Hydrogen Bonds in Silk Fibroin-Poly(acrylonitrileco-methyl acrylate) Blends: FT IR Study

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1 Hydrogen Bonds in Silk Fibroin-Poly(acrylonitrileco-methyl acrylate) Blends: FT IR Study YUYU SUN, ZHENGZHONG SHAO,* PING HU, TONGYIN YU Department of Macromolecular Science, Fudan University, Shanghai, , People s Republic of China Received 25 April 1996; revised 5 November 1996; accepted 27 November 1996 ABSTRACT: FT IR spectroscopy was used to study the specific interactions in polyacrylonitrile-silk fibroin ( PAN SF) and poly( acrylonitrile- co-methyl acrylate)-silk fibroin ( PANMA SF) blends. No specific interaction was found in PAN SF blends. In PANMA SF blends, however, a new 1703 cm 01 band, assigned to be hydrogen-bonded carbonyl groups of PANMA, appears, and its intensity depends on the compositions of the blends and the MA contents in PANMA. Furthermore, when the sample was heated, considerable changes in position and intensities of the hydrogen-bonded bands, in both stretching regions of the carbonyl group of PANMA and the hydroxl group of SF, were found, and these changes were irreversible on cooling. Finally, we suggested that the bands of hydrogen bonds in PANMA SF blends may be the average result of several kinds of possible hydrogen bondings John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: , 1997 Keywords: silk fibroin; FT IR spectroscopy; hydrogen bonds; polyacrylonitrile; poly( acrylonitrile- co-methyl acrylate) INTRODUCTION Polyacrylonitrile (PAN) and its copolymers (PAC) fibers are widely used as textile and reinforcement Although Bombyx mori silk fibroin ( SF) possesses fibers as well as the precursors of carbon fibers. many outstanding characteristics, it suffers from There have been a number of studies on blend fibers some inferior performances. Recently, besides inature of PAN, but to our knowledge, there is little liter- vestigations on the chemical modification of silk on blend system of PAC with SF. fibroin by graft copolymerization, 1 3 blends of silk Our interest here is to study the miscibility of fibroin with other polymers, such as poly (vinyl PANMA SF blends. It is widely accepted that FT alcohol), 4,5 chitosan, 6 sodium poly-glutamate, 7 IR spectroscopy is a sensitive tool for studying spe- sodium alginate, 8 and cellulose 9 have attracted cific interactions, particularly hydrogen bonds, in considerable academic and practical interests. We polymer blends This article is to study the hy- have reported the investigation of SF-poly ( vinyl drogen bonds in PANMA SF blends in relation to alcohol) blends also, but no information is the weight ratios of SF, the compositions of the coavailable on the study of the miscibility of SF with polymers, and the temperature, by FT IR spectros- other synthetic polymers. copy. We believed that this study may provide an important basis for the further investigation of PAC SF and even other synthetic polymer natu- * Present address: Department of Zoology, Institute of Bio- ral macromolecules blend systems. logical Sciences, University of Aarhus, DK-8000 Aarhus C Denmark. Correspondence to: T. Yu EXPERIMENTAL Contract grant sponsor: National Sciences Foundation of Materials China Contract grant sponsor: Target Basic Research 1997 John Wiley & Sons, Inc. CCC /97/ PAN and PANMA were prepared by the method described in the literature. 19 The [h] of the poly- 1405

