption is that the adsorption is in dynamic equilibrium, namely, that the adsorption is reversible. The fact that AFP and AFGP molecules are incorporated into ice suggests that irreversible adsorption is likely to occur.4,20,21 Further, it is reasonable to conclude that irreversible adsorption is necessary to completely stop the crystal growth of ice.22 However, adsorption kinetics should be taken into consideration because the antifreeze activity of AFPs and AFGPs depends only on the concentration of the solutions and on the degree of supercooling. If the adsorption was irreversible, the antifreeze activity would likely depend also on the time that ice crystals are exposed to the
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solution and also on the ratio of the surface area of the ice to the volume of the solution. Some experimental results have supported the assumption that the adsorption is reversible. Burcham et al.23 showed that the dependence of antifreeze activity of AFPs and AFGPs on the concentration is well-described by a simple Langmuir adsorption model based on the assumption of dynamic equilibrium. Recently, based on NMR experiments, Ba et al.24 reported evidence of reversible adsorption of AFP type I. Therefore, in our analysis here, we assume that the adsorption of PVA onto ice is also in dynamic equilibrium because PVA has the same effect on ice as AFPs and AFGPs, although further discussion is needed to determine whether the adsorption is reversible or irreversible. Conclusions The effect of several additives on the recrystallization of ice was examined quantitatively and then compared with the effect of AFP type I. PVA was found as effective as AFP type I in inhibiting the recrystallization of ice, whereas the other additives (Tweens, VTES, PEG, and PAA) had almost no effect on ice recrystallization. The effectiveness of PVA in inhibiting the recrystallization of ice increased with increasing molar concentration, molecular weight, or degree of hydrolysis of PVA. The effectiveness of PVA in inhibiting recrystallization was evident even at a concentration as low as about 5 × 10-7 mol/L, which is similar to the concentration needed for such inhibition by AFP type I. The function of PVA was discussed based on the Langmuir equation, assuming the PVA adsorption onto ice surfaces is in dynamic equilibrium. Acknowledgment. We thank Dr. Svein Grandum for many helpful discussions. This study was supported by the Industrial Technology Research Grant Program from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. References (1) Yeh, Y.; Feeney, R. E. Chem. Rev. 1996, 96, 601-617.
Inada and Lu (2) Raymond, J.; DeVries, A. L. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 2589-2593. (3) Davies, P. L.; Baardsnes, J.; Kuiper, M. J.; Walker, V. K. Philos. Trans. R. Soc. London B 2002, 357, 927-935. (4) Knight, C. A.; Cheng, C. C.; DeVries, A. L. Biophys. J. 1991, 59, 409-418. (5) Chao, H.; Houston, M. E., Jr.; Hodges, R. S.; Kay, C. M.; Sykes, B. D.; Loewen, M. C.; Davies, P. L.; So¨nnichsen, F. D. Biochemistry 1997, 36, 14652-14660. (6) Haymet, A. D. J.; Ward, L. G.; Harding, M. M.; Knight, C. A. FEBS Lett. 1998, 430, 301-306. (7) Zhang, W.; Laursen, R. A. J. Biol. Chem. 1998, 273, 3480634812. (8) Grandum, S.; Yabe, A.; Tanaka, M.; Takemura, F.; Nakagomi, K. J. Thermophys. Heat Transfer 1997, 11, 461-466. (9) Inada, T.; Yabe, A.; Grandum, S.; Saito, T. Mater. Sci. Eng. A 2000, 292, 149-154. (10) Lu, S. S.; Inada, T.; Yabe, A.; Zhang, X.; Grandum, S. Int. J. Refrig. 2002, 25, 563-569. (11) Matsumoto, K.; Okada, M.; Kawagoe, T.; Kang, C. Int. J. Refrig. 2000, 23, 336-344. (12) Matsumoto, K.; Shiokawa, Y.; Okada, M.; Kawagoe, T.; Kang, C. Int. J. Refrig. 2002, 25, 11-18. (13) Knight, C. A.; Wen, D.; Laursen, R. A. Cryobiology 1995, 32, 23-34. (14) Mastai, Y.; Rudloff, J.; Co¨lfen, H.; Antonietti, M. Chemphyschem 2002, 3, 119-123. (15) Kitamoto, D.; Yanagishita, H.; Endo, A.; Nakaiwa, M.; Nakane, T.; Akiya, T. Biotechnol. Prog. 2001, 17, 362-365. (16) Modak, P. R.; Usui, H.; Suzuki, H. HVAC&R Res. 2002, 8, 453-466. (17) Doi, M.; Edwards, S. F. In The theory of polymer dynamics; Oxford University Press: New York, 1986; Ch. 4, pp 91103. (18) Assender, H. E.; Windle, A. H. Polymer 1998, 39, 43034312. (19) Pakhomov, P. M.; Khizhnyak, S. D.; Nordmeier, E.; Nierling, W.; Lechner, M. D. Polymer Sci. B 2002, 44, 154-157. (20) Knight, C. A.; Driggers, E.; DeVries, A. L. Biophys. J. 1993, 64, 252-259. (21) Knight, C. A.; Wierzbicki, A.; Laursen, R. A.; Zhang, W. Cryst. Growth Des. 2001, 1, 429-438. (22) Knight, C. A.; Wierzbicki, A. Cryst. Growth Des. 2001, 1, 439-446. (23) Burcham, T. S.; Osuga, D. T.; Yeh, Y.; Feeney, R. E. J. Biol. Chem. 1986, 261, 6390-6397. (24) Ba, Y.; Wongskhaluang, J.; Li, J. J. Am. Chem. Soc. 2003, 125, 330-331.
CG0340300
