European Polymer Journal 36 (2000) 1055±1061
Crystallization of water in some crosslinked gelatins R.D. Patil a, J.E. Mark a,*, A. Apostolov b, E. Vassileva b, S. Fakirov b a
Department of Chemistry and The Polymer Research Center, The University of Cincinnati, Cincinnati, OH 45221-0172, USA b Laboratory on Structure and Properties of Polymers, So®a University, 1126 So®a, Bulgaria Received 10 July 1998; received in revised form 24 February 1999; accepted 12 May 1999
Abstract Five gelatin samples crosslinked with 1,4-diisocyanatobutane, 1,6-diisocyanatohexane, 1,12-diisocyanatododecane, 1,3-butadiene diepoxide and 1,2,7,8-diepoxyoctane were used to investigate the behavior of the gelatin±water system. The crosslink densities were estimated quantitatively by the values of the molecular weight between crosslinks Mc. Dierential scanning calorimetry indicated that the water was only partially crystallizable below 08C, and the fraction of non-crystallizable water depends on the nature of the crosslinking agent. This fraction tends to zero for high overall water fraction, approaching unity. The overall water weight fraction at which crystallizable water forms was found to be of the order of 0.35 for four of the samples, whereas for the sample crosslinked with 1,3-butadiene diepoxide it is surprisingly high, speci®cally 0.68. # 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Since water in polymers strongly aects their properties, it is of primary importance to analyze its state and amounts in polymer±water systems. According to Bershtein and Egorov [1], this is most often done by Dierential Scanning Calorimetry (DSC) [2±8]. Johnson et al. [2], for example, determined the amount of water forming as clusters in the microcavities of hydrophobic polymers. This is the simplest case for determining the amount of water since in hydrophobic polymers it forms a separate phase and consequently has no plasticizing eect. An increase in hydrophilicity leads to a more complicated picture of the state and amounts of water in the polymer. Some authors divide sorbed water into at least three types: (i) water I Ð in a `free' associated state with phase transition parameters close to those of melting ice; (ii) water II Ð
* Corresponding author. Fax: +1-513-556-9239. E-mail address:
[email protected] (J.E. Mark).
weakly bound to the polymer, but capable of freezing at quite reduced temperatures, and (iii) water III Ð strongly bound to the polar groups of the polymer, not freezing, and not registered calorimetrically [1]. Other authors [9±15] regard the absorbed water in hydrophilic polymers in two dierent states called bound and unbound water. In this case, water crystallizes only partially upon cooling below 08C, with this crystallizable form frequently called `unbound' water and the remaining part considered as non-crystallizable or `bound' water [16]. Recently, Rault and coworkers published several papers dealing with water in various hydrophilic polymers such as poly(vinyl alcohol), poly(vinyl pyrrolidone), polyacrylamide, and a polyether block copolymer amide [16±20]. They do not use the concept of bound and unbound water but designate the system polymer±water, in which the water acts as a plasticizer. Later, Rault et al. de®ned a critical weight fraction C of the water in the system: below C water does not crystallize, whereas above C it crystallizes partially, forming ice crystals. Since the non-crystalline water
0014-3057/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 4 - 3 0 5 7 ( 9 9 ) 0 0 1 4 4 - 5
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acts as plasticizer, the glass transition temperature of the system generally follows the Fox±Flory equation [21] ÿ ÿ p 1=Tg Cw =T w g
1 ÿ Cw =T g
1
