REACTIVE & FUNCTIONAL POLYMERS
Reactive & Functional Polymers 66 (2006) 931–943
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Crosslinked reactive macromonomers based on polyisobutylene and octadecyl acrylate copolymers as crude oil sorbers Ayman M. Atta *, Rasha A.M. El-Ghazawy, Reem K. Farag, Abdel-Azim A. Abdel-Azim Egyptian Petroleum Research Institute, Petroleum Application, Nasr City 11727, Cairo, Egypt Received 8 November 2005; received in revised form 15 December 2005; accepted 5 January 2006 Available online 21 February 2006
Abstract Cinnamoyl chloride was condensed with different glycols to produce five different of hydroxyalkyloxy cinnamate esters. Each cinnamate ester was reacted with polyisobutylene–succinic anhydride adduct to produce five different reactive macromonomers. The synthesized macromonomers were characterized by FTIR and 1HNMR spectroscopic analyses. These macromonomers were copolymerized with octadecyl acrylate (ODA) at 1, 2 and 4 wt% of trimethylolpropane triacrylate (TPT) crosslinker in presence of benzoyl peroxide as initiator and cobalt octoate as activator. Copolymerization of a cinnamoyloxyethyl methacrylate (CEMA) with octadecyl acrylate (ODA) was prepared by bulk polymerization in presence of ABIN initiator and TPT crosslinker. The crosslinked copolymers were evaluated for oil-absorbency application. The effect of monomer feed composition; crosslinker wt% and type of oil on swelling properties of crosslinked polymers were studied through the oil absorption tests. The network parameters, such as polymer solvent interaction (v), effective crosslink density (me), equilibrium moduli of elasticity (GT), average molecular weight between crosslinks (Mc) and theoretical crosslink density (mt) were determined and correlated with the structure of the synthesized sorbers. The values of crosslinking efficiency (b) and the efficiency of copolymer to form physical crosslinks (a) are also computed and discussed. 2006 Elsevier B.V. All rights reserved. Keywords: Crosslinking; Organogel; Reactive macromonomer; Reactivity ratios; Copolymerization; Swelling kinetics; Network parameters; Polyisobutylene
1. Introduction Water can be polluted by organic pollutants from oil fields and refinery areas and, in some cases process effluent from petroleum and petro*
Corresponding author. Tel.: +20 2747917; fax: +20 22747433. E-mail address:
[email protected] (A.M. Atta).
chemical plants [1]. The spilled oil contributes an undesirable taste and odor to drinking water and causes severe environmental damage [2,3]. The most urgent technique of elimination of emergency spread of oil and petroleum products is collecting of thin layers from the water surface with the help of sorbents. Sorbents should have oleophilic or hydrophobic character to use as sole cleanup
1381-5148/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.reactfunctpolym.2006.01.001
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method in small spills. Once sorbents have been used to recover oil, they must be removed from the water and properly disposed of or cleaned for reuse [4,5]. It was known that an effective mean to obtain oil absorbent is to synthesize the crosslinked polymer, which does not dissolve in oil [6]. In spite of the development of polymer for oil absorption, there have been few reports on the synthesis of such polymers. Synthesis of ethylene– propylene–diene polymer (EPDM) containing an aromatic moiety was reported [7]. Other kinds of polymers have been widely used to absorb oil spilled on water [8,9]. Among them alkyl acrylate and aromatic polymers, which have hydrophobicity and gel-type structure consisting of an elastic network and interstitial space, have been attracting much interest in the field of environment [10–15]. The copolymerization of acrylate monomers was carried out by electron-beam irradiation at different dose rates in a previous article. Furthermore, the crosslinking of these polymers by a high dose electron-beam irradiation in the presence of crosslinkers have been studied [10]. Synthesis and characterization studies of linear and crosslinked cinnamoyloxy ethyl methacrylate (CEMA)-isooctyl acrylate (IOA) copolymers for oil absorbency application was studied in a previous article [11]. In this respect, the copolymerization and crosslinking of CEMA with octadecyl acrylate (ODA) are the main goal of the present study to increase the oil absorbency of the prepared copolymers. On the other hand, the present study aims to modify polyisobutylene, PIB, with maleic anhydride followed by reaction with cinnamoyl moieties to introduce aromatic moieties to increase its solubility in crude oil. These macromonomers will be crosslinked with ODA to prepare oil sorbers having high oil swelling capacities. Determination of network parameters from the swelling measurement is another goal of the present work.
(DEG), triethylene glycol (TEG), tetraethylene glycol (TeEG), polyethylene glycol400 (PEG400) were obtained from Aldrich Chemical Co. Cinnamoyl chloride, octadecyl acrylate (ODA), trimethylolpropane triacrylate (TPT), 2,2-azobis isobutyronitrile (ABIN), benzoyl peroxide, triethylamine (TEA) were obtained from Aldrich Chem. Co., Germany. ODA was purified by washing with 5% aqueous sodium hydroxide, dried over anhydrous CaCl2 and distilled under vacuum. TEA was refluxed with acetic anhydride and with KOH and then distilled. ABIN, recrystallized from ethanol was used as a thermal polymerization initiator. 2.2. Synthesis of crosslinked reactive polymers 2.2.1. Synthesis of cinnamate esters Cinnamoyl chloride (1 mole) is reacted with 2 mole of each of five different glycols namely, ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol and polyethylene glycol 400 to produce five different compounds of hydroxy alkyloxy cinnamate. The reactions were carried out by adding 1 mole of cinnamoyl chloride at temperature below 25 C to 2 mole of the individual glycol in presence of TEA as a catalyst for 1 h. The reaction was continued for another 1 h at 25 C. Then, the reaction mixture was poured into water to dissolve the formed TEA salt. The products were extracted by adding the chloroform. The chloroform layer was washed with water diluted with sulfuric acid H2SO4,and aqueous magnesium sulfate to remove any unreacted materials. Chloroform was then removed by distillation under reduced pressure in a rotary evaporator. The products were designated as CM1, CM2, CM3, CM4 and CM9, the number 1–9 refers to number of ethylene oxide group. 2.3. Grafting of cinnamate ester monomers onto PIB– MA adduct
2. Experimental 2.1. Materials Cinnamoyloxy ethyl methacrylate (CEMA) was prepared and purified as reported in previous article [11]. Polyisobutylene1000, PIB, maleic anhydride were obtained from from B.D.H. Co. Ltd. (UK). Polyisobutylene–succinic anhydride adduct, PIB– MA was prepared as reported in previous article [16]. Ethylene glycol (EG), diethylene glycol
To 1 mole dm 3 pyridine solution of PIB–MA adduct, 2 mole of individual cinnamate ester were added. The reaction was carried out at 75 C for 21 h. The resulting mixture was poured in excess acetone to extract the products. The products were stored under nitrogen atmosphere in a refrigerator. The product was designed as PIB–MA–CM1, PIB–MA–CM2, PIB–MA–CM3, PIB–MA–CM4 and PIB–MA–CM9 and used to prepare crosslinked polymers by reaction with acrylate monomers.