2 1406 SUN ET AL. Table I. PAN and PANMA Used in the Study Thermal analysis was performed on a SET- ARAM DSC 92 differential scanning calorimeter. Approximate AN A heating rate of 20 C/min was employed using Polymer Content AN/MA a sample of approximately mg. Code (mol/mol) [h] PAN 100/ a MA 1 94/ RESULTS AND DISCUSSION MA 2 85/ MA 3 77/ PAN SF Blends MA 4 62/ Figure 1 shows the FT IR spectra in the range a M n Å 38018, calculated from the relation of Onyon 21 ([h] of 1000 to 2500 cm 01 of pure PAN (A) and PAN Å M n ). SF blends containing 10, 30, 50, and 100 wt % SF (B through E, respectively). PAN (A) shows mers in DMF at 25 C, and the AN contents in absorption bands at 2242, 1454, 1248, and 1073 the copolymers measured by pyrolytic chromatography 20 are listed in Table I. The AN/MA in cm 01, which are attributed to the n(cn), d(ch 2 ), this range is of particular interest because these polymers could be dissolved in concentrated aqueous solutions of salts, such as ZnCl 2, NaSCN, etc. Thus, it is possible to obtain blend solutions. Degummed silk fibroin from waste Bombyx mori silk fiber and PAN or PANMA were brought to dissolve in 60% (wt) aqueous ZnCl 2 solution at 40 C for 30 min and 50 C for an hour, respectively. Then the blend solutions were made up with water to a total polymer concentration of 8% by weight, and the relative polymer compositions, expressed as PAN/SF or MA i /SF (i Å 1, 2, 3, or 4, respectively) weight ratios, of 90/10, 70/30, and 50/50. After that, the blend solutions were precipitated with large excess of methanol (20/1, vol/vol). The resulting precipitates (powders) were filtered and dialyzed against distilled water for a week at 25 C, then dried under vacuum at 25 C for 4 days. All samples were stored under vacuum in a desiccator to minimize water adsorption. Measurements FT IR spectra were recorded on a MANGNA IR- 550 ( Nicolet) spectrometer by the method of transmission, and the spectra were stored in magnetic disc system. The samples were examined in KBr discs. In order to obey the Beer Lambert law, the samples were made thin enough, and the samples thus obtained were transparent. All discs were carefully dried under vacuum in a desiccator before use. A COMEGA ( Nicolet) high-temperature cell was used to record the spectra above Figure 1. FT IR spectra in the range of room temperature. All spectra presented here cm 01 of PAN SF blends containing: (A) 0, (B) 10, (C) were expanded to full scale. 30, (D) 50, and (E) 100 wt % SF.

3 HYDROGEN BONDS IN SILK FIBROIN 1407 PANMA SF Blends Room Temperature Spectra Figure 2 shows the FT IR spectra of MA 2 (A) and MA 2 SF blends containing 10, 30, and 50 wt % SF (B D) in the range of cm 01. The most striking feature of these spectra is that the carbonyl stretching vibration of pure MA 2 is at 1732 cm 01 ; however, upon blending with SF, a new band centered at approximately 1703 cm 01 appears and its intensity increases with increasing the concentration of SF. Because C O stretching mode does not couple significantly to backbone vibrations, such shifts to lower frequency are widely considered to be the acid test of the formation of hydrogen bonds. 18 In other Figure 2. FT IR spectra in the range of cm 01 of MA 2 SF blends containing: (A) 0, (B) 10, (C) 30, and (D) 50% SF. g w (CH), and n / (0) resonances, respectively, in agreement with the literature data. 22 SF(E) shows absorption at 1629 (amide I), 1530 (amide II), and 1265 ( amide III), assigned to silk II form, 23 and the bands at 1658 (amide I), 1235 (amide III), attributed to random coil 23 or silk I form. 24 Asakura and his co-workers 25 even claimed that distinction between the silk I and random coil forms from IR spectra is impossible. The blends (B D)show the absorption bands typical of the pure components, whose intensities are roughly related to the blending ratios. Although some authors reported that 26 the nitriles in PAN are capable of formating hydrogen bonds with water, our findings suggest that there is no specific Figure 3. FT IR spectra in the range of interaction between nitrile in PAN and SF, im- cm 01 of, (A) MA 1, (B) MA 2, (C) MA 3, and (D) MA 4 plying that these two polymers are incompatible. SF 50/50 wt % blends.

