Experimental Demonstration for the Morphological Evolution of Crystals Grown in Gel Media Yuya Oaki and Hiroaki Imai* Department of Applied Chemistry, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan Received April 5, 2003;
CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 5 711-716
Revised Manuscript Received June 10, 2003
ABSTRACT: The morphological evolution of the inorganic crystals (Ba(NO3)2, NH4Cl, H3BO3, and K2Cr2O7) was demonstrated in various kinds of organic gel media (agar, gelatin, pectin, and poly (vinyl alcohol)). As the gel density increased, the morphology grown in the gel matrix remarkably changed from polyhedral single crystals exhibiting specific habits into dendritic forms consisting of irregularly branched polycrystalline aggregates regardless of the sorts of inorganic compounds and gelling agents. The evolution from polyhedrons into dendrites via skeletal forms is ascribed to an increase in the influence of diffusion of the solutes on the crystal growth. Since gel media generally suppress the mobility of ions, densification of the media decreased the apparent diffusion rate of the solutes and finally promoted the formation of diffusion-limited morphologies including skeletal, dendritic, and branched forms. Peculiar curved and helical branches were observed in dendrites with crystals having a triclinic system (H3BO3 and K2Cr2O7) because the connections of subunits were deviated in the polycrystalline aggregates. Introduction Recently, much attention has been devoted to the total crystal design including a concept of controlling the size, morphology, and structure of crystals.1 Because many properties and functions of crystals depend on macroand microscopic structures, the design at specific scales is important for a variety of application fields. Particularly, the macroscopic morphology of crystals has attracted considerable interest because of their fundamental and technological importance.2 For solutionbased crystal growth methods, various kinds of crystal modifiers have been studied to control the macroscopic morphology of crystals. The presence of organic molecules,3-5 polyelectrolytes,6-8 surfactants,9-11 and inorganic ions12-14 has been reported to influence crystal morphologies with adsorption on specific surfaces. However, the morphological evolution with crystal modifiers usually resulted in a limited variation of the crystal habits of polyhedrons. It is widely known that crystal morphologies depend on the correlation between the driving force of crystallization and diffusion of atoms, ions, molecules, or heat. Variation in these experimental parameters changes the crystal shapes from polyhedrons into various dendritic morphologies through skeletal shapes.15-19 We summarize the morphological evolution with an increase in the driving force, such as the degree of supersaturation of the solutes, as shown in Figure 1. Specific polyhedral forms are created through a kinetic-controlled reaction near the equilibrium condition (Figure 1a). Skeletal (hopper) shapes (Figure 1b) are produced as the driving force of crystallization increases. Under a far-fromequilibrium condition, dendritic morphologies (Figure 1c) appear because of the instability of the growing surface. The regularity of dendrites that depend on a crystallographic symmetry disappears when the driving force is relatively high (Figure 1d). Fractal or dense * Corresponding author. Phone: +81 45 566 1556. Fax: +81 45 566 1551. E-mail:
[email protected].
Figure 1. Schematic model of morphological evolution with an increase in the driving force; (a) polyhedral form produced in the kinetic-controlled system near equilibrium, (b) skeletal morphology by the Berg effect, (c) single-crystalline ordered dendrite with crystallographic symmetry, (d) partially disordered dendrite having a single-crystalline ordered trunk and disordered polycrystalline side branches, (e) disordered polycrystalline dendrite as shown in diffusion-limited aggregation (DLA), and (f) dense branching morphology (DBM).