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2.4. Synthesis of crosslinked PIB–MA–CMn/ODA copolymers Copolymerizations and crosslinking of each (PIB–MA–CM) polymer and ODA monomer were performed through bulk polymerization. The monomers were mixed together with benzoyl peroxide initiator 0.02% (w/w), cobalt octoeate as activator, 0.02% (w/w), different weight ratio of TPT crosslinker ranging from 1% to 4% (w/w) and the mixture was bubbled with nitrogen. The copolymerization reactions were performed in siliconized test tubes at 333 K for 1.5 h and the crosslinked copolymer rods were post cured at 378 K in air oven. The rods were cut to thin discs and used for determining the soluble fraction (SF) and swelling parameters. 2.5. Synthesis of crosslinked CEMA/ODA copolymers The detailed procedures to synthesize linear and crosslinked CEMA with alkyl acrylate copolymers are described in a previous article [11]. This procedure was repeated with different monomer feed ratios (mole% CEMA/mole% acrylate) viz. 90/10, 70/30, 50/50, 30/70 and 10/90 in the preparation of crosslinked copolymers. The copolymerization reactions were performed in siliconized test tubes at 333 K for 3 h and the crosslinked copolymer rods were post cured at 378 K in an air oven. The rods were cut to thin discs that were used for determining the soluble fraction (SF) and swelling parameters.
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from oil, drained for 30 s, tapped with filter paper to remove excess oil from the bottom of the mesh, and then weighted. The oil absorbency (Q) and equilibrium toluene content (ETC) were calculated as described in a previous article [11]. The swelling kinetics of oil absorption was studied by repeating the previous measurements at different time intervals. The swelling parameters, Q and ETC, of the prepared gels were calculated from five measurements. Also, the maximum oil absorbency was determined by allowing the tests to stand for 24 h. To study the kinetics of swelling, gel samples in triplicate, were immersed in crude oil. After equilibration-swollen gel samples were placed into oven at 318 K for 12 h, which caused gels to deswell. The deswelling was then followed by weighing the gel at various time intervals. The reversibility of swelling and deswelling was determined using the same samples for consecutive swelling and deswelling experiments. 3. Results and discussion
The chemical structure of PIB–MA–CM macromonomers was determined from 1HNMR spectroscopy data. 1HNMR spectra were obtained with Varion NMR 300 model at frequency of 300 MHz on a using CDCl3 as a solvent. For the crosslinked xerogel discs, soluble fractions (SF) were extracted with chloroform until constant weights were achieved [10,11].
Polyisobutylene, PIB, is one of the most important polymers that have large industrial application. It is prepared through cationic polymerization using BF3 as a catalyst and in presence of organic solvent. It was proved that the polymer chains are ended with olefinic double bond. Maleic anhydride, MA, easily adds to polyisobutylene at high temperature or in presence of a radical catalyst [16]. In the present system, the reaction of MA onto PIB can be illustrated in Fig. 1. The reaction can be completed by the ene cyclo-addition reaction at high temperatures or by a hydrogen abstraction reaction on the a-CH2 [17]. The radical addition reaction yielded products have many complicated structures and the large portion of the products become insoluble but in the present system, the products were soluble in organic solvents and the insoluble product was not obtained. The chemical structures of the produced PIB–MA adduct can determined by IR and 1HNMR analyses as reported in a previous article [16].
2.7. Oil absorption test
3.1. Synthesis of PIB–MA–CM macromonomers
Oil absorbency of copolymers crosslinked with TPT were determined by ASTM (F726-81):0.1 g polymer was put in a stainless steel mesh (4 · 4 · 2 cm). The sample was immersed in pure or in crude oil solution (crude oil diluted with toluene, 10% oil). The sample and the mesh were together picked up
The advantage of using of cinnamate groups are: stability for long storage, polymerization is not affected by oxygen and antioxidants and its ability to copolymerize either by thermal or photo polymerization [18]. Therefore, it is desirable to synthesis crosslinked rubbers containing cinnamate
2.6. Characterization of the prepared polymers
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CH=CH-COCl
+
H(O-CH2-CH2)n-OH
n=1, 2, 3, 4 and 9
CH=CH-COO-(CH2-CH2-O)n-H
CH3
CO
O
CMn CH3
OC
H2C=C-(-CH2-C--)n-C=CH2 + O=C O C=O
CO O
CH2
CH3
CH3
o
180 C CH2
PIB-MA
CH3 CH2
+
OC
CMn
CH2
CO
O CO
CO O
CH3
H2C-C-(-CH2-C--)n-C-CH2
CH3 CH2
Ph-CO-CH=CH-COO-(CH2-CH2O)n-OC
+
CH3
H2C-C-(-CH2-C--)n-C-CH2
PIB-MA
CO
H2C-HC-(-CH2-C--)n-CH-CH2
CH3 CH3
PIB
CH2
COOH
COO-(CH2-CH2O)n-CO-CH=CHCOPh
COOH PIB-MA-CMn
Fig. 1. Reaction scheme of the prepared reactive macromonomer.
groups, which may have the advantages of both polyisobutylene and cinnamate groups. An attempt had been made in order to obtain cyclic polyisoprene–MA adduct [18] to form modified polyisoprene with substituted succinic anhydride groups. These groups were converted to cinnamate groups by reaction with hydroxy alkyloxy cinnamate. The aim of the present work was to synthesize new oilabsorptive polymers containing hydrophobic chains in the presence of different types of crosslinkers by chemical initiation. Accordingly, the present section aims to modify PIB–MA adduct with cinnamate moieties to introduce polymerizable aromatic moieties in order to obtain crosslinked PIB having high oil absorptivity, which can be applied in the field of oil sorbers. The base materials for an oil absor-
bent are as follows: fast oil absorption rate, high absorption oil capacity, good absorption selectivity of oil over water and low density compared to water to float with or without absorbed oil. In this work CMn ester derivatives were synthesized by the reaction of cinnamoyl chloride with different glycols in presence of triethyl amine (TEA) as a catalyst. The reaction scheme was represented in Fig. 1. The reaction between PIB–MA and CMn was carried out according to the procedure described in Section 2. In this respect, the succinic anhydride group of PIB–MA was apparently converted to mono (b-cinnamoyl alkyloxy) succinate groups. The chemical structure of CM esters was illustrated using IR analysis. The IR spectrum of CM esters with PEG were not represented here for brevity.