4 1408 SUN ET AL. (B), and as expected, only a subtle shoulder centered at about 1703 cm 01 could be seen in the FT IR spectrum of MA 1 [see Fig. 3(A)]. But in the case of MA 3 (C) or MA 4 (D), when there is increased opportunity for favorable intermolecular interactions, the intensity of the 1703 cm 01 band in the spectrum is weaker than that of MA 2 [see Fig. 3(B)], either. Similar results have also been found in other blends containing accessible carbonyl groups. 18,27 29 These findings are very interesting, and because the structure of SF is very Figure 4. DSC curves of MA 2 SF blends containing: (A) 0, (B) 10, (C) 30, and (D) 50 wt % SF. words, this band implies an intermolecular interactions involving the carbonyl groups of MA 2 and the proton donors of SF, such as the amide groups, the hydroxyl groups, and the amine groups, etc. There are two things worth noting about the 1703 cm 01 band. First, this shift to lower frequency (from 1732 to 1703 cm 01 ) implies a stronger interaction between the carbonyl group of PANMA and SF than that of free carbonyl group ( unhydrogen bonded carbonyl group). Second, the 1703 cm 01 band is significantly broader than that of the 1732 cm 01 band, which reflects a reasonably wide distribution of hydrogen bond distances and geometries in the blends. Besides, a more subtle shift to higher frequency (from 1732 to about 1734 cm 01 ) can also be observed in the major peak. This shift, however, may arise from the overlapping contribution of the 1703 cm 01 band, which has been demonstrated by Coleman et al. 18,27 in other similar systems. To provide further information regarding the influence of the compositions of the copolymers on the hydrogen bonds in the PANMA SF blends, we also examined the MA 1,MA 3, and MA 4 SF Figure 5. FT IR spectra in the range of blends under the same condition as mentioned cm 01 of pure MA 1 recorded at (A) room temperature, above. Figure 3 shows the FT IR spectra of the (B) 90, (C) 110, (D) 130, (E) 150, and (F) 180 C, as a 50/50 (wt %) blends of MA i (i Å 1, 2, 3, or 4, function of heating, and (G) 150 C, (H) 130 C, (I) respectively) SF. The molar concentration of car- 110 C, (J) 90 C, and (K) room temperature, as a function of bonyl groups in MA 1 (A) is less than that in MA 2 cooling.

5 HYDROGEN BONDS IN SILK FIBROIN 1409 the polarity of PAN with SF and increasing the opportunity of hydrogen bond formation ( increasing MA content in the copolymer) will both have favorable influence on the compatibility of the two polymers, which is similar to the results reported by Kwei et al. 30 in other systems. In the present system, PAN is more polar than SF, and its copolymerization with MA will thus decrease the value of 1 11, and hydrogen bond formation in the blends will raise 1 12, so, a favorable D1 will be expected. However, further increase in the MA content in the copolymer will disturb the balance between 1 11 and 1 12, and the compatibility of the blends will decrease, as shown in MA 3 SF and MA 4 SF blends. Figure 6. FT IR spectra in the range of cm 01 of pure SF recorded at (A) room temperature, (B) 90, (C) 130, and (D) 180 C, as a function of heating, and (E) 130 C, (F) 90 C, and (E) room temperature, as a function of cooling. complex, we can only give a qualitative discussion about the results presented above at present. Because the driving force for polymer miscibility comes largely from a favorable heat of mixing, we think it is worthwhile to reexamine the familiar expression D1 for the change in pair contact energy D1 Å 1 2(1 11 / 1 22 ) , (1) where 1 11, 1 22, and 1 12 are the energies of contact dissociation between like and unlike polymers, respectively. It is obvious from eq. (1) that matching Figure 7. FT IR spectra in the range of cm 01 of pure SF recorded at (A) room temperature, (B) 90, (C) 130, and (D) 180 C, as a function of heating, and (E) 130 C, (F) 90 C, and (G) room temperature, as a function of cooling.

6 1410 SUN ET AL. increasing of SF content. This finding is very likely, due to a favorable packing of the PANMA chains as a consequence of hydrogen bonding. The bondings may act as crosslinks in the system. As to the 50/50 samples, two T g s, at 93.3 C and C, were observed. The T g of 93.3 C corresponds to the MA 2 component. The C T g, however, must be attributed to a SF-rich phase in the blends. In other MA i (i Å 1, 3, or 4) SF blends, such kind of T g shifts to higher temperature can also be detected. These findings suggest that PANMA can mix with SF significantly, but the two T g s imply that these two polymers are only partially miscible. Figure 8. FT IR spectra in the range of cm 01 of MA 1 SF 50/50 wt % blends recorded at (A) room temperature, (B) 90, (C) 110, (D) 130, (E) 150, and (F) 180 C, as a function of heating. It is worthwhile to point out that hydrogen bond formation in PANMA SF blends will certainly allow significant molecular mixing, but not necessarily forms a single phase. Figure 4 shows the DSC curves of MA 2 (A) and MA 2 SF blends containing 10, 30 and 50 wt % SF (B through D, respectively). The T g of pure MA 2 is 93.8 C. Although some authors reported 31 that the T g of SF in the random coil conformation is 173 C, in our study, SF was in b form and a helix/random coil conformation, and it is difficult to get its T g. Figure 9. FT IR spectra in the range of However, the DSC curves of the blends still show cm 01 of MA 1 SF 50/50 wt % blends recorded at (A) some useful information. Upon blending, the T g room temperature, (B) 90, (C) 110, (D) 130, (E) 150, of the 90/10 and 70/30 samples increase with the and (F) 180 C, as a function of heating.

