Transport Properties of Crosslinked Acrylonitrile Butadiene Rubber/Poly(ethylene-co-vinyl acetate) Blends HIMA VARGHESE, S. S. BHAGAWAN,* SABU THOMAS School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam-686 560, Kerala, India Received 9 September 1998; revised 1 April 1999; accepted 2 April 1999 ABSTRACT: The diffusion and transport of organic solvents through crosslinked nitrile rubber/poly(ethylene-co-vinyl acetate) (NBR/EVA) blends have been studied. The diffusion of cyclohexanone through these blends was studied with special reference to blend composition, crosslinking systems, fillers, filler loading, and temperature. At room temperature the mechanism of diffusion was found to be Fickian for cyclohexanone–NBR/EVA blend systems. However, a deviation from the Fickian mode of diffusion is observed at higher temperature. The transport coefficients, namely, intrinsic diffusion coefficient (D*), sorption coefficient (S), and permeation coefficient (P) increase with the increase in NBR content. The sorption data have been used to estimate the activation energies for permeation and diffusion. The van’t Hoff relationship was used to determine the thermodynamic parameters. The affine and phantom models for chemical crosslinks were used to predict the nature of crosslinks. The experimental results were compared with the theoretical predictions. The influence of penetrants transport was studied using dichloromethane, chloroform, and carbon tetrachloride. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1815–1831, 1999 Keywords: acrylonitrile butadiene rubber; poly(ethylene-co-vinyl acetate); morphology; diffusion; crosslinking INTRODUCTION Diffusion and transport of organic solvents through polymeric materials have been a subject of fundamental interest1–5 and the technological importance of the molecular transport of solvents in polymers plays a vital role in a variety of applications such as separation process,6 food packaging,7 controlled drug release,8 reverse osmosis,9 and microelectronics.10 As far as these applications are considered, it is quite essential to evaluate the dimensional stability of the polymeric materials in the presence of aggressive liquids. * Present address: Propellant Engineering Division, V.S.S.C., Thiruvananthapuram, 695 022, Kerala, India Correspondence to: S. Thomas (E-mail: [email protected] vsnl.net.in) Journal of Polymer Science: Part B: Polymer Physics, Vol. 37, 1815–1831 (1999) © 1999 John Wiley & Sons, Inc. CCC 0887-6266/99/151815-17 The sorption behavior in polymer blends was first reported by Cates and White.11–13 They investigated the water sorption characteristics of polyacrylonitrile (PAN)/cellulose, PAN/silk, and PAN/cellulose acetate blends. The sorption of water in PAN/cellulose and PAN/cellulose acetate varied linearly with blend composition, whereas the blend of PAN/silk exhibited a complicated sorption behavior. Hopfenberg et al.14 –17 systematically examined the effects of temperature, penetrant activity, blend composition, and thermal history on the sorption kinetics of n-hexane in polystyrene/poly(2,6-dimethyl 1,4-phenylene oxide). The effect of fillers on the sorption behavior of elastomers is also reported extensively.18 –20 It is observed that the presence of an active filler reduces the extent of equilibrium swelling compared to the corresponding gum sample. Stannett and coworkers attempted to combine the properties of glassy polystyrene and cellulose 1815 1816 VARGHESE, BHAGAWAN, AND THOMAS Table I. Details of Materials Used Materials Nitrile rubber— (Aparene N553 NS) Poly(ethylene-covinyl acetate)— Pilene (1802) Characteristics Source Volatile matter (%) Antioxidant (%) Organic acid (%) Soap (%) Mooney viscosity (ML114 100°C) Bound acrylonitrile (%) Intrinsic viscosity (dl/g) Melt flow index (g/10 min) Density (g/cc) Vicat softening point (°C) Vinyl acetate (%) Intrinsic viscosity (dl/g) acetate by grafting styrene to cellulose acetate in a variety of configurations.21,22 These grafting techniques improved the compaction resistance of cellulose acetate. Although the excellent permselectivity of cellulose acetate was retained, the water sorption and, in turn, permeability to water were reduced. A membrane for the desalination of sea water was successfully prepared from blends of cellulose triacetate and cellulose diacetate by Saltonstall et al.23 These blend membranes have exhibited rejections in excess to 99.9% to aqueous feeds containing approximately 3.5% dissolved sodium chloride. Masuhara et al.24 developed a membrane from poly(vinyl pyrrolidone) and polyurethane blend suitable for dialysis. The dialysis rate was found to be approximately twice as high as rates normally achieved with conventional