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The appearance of two new strong bands at 1735 and 1145 cm 1 represent C@O and C–O stretching of ester group, indicates the formation of ester group when cinnamoyl chloride was reacted with glycol. On the other hand the appearance of strong band at 3445 cm 1 for OH stretching, indicates that the chemical structures of CM esters have terminal hydroxyl groups. The bands at 1620 and 900– 650 cm 1 which represent C@C stretching vibration and out-of-plane rotational vibration of aromatic C–H indicate the incorporation of cinnamate group in the structure of CMn esters. The present study aims to modify PIB with maleic anhydride followed by reaction with cinnamoyl moieties to introduce aromatic moieties to increase its solubility in crude oil. In this respect, PIB having an average molecular weight of 1000, reacts with maleic anhydride through an ene reaction which reacts with hydroxy alkyloxy cinnamate esters to give the reactive polyalkenylsuccinate macromonomers. The products were confirmed by 1HNMR analysis. The 1HNMR spectra of PIB–MA–CM1, PIB– MA–CM2, PIB–MA–CM3 and PIB–MA–CM9 were illustrated in Fig. 2(a)–(d), respectively. The peaks of cinnamate group were observed at 7.2–7.8 ppm for aromatic protons and 5.6–6.6 ppm for vinyl proton in all spectra. The peak at 3.8 ppm indicates the presence of OCH2–CH2O protons and their intensities are based on type of the used glycols. The peak
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at 8.9 ppm that represent COOH proton confirms the monoester formation between CMn and PIB– MA. Therefore, it was confirmed that the succinic anhydride group in PIB–MA was completely condensed to the cinnamate group by the reaction with hydroxy alkyloxy cinnamate. 3.2. Crosslinked copolymers Crosslinking is responsible for the three-dimensional network structure that is important for preparation of organogels and hydrogels. Elasticity and swelling properties are attributed to the presence of physical or chemical crosslinks within polymer chains. Hydrophobic network polymers are used as absorbents of oil as well as some organic solvents spilled on water in the field of environment. High conversion polymerization was performed for preparing different crosslinked copolymers. The crosslinked copolymers of CEMA/ODA copolymers were prepared via bulk polymerization in presence of 0.02% ABIN as initiator and different weight percentage of TPT crosslinker ranging from 0.5% to 4%. Different molar ratios of CEMA with each alkyl acrylates viz. 90/10, 70/30, 50/50, 30/70 and 10/90 (mole%/mole%) were used in each copolymer. To understand the distribution of crosslinks in the network, the reactivity of the various double bonds in the system must be determined. This
Fig. 2. 1HNMR spectra of (a) PIB–MA–CM1, (b) PIB–MA–CM2, (c) PIB–MA–CM3 and (d) PIB–MA–CM9 reactive macromonomers.
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includes the reactions between double bonds of CEMA and ODA, the initial double bonds of the crosslinker, and the various double bonds that are pendant to the polymer chain after incorporation of the crosslinker. The present copolymer system is composed essentially of CEMA with varying amounts of ODA comonomer to give certain hydrophibicity, which improves oil affinity. The yield of crosslinking reaction increases very rapidly at some extent of the reaction as the reaction proceeds, and the reaction product begins to form an infinite molecular weight network called gel point. In the gel state, chemical reaction can proceed and forms the network by crosslinking. The crosslink density or degree of crosslinking is a measure of the total links between chains in a given mass of substrate. In a crosslinking system, there are soluble portions and insoluble portions, the former can be extracted with suitable solvents and the latter cannot be extracted with any solvent due to crosslinking. It only swells in good solvent to give a gel. According to Flory’s swelling theory [19], swelling behavior is affected by rubber elasticity, affinity to solution and crosslinking density. The swelling behavior of gels with different amounts of the crosslinkers was studied. Generally, the crosslinker concentrations were ranged from 0.01% to 4% usually about 0.05–1% to provide super absorbents with high swelling capacity and low soluble polymer content. Some polymer chains are not attached to the infinite network can be extracted from the gel fraction. The effect of these chains is difficult to treat, and usually neglected in the theories. These chains do not contribute to the modulus but can be solvated and contribute to the swelling. Therefore, it is desirable to eliminate or minimize the content of these extractable molecules. The percentage of this extracted fraction (soluble fraction) depends on:
(a) the type and concentration of the monomers, and (b) the type and concentration of crosslinking agent [20]. In the present investigation, the polymer rods were post cured at 378 K in an air oven for 24 h to assure complete polymerization. The sol fractions of these polymeric materials were determined via Soxhlet extraction technique. In this respect, the dried xerogel discs were transferred into an extraction thimble and were subjected to Soxhlet extraction with chloroform. After extraction for 24 h, the samples were dried in atmosphere for several hours and then dried to a constant weight in vacuum oven at 308 K. However, no further extraction was found after 24 h, and this Soxhlet extraction time was adopted for all samples. In the present work, the reactivity of a crosslinker containing acrylate group (TPT) towards CEMA-ODA copolymer was investigated from polymerization conversion and SF measurements in chloroform. SF% values were determined and listed in Table 1. The effect of crosslinker concentrations on SF values was determined through crosslinking of CEMA(50 mole%)/ODA(50 mole%) copolymer with different contents of TPT viz. 0.5%, 1%, 2% and 4% (w/w). It was observed that, the percentage of SF for crosslinked copolymers is reduced when crosslinker content increases from 0.5% to 4% (w/w). The effect of copolymer compositions on SF% values were determined by crosslinking different compositions of CEMA-ODA copolymer using 1% (w/w) of TPT crosslinkers and 0.02% (w/w) AIBN as initiator. Regarding the data shown in Table 1, it is obvious that, for copolymers crosslinked with TPT, SF% decrease with increasing ODA percentage in the copolymer composition. This may be referred to the higher reactivity of ODA homopolymer towards either crosslinkers than that of CEMA/ODA copolymer. In other words, the alkyl acrylate poly-
Table 1 Absorption characteristics of the CEMA/ODA copolymers crosslinked with TPT crosslinker at 293 K Xerogel composition
Crosslinker content
SF (%)
90/10 70/30 50/50
1 1 0.5 1 2 4 1 1
39.57 32.55 32.91 30.98 17.6 14.11 20.57 13.25
30/70 10/90
Qmax (g/g)
ETC
Q (g/g)
k (h 1)
T (h)
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
22.260 26.030 33.556 27.8 27.398 24.242 29.812 34.832
20.662 22.034 29.572 24.982 24.342 19.214 26.356 32.472
