Biomacromolecules 2005, 6, 3373-3379
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Molecular Weight Effect on Liquid Crystalline Gel Formation of Curdlan Masahiro Nobe, Naomi Kuroda, and Toshiaki Dobashi* Department of Biological and Chemical Engineering, Faculty of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan
Takao Yamamoto Department of Physics, Faculty of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan
Akira Konno Department of Food and Nutrition, Faculty of Human Life Sciences, Senri Kinran University, Suita, Osaka 565-0873, Japan
Mitsuo Nakata Department of Polymer Science, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan Received June 17, 2005; Revised Manuscript Received August 10, 2005
Curdlan dissolved in alkaline solution forms a unique gel consisting of liquid crystalline gel (LCG) and amorphous gel (AG) in alternating layers by a dialysis into aqueous calcium chloride. The unique structure has been investigated by measuring the birefringence of the gel ∆n, the ratio q of the thickness of LCG layer δ to the gel radius R, and the calcium content in the gel CCa in a wide range of molecular weights of fractionated Curdlan, as well as unfractionated Curdlan as a control. With increasing molecular weight of Curdlan, ∆n increased and q ) δ/R decreased, and both became saturated at high molecular weight. ∆n and q for unfractionated Curdlan were smaller and larger, respectively, than those for fractionated Curdlan. CCa was constant irrespective of molecular weight and its distribution, which means that the abundance of calcium ions per glucose unit in the gel does not depend on the degree of orientation of mesogens. These results suggest that the amorphous phase appears when the size of the Curdlan molecules is larger than the average intermolecular distance, resulting from the random coil to triple helix transformation of Curdlan molecules associated with lowering hydroxide anion concentration in the dialysis process. I. Introduction The research field for systems with a semipermeable membrane has been intensively developed. In dilute solutions, the van’t Hoff equation can be applied, and analytical treatments of experimental data are possible. On the other hand, when the intradialytic solution is a concentrated polymer solution and the extradialytic solution is a concentrated ionic solution, it is difficult to analyze the data, and such a complex system has not been well-explored yet. The systems are, however, very interesting, since both equilibrium and nonequilibrium thermodynamic properties are involved because of the interactions of the polymers with their environments. Recently, we found that, in the process of dialysis of the concentrated polysaccharide Curdlan dissolved in aqueous sodium hydroxide put into an aqueous calcium chloride, a unique cylindrical gel consisting of liquid crystalline gel (LCG) and amorphous gel (AG) in alternating layers is produced.1 In the dialysis process, sodium cations and hydroxide anions are transferred from the intradialytic solution to the extradialytic solution, and calcium cations * To whom correspondence should be addressed. E-mail: dobashi@ bce.gunma-u.ac.jp. Fax: +81-277-30-1477.
and chloride anions are transferred from the extradialytic solution to the intradialytic solution. It is assumed that a certain amount of hydroxide groups in Curdlan molecules are dissociated in the intradialytic solution with high pH at the initial state. Hydroxides of 6C carbon of the glucose unit might be easily dissociated, analogous to the gelation of amylose.2 In the dialysis, the pH change associated with the outflux of hydroxide anions results in the conformational change of Curdlan molecules from random coil to triple helix.3 The influx of calcium cations cross-links the helical Curdlan molecules intermolecularly.4 It is interesting to discuss this unique structure on the basis of detailed characterization with variations of the controlling parameters, since the novel material could be used in functional drug delivery systems, food additives, and optical components.5 Especially, a variety of food processing containing Curdlan has been known since the FDA approved Curdlan as a food additive.6 One of the most important factors for controlling the structure of the Curdlan gel is apparently the molecular weight of Curdlan, because the thresholds of calcium cations and pH for forming the gel and the triple helix, as well as the size of the mesogens, i.e., the units of an oriented mesoscale domain, could be varied
10.1021/bm050420m CCC: $30.25 © 2005 American Chemical Society Published on Web 10/01/2005
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Nobe et al.