branching forms are produced with a further increase in the driving force (Figure 1e,f). The variation of macroscopic morphologies, which is attributed to an increase in the influence of diffusion on the growth behavior, has been mainly studied by theoretical investigation.17,20 On the other hand, few reports exist on the experimental demonstration of the morphological evolution because strict control of the driving force is difficult in practice. A gel matrix has been used for the control of nucleation and morphology on aqueous solution-based crystal growth.16,21-24 In the early stage, PbI2, AgI, Ag2Cr2O7, PbSO4, and PbCl2 crystals were produced in various gels because the media provide appropriate conditions for the growth of large defect-free single crystals.16 The advantage of gel media is believed to be the reduction of the nucleation rate and suppression of convection. In recent years, the production of peculiar and complex crystal morphologies, such as dendritic and helical shapes, in gel media has been reported for various materials, such as K2Cr2O7,25 NH4Cl,26 AgBr,27 ascorbic acid,28 and glucose.29 Very recently, Petrova and Swift showed that the habit changes of NaBrO3 grown in
10.1021/cg034053e CCC: $25.00 © 2003 American Chemical Society Published on Web 06/27/2003
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Table 1. Combination of Inorganic Crystals and Gelling Agents for Demonstration inorganic crystals
crystal system
solubility g/100 g of water 60 °C 25 °C
Ba(NO3)2 NH4Cl H3BO3 K2Cr2O7
cubic cubic triclinic triclinic
20.3 55.3 14.9 46.4
10.2 39.3 5.7 14.9
initial concentration range
gelling agents
g/100 g of water (degree of supersaturation)a
agar 0-8
gelatin 0-40
pectin 0-3
PVA 0-24
12 (0.17)-21 (1.05) 41 (0.04)-53 (0.35) 7 (0.22)-13 (1.26) 25 (0.67)-40 (1.68)
Ob O O O
-c O O
O
O
a The degree of supersaturation (σ) was calculated using the follow equation: σ ) C - C /C (C: initial solute concentration, C : o o o saturated concentration at 25 °C). b O: Morphological variation was successfully observed. c -: Crystal growth was not demonstrated because the gelling agents were not dissolved.
various gels occurred with an increase in the gel density.30 Liu and Swant described the branched fibrous structure of an organic crystal grown in viscous gel media.31 These reports suggest that gel media obviously affect the crystal morphologies. Details of the effects of gel on crystal growth have not been completely clarified; however, it is well-known that the growth rates decrease in the media. In this work, we performed a systematic investigation of crystal growth in a gel matrix for a general understanding of the formation mechanisms for a variety of morphologies. Four kinds of inorganic crystals (Ba(NO3)2, NH4Cl, H3BO3, and K2Cr2O7) were grown in various sorts of organic gel media (agar, gelatin, pectin, and poly (vinyl alcohol)). Crystals having a cubic (Ba(NO3)2 and NH4Cl) or triclinic (H3BO3 and K2Cr2O7) system were selected to study the influence of the crystallographic symmetry on the macroscopic morphology. We successfully provided an experimental demonstration of the morphological evolution of crystals, as shown in Figure 1, with variation of the degree of supersaturation and density of the gelling agents. The diffusion rates controlled by the gel density were found to be essential for the evolution of the crystal growth. Experimental Procedures Materials and Crystallization Method. Table 1 shows the inorganic materials used for crystal growth and the gelling agents used as growth media. Barium nitrate (Ba(NO3)2; Koso Chemical, 99.0%), ammonium chrolide (NH4Cl; Kanto Chemical, 99.0%), boric acid (H3BO3; Kanto Chemical, 99.5%), and potassium dichromate (K2Cr2O7; Kanto Chemical, 99.5%) were selected as the inorganic materials by considering their solubility in water. The solubility of these inorganic crystals varied greatly with the solution temperature as listed in Table 1. Thus, crystallization of these materials was achieved by lowering the temperature from 60 to 100 °C to 25 °C. The gelling agents adopted as media have various physical structures and chemical properties, as described in the following. Agar gel has a three-dimensional porous network structure at temperatures below 40 °C. Galactose-based polymer chains form a double-helix structure by hydrogen bonding, and the aggregation of these helices produces a network with intermolecular hydrogen bonding.32 The structure of gelatin gel turns a random coil into a three-dimensional porous network with sol-gel transition. Gelation occurs at temperatures below 30 °C. Part of this network structure consists of left-handed triple helices that are composed of righthanded protein fibrils mainly obtained from glycine, proline, hydroxyproline, and alanine.33 Pectin molecules are a polysaccharide derivative. Hydrogen bonding between the molecules or egg-box junction containing various cations induces gelation and the formation of network structures.34 Poly (vinyl alcohol) (PVA) provides a highly viscous solution with slight fluidity. Since aggregation of PVA molecules forms many partially
crystalline regions, these microcrystalline parts and free molecular chains create network frames.35 Thus, an aqueous solution with a high PVA concentration can interact with inorganic ions in the same manner in the other gel matrixes. When the concentration of these gelling agents was relatively low, solidification did not occur. We describe the concentration of the gelling agents (g/100 g of water) as gel density regardless of the state of the media. Procedure. A certain amount of inorganic crystals was dissolved in 10 dm3 of purified hot water (60-100 °C). After the inorganic crystals were completely dissolved, a specified amount of gelling agents was added to this hot solution. The mixture was then poured into a flat polystyrene vessel and maintained at 25 °C for several days. The solutions were transformed to gel during the cooling process. The apparent degree of supersaturation of the solutes and the concentration of the gelling agents are listed in Table 1. The morphologies of grown crystals were characterized with the use of an optical microscope (OM) and scanning electron microscope (FESEM, Hitachi S-4700). X-ray diffraction analysis (Rigaku RAD-C diffractometer with CuKR radiation) was used for the determination of the crystallographic direction.