95.507 96.158 97.019 96.402 96.350 95.874 96.645 97.129
95.160 95.461 96.618 95.997 96.053 94.795 96.205 96.920
14.068 16.450 21.207 17.569 17.315 15.320 18.841 22.013
13.058 13.925 18.689 15.788 16.016 12.143 16.656 20.522
1 0.75 0.5 0.6 0.7 0.75 0.5 0.4
0.9 0.8 0.4 0.75 0.80 0.85 0.6 0.5
0.999 1.33 1.99 1.66 1.428 1.333 1.99 2.499
1.11 1.249 2.499 1.33 1.249 1.176 1.666 1.999
A.M. Atta et al. / Reactive & Functional Polymers 66 (2006) 931–943
mers are used up before a significant number of CEMA would incorporate in the network structure. In a previous section we have reported on esterification of hydroxy alkoxycinnamate with polyisobutylene succinate adduct. These products were reacted with ODA monomer in presence of TPT, cobalt octoeate (Co) and benzoyl peroxide as crosslinker, activator and initiator, respectively. Accordingly, we suggest a new method to crosslink PIB by chemical method through introducing cinnamoyl derivatives into its macromolecular chains. The crosslinking efficiencies of PIB–MA–CMn/ODA copolymers were determined from the SF measurements which were determined from Soxhlet extraction with chloroform after 24 h of extraction. In this respect, the results obtained via Soxhlet extraction for the crosslinked (50 mole%) BIP-MA-CMn/ (50 mole%) ODA (where n = 1, 2, 3, 4 or 9) with 1, 2 and 4% TPT crosslinker were listed in Table 2. It is obvious that, the percentage of SF for crosslinked copolymers decreased with increasing the TPT wt% from 1% to 4%. It is also observed that, SF% values for PIB–MA–CMn/ODA decreases from n = 1 to n = 9. This may be attributed to the difference in the reactivity of the crosslinker towards the copolymers. This indicates that increasing number of ethylene oxide units for PIB–MA–CMn macromonomers increases their ability to crosslink with TPT. Accordingly, the crosslinking efficiency of ODA with reactive macromonomers increases
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in the order PIB–MA–CM9 > PIB–MA–CM4 > PIB–MA–CM3 > PIB–MA–CM2 > PIB–MA–CM1. Comparing SF% values for the reactive copolymers with those of CEMA/ODA copolymers, it is obvious that high SF% values are higher for the former. This may be due to lower expected collisions of reactants in the case of reactive copolymers. 3.3. Oil absorbency There are different parameters that can be selected to control the oil absorptivity of oil sorbers. The excellent oil absorptivity of materials depends on the bulkiness and length of the alkyl substituents and the porosity of the microstructure, which can be controlled by crosslinking. It is also reported that, the driving force for oil absorption of hydrophobic networks is caused mainly due to the van der Waals interaction between the material and the oil, therefore, the materials with the proper porosity can effectively contain oil in their structures. The swelling characteristics of crosslinked networks are controlled by a balance of opposing forces, swelling forces driven by osmotic pressure, and restoring forces from a variety of physical, covalent, or ionic crosslinks. The crosslinks are typically incorporated during the polymerization by the use of copolymerized multifunctional crosslinkers. Swelling kinetics of the crosslinked copolymers were determined according to a previous article [11]. The swelling
Table 2 SF and absorption characteristics of the crosslinked PIB–MA–CMn/ODA copolymers having different crosslinker weight contents in toluene at 293 K Sample
Crosslinker content
SF (%)
Qmax (g/g)
Q (g/g)
ETC
T
Tmax
k (h 1)
PIB–MA–CM1/ODA
1 2 4
41.53 40.13 38.45
45.90 42.22 38.70
29.008 26.683 24.458
97.82 97.63 97.41
0.25 0.33 0.5
1 1 1
3.99 2.99 1.99
PIB–MA–CM2/ODA
1 2 4
38.63 34.43 32.65
35.55 33.50 32.50
22.467 21.172 20.54
97.18 97.01 96.92
0.3 0.4 0.5
1 1 1
3.33 2.49 1.99
PIB–MA–CM3/ODA
1 2 4
34.73 32.83 30.85
28.05 26.90 26.23
17.731 17.00 16.577
96.343 96.28 96.18
0.33 0.42 0.58
2 2 2
3.00 2.39 1.71
PIB–MA–CM4/ODA
1 2 4
32.98 31.86 30.11
26.99 25.30 25.05
17.062 15.989 15.830
96.29 96.04 96.00
0.33 0.45 0.75
2 2 2
3.029 2.22 1.33
PIB–MA–CM9/ODAz
1 2 4
26.62 24.76 20.15
24.30 23.10 22.86
15.362 14.599 14.44
95.88 95.67 95.62
0.33 0.5 0.75
2 2 2
2.99 1.99 1.33
A.M. Atta et al. / Reactive & Functional Polymers 66 (2006) 931–943
rate, maximum oil absorbency (Qmax) and swelling kinetic constant (k) were calculated as reported in a previous article [11]. The oil used in this experiment is diluted with toluene (10%). For the real application to clean up an oil spill, the oil absorption test has to be operated using not only light or medium oil but also heavy oil, because the spilt crude oil has a high viscosity. On the other hand, the materials used to absorb the oil do not have a sponge like structure with open pores. It has only a network structure, which formed by the crosslinking reaction. Therefore, heavy oil with high viscosity, like Belayium crude oil, cannot easily diffuse from the surface of the samples into the internal space of network. On the other hand, toluene is the most applicable solvent that can be used to dissolve the asphaltene of crude oil. For these reasons, we have used diluted crude oil with toluene in this experiment so that the swelling behavior of the samples could be easily evaluated. In the previous publication [11], we have reported on the swelling characteristics of crosslinked CEMA isooctyl acrylate copolymers using different types and concentrations of crosslinkers. It was reported that, the swelling characteristics are affected by crosslinker types and concentrations [11]. It was noted that the oil uptake increased when TPT used as crosslinker [11]. In this respect, the present investigation aims to use TPT crosslinker to increase the oil uptake of the prepared organogels. The oil absorbance of the crosslinked copolymers with TPT as a function of immersion time upon using pure toluene as an oil medium for CEMA/ODA was selected and represented in Fig. 3. In this figure, the oil absorbency increases with increasing the immersion time and attains the maximum swelling values during 3 h for CEMA/ ODA copolymers. Also, the higher ODA content increases the oil absorbency. This may be explained on the basis that, the high acrylate content in the crosslinked copolymer increases the hydrophobicity of crosslinked network. This indicates that, the swelling capacities are affected by the hydrophobicity of copolymers. On the other hand, Qmax values are largely affected by the sorption medium. It is noticed that, the oil absorbency decreases slightly upon using 10% crude instead of pure toluene. This can be attributed to the higher viscosity of crude oil, which causes two opposite effects: decreased sorption during the penetration through interior of network and improved sorption since the oil is better adhered to the material [21,22]. Swelling kinetic
55 (90/10) 50
(50/50) (30/70)
45
(10/90) (70/30)
40
Oil abso. (g/g)
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35 30 25 20 15 10 0
20
40
60
80
Time (hr)
Fig. 3. Oil Absorbency for CEMA/ODA copolymers having different mole ratios of CEMA to ODA as a function of immersion time using 1%TPT crosslinker in toluene at 298 K.