Table 1. sample
[η] (ml/g)
Mw × 10-5
CUD02
403
14.3
CUD1F1 F2 F5 F8 F9 F10 F11
703 665 520 387 343 295 217
28.4 26.5 19.6 15.0 14.8 12.7 11.5
CUD3F4 F6 F7 F8
200 140 129 95.5
CUD5F2
545
6.01 3.74 3.70 2.19 20.8
by the molecular weight of Curdlan. It is well-known, however, that it is very difficult to examine the molecular weight effect of polysaccharide solutions because of the difficulty in purifying or fractionating polysaccharide samples. Fortunately, in the case of Curdlan, an appropriate set of good and poor solvents for fractionation has been found recently.7 In this study, we have measured the characteristic quantities of the birefringence of the gel ∆n, the ratio q of the thickness of the LCG layer δ to the gel radius R, and the calcium content in the gel CCa in a wide range of molecular weights of fractionated Curdlan. On the basis of the experimental results combined with a simple theoretical argument, the unique characteristics of the LCG/AG structure of Curdlan are discussed. II. Experimental Section Purification of Curdlan Samples and Their Characterization. The original sample of Curdlan was supplied in the form of a spray-dried powder from Takeda Chemical Industries, Ltd., Osaka, Japan. To prepare Curdlan samples with a narrow molecular weight distribution for a wide range of average molecular weights, an amount of Curdlan was sonicated, and then, both sonicated and unsonicated samples were fractionated. The mixture of dimethyl sulfoxide (DMSO) + LiCl at 0.05 g/mL in LiCl concentration was used as a good solvent, and acetone was used as a poor solvent. The samples were designated as listed in Table 1. The series of CUD1 was prepared from an unsonicated Curdlan sample (hereafter denoted CUD01) used for ref 7, as follows. CUD01 weighing 7 g was dissolved in 1 400 mL of the solvent DMSO + LiCl. By adding acetone to the solution little by little while stirring gently at room temperature, the viscosity of the solution decreased gradually. When the amount of added acetone reached ca. 1 570 mL, the solution became turbid. The turbidity did not change when either raising or lowering the temperature. After stirring the solution for 1 h, we settled the solution in a thermal bath at 25 °C overnight. Then, a clear, flat meniscus appeared between two transparent solution phases. The upper phase was transferred into another flask for further fractionation. The lower phase, rich in Curdlan, was diluted moderately by the solvent DMSO + LiCl and precipitated into 1 L of acetone to collect
Figure 1. Photographs of cross-section of Curdlan gel observed under crossed nicols (upper panel) and natural light (lower panel) for different samples denoted under the photographs. δ and R are the thickness of the outermost LCG layer and the radius of the gel, respectively, and A and B are the points for the measurement of birefringence ∆n.
the cotton-like Curdlan. To remove the LiCl precipitates, the supernatant fluid was sucked away. Then, the mixture of acetone + water (1:1 by volume) was added with stirring. The Curdlan precipitates were washed four times in the acetone + water mixture and finally in acetone for vacuumdrying. This fraction was labeled CUD1-F1. From the upper phase transferred into the other flask, the second fraction, CUD1-F2, was obtained by adding acetone as in the case of CUD1-F1. The total number of fractions was twelve, and the total weight finally obtained was 5.0 g. The preparation protocol for the series CUD3 prepared from a sonicated Curdlan of lower molecular weight has been described elsewhere.7 We also used another unsonicated Curdlan sample, CUD02. The purified series of samples from CUD02 obtained by sonicating and following a protocol similar to the above was designated CUD5. The weight-average molecular weights of the purified samples in 0.3 M NaOH were determined by light-scattering measurements carried out at 25 °C with unpolarized incident light at 435.8 nm. Viscosity measurements were performed at 25 °C with the Ubbelohde-type viscometer just after the solution preparation to determine the intrinsic viscosity for Curdlan in 0.3 M NaOH. The details of the apparatus and the experimental procedure were described in ref 7. The samples that were not used for the study of ref 7 were stored in a desiccator in a dark place and a vacuum-dried state. The characteristic values of the samples used for this study are summarized in Table 1. Gel Preparation and Characterization. Reagent-grade NaOH and calcium chloride and MilliQ water were used for the preparation. A desired amount of each Curdlan sample was dissolved at 5 wt % in 0.3 M NaOH. A measured quantity (10 mL) of the Curdlan solution was poured into a seamless cellulose tubing with the diameter of 14.3 mm (UC36-32, Sanko Junyaku Co., Ltd., Japan), immersed into 200 mL of an 8 g/dL calcium chloride bath at 25 °C and dialyzed for 24 h to make a gel. A round slice of the gel with the thickness of 3 mm was excised out perpendicularly to the long axis of the dialysis tubing. The gels were observed under both natural light and crossed nicols, and their photographs taken by a digital camera are shown in Figure 1. LCG/AG alternating layers appeared in all the gels. The birefringence