p where Tg, T w g and T g are the glass-transition temperatures of the gelatin±water system, water, and dry polymer, respectively, and Cw is the water weight fraction. The critical water weight fraction C is determined as the abscissa of the intersection of the glass transition temperature versus concentration curve (Tg vs. Cw) and the melting curve of the ice, namely the melting temperature of ice T ice m vs. Cw [16]. Gelatin has been the focus of much research for many years since it is a biodegradable and environmental friendly biopolymer, and possesses attractive properties in terms of commercial applications [22]. Modern technological applications of gelatin depend on its high solubility in hot water, polyampholyte character, availability in a wide range of viscosities, and ability to form thermally reversible gels. Usually, however, it is necessary to crosslink gelatin to transform it into a useful material, and this introduces stable covalent bonds between the chains, in addition to the aggregates responsible for the usual physical network structure [23]. Water plasticizes gelatin and since it is highly hydrophilic, its glass transition temperature strongly decreases upon uptake of water. Speci®cally, its glass transition temperature decreases approximately from 2178C for dry gelatin to 08C for water concentration of 25 wt% [24]. Neither the Fox±Flory Eq. (1) nor the Ten Brinke equation [25] match the experimental curve of Tg vs. Cw. That is why it is better to use the experimental curve itself for de®ning C for the system gelatin±water. It is well known that the glass transition temperature depends also on whether the polymer is uncrosslinked or crosslinked, and in the latter case, on the crosslink density. In order to increase the crosslink density of gelatin, identi®cation of a more versatile chemical crosslinking approach (in addition to the formation of a physical network) is required [26]. There is, for example, the possibility of crosslinking with a bifunctional reagent via the free amino and hydroxy groups from amino acid residues. Various crosslinking agents are known to serve this purpose and were used in this study to obtain networks diering in both structure and crosslink density. The system gelatin±water has been thoroughly investigated by Rehage [27] and later by Borchard et al. [28±30]. They investigated native (chemically uncrosslinked gelatin) and found that gelatin and water form a state diagram of an eutectic type, where the eutectic point is shifted to extremely low polymer concentration [28]. In fact, the eutectic temperature and the melting
temperature of water are practically identical, which is usual for a system in which a big dierence between the melting temperatures of the components is observed (it is nearly 2308C for the gelatin±water system). Therefore, pure water crystallizes when mixtures are cooled to temperatures below the freezing point of pure water if the polymer concentration is not too high. A linear concentration dependence of the eutectic enthalpy of fusion is observed in the range of 0.1±0.4 gelatin weight fraction. The straight line intersects the concentration axis at a weight fraction of 0.67, which means that gelatin forms a compound with water at this composition. For gelatin, which is a collagen-like product, a certain amount of water is necessary to rebuild the collagen triple helical structure. Using Xray and calorimetric studies Reutner et al. [30] further prove that the collagen-like structure of gelatin is presumably possible only if water is a part of the crystals formed. In brief, the important ®ndings of Borchard et al. [28±30] were: . gelatin forms mixed crystals with water . the Tg vs. Cw curve is situated very close to, but below the solidus curve . in addition to the glass transition of the mixed crystal there is another morphologically originating glass transition which is generated by the crystallization of pure water. In our previous work we investigated the behavior of the system gelatin±water with regard to two processes: the crystallization of water upon cooling and its evaporation upon heating [31]. This was done as a function of the overall water content, for uncrosslinked samples and some crosslinked with glutaric aldehyde. The aim of the present study is to investigate the water behavior in gelatin samples, crosslinked with diisocyanates and diepoxides. As was done previously [31], the method of Rault and coworkers [16±20] was closely followed.
2. Experimental 2.1. Materials The gelatin was type A, Bloom value 300 (Sigma). 1,4-diisocyanatobutane (DICB), 1,6-diisocyanatohexane (DICH), 1,12-diisocyanatododecane (DICDD), 1,3-butadiene diepoxide (BDE), and 1,2,7,8-diepoxyoctane (DEO) were purchased from Aldrich. Triethylamine was purchased from Fluka, 2,2,2-tri¯uoroethanol (TFE) from Aldrich, and potassium thiocyanate (KCSN) from REACHIM, USSR.