constant values (k), listed in Table 1, increase with decreasing crosslinker wt%. This result can be explained on the base that the high crosslinker content forms stiffer crosslinked polymers having smaller cavities at the gel surfaces. Considering that the swelling kinetics may be dependent not only on the surfaces of the polymer but also on the number and volume of the pores in the polymer. The smaller cavities provide larger absorption surfaces which give higher swelling rate of the polymeric network. In other words, the polymer with higher swelling rate may have suitable structure for oil absorption [23]. The equilibrium toluene content (ETC), listed in Table 2, increases with increasing alkyl acrylates mole%. This high oil absorptivity of the polymer depends on the blockness of the alkyl constituent. In our investigation the oil absorbency of the crosslinked PIB–MA–CMn/ODA were determined using toluene and 10% crude oil. Fig. 4 represent swelling kinetic curves for PIB–MA–CM1/ODA in either toluene or 10% crude oil as representative. The data of the maximum oil absorbency Qmax, equilibrium swelling time (Tmax) for all reactive crosslinked macromonomer sorbers in pure toluene and 10% crude oil media are listed in Tables 2 and 3, respectively. As shown from the data, the maximum oil absorbency decreases with increasing the crosslinker concentration from 1 to 4 wt% in both media. This behavior can be attributed to more restricted polymeric chains upon using higher crosslinker concentration. Another factor, the
A.M. Atta et al. / Reactive & Functional Polymers 66 (2006) 931–943
a
53 48
oil absorbancy g/g
43 38 33 28 23
TPT 1%
18
TPT 2 %
13
TPT 4 %
8 3 0
20
40
60
80
100
120
time (min)
b
35
oil absorbancy (g/g)
30 25 20 15 TPT 1 %
10
TPT 2 % 5
TPT 4 %
0 0
20
40
60
80
100
120
140
time (min)
Fig. 4. Oil absorbency for (50 mole%) PIB–MA–CM1/ODA(50 mole%) crosslinked reactive copolymer as a function of immersion time using 1, 2 or 4 wt% TPT in (a) pure toluene and (b) 10% diluted crude oil in toluene at 298 K.
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influence of surrounding medium on the sorption capacity was also studied. From the listed data, the sorption capacity of all tested crosslinked copolymers for pure toluene is always higher than for 10% oil medium. As an example Qmax for PIB– MA–CM1/ODA in toluene is equal 45.9 g/g sample while in 10% oil is equal 31.46 g/g sample. This increased restriction can be also illustrated in the average molecular weight between crosslinks Mc as will be discussed in following section. It was also suggested that the low rate of diffusion of toluene at room temperature and the high energy of activation for this process is associated with the nature of interaction between toluene with polyisobutylene macromolecules [24]. The effect of alkyloxy chain length were introduced namely n = 1, 2, 3, 4 and 9 into crosslinked PIB–MA–CMn/ODA copolymer. The data presented in Tables 2 and 3 show that, upon increasing the ethyloxy chain length a remarkable decrease in the sorption capacity was observed. While the sorption capacity in toluene for PIB–MA–CM1/ODA (1 mole%) crosslinked with 1% TPT is 45.9 g/g polymer, PIB–MA–CM9/ODA (1 mole%) crosslinked with 1% TPT is 24.3 g/g polymer. The same behavior was observed for the sorption capacity in 10% crude oil regarding the data shown in Table 3. Maximum sorption of 10% crude oil observed by PIB– MA–CM1/ODA crosslinked with 1% TPT is 31.46 g/g polymers, compared by 19.40 g/g polymer attained by PIB–MA–CM9/ODA crosslinked with 1% TPT at same conditions.