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MW Effect on Gel Formation of Curdlan
∆n of the LCG layer was measured at two fixed points, A near the interface with the extradialytic solution and B near the interface with the turbid ring of AG, by a laboratorymade apparatus. A He-Ne laser with wavelength in vacuo λ ) 632.8 nm was used as the light source. A polarizer was set perpendicular to the light path and the direction of the polarization was set perpendicular to that of the laser light so as to make crossed nicols. The detector of the transmitted light intensity was a photodiode. The sliced gel with thickness d ) ∼1 mm was set just in front of the polarizer. From the observed transmitted light intensity under crossed nicols Ic and that under open nicols Io, the retardation Re and the birefringence ∆n were determined using the equations of
( )
(1)
Re d
(2)
Ic ) Io sin2
πRe λ
and ∆n )
The thickness of the outermost LCG layer δ and the gel radius R were measured by an image-analyzing software (Image Pro Plus, Media Cybernetics, Japan). To estimate the calcium content in the gel, 0.01 g of the gel sheet was excised from the outermost LCG layer near the interface with the dialysis tubing and rinsed several times in pure water to remove the unreacted free calcium cations. Then, the gel sheet was dissolved in 10 mL of 0.01 M EDTA-4Na. The solution was mixed with 2 mL of ammonium buffer at pH 10 with two drops of eriochrome black T (EBT) as the indicator and diluted with an appropriate amount of pure water to make a 30 mL solution. The calcium content of the gel layer was determined by back-titration with 0.01 M MgCl2 standard aqueous solution. III. Results Figure 1 shows the upper view of the slice of the gel. The gel consists of alternating concentric transparent and turbid layers from the rim to the center of the gel, as observed under natural light, and more clearly under crossed nicols, for all the samples shown in Figure 1. Those rings were observed from one end of the dialysis tube to the other end continuously, making concentric “pipes”. In the upper panel observed under crossed nicols, two orthogonal lines appear, except near the center. The outermost layer consists of multiple concentric layers with various colors in the upper panel and corresponds to the first (outermost) transparent layer observed in the lower panel. The thickness of each fine layer with the same color is around 10 µm at the rim and gradually increases with approach toward the center. The central line observed in the innermost layer was swirled by rotating the sample around the center under crossed nicols, indicating a large optical rotation. The direction of the mesogens composed of Curdlan molecules in the ordered structure was proven to be perpendicular to the circumference of the circle on which the molecules sit, i.e., the ordering of mesogens extending radially out from the center of the tube,
Figure 2. Molecular weight dependence of birefringence observed in the LCG layer; at the point near the interface with extradialytic solution (a) and with the inner turbid ring (b), indicated as A and B, respectively, in Figure 1. Open circles and a closed circle denote fractionated and unfractionated samples, respectively.
by means of the observation of strips excised out in different directions, as reported in a previous paper.1 The color intensity of the outermost LCG layer decreased with decreasing molecular weight, and no color was observed for Mw less than 600 000. The birefringence ∆n was almost zero for Mw less than 370 000. The gel prepared from CUD3F8 with Mw ) 219 000 was entirely turbid, so no rings were discriminated. This gel was brittle and fragile with a weak force, indicating that neither ordered nor homogeneous polymer networks could be constructed from low molecular weight Curdlan molecules at the present Curdlan concentration of 5 wt %. Figure 2 shows that the molecular weight dependence of the birefringence ∆n is S-shaped at both sampling points A and B, though ∆n at B is around 2/3 of that at A. ∆n for A and B approach 0 at different rates. That is, the low molecular weight tail of the S-shaped profile for A approaches 0 faster than the similar curve region of B, which also is reflected in the lower inflection point around Mw ) 900 000 for A than 1 500 000 for B. It is also noted that ∆n becomes saturated above Mw ) 1 500 000 at A and 2 000 000 at B, and ∆n of the unfractionated sample is around 1/2 of the fractionated one with similar weight-average molecular weight. Figure 3 shows the molecular weight dependence of the ratio q of the thickness of the outermost LCG layer δ and the gel radius R. The ratio q decreased with increasing molecular weight up to a molecular weight of about Mw ) 600 000 and then held constant at a value of 0.37 for the remainder of the molecular weight range examined. The ratio q for the unfractionated sample seems to be larger than that for fractionated one, but we decline to comment further because of the experimental error.