7 HYDROGEN BONDS IN SILK FIBROIN 1411 range of cm 01. The results are very similar to that of the MA 1 : upon heating, the band shift to a higher frequency, and in the cooling process, it progressively decreases to a lower frequency. The spectra of pure SF in the range of cm 01 are shown in Figure 7. Upon heating, the relative intensity of the 1629 cm 01 band has a slight increase, at the expence of the 1658 cm 01 band. On cooling, this change is irreversible. This change may be reasonably attributed to the random coil r b form conformation transition of SF. 30 The high-temperature spectra of PANMA SF blends were also examined in this study. Figure Figure 10. FT IR spectra in the range of cm 01 of MA 1 SF 50/50 wt % blends recorded at (A) 180 C, (B) 150 C, (C) 130 C, (D) 110 C, (E) 90 C, and (F) room temperature, as a function of cooling, and (G) after conditioned in the air for a week, (H) after dried in vaccum for 4 days (see text). High Temperature Spectra Before going further, lets examine the high temperature spectra of the pure components of SF and PANMA first. Figure 5 shows the FT IR spectra of MA 1 in the range of cm 01 as a function of temperature. Upon heating, the carbonyl band has a subtle shift to higher frequency ( A through F, from to cm 01 ). In the cooling process, the cm 01 band decreases to lower frequency progressively Figure 11. FT IR spectra in the range of (F through K, from to cm 01 ). No cm 01 of MA 1 SF 50/50 wt % blends recorded at (A) other obvious changes can be detected in this re- 180 C, (B) 150 C, (C) 130 C, (D) 110 C, (E) 90 C, and gion. Figure 6 shows the spectra of pure SF in the (F) room temperature, as a function of cooling.

8 1412 SUN ET AL. Figure 12. Graph of absolute absorptivities ( areas) of the carbonyl groups of MA 1 in MA 1 SF blends vs. temperature. : 1734 cm 01 band, heating process, : 1734 cm 01 band, cooling process; l: 1716 cm 01 band, heating process, : 1716 cm 01 band, cooling process; : 1699 cm 01 band, heating process, : 1699 cm 01 band, cooling process. age of all the possible kinds of hydrogen bonds. From 110 to 180 C, the system reaches the T g and the two polymers begin to mix intimately. Because the intensities of the several kinds of possible hydrogen bands could not be the same, so the 1703 cm 01 band splits into two new bands whose intensity increases with the increasing of temperature. These new bands, however, may also be a result of average effect. We think the word average has two meanings here. First, it is difficult to follow the formation and break of hydrogen bonds in the time scale of FT IR, so the 1716 and 1699 cm 01 bands can only characterize an average structure. Second, the two bands may represent an average structure of several kinds of possible hydrogen bonds in the blends. The average idea is further strengthened by the spectra shown in Figure 9 obtained on the same sample in the 3000 to 4000 cm 01 region. At room temperature (A), the 3288 band and the broad band centered from 3450 to about 3505 cm 01 are attributed to the stretching frequencies of the amine and the hydroxyl groups of SF. Upon heating, the intensity of the 3288 and 3450 cm 01 band decreases, which is the result of the breaking of intramolecular and intermolecular hydrogen bonds of SF. 30 On the other hand, two new bands centered at about 3748 and 3850 cm 01, appear, and their intensities increase with the increase of temperature. These bands may indicate the hydrogen bonds between SF and MA 1 is weaker than that within SF, which may be the result of competition ( i.e., the carbonyl groups of MA 1 and amide groups of SF competing for interaction with the NH and OH groups of SF). Fur- 8 shows the spectra of a 50/50 wt % MA 1 SF blend in the carbonyl range of MA 1 (from 1690 to 1760 cm 01 ). At room temperature, the 1734 cm 01 band (the carbonyl stretching frequency of MA 1 ) is very strong, while the 1703 cm 01 band (hydrogen-banded carbonyl) is weak [as shown in Fig. 8(A)].Upto90 C, little change could be observed. However, from 110 to 180 C, the 1703 cm 01 band splits into two new bands, centered at 1716 and 1699 cm 01, respectively, and their intensities in- thermore, from 90 to 180 C (B F), in the region crease progressively, at the expense of the 1734 of 3500 to 3700 cm 01, several weak bands, which cm 01 band. To our knowledge, this is, for the first may indicate other kinds of hydrogen bonds in time, a presentation of this kind of results. MA 1 SF blend and in SF and (or) the overlapping It is widely accepted that the best way to mix contribution of the 3748 and 3850 cm 01 bands, can two polymers intimately is to evaporate a common be detected. solvent from their solution, whereas in this study Figure 10 shows the FT IR results in the carbonyl we have no other choice except coprecipitation. transmission range of MA 1 (from 1690 to Because the T g of the system is about 90 C, the 1760 cm 01 ) obtained upon cooling the same sample two polymers do not have enough mobility to mix from 180 C to room temperature. As the samtwo and their structure are effectively frozen in un- ple was cooled, the intensities of the 1734 and der 90 C. Accordingly, the 1703 cm 01 band is relatively 1699 cm 01 bands increase, while that of the 1716 weak in spectrum A (Fig. 8). On the other cm 01 band decreases. It is reasonable to think that hand, there are several kinds of groups of SF, such the 1699 cm 01 band implies a stronger intermolec- as amine groups, hydroxyl groups of serine and ular interaction than the 1716 cm 01 band. Upon tyrosine, carboxyl groups of glutamic acid, and cooling, the mobility of the two polymers decrease, aspartic acid, etc., 32 prefer to form hydrogen and some of the weaker hydrogen bonds may bonds with the carbonyl groups of MA 1, so the break or change into stronger ones. So the intensi- weak band centered at 1703 cm 01 may be the aver- ties of the 1734 and 1699 cm 01 bands increase,