Table 3 Absorption characteristics of the crosslinked PIB–MA–CMn/ODA copolymers having different crosslinker weight contents in 10% crude oil at 293 K Sample
Crosslinker content
Qmax (g/g)
Q (g/g)
EOC
T
Tmax
k (h 1)
PIB–MA–CM1/ODA
1 2 4
31.46 27.37 25.02
19.88 17.301 15.81
96.82 96.34 96.00
0.33 0.40 0.45
1 1 1
2.99 2.49 2.22
PIB–MA–CM2/ODA
1 2 4
25.34 23.28 20.11
17.34 14.71 12.71
96.35 95.70 95.03
0.4 0.5 0.5
1 1 1
2.49 1.99 1.99
PIB–MA–CM3/ODA
1 2 4
24.45 23.132 19.56
15.45 14.61 12.36
95.92 95.67 94.88
0.5 0.5 0.5
2 2 2
1.99 1.99 1.99
PIB–MA–CM4/ODA
1 2 4
24.534 21.82 17.31
15.50 13.79 10.93
95.91 95.41 94.22
0.33 0.5 0.5
2 2 2
1.99 1.99 1.99
PIB–MA–CM9/ODA
1 2 4
19.406 18.046 17.022
12.26 11.40 10.75
94.84 94.22 94.13
0.6 0.6 0.75
2 2 2
1.66 1.66 1.33
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According to Yao and Zhou [25], the swelling kinetic of the investigated reactive crosslinked polymers PIB–MA–CMn/ODA was studied. The swelling parameters were determined from the swelling curves and listed in Tables 2 and 3. These tables show the equilibrium toluene or oil content, (ETC) or (EOC), characteristic time required for the swelling (T), maximum swelling time (Tmax) required to reach equilibrium and swelling kinetic constant (k) for the prepared reactive crosslinked copolymers. Regarding Tmax values in either toluene or oil medium cases (diluted 10% crude oil in toluene), it is noticeable that generally as the ethyloxy chain length increase the Tmax was increased. This behavior can be explained easily by considering the increase in the hydrophilic nature of the polymer matrix by increasing the ethyloxy chain length. On the other hand, the rate constant values decrease with increasing the ethyloxy chain length from n = 1 to n = 9. This may be explained on the basis of swelling mode. The swelling process of polymeric networks is primarily due to oil solution penetrating into the polymeric gel through diffusion. Here, increasing the ethyloxy chain length increases the hydrophilicity of the polymeric networks, thus increasing the difficulty of oil diffusion. The swelling rate constant for PIB–MA–CM1/ ODA is only 2.99 (h 1) swelled in 10% crude oil where as that swelled in pure toluene is 3.99 (h 1). Comparing the swelling rate constants between the gels swelled in 10% crude oil and those swelled in pure toluene, the latter always show higher values. This behavior can be easily explained on the basis of different viscosity values of either pure toluene or 10% crude oil that cannot easily diffuse from the surface of the gels into the internal space of the network. A comparison of rate constant values for the crosslinked reactive polymer with those of CEMA/ODA copolymers crosslinked with the same crosslinker content in toluene was held. As an example, k = 3.99 h 1 for PIB–MA– CM1/ODA, whereas k = 1.66 h 1 for CEMA/ ODA. This behavior can be easily explained on the basis of, in case of crosslinked reactive polymer more hydrophobic chain nature due to PIB moiety enhances oil diffusion than that of CEMA/ODA copolymer (less hydrophobic). The ability of the swelled gels to undergo several cycles of swelling and deswelling is investigated. We can see that after the first cycle the gel did not achieve the original swollen state but that in all of the following cycles it swelled back to its previous swollen state. This
indicates that a small amount of soluble fractions still remains in the crosslinked gels which could have leached out upon deswelling and reducing the degree of successive swelling [26]. 3.4. Network parameters of gels Network parameters of crosslinked polymers include the theoretical crosslink density mt, Flory– Huggins type interaction parameter v, effective crosslink density me, and molar mass between crosslinks (Mc). From the temperature dependence of transport coefficients, attempts were made to predict the activation parameters, Flory–Huggins type interaction parameter (v) and molar mass between crosslinks (Mc) of the polymer and effective crosslink density me of the polymer. Also, the theoretical crosslink density mt has been calculated from: vt = Cf/2 where, C (mol dm 3) is the concentration of crosslinking agent of functionality f. For TPT, f = 6. The value of C was determined from the weight concentration of TPT and the density q of the xerogel. The latter was determined by direct weighing and micrometrically measured dimensions of the dried discs and pellets used. The Flory–Rehner swelling mode [19,27] has been used in the literature to predict the molar mass between crosslinks (Mc). This needs accurate values of Flory–Huggins type interaction parameter v. Bristow and Watson [28] have attempted to compute it from the solubility parameter concept as developed by Hildebrand [29]. This approach being strictly empirical which sometimes leads to wrong predictions for v. Also, for some penetrants it would be cumbersome to find reliable literature [30] solubility parameters data of solvents. Instead, we suggest using an alternative phenomenological theory to calculate v. The molar mass between crosslinks and me were calculated from swelling parameter [31]. The network parameters me, Mc and v were determined from the swelling measurements of copolymers with pure toluene or 10% crude oil and are listed in Tables 4 and 5. The compression moduli GT values were obtained from swelling parameters [32]. In this respect GT values were calculated for the copolymer gels and listed in Table 4 It is well known that the lower GT values indicate that the prepared gels have an elastic network. This will increases the interaction between toluene and the copolymer networks. Bastide et al. [32] showed that the presence of dangling chains or pendant chains in the polymeric network affected the compression moduli of elasticity.