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Figure 3. Molecular weight dependence of the ratio of the thickness of the LCG layer δ and the radius of the gel R. Open circles and a closed circle denote fractionated and unfractionated samples, respectively.
Figure 4. Molecular weight dependence of calcium cation concentration in the gel. Open circles and a closed circle denote fractionated and unfractionated samples, respectively.
Figure 4 shows the molecular weight dependence of calcium concentration CCa in the LCG layer. CCa was constant irrespective of molecular weight and its distribution. It is suggested that the amount of calcium cations in the gel does not correlate with the orderedness of the Curdlan molecules.
IV. Discussion The experimental results show that LCG is formed from both fractionated and unfractionated Curdlan, though the degree of orientation is higher for the fractionated material, as shown in Figure 2. According to our screening test of intra- and extradialytic solutions, alkaline metal monovalent cations cannot induce LCG.8 These results suggest that, even if there are a small amount of lithium anions remaining in Curdlan brought in by the process of fractionation, they do not play a deterministic role for forming LCG, although we cannot exclude the possibility of a certain effect in combination with calcium cations. At low molecular weight, no birefringence was observed. This indicates that the molecular weights of Curdlan need to be above a threshold value to form LCG, though the threshold could be dependent on the Curdlan concentration. The degree of orientation of Curdlan molecules increases with molecular weight around the threshold molecular weight and saturates at high molecular weight, as indicated in the behavior of ∆n. The key factors for forming Curdlan LCG by means of dialysis are the change of the Curdlan conformation from random coil to triple helix due to the outflux of Na+ and
Nobe et al.
OH- and the cross-linking between different Curdlan molecules due to the influx of Ca2+ and Cl-. The experimental results show that the calcium concentration in the gel is constant irrespective of the molecular weight of Curdlan at constant weight fraction of Curdlan. Therefore, the effect of pH change resulting from the outflux of Na+ and OH- should be examined in detail in a discussion of the molecular weight effect. According to the viscosity measurements,7 the intrinsic viscosity of Curdlan (CUD3F4, Mw ) 1 810 000) solutions is 190 cm3/g at 0.45 M NaOH; and with decreasing OHconcentration COH, it increases slightly, suddenly decreases from 190 to 160 cm3/g at 0.25-0.21 M NaOH, and then increases sharply to a saturated value of 290 cm3/g at 0.15 M NaOH. This COH dependence of the intrinsic viscosity might be corresponding to the conformation change of Curdlan from random coil to triple helix via a certain intermediate state. Since the radius of gyration of Curdlan molecules increases with intrinsic viscosity monotonically at 0.3 M NaOH,7 COH dependence of the intrinsic viscosity could be translated to that of the radius of gyration. According to our screening test for a variety of macromolecules, it is suggested that only rodlike molecules such as double helical DNA, R-helical polypeptides, and polysaccharides can form liquid crystalline gel (LCG) by the present dialysis method. Therefore, we speculate that only the triple helix Curdlan (not the single strand Curdlan) can form mesogens, which compose LCG. In the dialysis process, COH of the Curdlan solution in the dialysis tubing decreases with time and goes to a value less than that corresponding to the threshold for the coil-to-helix transition.9 It seems to be reasonable to assume that, in the case of concentrated Curdlan solutions, triple helix alignment is formed locally during the dialysis process, which becomes the mesogen. It is difficult to presume mesogens consisting of a single molecule even at extremely high molecular weight, because the solution and the gel are not dilute and such high molecular weight molecules may entangle each other easily. When the molecular weight of Curdlan is high, the threshold COH could be raised. The entanglement effect could help local alignments of the molecules. Therefore, higher molecular weight Curdlans form higher-order structures. The entanglement effect, however, saturates, and no molecular weight dependence appears when the molecular weight is high enough. Fractionated Curdlan molecules should orient with each other more easily than the unfractionated molecules. These arguments are consistent with Figure 2. The sequential change in color in the outermost LCG layer is attributed to the slight change in the orderedness. That is, since the color corresponds to the wavelength satisfying the diffraction condition, the slight change of the orderedness is consistent with the sequential color variation. The experimental fact that the ratio q of the thickness of the LCG layer to the gel radius decreases with increasing molecular weight must be explained from the above properties of Curdlan molecules. The randomly directed Curdlan molecules in the sol state may align parallel to each other during the gelation process. The local alignments can form