cellophane dialysis membranes. Gregor and coworkers prepared polymer blend membranes from poly(styrene sulfonic acid) and poly(vinylidene fluoride) as ultrafiltration membranes for concentration of biological proteins,25 purification of primary sewage effluents,26 and purification of effluents from pulp and paper mills.27 Gregor et al.28 –30 also reported the synthesis and properties of ion-selective blend membranes prepared from a polyelectrolyte component and an uncharged, second polymeric component. Hollow fiber dialysis membranes from a complicated blend of quaternized acrylonitrile–methyl vinyl pyridine copolymer and an acrylonitrile–vinyl acetate copolymer was reported by Sayler et al.31 Molecular transport of alkanes32 and haloalkanes33 through blends of ethylene–propylene random copolymer and isotactic polypropylene has been reported by Amin- : 0.130 : 1.400 : 0.250 : 0.004 : 40.000 : 34.000 : 1.527 : 2.000 : 0.937 : 59.000 : 18.000 : 0.170 Gujarat Apar Polymers Ltd., Mumbai Polyolefins Industries Ltd., Chennai abhavi et al. The sorption, desorption, resorption, and redesorption characteristics were influenced by the nature of the liquid and the temperature. The blends of nitrile rubber (NBR) and poly(ethylene-co-vinyl acetate) (EVA) combine the excellent oil resistance of NBR and the ozone resistance and mechanical properties of EVA. In our earlier studies,34,35 we have reported the morphology, mechanical properties, viscoelastic behavior, failure mechanism, and reprocessability of NBR/EVA blends. The aim of the present work is to investigate the diffusion and sorption behavior of organic solvents through crosslinked nitrile rubber/poly(ethylene-co-vinyl acetate) (NBR/ EVA) blends. The effects of blend composition, crosslinking systems, filler type, loading, temperature, and nature of penetrants on the diffusion process have been investigated. EXPERIMENTAL Materials NBR (Aparene-N 553 NS), with a bound acrylonitrile content of 34%, was supplied gratis by Gujarat Apar Polymers Ltd., Mumbai. EVA (Pilene1802), with a vinyl acetate content of 18%, was procured from Polyolefins Industries Ltd., Chennai. The basic characteristics of NBR and EVA are given in Table I. The rubber chemicals such as dicumyl peroxide, zinc oxide, stearic acid, mercaptobenzothiazyl disulfide (MBTS), sulfur, and fillers such as high-abrasion furnace black (HAF) and semireinforcing furnace black (SRF) were of commercial grade. Solvents (laboratory grade re- TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1817 Table II. Compounding Recipe for NBR/EVA Blends Ingredients (phr)a Peroxide System (P) Sulfur System (S) Mixed System (M) 10 S 10 C 10 BS 10 BH 20 BH 30 BH Polymer Zinc oxide Stearic acid MBTSb Sulfur DCPc Silica Clay SRF HAF 100 — — — — 4.0 — — — — 100 5.0 1.5 1.5 1.5 — — — — — 100 5.0 1.5 1.5 1.5 4.0 — — — — 100 — — — — 4.0 10.0 — — — 100 — — — — 4.0 — 10.0 — — 100 — — — — 4.0 — — 10.0 — 100 — — — — 4.0 — — — 10.0 100 — — — — 4.0 — — — 20.0 100 — — — — 4.0 — — — 30.0 a Parts per hundred rubber by weight. Mercaptobenzo thiazyl disulfide. c Dicumyl peroxide. b agent) used were cyclohexanone, dichloromethane, chloroform, and carbon tetrachloride. The solvents were dried over anhydrous calcium chloride before use. Blend Preparation The blends of NBR/EVA with different crosslinking systems and blend ratio were prepared on a two-roll mixing mill of friction ratio 1 : 1.4. The compounding recipes of the blends are given in Table II. The different crosslinking systems used, namely, peroxide system (DCP), sulfur system (S), and mixed system (DCP 1 S) are indicated using letters P, S, and M, respectively. Dicumyl peroxide can be used for the crosslinking of both NBR and EVA; hence, in the peroxide-cured system both NBR and EVA phases are crosslinked and interwoven, resulting in the formation of a full interpenetrating network. But sulfur can crosslink only NBR and not EVA due to its saturated backbone structure. So in the sulfur-cured system only one phase, i.e., NBR is crosslinked and results in the formation of a semi-interpenetrating network. A mixed-cure system, containing both peroxide and sulfur, was also selected for an effective curing of both the phases. The mixedcure system also results in the formation of a full interpenetrating network. The compounds containing a mixed-cure system are designated as N0M (pure EVA), N30M (30/70 : NBR/EVA), N50M (50/50 : NBR/EVA), and so forth. The subscript indicates the weight percentage of NBR in the blend. The peroxide-cured 50/50 : NBR/EVA blend (N50P) was selected for studying the effect of fillers. The different fillers used were HAF, SRF, silica, and clay and are designated as BH, BS, S, and C, respectively. The loading is indicated