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Table 4 Network parameters of different compositions CEMA/ODA copolymers crosslinked with various concentrations of TPT crosslinker at 298 K Xerogel composition
Crosslinker content
Density (kg/dm3)
90/10 70/30 50/50
1 1 0.5 1 2 4 1 1
0.65 0.62 0.60 0.62 0.64 0.68 0.60 0.54
30/70 10/90
Up
GT (MN m 2)
me · 103 mol/dm3
Mc (g/mol)
v
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
Toluene
Crude oil
0.0449 0.0384 0.0298 0.0359 0.0365 0.0412 0.0335 0.0287
0.0483 0.0453 0.0338 0.0400 0.0411 0.0520 0.0379 0.0307
14.189 9.748 6.928 7.820 8.091 9.316 7.0966 5.898
17.037 14.546 7.230 10.747 11.434 19.069 9.466 6.924
16.453 11.909 9.211 9.765 10.054 11.11 9.070 7.935
19.271 16.810 9.217 12.951 13.660 21.053 11.612 9.106
39.505 52.059 65.135 63.491 63.358 61.183 66.149 68.049
33.728 36.880 65.096 47.870 46.850 32.298 51.669 59.301
0.353 0.349 0.298 0.358 0.359 0.382 0.346 0.312
0.355 0.353 0.346 0.350 0.351 0.368 0.349 0.314
Table 5 Network parameters from swelling measurements of the crosslinked PIB–MA–CMn/ODA copolymers in toluene with various concentrations of TPT crosslinker at 298 K Sample
Crosslinker content
mt (mol/dm3)
me · 103 mol/dm3
Mc · 10 g/mol
PIB–MA–CM1/ODA
1 2 4
0.581 0.667 0.719
9.043 10.620 11.557
PIB–MA–CM2/ODA
1 2 4
0.735 0.790 0.821
PIB–MA–CM3/ODA
1 2 4
PIB–MA–CM4/ODA
PIB–MA–CM9/ODA
3
GT (MN m 2)
Density (kg/dm3)
v
Up
63.361 61.956 61.433
0.124 0.125 0.156
0.0217 0.0236 0.0258
6.120 7.390 8.279
0.573 0.658 0.710
13.655 14.909 15.599
53.093 52.314 51.926
0.157 0.168 0.173
0.2812 0.0298 0.0307
10.062 11.206 11.843
0.725 0.78 0.81
0.757 0.807 0.831
21.011 22.576 23.337
35.552 35.258 35.136
0.175 0.181 0.187
0.0356 0.0371 0.0381
16.752 18.256 19.032
0.747 0.796 0.82
1 2 4
0.791 0.811 0.821
22.406 23.286 23.693
34.811 34.354 34.186
0.181 0.212 0.213
0.0370 0.0395 0.0399
18.097 19.219 19.620
0.78 0.80 0.81
1 2 4
0.902 0.922 0.943
27.031 27.839 28.470
32.924 32.687 32.665
0.192 0.2180 0.2182
0.0411 0.0432 0.0437
22.610 23.685 24.303
0.89 0.91 0.93
They found that the values of moduli decrease drastically when the proportion of pendant chains increase. For the same reason, values of GT and me decrease with increasing the alkyl acrylate proportion in the copolymer composition and increase with increasing the crosslinker weight content. This can be proved from measuring polymer–solvent interaction parameter (v). The values of v were calculated for all copolymers and are listed in Tables 4 and 5. The decreasing of v values indicates the good interaction between the crosslinked copolymers with toluene. This indicates that crosslinking with TPT introduces dangling hydrophobic groups to network at crosslinking [33]. Since Mc is used to determine the distance between two successive crosslinks, the smaller its
value the higher the crosslinking density of the networks. As the crosslinking density increases, the oil sorber capacities are reduced. It was also observed that the b-values are less than unity. It is due to the fact that toluene is a better swelling agent for this system. This is because b is not only a measure of chemical crosslinking but also of physical interaction between the chains when the values are greater than unity [34]. Tables 4 and 5 show effective crosslink density (me), theoretical crosslink density (mt), molecular weight of the chains between two successive crosslinks (Mc), polymer–solvent interaction parameter (v), volume fraction of the polymeric material in the xerogels (Up), equilibrium moduli of elasticity for xerogels (GT), and density of the xerogels. The Flory–Rehner swelling model [19,27]
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has been used in the literature to predict the molar mass between crosslinks (Mc). To do this we need to have accurate values of (v). Several researchers [27,35] have attempted to compute v from the solubility parameter concept. This approach being strictly empirical sometimes leads to wrong predictions for v also, for some penetrates it would be cumbersome to find reliable literature data on solubility parameters of solvents. Instead, it was suggested by Aithal and Aminabhavi [36] using an alternative phenomenological theory to calculate v. This approach starts from Flory–Rehner equations in Section 2. Where the temperature coefficient of polymer volume fraction (dUp/dT) was determined and utilized to calculate v. As shown in Tables 4 and 5, v have values always <0.3 for PIB–MA– CMn/ODA at 1% crosslinker, where v = 0.124 for PIB–MA–CM1/ODA whereas for PIB–MA–CM9/ ODA v = 0.192 at the same crosslinker concentration where the samples are swelled in Toluene. However the lower the values of v, the higher the polymer–solvent interaction. This behavior runs in harmony with the equilibrium swelling results, where Qmax values are shifted to higher values as v decreases. In other words, toluene is a thermodynamically good solvent for these polymers when v is always less than 0.3. It is also observed from Table 5 that, the lowest value of v(0.124) was exhibited at the lowest TPT (crosslinker) content for PIB–MA–CM1/ODA polymer swelled in toluene. A similar behavior for v parameter and its effects was observed for samples swelled in 10% crude oil. A comparison of v parameter values of the reactive polymer with those of CEMA/ODA copolymers crosslinked with the same crosslinker content in toluene was held. It was observed that the increased polymer–solvent interaction for reactive polymers than that for CEMA/ODA copolymer. This in turn affects on the swelling behavior of either cases. In reactive polymers the swelling is shifted to higher values of Qmax for PIB–MA–CM1/ODA = 45.9 g/g polymer where as for CEMA/ODA Qmax = 27.8 g/g polymer upon using 1% TPT. This may be attributed to the compositional drift of the reactive polymer (hydrophobic and the elastic nature of the polyisobutylene moiety). Values of Up listed in Table 5 measured at 298 K using pure toluene as oil medium increases with increasing content of crosslinking agent (from 1 to 4 wt%). Also, Up increase with increasing ethyloxy chain length moiety which may be explained as previously mentioned for v values. Increase in Up val-