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MW Effect on Gel Formation of Curdlan
mesogens of LCG. Then, we pay attention to the relationship between the alignment and the molecular weight of Curdlan molecules. For rodlike particles, the lyotropic effect (the excluded volume effect) arranges the long-axis direction of the particles in one direction. The stability of the orientation alignment against the thermal fluctuation increases with increasing ratio between the length L and the diameter D of the rod, L/D (this ratio is called the length-to-breadth ratio).10 This shows that when the rodlike particles are directed randomly in the initial condition, the particles with smaller length-to-breadth ratio are directed along the same direction more easily. Thus, the particles whose ratio is large enough never align parallel to each other. For polymers, the similar analysis for the orientation order based on the length-to-breadth ratio can be possible when the polymers are stiff enough and are not so long.10 The Curdlan molecules in the present analysis, however, are too long, and the stiffness of them changes widely depending on the pH condition. It is also difficult to obtain the molecular weight dependence of the length-to-breadth ratio. We choose the radius of gyration Rg instead of the length-to-breadth ratio to discuss the orientation order. The radius of gyration for rodlike particles with large length-to-breadth ratios is large. Then, qualitatively, the length-to-breadth ratio and the radius of gyration express the same intrinsic property of the molecules. The molecular weight dependence of the radius of gyration is also clear. So, let us discuss the relation between the radius of gyration of the molecules and the degree of order of the final orientation alignment of the molecules with random initial orientations. It seems to be natural to assume that the amorphous phase appears when the radius of gyration Rg is larger than the average intermolecular distance l, since the large gyration radius could prohibit the Curdlan molecules from aligning parallel to each other. In terms of the average segment number of Curdlan N, the radius of gyration Rg for a Curdlan molecule is expressed as11 Rg = Rg0Nν
(3)
where ν is the exponent characterizing the Curdlan conformation. The Curdlan conformation dependence on the hydroxide anion concentration can be described by the functional relation between the exponent ν and the hydroxide anion concentration COH; ν ) ν(COH). The exponent ν is in the range between 1 at the triple helix state and 0.588 at the random coil state,11 and is expected to be a monotonically decreasing function of COH, since Curdlan conformation changes from triple helix to random coil with increasing COH.3,12 In eq 3, the constant Rg0 may depend on COH weakly. The average molecular weight of Curdlan Mw is also expressed as Mw ) M0N
(4)
where M0 is a constant. The number of the Curdlan molecules in unit volume n is proportional to the ratio between the number density of segments in the intradialytic solution c and the molecular weight M; then, n ) (1/c0)(c/M), where
1/c0 is a proportional constant. The intermolecular distance l is proportional to n-1/3. Therefore, we have l = l0
( ) c0 M c w
1/3
) l0M01/3
() c0 c
1/3
N1/3
(5)
where l0 is a proportional constant. Let us introduce the ratio y ≡ Rg/l as a function of the concentration COH y(COH) )
()
Rg0(COH) c l0M01/3 c0
1/3
Nν(COH)-1/3
(6)
and assume that the amorphous structure appears if the value of y is larger than a threshold value yc. Then, the “threshold” value C/OH of the hydroxide anion concentration (the concentration of hydroxide anion for transforming to the amorphous state) is obtained from the equation
()
Nν(COH)-1/3
(7)
() [
]
(8)
Rg0(C/OH) c yc ) l0M01/3 c0
1/3
/
or c 1 1 + ν(C/OH) - ln N ) 0 ln Rˆ g0(C/OH) + ln 3 c0 3
where Rˆ g0 ) Rg0/l0M01/3yc. As the COH dependence of the term (ν - 1/3) is much larger than that of ln Rˆ g0, we regard ln Rˆ g0 to be a constant, ln Rˆ g00, independent of COH. Then, eq 8 reduces to
1 ν(C/OH) - ) 3
()
1 c ln Rˆ g00 + ln 3 c0 ln N
(9)
This equation indicates that the exponent value ν* ≡ ν(C/OH) at the threshold hydroxide anion concentration is a function of N. Since 1 g ν* g 0.588, we have ν* - 1/3 > 0. This shows
()