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Table 1 Sample designations and conditions of preparation, for all samples obtained from a 5.5 wt% solution of gelatin at 258C Sample Solvent
Concentration (M) Type of crosslinking agent Addition of triethylamine Duration of crosslinking (min)
1 2 3 4 5
0.0127 0.0127 0.0127 0.0121 0.0121
TFE TFE TFE 2 M KSCN 2 M KSCN
DICB DICH DICDD BDE DEO
Yes Yes Yes No No
2.2. Preparation of samples Five cross-linked samples were prepared using dierent cross-linking agents. Samples 1±3 were crosslinked by adding selected quantities of one of the cross-linking agents DICB, DICH, and DICDD. Triethylamine as catalyst was added (1/3 amount of the crosslinking agent) to a 5.5 wt% solution of gelatin in TFE at room temperature (258C). The resulting mixtures were stirred for 2 h to obtain homogeneous mixtures (only 80 min for the mixture containing DICDD since it gelled when stirred longer). They were subsequently poured into aluminum dishes and kept under ambient conditions in order to obtain dry ®lms. Samples 4 and 5 were crosslinked by adding BDE and DEO, respectively, to a 5.5 wt% solution of gelatin in 2 M water solution of KCSN at room temperature and stirring for 2 h. The solutions were then poured into aluminum dishes and kept under ambient conditions in order to obtain dry ®lms. Since these ®lms contained some crystals of KCSN, they were subsequently rinsed in distilled water. The sample designation and conditions of preparation are given in Table 1. Room-conditioned gelatin ®lms typically contain 15±17 wt% water. Samples with higher water concentrations were prepared by swelling the samples for several minutes to a few hours between moistened sheets of ®lter paper. They were then immediately tested in a DSC instrument (PL-DSC of Polymer Laboratories). Samples with water concentration less than 15±17 wt% were obtained by drying ®lms at various temperatures for the required durations. 2.3. Investigation of thermal behavior The thermal behavior of the gelatin±water system was investigated by DSC, using sample weights between 2 and 15 mg. All water concentrations were speci®ed by weight and calculated from Cw
W ÿ Wi =W
2
where W is the weight of the swollen sample and Wi is the initial weight of the dry sample. The accuracy of
120 120 80 120 120
Cw depends on W, Wi and the accuracy of the balance (0.1 mg) and in the least accurate case was found to be 0.02. The temperature ramp was ÿ40 to 1508C at a heating rate of 108C/min in a nitrogen atmosphere. All DSC traces were normalized and redrawn according to the sample weight and the heat ¯ow sensitivity. In this way, curves of every set of traces for each of the ®ve samples re¯ect only the eects of the water concentration. The fraction of the crystallizable water was calculated from the ideal ice melting enthalpy, which was taken to be 334 J/g [32]. In order to obtain the real ice melting enthalpy, the peak area was taken between the base line as a straight line between the onset and the end of the melting interval and the DSC trace. Since the glass transition occurs in the same temperature interval, this method leads to some small systematic error in the determination of the peak area; generally the higher the area (i.e., the higher Cw) the smaller the error. 2.4. Evaluation of the network density Gelatin samples (squares of 10 10 0.25 mm) were swollen at 208C for 48 h in distilled water in order to achieve equilibrium swelling. The gelatin volume fraction in swollen samples nG was determined assuming an additivity of speci®c volumes of gelatin and water: nG Wi rw = Wr ÿ Wi
r ÿ rw
3 where rw is the density of the water at 208C and r is the density of the dry, chemically uncrosslinked gelatin. In the ®rst approximation this latter value was also used for the crosslinked gelatin samples. The weight of the swollen sample was measured after removing the excess liquid on the surface of the sample by a piece of ®lter paper. With nG thus obtained, to estimate the network density, the average molecular weight between crosslinks Mc was calculated from the Flory±Rehner equation [33] 2 Mc ÿrV1 n1=3
4 G = wnG =2 ln
1 ÿ nG nG
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where V1 is the molar volume of the solvent and w 0:49 [34] is the polymer±solvent interaction parameter.