Results The nucleation of crystals was clearly observed to start within several days, and crystal growth finished within an hour after the nucleation. The morphologies of inorganic crystals grown in gel media were investigated as a function of the degree of solute supersaturation and gel density. Generally, the degree of supersaturation depending on the initial concentration of the solutes slightly influenced the final morphology, whereas the number of nuclei increased as the degree increased. On the other hand, the gel density had a substantial effect on the morphologies regardless of the type of gelling agent used. A decrease in the number of nucleation was also observed as the gel density increased. Ba(NO3)2 Crystal Morphology. Figure 2 shows the morphological evolution of Ba(NO3)2 crystals as a function of the agar gel density. Regular octahedral forms surrounded by {111} planes, which are the most closely packed faces, were produced at a low agar density (Figure 2a). As the density increased, skeletal shapes having a stair-like pit on the {111} planes (Figure 2b) were formed. We then observed regular dendrites oriented along and (Figure 2e). Figure 2c,d shows intermediate structures including both skeletal and dendritic forms. With a further increase in the agar gel density, highly ordered dendrites gradually developed into partially disordered dendrites (Figure 2f,g). Irregularly branched dendrites consisting of polycrystalline aggregates were formed at the highest agar density (Figure 2h). This morphological variation is consistent with the model shown in Figure 1. In
Evolution of Crystals Grown in Gel Media
Figure 2. OM and SEM images for the morphological evolution of Ba(NO3)2: (a) regular octahedron at CBa ) 15/Cag ) 0.4, (b) skeletal form at CBa ) 15/Cag ) 1.0, (c and d) intermediate structure between skeleton and dendrites at CBa ) 15/Cag ) 2.0, (e) regular dendrite at CBa ) 15/Cag ) 3.0, (f) partially disordered dendrite at CBa ) 15/Cag ) 4.0, (g) magnification of panel f, and (h) CBa ) 15/Cag ) 8.0. CBa and Cag indicate the initial concentrations (g/100 g of water) of Ba(NO3)2 and agar, respectively.
contrast, the basis of morphology, such as polyhedrons, skeletons, and dendrites, was not changed with raising the Ba(NO3)2 concentration from 12 to 21 g/100 g of water although the roughness of the surface of polyhedrons and frequency of branching in dendrites increased. The number of the nuclei increased as the concentration was raised. NH4Cl Crystal Morphology. Figure 3 shows the morphological evolution of NH4Cl in an agar gel matrix. In this case, polyhedron shapes were not produced in solutions even with an extremely low degree of supersaturation because of the low surface energy of the crystal. The default morphology showed regular dendrites growing along the directions (Figure 3a,b). As the agar gel density increased, growth along the directions was observed (Figure 3c,d). This change in the direction of growth had already been reported to occur when the growth rate increased.36 An increase in the gel density produced a partially disordered dendritic morphology (Figure 3e,f). An irregularly branching morphology was produced with a further increase in the agar density (Figure 3g,h). Remarkable morphological evolution was not achieved with raising the NH4Cl concentration from 41 to 53 g/100 g of water
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Figure 3. OM images of NH4Cl morphological evolution: (a and b) dendrite oriented along the directions at CNH ) 41/Cag) 0.4, (c and d) dendrite oriented along the directions at CNH ) 41/Cag ) 0.6, (e and f) partially disordered dendrite at CNH ) 41/Cag ) 2.0, and (g and h) irregularly branched dendrite at CNH ) 41/Cag ) 4.0. CNH and Cag indicate the initial concentrations (g/100 g of water) of NH4Cl and agar, respectively.