by prefixing numbers, that is, 10 BH indicates a 10 phr HAF loaded system; 20 BH, a 20 phr loaded system; and so on. The compounded blends were compression molded at 160°C for the optimum cure. Circular samples (diameter ' 2 cm) were punched by means of a sharp-edged die from the molded sheets. The thickness of the samples was measured using a micrometer screw gauge. Diffusion Experiments Samples were immersed in the solvent taken in the test bottles. The samples were withdrawn periodically from the solvent; any solvent adhering to the surface was rubbed off. The samples were weighed on a highly sensitive electronic balance and then replaced in the test bottle. This process was continued till equilibrium was reached. To minimize the error due to the evaporation of solvent from the sample, the time for weighing was kept to a minimum of 30 s in all the experiments. For the experiments above room temperature, the samples were kept in a thermostatically controlled air oven. The mol % uptake (Q t ) for the solvent by 100 g of the polymer was plotted against the square root of time and the results were analyzed. When equilibrium was reached, Q t was taken as Q ` , i.e., mol % uptake at infinite time. 1818 VARGHESE, BHAGAWAN, AND THOMAS expected for the dispersed phase. The sorption behavior of N70P, where NBR is the continuous phase, is similar to that of NBR (N100P). Again, the sorption behavior of EVA rich blend (N30P) is Figure 1. Sorption curves of NBR/EVA blends. RESULTS AND DISCUSSION The swelling behavior of NBR/EVA blends in cyclohexanone as a function of blend composition, crosslinking systems, filler type, and filler loading is studied. The effect of blend composition on the sorption behavior of a peroxide-crosslinked system is presented in Figure 1. From Figure 1, it is observed that EVA has the lowest equilibrium uptake. There is an increase in the equilibrium uptake with the increase in NBR content. This can be related to the morphology of the system. The scanning electron micrographs of NBR/EVA blends is given in Figure 2. In N30 and N70, the major component tends to be the continuous phase. The N50 exhibits a cocontinuous morphology. In the case of crosslinked samples, the extraction of the rubber phase was rather difficult; therefore, SEM analysis of the morphology of the system is difficult. The morphology of the crosslinked systems is speculated based on the morphology of uncrosslinked systems and is given in Figure 3. When N30 (Fig. 3a) is crosslinked, a particle size reduction is expected for the dispersed NBR phase. In N50 (Fig. 3b), when sulfur is the curing agent, only NBR is crosslinked and results in the formation of a semi-interpenetrating network. For the peroxide and mixed-cure systems, both phases are crosslinked, resulting in the formation of a full-interpenetrating network. In N70 (Fig. 3c), a particle size reduction is also Figure 2. Scanning electron micrographs showing the morphology of (a) N30, (b) N50, and (c) N70. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1819 Figure 3. Schematic model for the morphology of crosslinked NBR/EVA blends. similar to that of EVA (N0P). The N50P, where both phases are continuous, exhibits an intermediate sorption behavior between those of the pure components. This clearly indicates that one can study the phase continuity from transport studies. But N70P (i.e., 70/30 : NBR/EVA) exhibits a higher equilibrium uptake than N100P. This can be explained on the basis of crosslink density. The crosslink density of the samples was calculated from the tensile measurements using the equation: n5 F 2A 0r pRT~ a 2 1/ a 2! (1) where F is the load; A 0 , cross-sectional area of the sample; r p , density of the polymer; R, gas con- 1820 VARGHESE, BHAGAWAN, AND THOMAS Table III. Crosslink Density (n) and Volume Fraction of Rubber (f) in Swollen Mass of NBR/EVA Blends Samples f n 3 104 (gmol/cc) N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 0.72 0.48 0.38 0.19 0.22 0.39 0.40 0.44 0.44 0.45 0.46 0.48 0.49 3.69 3.02 2.18 1.44 1.68 2.27 2.31 5.54 5.23 5.59 6.44 7.52 8.57 stant; T, the absolute temperature; and a, the extension ratio. The crosslink density values are given in Table III. The higher equilibrium uptake of N70P is due to its lower crosslink density than N100P. The equilibrium uptake is also affected by the crystallinity of the sample. EVA (N0P), which is crystalline, shows the lowest equilibrium uptake. As NBR is added to EVA, the crystallinity is reduced and the equilibrium uptake increases accordingly. Volume fraction of rubber f in the solvent swollen sample was calculated using the equation36: f5 W1 r1 W1 W2 1 r1 r2 Table IV. Dependence of Equilibrium Uptake (Q ` ) on Temperature for NBR/EVA