Table 2 Critical water weight fraction C , molecular weight between crosslinks Mc, and maximum water weight fraction achievable C max w
3. Results and discussion
Sample
C
Mc
C max w
Fig. 1 shows the DSC traces for sample 1, for various values of the overall water weight fraction Cw. There are two endothermal downward peaks in these traces in all curves having Cw r0:46, one around 08C and the other around a higher temperature. A higher temperature downward peak can also be seen for Cw 0:33: The low-temperature peak increases gradually with increase in the total water content. This peak is always around 08C and obviously re¯ects the melting of the ice in the sample. The amount of crystalline water for each curve can be calculated from
1 2 3 4 5
0.30 0.35 0.34 0.64 0.39
4450 3200 1400 2600 1970
0.95 0.96 1.00 0.86 0.95
Ccr DH=DH0
5
where DH is the measured melting enthalpy and DH0 334 J/g [32] is the value for ideal ice melting. Generally, the high-temperature endothermal peak moves to higher temperatures with increase of the water content (curves Cw 0.50 and 0.76 being exceptions). This peak originates from the overlapping of several processes: (i) evaporation of both crystalline and non-crystalline water as shown elsewhere [35] (evaporation of only non-crystalline water for Cw 0:33); (ii) continuous melting and recrystallization of small and/or imperfect gelatin crystallites [36]; and (iii) the so-called ®rst glass transition in gelatin, which is located around 1008C and corresponds to the association of the glass transition of a-amino acid blocks in the polypeptide chain [37]. Rehage and Borchard [38] explain this glass transition with relaxation of the enthalpy. Generally, the glass transition
Fig. 1. DSC traces for samples of gelatin crosslinked with 1,4diisocyanatobutane (sample 1), diering in overall weight water fraction Cw (taken immediately before the DSC run).
temperature depends on the water content [26,28]. Most probably, the evaporation of water and speci®cally of the crystallizable water prevails above the other processes, giving rise to this endothermal peak, as was shown for similar crosslinked gelatins using thermogravimetric analysis [31]. It was demonstrated there, that for high water content the water leaves the system in two steps: the ®rst one from heating to approximately 1008C and the second during the subsequent heating to 3008C. Since the prevailing amount of water leaves the system during the ®rst step, it was concluded that this was the crystallizable portion [31]. The so called morphologically generated glass transition (i.e., the transition caused by the crystallization of water [30]) can also be seen in Fig. 1. It occurs around ÿ108C in accordance with the ®ndings of Reutner et al. [30] for uncrosslinked gelatin. It seems that in our case of DICB crosslinked gelatin (sample 1) the network is relatively loose and the helix formation inside the gel is only little in¯uenced. A low degree of crosslinking is also indicated by the high Mc value of sample 1 (Table 2). DSC traces similar to Fig. 1 were obtained for the other four samples. Fig. 2 shows the ice melting enthalpy DH versus
Fig. 2. Ice melting enthalpy DH versus overall weight water fraction for gelatin crosslinked with 1,4-diisocyanatobutane (sample 1). See Section 2 for the accuracy in the data points.