9 HYDROGEN BONDS IN SILK FIBROIN 1413 while the 1716 cm 01 band, decreases. Anyhow, the with SF. At high temperature (from 110 to 1716 cm 01 band exists even at room temperature. 180 C), the number of hydrogen-bonded carbonyl [ note particularly the contrast between Fig. 8( A) groups increases. When the heated sample is and Fig. 10(F)]. After the sample was conditioned cooled to room temperature, it could not reverse in the air for a week, due to the disturbance to the original structure. Finally, we suggest that of water, the 1716 and 1699 cm 01 band disappear, there are several kinds of groups in SF can form and the 1734 cm 01 band is very broad [Fig. hydrogen bonds with PANMA, and the hydrogen 10(G)]. However, when the same sample was bands detected by FT IR spectroscopy in the then dried under vacuum at 25 C for 4 days, the blends may be the result of the average structures 1699 cm 01 band can be detected again [Fig. of these possible hydrogen bonds. 10(H)], but the 1716 cm 01 band becomes very weak. This may be due to the fact that the 1716 cm 01 band represents weak hydrogen bond, and This article is supported by National Science Founda- after it was broken by water, it is difficult to come tion of China and Target Basic Research. back to the former structure. Figure 11 shows the spectra of the same sample in the 3000 to 4000 cm 01 region as a function of decreasing temperature. There are three things worth mentioned. First, as the temperature decreases, REFERENCES AND NOTES the intensities of the 3748 and 3850 cm 01 bands increase. Second, from 180 C to room tem- 1. M. Tsukada, J. Appl. Polym. Sci., 35, 2133 (1988). perature (A F), in the range of 3500 to M. Tsukada, M. Nagura, H. Ishikawa, and H. Shio- cm 01, the above-mentioned several weak bands zaki, J. Appl. Polym. Sci., 49, 593 (1993). ( see Fig. 5) progressively change into two bands 3. J. Liu and T. Yu, Fudan Xue Bao (Ziran Kexue centered at about 3620 and 3670 cm 01, respec- Ban) (Chinese), 33, 371 (1994). 4. K. Yamaura, N. Kuranuki, M. Suzuki, T. Tanigami, tively. These two new bands may also indicate and S. Matsuzawa, J. Appl. Polym. Sci., 41, 2409 the presence of some average structures. Third, (1990). hydrogen bonds formed upon heating are irrevesi- 5. M. Tsukada, G. Freddi, and J. S. Crighton, J. ble on cooling [note particularly the contrast be- Polym. Sci., Polym. Phys. Ed., 32, 243 (1994). tween Fig. 9(A) and Fig. 11(F)]. 6. C. X. Ling and K. Hirabayashi, Sen-i Gakkaishi, The changes of the absolute absorptivities 47, 334 ( 1991). (areas) of the 1734, 1716, and 1699 cm 01 bands 7. C. X. Ling and K. Hirabayashi, Sen-i Gakkaishi, vs. temperature are summarized in Figure 12. It 46, 535 (1990). is worth noting that in this study we cannot tell 8. C. X. Ling and K. Hirabayashi, J. Appl. Polym. which groups in SF play more important roles in Sci., 45, 1937 (1992). the formation of hydrogen bonds with the carkada, J. Appl. Polym. Sci., 56, 1537 (1995). 9. G. Freddi, M. Romano, M. R. Massafra, and M. Tsu- bonyl groups of PANMA. We believed that the 10. Y. Liu, H. Liu, J. Qian, J. Deng, and T. Yu, J. study on the blends of PANMA with the high mo- Macromol. Sci., Pure Appl. Chem., A33, 209 lecular weight polypeptides, such as polyalanine, (1996). polytyrosine, polyserine, etc., will give further in- 11. Y. Liu, J. Qian, H. Liu, J. Deng, and T. Yu, Appl. formation, which is the main subject of our further Biochem. Biotechnol., to appear. study. 12. Y. Liu, J. Qian, H. Liu, J. Deng, and T. Yu, J. Appl. Polym. Sci., to appear. 13. D. M. Cates and H. J. White, Jr., J. Polym. Sci., CONCLUSION 20, 155 (1956). 14. D. M. Cates and H. J. White, Jr., J. Polym. Sci., FT IR results show that PAN is incompatible 21, 125 (1956). 15. P. Lennox Keer, Tex. Inst. Ind., 19, 83 (1983). with SF, but after PAN is chemically modified 16. J. Qin, J. Appl. Polym. Sci., 44, 1095 (1992). with MA, it would form hydrogen bonds with SF, 17. A. Garton, Polym. Eng. Sci., 24, 112 (1984). and increasing compatibility in the blends could 18. M. M. Coleman and P. C. Painter, Appl. Spectrosc. be expected. Furthermore, at room temperature, Rev., 20, 255 ( 1984). only when the content of MA in PANMA is within 19. N. Grassie and R. Mcguchan, Eur. Polym. J., 8, 865 a certain range, considerable amounts of carbonyl (1972). groups of PANMA could form hydrogen bonds 20. M. Seglam, J. Appl. Polym. Sci., 32, 5719 (1986).