Blends Samples 27°C 40°C 50°C 60°C N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 0.39 1.05 1.61 3.81 3.39 1.54 1.46 1.14 1.19 1.17 1.12 1.01 0.92 0.69 1.56 2.03 3.89 3.40 1.82 1.84 1.42 1.50 1.42 1.45 1.24 1.11 1.59 3.16 4.09 5.60 4.28 2.84 2.80 1.99 2.28 2.16 2.18 1.92 1.77 2.33 5.39 5.32 7.52 5.05 4.23 3.82 3.12 3.59 3.02 3.45 2.60 2.03 bility of the solvent in the polymer. The difference in solubility parameters of the solvent and the polymer ( d s 2 d p ) is plotted against the equilibrium uptake and is given in Figure 4. It is clear from the figure that as ( d s 2 d p ) increases, equilibrium uptake decreases. The higher equilibrium uptake of N70P has been discussed earlier. The equilibrium uptake values of different NBR/EVA blends at various temperatures are given in Table IV. As expected, the equilibrium values increase with temperature. Figure 5 shows the sorption (2) where W 1 the weight of the rubber sample; r1, the density of the rubber; W 2 , the weight of solvent in the swollen sample; and r2, density of the solvent. A high value of f is an indication of high crosslink density. The f values are given in Table III. The f value also supports the higher equilibrium uptake of N70P. In spite of its higher equilibrium uptake value, N70P shows a lower initial rate of uptake than that of N100P. This is due to the difference in solubility parameters (d) of the samples, i.e., d(cyclohexanone) 2 d(N70P) 5 0.36 and d(cyclohexanone) 2 d(N100P) 5 0.12. The greater the difference in solubility parameter, the lesser the solu- Figure 4. d s – d p vs. equilibrium uptake curve of NBR/ EVA– cyclohexanone system. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1821 sample; r p , the density of the polymer; r s , the density of the solvent; and A s , the amount of solvent absorbed. For an unfilled system, f 5 0. Substituting this in eq. (4), we get the expression for the volume fraction of rubber in the solventswollen unfilled sample (V r0 ) V r0 5 Figure 5. Sorption curves of various crosslinked NBR/EVA blends. V r0/V rf 5 1 2 [email protected]/1 2 f# (5) Since eq. (3) has the general form of an equation for a straight line, a plot of V r0 /V rf as a function of f/1 2 f should give a straight line, whose slope (m) will be a direct measure of the reinforcing ability of the filler used. According to the theory developed by Kraus20 for highly reinforcing carbon blacks, negative higher slope values indicate a better reinforcement. A constant C, characteristic of the filler, is also calculated using the equation: C5 curves of N50P with different crosslinking systems. Here the mixed-cure system shows the lowest equilibrium uptake and the peroxide-cure system the highest. The sulfur-cure system takes the intermediate position. The lowest equilibrium uptake of the mixed-cure system is due to its high crosslink density (Table III). The sorption curves of various filled systems (10 phr loading) and unfilled (N50P) are given in Figure 6. The presence of fillers reduced the equilibrium uptake values considerably due to reinforcement. Among the various fillers, the HAF black filled system (10 BH) with the highest crosslink density shows the lowest equilibrium uptake. The equilibrium uptake of all the other filled systems (SRF black, silica, and clay) are comparable. The extent of reinforcement is assessed using Kraus’s equation.20 According to this equation: d r 21 p d r 1 A sr 21 s 21 p m 2 V r0 1 1 1/3 3~1 2 V r0 ! (6) The Kraus plots for various fillers are shown in Figure 7 and the values of slope and C are given in Table V. It was observed that the amount of solvent absorbed ( A s ) decreases as the filler loading increases. This results in an increase in the (3) where V rf is the volume fraction of rubber in the solvent-swollen filled sample and is given by the equation: V rf 5 ~d 2 fw! r 21 p 21 ~d 2 fw! r 21 p 1 A sr s (4) where d is the deswollen weight; f, the volume fraction of the filler; w, the initial weight of the Figure 6. Sorption curves of unfilled and various filled NBR/EVA blends. 