1 c Mmin, and becomes a constant in the region Mw > Mmax. The above-mentioned theory giving the relation eq 16 could explain the molecular weight dependence of q for low molecular weight range qualitatively but not explain the saturation of the molecular weight dependence shown by the experiment at high molecular weight. The saturation of q is expected to be due to the collisions between molecules, which are neglected in the present theory. Since it is quite difficult to treat the many-body effect as the collision effect directly, let an “effective” theory be introduced. The essence of the collision effect is that the collisions between the molecules prohibit the free elongation of the entire molecular chain as shown by eq 3. Therefore, we introduce the segment number Nmax of the freely elongating part in a molecule to take the collision effect into account. For the molecule of segment number N > Nmax, we assume that a part of it consisting of Nmax segments freely elongates and the rest remains crumpled; the intermolecular collision reduces the number of segments contributing the elongation from N to Nmax. Paying attention to the Nmax segments contributing to the elongation effectively makes the present theory applicable to higher molecular weight molecules. The value of Nmax generally depends on the concentration c. In the molecular weight range for N > Nmax , q remains constant, i.e., at the value for the molecules with N ) Nmax. This means q saturates at N ) Nmax. The entanglement effect and the collision effect probably appear simultaneously; Mmin ≈ M0Nmax. The molecular weight Mmin corresponds to the molecular weight at the rising point of ∆n and M0Nmax at the saturation point of q. These characteristic molecular weights have been discussed in section III. From Figure 2, we roughly estimate Mmin ≈ 600 000, and from Figure 3, M0Nmax ≈ 600 000. This agreement supports the present theoretical analysis. V. Conclusion Experimental results of the molecular weight effect on LCG characteristics, i.e., ∆n increased and δ/R decreased with molecular weight, and both became saturated at high molecular weight, together with constant CCa irrespective of molecular weight and its distribution, were analyzed in analogy with the theory based on the length-to-breadth ratio of rodlike molecules. During the dialysis, the hydroxide anion concentration COH decreases, resulting in the conformational change of Curdlan from coil to helix to form local alignment. The Curdlan conformation dependence on the hydroxide anion concentration can be described by a functional relation
MW Effect on Gel Formation of Curdlan
between the exponent for end-to-end distance ν and COH. The theoretical consideration resulted in eq 9, which reads inequalities of eqs 16 and 17. The consistency of experimental and theoretical results suggests that the current application of the general liquid crystalline formation idea to the unique LCG formation is reasonable, at least qualitatively. The results also suggest that the amorphous phase appears when the size of the Curdlan molecules is larger than the average intermolecular distance resulting from the random coil to triple helix transformation of Curdlan molecules associated with lowering hydroxide anion concentration in the dialysis process. For the saturation at high molecular weight, we developed the discussion based on the many-body effects such as the entanglement and collision between molecules. This discussion suggests that the molecular weights at the rising point of ∆n and at the saturation point of q are the same; that is also consistent with the experimental results. Acknowledgment. This work was partly supported by Grant-in-Aid for Science Research from The Ministry of
Biomacromolecules, Vol. 6, No. 6, 2005 3379
Education, Culture, Sports, Science and Technology in Japan (grant no. 16540366). References and Notes (1) Dobashi, T.; Nobe, M.; Yoshihara, H.; Yamamoto, T.; Konno, A. Langmuir 2004, 20, 6530-6534. (2) Rao, V. S.; Foster, J. F. Biopolymers 1963, 1, 527-544. (3) Ogawa, K.; Tsurugi, J.; Watanabe, T.; Ono, S. Carbohydr. Res. 1972, 23, 399-405. (4) Konno, A.; Kimura, H. Kinran Tanki Daigaku Kenkyushi 1992, 23, 173-182. (5) Dobashi, T.; Yoshihara, H.; Nobe, M.; Koike, M.; Yamamoto, T.; Konno, A. Langmuir 2005, 21, 2-4. (6) Jezequel, V. Cereal Foods World 1998, 43, 361-364. (7) Nakata, M.; Kawaguchi, T.; Kodama, Y.; Konno, A. Polymer 1998, 39, 1475-1481. (8) Sato, M.; Nobe, M.; Dobashi, T.; Yamamoto, T.; Konno, A. Colloid Polym. Sci. 2005, in press. (9) Nobe, M.; Dobashi, T.; Yamamoto, T. Langmuir 2005, 21, 81558160. (10) Vroege, G. J.; Lekkerkerker, H. N. W. Rep. Prog. Phys. 1992, 55, 1241-1309. (11) Doi, M.; Edwards, S. F. The theory of Polymer Dynamics; Oxford University Press: New York, 1986. (12) Tada, T.; Matsumoto, T.; Masuda, T. Chem. Phys. 1998, 228, 157-166.
BM050420M