while the frequency of branching in dendritic forms increased. We also prepared NH4Cl crystals in gelatin. The morphological change that occurred as the gelatin density increased was fundamentally the same as that with agar. H3BO3 and K2Cr2O7 Crystal Morphology. The morphological evolution of triclinic crystals (H3BO3 and K2Cr2O7) was basically similar to that of cubic crystals (Ba(NO3)2 and NH4Cl). A hexagonal prism of H3BO3 having the (100), (010), (001), and (-110) planes (Figure 4a) and a platy form of K2Cr2O7 surrounded with the (2-11), (010), and (001) planes (Figure 5a) were produced at a low gel density. Irregularly branching dendrites were formed at the highest density (Figures 4f and 5f). Partially ordered dendrites of H3BO3 (Figure 4b,c,e) and K2Cr2O7 (Figure 5b,e) with an assembly of platy crystals were produced instead of the skeletal and ordered dendrites of Ba(NO3)2 and NH4Cl. Although the fundamental variation of dendritic forms was similar to that of the cubic systems in a medium gel density range, unique morphologies, such as curved (Figures 4c,e and 5b,d,e) and twisted (Figures 4d and 5c) structures, were observed in the aggregates. SEM images in insets of Figures 4c,d and 5c show that these dendritic morphologies consisted of the fundamental
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Figure 4. OM and SEM images of H3BO3 morphological evolution: (a) hexagonal prism grown from the evaporation of 3 wt % aqueous solution, (b) partially ordered polycrystalline dendrite at CHB ) 9.0/Cag ) 0.2, (c-e) macroscopic irregular dendritic forms having curved, twisted, and microscopic helical structures at CHB )7.0/Cag ) 0.2, CHB ) 7.0/Cag ) 0.6, and CHB ) 9.0/Cag ) 1.0, respectively (insets of panels c and d), magnified images of the curved and helical morphology, and (f) polycrystalline dendrite at CHB ) 7.0/Cag ) 4.0. CHB and Cag indicate the initial concentrations (g/100 g of water) of H3BO3 and agar, respectively.
platy units as shown in Figures 4a and 5a. The angles at the connections were regular in the helical morphologies (insets of Figures 4d and 5c). These samples used for the SEM observation were prepared by evaporation of water from the gel media to prepare a bare surface of the helical crystals. The morphology obtained by the evaporation method was almost the same as that by the regular technique. These results indicate that these helical morphologies were formed with the repetition of the twins. It has been reported that the formation of a growth twin was enhanced in a diffusion field.37 The detailed structure of these unique morphologies is now under investigation. The crystal growth of K2Cr2O7 was also demonstrated in agar, pectin, and poly (vinyl alcohol). The effect of the density of these gelling agents was almost the same as that of gelatin. In contrast, the influence of the solute concentration on the morphological evolution was small in the range listed in Table 1, whereas the number of the nuclei increased as the concentration was raised. Discussion Morphological evolution from polyhedral forms into dendritic morphologies, as shown in Figure 1, is commonly attributed to an increase in the driving force of crystallization, such as the degree of supersaturation and supercooling. In this study, however, an increase in the degree of supersaturation controlled by the initial concentration of the solutes hardly influenced the shape of crystals because an increase in the nucleation practi-
Oaki and Imai
Figure 5. OM and SEM images of K2Cr2O7 morphological evolution: (a) platy form at CKC ) 25/Cge ) 5, (b) macroscopic irregular branching structure with microscopic helical morphology at CKC ) 25/Cge ) 25, (c) magnification of panel b (the inset of panel c), detail of the helical morphology, (d and e) macroscopic irregular morphology having curved and twisted structures at CKC ) 35/Cge ) 30 and CKC ) 40/Cge ) 25, respectively, and (f) polycrystalline dendrites at CKC ) 25/Cge ) 35. CKC and Cge indicate the initial concentrations (g/100 g of water) of K2Cr2O7 and gelatin, respectively.