1822 VARGHESE, BHAGAWAN, AND THOMAS Figure 7. Plots of V r0 /V rf vs. f/1 2 f for various filled N50P. V rf values (with filler loading) calculated using eq. (4). Since V r0 remains constant, the ratio V r0 / V rf decreases with the filler loading, resulting in a negative slope (Figure 7). It is observed that the negative slope value, which is a direct measure of the reinforcing ability of the fillers, decreases in the order of HAF . SRF . silica . clay. This shows that as far as the extent of reinforcement is concerned, HAF is superior to other fillers; thus, the lower uptake of the HAF-filled system is supported by its reinforcing ability. With filler loading, there is a decrease in equilibrium uptake value (Figure 8). This is due to the increase in reinforcement upon loading. A schematic representation of the unfilled and filled blend before and after swelling is given in Figure 9. During mixing, carbon black forms bound rubber in the blend. Bound rubber represents the amount of polymer insolubilized by the carbon black. The decrease in equilibrium uptake of the Figure 8. Effect of filler loading on the sorption curves. filled system is due to the formation of bound rubber. As the reinforcement increases, the bound rubber content also increases. The effect of tem- Table V. Values of Negative Slope and C for Filled N50P Fillers Negative Slope C HAF SRF Silica Clay 0.72 0.23 0.19 0.17 1.44 0.94 0.90 0.88 Figure 9. Schematic representation of unfilled and filled blends before and after swelling. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1823 Table VI. Values of n and k for NBR/EVA Blends k 3 10 2 (min2n ) n Samples 27°C 40°C 50°C 60°C 27°C 40°C 50°C 60°C N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 0.45 0.43 0.42 0.45 0.51 0.44 0.43 0.53 0.52 0.55 0.54 0.53 0.57 0.50 0.54 0.55 0.54 0.62 0.56 0.57 0.53 0.57 0.56 0.55 0.56 0.57 0.58 0.57 0.61 0.63 0.65 0.62 0.64 0.56 0.54 0.55 0.49 0.52 0.50 0.56 0.65 0.62 0.60 0.59 0.62 0.52 0.65 0.64 0.60 0.62 0.58 0.56 1.8 2.1 2.0 1.2 2.0 1.9 1.8 1.5 1.4 1.3 1.2 1.4 1.4 2.0 1.6 1.4 1.3 1.5 1.4 1.5 1.6 1.4 1.3 1.4 1.3 1.4 1.3 1.0 0.8 0.9 1.3 1.2 0.9 1.5 1.6 1.6 1.8 1.7 1.9 1.5 0.6 0.7 0.9 1.5 1.2 1.6 0.8 0.8 1.0 1.1 1.2 1.5 perature on the sorption curves of N50P is shown in Figure 10. The rate of diffusion and equilibrium uptake increase with increase in temperature. This behavior is attributed to the increase in free volume and segmental mobility at higher temperature. To follow the mechanism of sorption, the values obtained were fitted to the equation37: log~Q t/Q `! 5 log k 1 n log t blend systems. However, a deviation from the Fickian mode of diffusion is observed as the temperature increases. This is due to the increased rate of diffusion of the penetrant molecules at higher temperatures. No systematic trend is observed for the values of k at room temperature as well as at higher temperatures. From the swelling data, the diffusion coefficient D was calculated using the equation38: (7) where Q t is the mol % increase in uptake at time t; Q ` , the mol % increase in uptake at equilibrium; t, the time; k, a constant characteristic of the polymer, which indicates the interaction between polymer and solvent; and n indicates the mechanism of sorption. The values of n and k were determined by linear regression analysis and are given in Table VI. If value of n is 0.5, it means that the rate of diffusion of penetrant molecules is much less than the rate of relaxation of polymer chains. This mode of transport is termed as Fickian. On the other hand, if the value of n is unity, the mode of diffusion is termed as non-Fickian, where the rate of diffusion of penetrant molecules is much faster than polymer relaxation. When the rates of both processes are similar, the values of n will fall between 0.5 and 1, presenting an anomalous behavior. From the table, it is observed that the values of n range from 0.42 to 0.65. For all the systems, the n value is close to 0.5 at room temperature. This suggests the mode of diffusion is close to Fickian for cyclohexanone–NBR/EVA D 5 p ~h u /4Q `! 2 Figure 10. curves. (8) Effect of temperature on the sorption 1824 VARGHESE, BHAGAWAN, AND THOMAS Table VII. Values of Intrinsic Diffusion, Sorption, and Permeation Coefficients for NBR/EVA Blends D* 3 10 7 (cm2 sec21) P 3 10 6 (cm2 sec21) S Samples 27°C 40°C 50°C 60°C 27°C 40°C 50°C 60°C 27°C 40°C 50°C 60°C N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 0.63 1.43 2.11 5.52 17.27 2.04 1.95 4.79 4.86 4.93 4.91 4.49 4.77 4.04 9.04 13.23 34.11 63.69 12.44 14.85 9.94 9.66 9.72 9.96 9.53 9.40 18.64 24.50 42.18 124.82 121.62 45.47 39.11 24.79 21.91 23.83 19.32 18.80 15.87 24.06 66.44 67.15 174.79 118.94 97.88 52.89 48.67 41.38 41.29 62.35 37.11 30.17 0.38 1.03 1.58 3.75 3.32 1.51 1.42 1.11 1.17 1.14 1.09 0.98 0.90 0.67 1.53 1.98 3.81 3.31 1.78 1.87 1.38 1.47 1.39 1.42 1.21 1.09 1.56 3.09 4.00 5.48 4.20 2.78 2.85 1.94 2.23 2.12 2.13 1.87 1.73 2.29 5.28 5.22 7.36 4.94 4.14 3.74 3.06 3.51 2.95 3.38 2.55 1.99 0.02 0.15 0.33 2.07 5.73 0.31 0.28 0.53 0.57 0.56 0.53 0.44 0.43 0.27 1.38 4.62 12.99 21.08 3.02 2.77 1.37 1.42 1.28 1.41 1.15 1.02 2.91 7.57 16.87 68.40 51.08 12.64 11.15 4.81 4.89 5.05 4.11 3.52 2.69 5.51 35.08 35.06 128.64 58.75 40.52 19.78 14.52 14.52 12.18 21.07 9.46 6.00 where u is the slope of the sorption curves before attainment of 50% equilibrium and h is the initial thickness of the sample. The value of D depends on the polymer segmental mobility. Equation (8) holds for systems without appreciable swelling. For considerable swelling, a correction for the swelling of the polymer can be made by incorporating f, the volume fraction of the polymer in the swollen mass, thus giving the intrinsic diffusion coefficient, D*. 