R.D. Patil et al. / European Polymer Journal 36 (2000) 1055±1061
water weight fraction Cw for sample 1. A least-squares straight line was drawn through the data in the region where DH increases with Cw. The critical water weight fraction C 0:30 was obtained by extrapolating this straight line to DH 0 (see [19,31]). A similar curve was obtained for uncrosslinked gelatin by Reutner et al. [30]. Below this fraction, the water can exist only in the non-crystalline state, whereas part of it is crystallizable for fractions higher than C. Similar extrapolations were made for the other four samples, and the respective C values determined. The DH vs. Cw plots for samples 2, 3 and 5 look quite similar to those in Fig. 2 but, as shown in Fig. 3, the DH vs. Cw plot for sample 4 diers signi®cantly. By comparing Fig. 3 with Fig. 2, some dierences can be found: (i) much higher C of 0.86 for sample 4 vs. C of the order 0.35 for samples 1±3, and 5; (ii) much larger slope, of the order 400 for sample 4 versus slope of the order 100 for samples 1±3, and 5, and (iii) straight lines approaching Cw 1 for the highest possible value of DH 334 J/g for samples 1±3, and 5, which means that a very large degree of swelling can be reached. This is not the case with sample 4, where the maximal possible water weight fraction achievable is 0.86. Fig. 4 shows the weight fraction of the crystalline water Ccr and that of the non-crystalline water Cnc versus overall water weight fraction Cw for sample 1. The value of Cnc was calculated from Cnc Cw ÿ Ccr
6
where Ccr is obtained from Eq. (5). As already stated, Ccr 0 up to the critical fraction C and increases linearly above it. Quite dierent behavior is observed for the non-crystalline water concentration Ð it increases linearly from zero up to C and decreases gradually to zero for the highest overall fraction. This dependence
Fig. 3. Ice melting enthalpy DH versus overall weight water fraction Cw for gelatin crosslinked with 1,3-butadiene diepoxide (sample 4). See Section 2 for the accuracy in the data points.
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Fig. 4. Fraction of non-crystalline Cnc and crystalline Ccr water versus overall weight water fraction for gelatin, crosslinked with 1,4-diisocyanatobutane (sample 1).
(Fig. 4) is valid for temperatures below and close to 08C. It is interesting to note that such decreasing of Cnc above a certain overall fraction was not reported by Rault and coworkers for the other hydrophilic polymers [16±19]. Similar ®gures (not shown here) were constructed for the other four samples. The maximum water concentration achievable, C max w , was determined for sample 1 from Fig. 2 (and similarly for the other four samples) as the abscissa of the data point with ordinate of 334 J/g (which, being the ice melting enthalpy, is the maximum possible enthalpy for the system gelatin±water). Data from the above measurements and calculations are summarized in Table 2. As seen from Table 2, there is no direct connection between the critical concentration C and the molecular weight between crosslinks Mc. For chemically uncrosslinked gelatin, Reutner et al. [30] discussed the composition of the mixed (gelatin±water) crystals from the molecular point of view. They calculate water contents of 15.1, 26.2 and 34.7 wt%, if every amino acid residue binds one, two or three water molecules, respectively, by hydrogen bonding (while the experimentally obtained value is 33 wt%). Hence, they concluded that the total water content cannot be bound stoichiometrically to the polymer chain. Further, using X-ray diraction measurements, Reutner et al. [30] conclude that the uncrosslinked gelatin occupies 67% of the total volume, which corresponds to 74 wt%, and the remaining empty place is ®lled with water. This value is close to 72 wt%, which can be taken from the solidus curve of the phase diagram of the system gelatin± water, obtained by the same authors. Hence, the conception of the empty place in the gelatin, ®lled with water, explains the experimentally observed water content.