10 1414 SUN ET AL. 21. P. F. Onyon, Trans. Faraday Soc., 52, 80 (1956). 27. M. M. Coleman and E. J. Moskala, Polymer, 24, 22. C. Y. Liang and S. Krimm, J. Polym. Sci., 31, (1983). (1958). 28. S. P. Ting, B. J. Bulkin, E. M. Pearce, and T. K. 23. J. Magoshi, M. Mizuide, Y. Magoshi, K. Takahashi, Kwei, J. Polym. Sci., Polym. Chem. Ed., 19, 1451 M. Kubo, and S. Nakamura, J. Polym. Sci., Polym. (1981). Phys. Ed., 17, 515 (1979). 29. E. J. Moskala, S. E. Howe, P. C. Painter, and M. M. 24. T. Hayakawa, K. Kondo, S. Yamamoto, and J. No- Coleman, Macromolecules, 17, 1671 ( 1984). guchi, J. Kobunshi Kagaku, 27, 300 (1970). 30. S. R. Fahrenholtz and T. K. Kwei, Macromolecules, 25. T. Asakura, A. Kuzuhara, R. Tabeta, and H. Saito, 14, 1076 (1981). Macromolecules, 18, 1841 ( 1985). 31. J. Magoshi and Y. Magoshi, J. Polym. Sci., Polym. 26. Z. Bashir, S. P. Church, and D. Waldron, Polymer, Phys. Ed., 15, 1675 ( 1977). 35, 967 (1994). 32. B. Lotz and F. C. Cesari, Biochimie, 61, 205 (1979).

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