39 D* 5 D f 7/3 where M ` is the mass of the solvent taken up at equilibrium swelling and M p is the mass of the polymer sample. The permeability coefficient (P), which implies the net effect of sorption and diffusion, is given by the relation36: P 5 D*S (11) The values of S and P are also given in Table VII. A similar trend as that of D* is observed for S and P values with the change in blend composition, (9) The values of intrinsic diffusion coefficients are given in Table VII. It is observed that the D* value increases with an increase in NBR content in the blend. For the different crosslinking systems, the peroxide-cured system (N50P) exhibits the highest D* value. Among the filled systems, the silica-filled system (10 S) shows a low D* value as the filler loading increases. For all the systems, the D* value increases with an increase in temperature, which indicates the activation of diffusion process at higher temperatures. The permeability of a penetrant in a polymer membrane depends on the diffusivity as well as solubility or sorption of the penetrant in the polymer membrane. Therefore, the sorption coefficient that is related to the equilibrium sorption of the penetrant is calculated using the equation40: S5 M` Mp (10) Figure 11. Variation of S with the weight percentage of NBR. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1825 P d 1 2P m 2 2 f d~P m 2 P d! P d 1 2P m 1 f d~P m 2 P d! (14) P# c 5 P m where the subscripts d and m correspond to dispersed phase and matrix, respectively. Robeson extended42 Maxwell’s analysis to include the continuous and discontinuous characteristic of both phases at intermediate compositions and expressed the equations, F P# c 5 x aP# 1 P# 2 1 2P# 1 2 2 f 2~P# 1 2 P# 2! P# 2 1 2P# 1 1 f 2~P# 1 2 P# 2! F 1 x bP# 2 Figure 12. Variation of D* and P with the weight percentage of NBR. G P# 1 1 2P# 2 2 2 f 1~P# 2 2 P# 1! P# 1 1 2P 2 1 f 1~P# 2 2 P# 1! G (15) where x a and x b are fractional contributions to continuous phase so that x a 1 x b 5 1. Figure 13 shows the variation of permeation coefficient with volume fraction of NBR. The experimental values are close to the Maxwell model crosslinking systems, filler type, loading, and temperature. The variation in sorption coefficient (S) with the weight percentage of NBR is given in Figure 11. The value of S increases with NBR content. The effect of weight percentage of NBR on intrinsic diffusion (D*) and permeation (P) coefficients is shown in Figure 12. D* and P increase regularly up to 50 wt % of NBR. Beyond that the properties increase sharply. This can be attributed to the phase inversion in morphology of the system. In the case of heterogeneous blends, the permeability can be interpreted in terms of various theoretical models. Robeson’s two limiting models (i.e., series and parallel models) are generally used in the case of polymer blends. According to the parallel model P c 5 P 1f 1 1 P 2f 2 (12) and by the series model P c 5 P 1P 2/~ f 1P 2/ f 2P 1! (13) where P c , P 1 , and P 2 are the permeation coefficients of blend, component I, and component II, respectively, and f1 and f2 are the volume fractions of components I and II, respectively. Further, for a conducting spherical filler, the overall composite permeation coefficient is given by Maxwell’s equations as41,42 Figure 13. Theoretical modeling for the permeation coefficient of NBR/EVA blends. 1826 VARGHESE, BHAGAWAN, AND THOMAS Table VIII. Activation Energies for Permeation and Diffusion of NBR/EVA Blends Samples E P (kJ mol21) E D (kJ mol21) N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 96.9 95.9 90.7 90.8 50.9 99.8 85.5 59.9 55.2 56.4 62.8 53.6 46.2 144.2 139.4 122.1 108.5 61.5 124.3 110.7 85.4 83.1 80.3 91.5 78.6 67.7 up to fNBR 5 0.6; beyond that, it is close to the Robeson model. The temperature dependence of transport coefficients (D*, S, and P) can be used to calculate the energy of activation for the processes of diffusion and permeation from the Arrhenius relationship40: X 5 X 0exp~2E x/RT! (16) where X is D*, S, or P; X 0 represents D *0 , S 0 , or P 0 , which are constants; E x , the activation energy; R, the universal gas constant; and T, the absolute temperature. The values of activation Table IX. Thermodynamic Parameters Samples DH (kJ mol21) DS (Jmol21 k21) N0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 47.2 42.4 32.2 17.8 10.5 26.1 25.1 25.3 25.1 24.5 28.5 24.7 