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One can see from Table 2 that the stoichiometric description of the total bound water is not acceptable. In the case of crosslinked gelatin an additional complication occurs due to the presence in the crosslinks of chemical groups, which are able to form hydrogen bonds with water molecules (OH in the case of diepoxydes and NH and CO in the case of diisocyanates), thus also aecting C. On the other hand, it seems that the voids in the system and the critical concentration, respectively, are strongly aected by the nature and concentration of the crosslinking agent (see Table 2 and Figs. 2 and 3). Since the maximum possible enthalpy for the system gelatin±water is the ideal one (334 J/g), the abscissa of the data point with ordinate of 334 J/g (Fig. 2) gives the maximum water concentration achievable C max w : It was determined for sample 1 from Fig. 2 and similarly for the other four samples. The data and results from the above measurements and calculations are also shown in Table 2. According to Rault [20] the intersection of the gelatin±water glass transition temperature curve with the ice melting temperature curve gives the critical water weight fraction C. When the glass transition temperature of the gelatin±water increases, this intersection shifts to the right, i.e., to higher C. One possible way to increase Tg is by increasing the crosslink density [39]. As seen from Table 1 one must compare samples 1± 3 as well as samples 4 and 5 due to their similar chemical structures. The crosslinking chains for samples 1, 2, and 3 are very similar in character but dier in length (4, 6, and 12 methylene groups, respectively). The longer the crosslinker, the higher its ¯exibility and the lower the glass transition temperature of the polymer [39]. For this reason, one should expect the lowest glass transition temperature for sample 3. On the other hand the longer the crosslinker, the lower the Mc (see Table 2), i.e., the denser the network and consequently the higher the glass transition temperature. Due to these opposing eects of the ¯exibility and the crosslink density on the glass transition temperature, one can hardly expect any signi®cant eect on C, which is actually the case (see Table 2, samples 1±3). The crosslinker length in the case of diisocyanate crosslinked samples (samples 1±3, Table 1) has a remarkable eect on the crosslink density and a negligible eect on the critical water fraction (Table 2). The chains of sample 5 are connected with crosslinker similar to that in sample 4 but being twice as long. There is, however, a striking dierence in C Ð its value for sample 5 is lower by 40% than that for sample 4. Since Mc for these two samples are similar (Table 2), the relatively low value of C for sample 5 could be explained with the lower glass transition tem-
perature, due in turn, to the much higher ¯exibility of the crosslinker. 4. Conclusions In this work we investigated gelatin crosslinked with one of either three diisocyanates or two diepoxides. Again, as in our previous work on native gelatin and gelatin crosslinked with glutaric aldehyde [31], it seems appropriate to consider water in gelatin as crystallizable or non-crystallizable, instead of unbound or bound. The gelatins used in the present work behave similarly to many other hydrophilic polymers [16±19], where the process of crystallization of water is ruled by the relative position of the two curves Tg vs. Cw and T ice m vs. Cw. For temperatures below 08C and low water concentrations, the water (which acts as a plasticizer) in the crosslinked gelatins is included in mixed polymer crystals. After reaching a critical value of C, water starts partially to crystallize, thus forming a second phase. For four out of the ®ve samples, overall water fractions close to unity can be reached. An exception is the sample crosslinked with butadiene diepoxide, for which the maximum water concentration achievable is only 0.86. Additional measurements of the glass transition temperature by dynamic mechanical thermal analysis would possibly clarify the results on the critical and the maximum achievable water fractions. On the other hand, we clari®ed the behavior of the system gelatin±water for relatively high values of Cw, speci®cally 0.85±0.9, whereas Rault and coworkers reached values only as high as 0.6 for poly(vinyl alcohol), poly(vinyl alcohol)±poly(vinyl pyrrolidone) blends and copolymer polyamide±poly(ethylene) glycol copolymer [17,18]. Thus, we showed that at least in the present case of crosslinked gelatins, the fraction of the crystalline water increases linearly with the overall water fraction not only in the intermediate region of Cw, but also for higher values, and subsequently the fraction of the non-crystalline water decreases to nearly zero. It is an open question whether this is valid for other hydrophilic polymers or is a speci®c feature only of gelatin. Acknowledgements It is a pleasure to acknowledge the ®nancial support provided by the National Science Foundation through Grant INT-9514149 and by the Bulgarian Ministry of Education, Science and Technology under contract TH-714. R.D. Patil appreciates the hospitality of the Laboratory on Structure and Properties of Polymers of the University of So®a, Bulgaria, where part of this work was carried out.