cally decreased the driving force depending on the concentration. On the other hand, the morphological evolution of crystal morphologies was achieved by changing the gel density. Since the variation including skeletal and dendritic forms was independent of the types of inorganic compounds and organic gelling agents used, the habit change and dendritic growth because of instability of the growing surface are ascribed to the influence of the gel media rather than the specific adsorption of gelling agents on specific crystal surfaces. Moreover, polycrystalline aggregates exhibiting disordered dendrites were produced at a high density of gel media, although single crystals were grown in a lowdensity matrix. The formation of skeletal and dendritic forms with an increase in the gel density indicates that diffusion-limited crystal growth dominates in the gel media. Since viscous media, such as gel, suppress the convection, diffusion is relatively predominant for the transformation process of the solutes.16,21-24 Moreover, solute anions and cations interact with the molecules of gelling agents having -OH, -COOH, and -NH2 groups via a complex formation.23,24 Thus, an increase in the gel density reduces the apparent diffusion rate of the solutes. Actually, we confirmed that the apparent diffusion rate of Cr2O72- was reduced as the gel density increased by measuring the penetration rate of the front of the yellowish K2Cr2O7 solution into gelatin gel. The reduction of the apparent diffusion rate of the solutes decreased the nucleation and induced crystal growth through the diffusion-limited process. The habit change of NaBrO3 crystals grown in various gels30 was at-
Evolution of Crystals Grown in Gel Media
tributed to a reduction in the diffusion rate with the media. In our study, polyhedral forms were changed into a skeletal morphology because of the Berg effect with increasing the effect of the diffusion for the growth process. The formation of dendrites was ascribed to instability of the growing surface in a diffusion field formed in the viscous gel media. Polyhedral, skeletal, and ordered dendritic morphologies were composed of a single crystal. However, a decrease in the regularity of the dendrites, as shown in Figures 2g-h and 3e-h, indicates the formation of polycrystalline aggregates with growth twins. Densification of the gel matrix decreases the diffusion rate, and thus, promotes the formation of irregularly branched polycrystalline aggregates. Theoretical studies have also indicated that a decrease in the diffusivity changes the morphology of a diffusion-limited aggregate (DLA) from an anisotropic shape into an irregularly branching pattern.20 It has also been speculated that densification of gel media increases the random noise for crystal growth because the polymer backbone of gel matrixes disturbs the progress of the growing surface. Partially disordered dendritic forms, as shown in Figure 3f, were formed by decreasing the anisotropy of the growth direction with an increasing random noise. This behavior agrees with a variation of the morphology of DLA with a change in the random noise on computer simulation.38 Liu and Swant have proposed that the selective adsorption of additives and the crystallographic mismatch model produced a branched structure of various compounds in a high-density matrix.31 In this work, however, the formation of irregularly branched dendrites was observed regardless of the types of gelling agents used. Thus, the adsorption model for branching is not plausible for our experiments. In the case of the triclinic crystal system (H3BO3 and K2Cr2O7), macroscopically curved and helical shapes were produced instead of skeletal or regular dendritic forms. These unusual architectures are tentatively attributed to the lowest symmetry of the crystal units. In a diffusion field, the connections of twinned crystals would be deviated because of the asymmetry of the subunits. As a further increase in gel density, DLA-like unique morphologies containing twisted branches were observed. Details of the formation process and growth mechanism of the helical morphologies are now under investigation. Conclusion We experimentally demonstrated the