21.5 110.6 102.4 72.3 45.6 6.5 51.1 47.9 46.2 55.8 44.1 56.8 43.3 32.1 energy of permeation (E p ) and the activation energy of diffusion (E D ) are given in Table VIII. Pure EVA (N0P) exhibits the highest activation energy for both permeation and diffusion. This is because of the crystalline nature of EVA. The E p and E D decrease as the wt % of NBR increases. As the NBR content is increased, the crystallinity of the sample is reduced and hence the blends exhibit a drop in activation energies. This is evident from the X-ray diffraction patterns given in Figure 14. The X-ray diffraction patterns were separated into two parts, crystalline and amorphous, by taking nitrile rubber as fully amorphous. The areas under the crystalline and amorphous portions were measured in arbitrary units, and the degree of crystallinity X c of the samples was calculated using the relation: Table X. Comparison of Network Structure Figure 14. XRD patterns of NBR/EVA blends. Sample M c (chem.) M c (affine) M c (phantom) N 0P N30P N50P N70P N100P N50S N50M 10S 10C 10BS 10BH 20BH 30BH 296 960 1761 8324 5295 1658 1536 1214 1243 1169 1098 998 985 288 935 1715 8101 5153 1557 1411 1116 1142 1073 1008 867 813 96 311 572 2700 1717 579 470 371 381 358 336 289 271 TRANSPORT IN CROSSLINKED NBR/EVA BLENDS 1827 Figure 16. Sorption behavior of NBR/EVA blends in dichloromethane. The enthalpy and entropy of sorption have been calculated using the van’t Hoff relation38 Figure 15. Comparison of theoretical and experimental sorption curves. Xc 5 Ic Ic 1 Ia (17) where I c and I a represent the integrated intensities corresponding to the crystalline and amorphous phases respectively, i.e., the areas under the respective curves. The degree of crystallinity (X c ) of N0P, N30P, N50P, and N70P is 35, 23, 20, and 8%, respectively. Usually the activation energies for permeation and diffusion increase with loading of filler. But in the case of N50P, as the carbon black loading is increased from 10 BH to 30 BH, it is seen that there is a decrease in E P and E D . This is due to the presence of polar groups on the surface of carbon black, which enables a high interaction with cyclohexanone, a polar solvent. As the loading is increased, the number of filler particles per unit volume increases, thereby increasing the sites of interaction. However, the equilibrium uptake exhibits the normal trend, that is, it decreases with filler loading as observed earlier. ln K s 5 DS DH 2 R RT (18) The values obtained by the linear regression method are given in Table IX. It is found that the values of DH and DS are positive for the different NBR/EVA systems. Determination of the Network Structure The investigation of swelling equilibrium can help to elucidate the structure of the polymer network. Flory and Rehner43 relations were developed for a network deforming affinely, i.e., the Table XI. Solubility Parameters (d) of Solvents and Polymers Reference d (cal/cm3)1/2 Dichloromethane Chloroform Carbon tetrachloride N0 (pure EVA) N50 (50/50 : NBR/EVA) N100 (pure NBR) 9.7 9.3 8.6 8.99 9.38 9.78 1828 VARGHESE, BHAGAWAN, AND THOMAS Figure 17. Sorption behavior of NBR/EVA blends in chloroform. components of each chain vector transform linearly with macroscopic deformation and the junction points are assumed to be embedded in the network without fluctuations. Then the molecular weight between crosslinks (M c ) for the affine Figure 18. Sorption behavior of NBR/EVA blends in carbon tetrachloride. Figure 19. d s – d p vs. equilibrium uptake curve for NBR/EVA– dichloromethane system. limit of the model [M c (aff)] was calculated by the formula,44 S D m 1/3 n n 2m M c~aff! 5 2 2~ln~1 2 n 2m! 1 n 2m 1 xn 2m ! 2/3 1/3 r V sn 2c n 2m 1 2 (19) Figure 20. d s – d p vs. equilibrium uptake curve for NBR/EVA– chloroform system. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS Table XII. Values of Q ` in Different Solvents Samples Dichloromethane Chloroform Carbon Tetrachloride N0 N50 N100 2.38 5.28 6.77 7.03 7.45 5.87 4.95 2.41 1.08 where V s is the molar volume of the solvent; m and n are called the number of effective chains and junctions; n 2m , the polymer volume fraction at swelling equilibrium; n 2c , the polymer volume fraction during crosslinking; and r, the polymer density. James and Guth45 proposed the phantom network model, where the chains may move freely through one another. According to the theory, the molecular weight between crosslinks for the phantom limit of the model [M c (ph)] was calculated by44 S D 2 2/3 1/3 r V sn 2c n 2m f M c~ph! 5 2 2~ln~1 2 n 2m! 1 n 2m 1 xn 2m ! 