ues was also observed upon using 10% crude oil instead of pure toluene (Table 5). The densities of the prepared PIB–MA–CMn/ODA sorbers (qp) crosslinked with 1, 2 or 4 wt% TPT crosslinker were determined and listed in Table 5. The listed data show that the densities of xerogels are all less than unity. This indicates that the prepared xerogels can be floated on sea’s surface. The most important property of an absorbent polymer is its sorption capacity. On the basis of Flory–Rehner theory [27] the key variables, which control this property are crosslink density me, average molecular weight between crosslinks Mc, equilibrium moduli of elasticity GT. The values of me and mt for PIB–MA– CMn/ODA sorbers crosslinked with 1, 2 or 4 wt% TPT crosslinker using pure toluene or 10% crude oil are listed in Table 5. The data show that, me increases with increasing ethyloxy chain length from n = 1 to n = 9. This runs in harmony with Qmax values obtained by PIB–MA–CMn/ODA. This may be explained by the increased possibility of physical crosslinks with increasing the alkyloxy chain length, from n = 1 to n = 9. Also, me increases with increasing crosslinker weight content (increased chemical crosslinks). This conclusion is supported by the data of Mcfor the crosslinked reactive polymer by different weight content of TPT crosslinker using toluene or 10% crude oil (see Table 5). The data show that Mc values decrease as crosslinker weight content increase and with increasing ethyloxy chain length for PIB–MA–CMn/ODA crosslinked reactive polymer. The reason may be that the increase in the amount of the crosslinking agent led to formation of a denser network of the crosslinked reactive copolymer and reduced Mc (average molecular weight between successive crosslinks). In other words, the smaller Mc value indicates the higher crosslinking density network. On the other hand, the crosslinking density increase, the oil sorber capacity is reduced. The data show that, GT increases with increasing ethyloxy chain length and by increasing crosslinker weight content. This may be due to, the decreased probability of forming dangling chains or pendant groups as ethyloxy chain length increase and with increased crosslinker weight content. The presence of pendant chains or dangling chains in the polymeric network affects the compression moduli. The values of moduli decrease drastically when the proportion of pendant chains increase [32]. The lower GT and me values for PIB–MA–CMn/ODA crosslinked reactive polymers indicate that the prepared
A.M. Atta et al. / Reactive & Functional Polymers 66 (2006) 931–943
gels have elastic networks. This will increase interaction between toluene and prepared networks and hence increased absorption capacity for PIB–MA– CMn/ODA crosslinked reactive polymer. 4. Conclusions The following conclusions are drawn from the present investigation: (1) Oil absorbency increased by higher incorporation of hydrophobic acrylate units and by decreasing amount of either crosslinking agent (TPT). (2) Polymer solvent interaction (v) decreased by increasing the hydrophobic alkyl acrylate units and by decreasing the amount of either crosslinking agent (TPT). (3) Maximum oil absorbency for PIB–MA–CMn/ ODA sorbers decreases by increasing the alkyloxy chain length grafts and by increasing crosslinker weight content. (4) The oil absorbency and absorption rate constant for PIB–MA–CMn/ODA reactive copolymer sorbers is higher than that for CEMA/ ODA copolymers crosslinked at the same conditions. (5) More elastic networks are obtained by PIB– MA–CMn/ODA reactive copolymer sorbers than CEMA/ODA sorbers as illustrated by network parameters data (GT, me and v).
References [1] R.F. Johnson, T.G. Manjrekar, J.E. Halligan, Environ. Sci. Technol. 7 (5) (1973) 439. [2] M. Blumer, in: D.P. Hoult (Ed.), Oil on the Sea, Plenum Press, New York, 1969, p. 6. [3] M. Morita, M. Higuchi, I. Sakata, J. Appl. Polym. Sci. 34 (1987) 1013. [4] T. Shimizu, S. Koshiro, Y. Yamada, K. Tada, J. Appl. Polym. Sci. 65 (1997) 179. [5] J. Jang, B.S. Kim, J. Appl. Polym. Sci. 77 (2000) 903.
943
[6] Y. Liu, R. Mao, M.B. Huglin, P.A. Holmes, Polymer 37 (8) (1996) 1437. [7] S.C. Davis, W.V. Hellens, H.A. Zahalka, in: J.C. Salamone (Ed.), Polymeric Materials Encyclopedia, vol. 4, CRC Press, New York, 1996, pp. 2264–2271. [8] P.A. Bertrand, J. Mater. Res. 8 (1993) 1749. [9] W.S. Anthony, Appl. Eng. Agr. 10 (3) (1994) 357. [10] A.M. Atta, K.F. Arndt, J. Appl. Polym. Sci. 97 (2005) 80. [11] A.M. Atta, A.M. Rasha, R.K. Farag, A.F. El-Kafrawy, A.A. Abdel-Azim, Polym. Int. 54 (7) (2005) 1088. [12] M.H. Zhou, W.J. Cho, Polym. Int. 49 (2000) 17. [13] S. Champ, W. Xue, M.B. Huglin, Polymer 42 (2001) 6439. [14] C. Sayil, O. Okay, Polymer 42 (2001) 7637. [15] S. Saito, M. Kanno, H. Inomoto, Adv. Polym. Sci. 109 (1993) 207. [16] A.M. Al-Sabagh, A.M. Atta, J. Chem. Technol. Biotechnol. 74 (1999) 1075. [17] C. Azuma, N. Hashizume, K. Sanui, N. Ogata, J. Appl. Polym. Sci. 28 (1983) 543. [18] C. Azuma, K. Sanui, N. Ogata, J. Appl. Polym. Sci. 25 (1980) 1273. [19] P.J. Flory (Ed.), Principles of Polymer Chemistry, Cornell University Press, Ithaca, NewYork, 1953 (Chapter 13). [20] T.M. Kossmehl, E.M. Abdel-Bary, A.A. Sarhan, M.Y. Abdelaal, Die Angew. Makromol. Chem. 215 (1994) 59. [21] A.M. Atta, K.F. Arndt, Polym. Int. 50 (2001) 1360. [22] H.M. Choi, R.M. Cloud, Environ. Sci. Technol. 26 (1992) 772. [23] M.H. Zhou, W.J. Cho, Polym. Int. 50 (2001) 1193. [24] A.A. Tager, A.I. Podlisnyak, Vysokomol. Soedin. B 1 (1963) 87. [25] K.J. Yoa, W.J. Zhou, J. Appl. Polym. Sci. 53 (1994) 1533. [26] A.M. Atta, Polym. Adv. Technol. 13 (2002) 567. [27] P.J. Flory, J. Rehner, J. Chem. Phys. 11 (1943) 512. [28] G.M. Bristow, W.F. Watson, Trans. Faraday Soc. 54 (1987) 1731. [29] J.H. Hildebrand, R.L. Scott (Eds.), Regular Solutions, Prentice-Hall, Englewood Cliffs, NJ, 1962 (Chapter 2). [30] J. Crank (Ed.), The Mathematics of Diffusion, second ed., Clarendon Press, Oxford, 1975 (Chapter 2). [31] T.P. Davis, M.B. Huglin, Makromol. Chem. 191 (1990) 331. [32] J. Bastide, C. Picot, S. Candau, J. Polym. Sci., Polym. Phys. Ed. 17 (1979) 1441. [33] A.M. Atta, K.F. Arndt, Polym. Int. 52 (2003) 389. [34] K. Yokota, A. Abe, S. Hosaka, I. Sakai, H. Saito, Macromolecules 11 (1978) 95. [35] M.C. Gupta, V.P. Bansod, I.D. Patil, Polym. Commun. 28 (1987) 204. [36] U.S. Aithal, T.M. Aminabhavi, Polymer 31 (1990) 1757.