systematic variation of crystal morphology by varying the density of the gel matrix. The morphology of crystals changed from specific polyhedral habits into various dendritic forms as the gel density increased, regardless of the types of inorganic materials and organic gelling agents used. This morphological evolution with an increase in the gel density indicates that diffusion was relatively dominant for crystal growth in a densified gel matrix because of the interaction between inorganic ions and organic molecules of the gelling agents. A decrease in the diffusion rate reduced the regularity of the dendrites with the promotion of twinned crystals. In the case of the lowest symmetry of a crystal system (triclinic
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system), unique curved and helical morphologies were produced in the branched morphologies. Acknowledgment. This work was supported by Grant-in-Aid for Scientific Research (15560587) and 21st Century COE program “KEIO Life Conjugate Chemistry” from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References (1) Mann, S. Angew. Chem., Int. Ed. 2000, 39, 3392-3406. (2) (a) Weiner, S.; Addadi, L. J. Mater. Chem. 1997, 7, 689702. (b) Estroff, L. A.; Hamilton, A. D. Chem. Mater. 2001, 13, 3227-3235. (3) Coveney, P. V.; Davey, R.; Griffin, J. L.; He, Y.; Hamlin, J. D.; Stackhouse, S.; Whiting, A. J. Am. Chem. Soc. 2000, 122, 11557-11558. (4) Fukuyo, T.; Imai, H. J. Cryst. Growth 2002, 241, 193-199. (5) Gower, L. A.; Tirrell, D. A. J. Cryst. Growth 1998, 191, 153160. (6) Marentette, J. M.; Norwig, J.; Sto¨ckelmann, E.; Meyer, W. H.; Wegner, G. Adv. Mater. 1997, 9, 647-651. (7) Qi, L.; Co¨lfen, H.; Antonietti, M. Angew. Chem., Int. Ed. 2000, 39, 604-607. (8) Qi, L.; Co¨lfen, H.; Antonietti, M.; Li, M.; Hopwood, J. D.; Ashley, A. J.; Mann, S. Chem.sEur. J. 2001, 7, 3526-3532. (9) Li, M.; Mann, S.; Langmuir 2000, 16, 7088-7094. (10) Bujan, M.; Sikiric, M.; Filipovic-Vincekovic, N.; Vdovic, N.; Garti, N.; Fu¨redi-Milhofer, H. Langmuir 2001, 17, 64616470. (11) Wang, C.; Chen, D.; Huang, T. Colloid Surf. A 2001, 89, 145-154. (12) Benton, W. J.; Collins, I. R.; Grimsey, I. M.; Parkinson, G. M.; Rodger, S. A. Faraday Discuss. 1993, 95, 281-297. (13) Garcia-Ruiz, J. M. J. Cryst. Growth 1985, 73, 251-262. (14) Imai, H.; Terada, T.; Yamabi, S. Chem. Commun. 2003, 484-485. (15) Kuroda, T.; Irisawa, T.; Ookawa, A. J. Cryst. Growth 1977, 42, 41-46. (16) Henisch, H. K. C. N.Crystals in Gels and Liesegang Rings; Cambridge University Press: Cambridge, 1988. (17) Saito, Y.; Ueta, T. Phys. Rev. A 1989, 40, 3408-3419. (18) Dirksen, J. A.; Ring, T. A. Chem. Eng. Sci. 1991, 46, 23892427. (19) Nanev, C. N. Prog. Cryst. Growth Charact. 1997, 35, 1-26. (20) Bogoyavlenskiy, V. A.; Chernova, N. A. Phys. Rev. E 2000, 61, 1629-1633. (21) Dennis, J.; Henish, H. K. J. Electrochem. Soc. 1967, 114, 263-266. (22) Robert, M. C.; Lefaucheux, F. J. Cryst. Growth 1988, 90, 358-367. (23) Cecal, A.; Palamaru, M.; Juverdeanu, A.; Giosan, M. J. Cryst. Growth 1996, 158, 181-184. (24) Moreno, A.; Jua´rez-Martı´nez, G.; Herna´ndez-Pe´rez, T.; Batina, N.; Mundo, M.; Mcpherson, A. J. Cryst. Growth 1999, 205, 375-381. (25) Suda, J.; Matsushita, M. J. Phys. Soc. Jpn. 1995, 64, 348351. (26) Hojo, H.; Ohta, S.; Matsushita, M. J. Phys. Soc. Jpn. 1986, 55, 2487-2490. (27) Doxsee, K. M.; Chang, R. C.; Chen, D.; Myerson, A. S.; Huang, D. J. Am. Chem. Soc. 1998, 120, 585-586. (28) Rastogi, R. P.; Das, I.; Sharma, A. J. Chem. Educ. 1994, 71, 694-696. (29) Das, I.; Sharma, A.; Kumar, A.; Lall, R. S.; J. Cryst. Growth 1997, 171, 543-547. (30) Petrova, P. I.; Swift, J. A. Cryst. Growth Des. 2002, 2, 573578. (31) Liu, X. Y.; Swant, P. D. Angew. Chem., Int. Ed. 2002, 41, 3641-3645. (32) (a) Djabourov, M.; Clark, A. H.; Rowlands, D. W.; RossMurphy, S. B. Macromolecules 1989, 22, 180-188 (b) Nijenhuis, K. Adv. Polym. Sci. 1997, 130, 194-202. (33) (a) Pezron, I.; Djabourov, M.; Boiso, J.; Leblond, J. J. Polym. Sci. B Polym. Phys. 1990, 28, 1823-1839. (b) Nijenhuis, K. Adv. Polym. Sci. 1997, 130, 160-193. (34) Thakur, B. R.; Singh, R. K.; Handa, A. K. Crit. Rev. Food Sci. 1997, 37, 47-73.
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CG034053E