12 (20) where f is the junction functionality. Mc(aff) and Mc(ph) were compared with Mc(chem) and the values are given in Table X. It is seen that Mc(chem) values are close to Mc(aff). This suggests that in the highly swollen state, the chains in NBR, EVA, and the blends deform affinely. The experimental diffusion results were compared with theoretical predictions in order to find the deviation from the regular Fickian mode described by the equation46 Mt 8 512 2 M` p 1829 trants. The sorption curves as a function of blend composition are given in Figure 16 –18. In dichloromethane N0P (pure EVA) exhibits the lowest uptake (Figure 16). The rate of diffusion as well as the equilibrium uptake increase with the increase in NBR content. This can be explained on the basis of solubility parameters of the solvent and polymers. The closer the solubility parameters, the greater will be the solubility of the solvent in the polymer. The solubility parameters of the solvents and polymers are given in Table XI. In the case of chloroform (Figure 17) the equilibrium uptake is higher for the blend than that of the pure components. This is because of the closeness in solubility parameters of N50P and chloroform. In carbon tetrachloride, the rate of diffusion as well as the equilibrium uptake increase with the increase in EVA content (Figure 18). The values of Q ` in different solvents are given in Table XII The equilibrium uptake of the blends in dichloromethane, chloroform, and carbon tetrachloride is plotted against the difference in solubility parameters of the solvent and polymer in Figure 19 –21,. The greater the difference, the lesser the equilibrium uptake. The sorption curves of N50P for different penetrants are shown in Figure 22. Here, too, the solubility parameter is the deciding factor for the rate of diffusion and equilibrium uptake. The mechanism of sorption was followed by fitting the values obtained in eq. (7). The values of O ~2n 11 1! expF 2D~2nh1 1! p tG n5` 2 2 2 2 n50 (21) The given equation represents a Fickian mode of diffusion. Figure 15 shows the experimental (at room temperature) and theoretical sorption curves. This is an excellent fit at the early stages of diffusion, indicating Fickian behavior. Effect of Penetrants Dichloromethane, chloroform, and carbon tetrachloride were used to study the effect of pene- Figure 21. d p – d s vs. equilibrium uptake curve for NBR/EVA– carbon tetrachloride system. 1830 VARGHESE, BHAGAWAN, AND THOMAS Figure 22. Sorption curves of N50P in different solvents. Figure 23. Sorption-desorption-resorption-redesorption curves of N50P in carbon tetrachloride. n and k are given in Table XIII. The values of n lie between 0.5 and 1 for all the solvents, indicating a deviation from a Fickian mode of diffusion. In order to understand the stability of the blends, the sorption– desorption–resorption– desorption pattern of N50P in carbon tetrachloride was followed and is presented in Figure 23. The figure reveals that the rate of desorption (desorption and redesorption) is greater than that of sorption (sorption and resorption). In the sorption process, the solvent molecules have to penetrate into the tightly packed network and hence the rate of the sorption process is low. While in the desorption process, the escape of solvent molecules from the relaxed polymer chain takes place more easily. So the rates of the desorption processes are greater than those for sorption processes. Table XIII. Values of n and k in Different Solvents Samples Dichloromethane Chloroform Carbon tetrachloride N0 N50 N100 N0 N50 N100 N0 N50 N100 n k 3 10 2 (min2n ) 0.55 0.62 0.68 0.65 0.66 0.63 0.64 0.57 0.54 4.1 3.1 4.6 1.4 1.8 4.0 0.9 1.4 2.1 CONCLUSIONS The diffusion of organic solvents through crosslinked NBR/EVA blends has been studied. The influence of blend composition, crosslinking systems, filler type, loading, temperature, and penetrants on the diffusion process has been analyzed. At room temperature, the mode of diffusion was found to be Fickian for the cyclohexanone–NBR/EVA blend systems. At higher temperatures a deviation from the Fickian mode of diffusion is observed. The sorption behavior of the blends was related to the morphology of the system. The variations in the equilibrium uptake values were explained on the basis of the blend morphology, volume fraction of polymer in the swollen mass, crosslink density, and crystallinity. The equilibrium uptake of the filled system decreases upon loading due to reinforcement. The extent of reinforcement was assessed using the Kraus equation. The transport coefficients increase with the increase in NBR content. The activation energies for the processes of diffusion and permeation were estimated. TRANSPORT IN CROSSLINKED NBR/EVA BLENDS Thermodynamic parameters were determined using van’t Hoff’s relationship. 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