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References [1] Bershtein VA, Egorov VM. In: Dierential scanning calorimetry of polymers. New York: Ellis Horwood, 1994. p. 224. [2] Johnson G, Bair H, Matsuoka S, Anderson E, Scott J. In: Rowland S, editor. Water in polymers. Washington, DC: American Chemical Society, 1980. p. 361. [3] Nakamura K, Hatakeyama T, Hatakeyama H. Polymer 1983;24:871. [4] Krushitsky NN, Polishchuk TN, Privalko VP, Vyazmitina OM. Ukr Khim Zh 1985;51:1250. [5] Ohno H, Shibayama M, Tsuchida E. Macromol Chem 1983;185:1017. [6] Gossman S, Tirrell D, Vogl O. In: Rowland S, editor. Water in polymers. Washington, DC: American Chemical Society, 1980. p. 451. [7] Higuchi A, Iijima T. Polymer 1985;26:1207. [8] Nishioka N, Yoshimi S, Iwaguchi T, Kosai K. Polymer J 1984;16:877. [9] Sakurada I, Nakajima A, Fujiwara H. J Polym Sci 1959;35:497. [10] Kenney JF, Willcockson GW. J Polym Sci 1966;A4:679. [11] Tazikawa A, Negishi T, Ishikawa K. J Polym Sci 1968;A6:475. [12] Peppas NA, Merrill EW. J Appl Polym Sci 1968;20:1457. [13] Hatakayama T, Hirose S, Hatakayama H. Makromol Chem 1987;188:1875. [14] Fushimi H, Lijima T. Polymer 1991;32:241. [15] Roadehed C, Randy B. J Appl Polym Sci 1986;32:3309. [16] Rault J, Gref R, Ping ZH, Nguyen QT, Neel J. Polymer 1995;36:1655. [17] Rault J, Ping ZH, Nguyen QT. Polym Bull 1995;35:649. [18] Rault J, Ping ZH, Nguyen QT. J Non-Cryst Solids 1994;172:733. [19] Ponomariova T, Melnichenko Y, Albouy PA, Rault J. Polymer 1997;38:3561. [20] Rault J. In: Bellissent-Funel M-C, Dore JC, editors.
[21] [22]
[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
1061
Hydrogen bond networks. Dordrecht, The Netherlands: Kluwer, 1994. p. 441. Fox TG, Flory PJ. J Polym Sci 1954;14:315. Rose PJ. In: Mark HF, Bikales NM, Overberger CG, Menges G, Kroschwitz, JI, editors. Encyclopedia of polymer science and engineering, vol. 7, 2nd ed. New York: Wiley, 1985. p. 488. Zhao W, Kloczkowski A, Mark JE, Erman B, Bahar I. Chemtech 1996;26:32. Rose PI. In: James TH, editor. The theory of the photographic process, 4th ed. New York: MacMillan, 1977. p. 67. Ten Brinke G, Karasz FE, Ellis TS. Macromolecules 1983;16:244. Davis P, Tabor BE. J Polym Sci Part A 1963;1:799. Rehage G. Prog Colloid Polym Sci 1975;57:7. Borchard W, Bremer W, Keese A. Colloid Polym Sci 1980;258:516. Borchard W, Luft B, Reutner P. Ber Bunsenges Phys Chem 1984;88:1010. Reutner P, Luft B, Borchard W. Colloid Polym Sci 1985;263:519. Apostolov AA, Vassileva E, Fakirov S, Patil RD, Mark JE. J Appl Polym Sci 1998;71:465. Windholz M, editor. The Merck index, 9th ed. Rahway: Merck, 1976. p. 1294. Flory PJ, Rehner JJ. Chem Phys 1943;11:521. Bohidar HB, Jena SS. J Chem Phys 1993;98:8970. Fakirov S, Sarac Z, Anbar T, Boz B, Bahar I, Evstatiev M, Apostolov AA, Mark JE, Kloczkowski A. Colloid Polym Sci 1997;275:307. Fakirov S. Vysokomol Soed 1990;37:878. Chatterji PR. J Appl Polym Sci 1989;37:2203. Rehage G, Borchard W. In: Haward RN, editor. The physics of glassy polymers. London: Applied Science Publishers, 1973. p. 54. Plazek DJ, Ngai KL. In: Mark JE, editor. Physical properties of polymers handbook. New York: Springer, 1996. p. 139.