Through EVA Membranes

Transcription

1 Through EVA Membranes Chapter 4 Sorption and Diffusion of Aliphatic Hydrocarbons Summary The sorption and diffusion of n-alkanes viz. pentane, hexane and heptane through EVA membranes have been studied at 30, 40, 50 and 60 o C with special reference to the effects of crosslinking and penetrant nature. Among the crosslinked samples, the system with maximum crosslink density exhibited the lowest solvent uptake. The differences in the transport behaviour of the samples have been discussed in terms of the molecular weight between crosslinks, M c. The M c values were found to decrease with increase in the amount of dicumyl peroxide used for crosslinking. Heptane exhibited higher interaction with samples than n- pentane and n-hexane. The polymer-solvent interaction parameter has also been deduced from diffusion experiments. The content of this chapter has been accepted in the Journal of Polymer Science Part B : Polymer Physics and an extension of this work is communicated to Packaging Science and Technology.

2 136 Chapter Introduction The dimensional stability and integrity of polymeric materials in an aggressive liquid environment are highly essential for their successful technological and engineering applications [1-3]. The transport characteristics of aliphatic hydrocarbons have been studied by several researchers. Neway et al. [4] examined the sorption and desorption of n-hexane through heterogeneous poly (ethylene-co-octene) (PEO) with hexyl branch contents between 0.8 and 3.9 mol% and crystallinities between 30 and 60%. The dependence of the fractional free volume of the penetrable phases on the phase composition suggested that mass transport took place from the liquid-like component to the interfacial component and that the penetrant molecules were trapped at the interfacial sites. J. Hao [5] studied the transport properties of sulphonyl containing polyimide membranes with aromatic / aliphatic hydrocarbon mixtures. The sorption amounts of benzene and toluene were 11 and 15 g/100 g dry polymer, and those of aliphatic hydrocarbons were much lower. The diffusion coefficient of pure liquid was in the order of n-hexane > n-octane > benzene > toluene > cyclohexane > iso-octane. The membranes were preferentially permeable to aromatics over aliphatics. Aminabhavi and Munnoli [6] carried out the transport of n-alkanes through bromobutyl rubber membranes and found that diffusivity was dependent on the size of the alkanes, their interaction with the polymer chains and temperature. Swamy et al. [7] investigated the molecular transport of n-

3 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 137 alkanes by calculating sorption, diffusion, and permeation of liquids through diol chain extended polyurethane membranes and showed that transport is dependent on the nature and size of interacting n-alkane molecules as well as on the morphology of the chain-extended polyurethanes. Kwan et al. [8] investigated the diffusion behaviour of n-alkanes through a polyamide-type polymeric matrix and found that diffusion follows a Fickian mode and proceeds via a Henry s law type mechanism. Kariduraganavar [9] examined the molecular transport of n-alkanes through poly (tetraflouroethylene-co- propylene) elastomers in the temperature range of o C. A. Sujith and Unnikrishnan [10] studied the sorption of n-alkanes through crosslinked natural rubber / poly (ethylene-co-vinyl acetate) (NR/EVA) blends and found that solvent transport was influenced by the EVA content in the blends. Our group also examined the interaction of aliphatic hydrocarbons with different polymeric systems [11-13]. This chapter deals with the investigation of the transport behaviour of three aliphatic hydrocarbons, n-pentane, n-hexane and n-heptane through uncrosslinked and DCP crosslinked EVA samples in the temperature range of o C. Special attention is being given to the effect of crosslinks and penetrant interaction. The polymer-solvent interaction parameter and molecular mass between crosslinks have been determined. The phantom and affine models were used to analyse the deformation of the networks during swelling.

4 138 Chapter Results and Discussion Transport analysis Effect of crosslinks on diffusion Figure 4.1 shows the liquid sorption behaviour of uncrosslinked and crosslinked samples at 30 o C. The solvent used was heptane. It is clear from the figure that D 1 system possesses higher equilibrium penetrant uptake than the uncrosslinked system (D 0 ). The crystalline regions of EVA put up stiffer resistance to the penetrant molecules leading to lower solvent uptake. When moderate amounts of DCP were introduced, the crystallinity was reduced due to the formation of C-C crosslinks. When the crystalline fraction of the polymer decreases, there is an increase in the volume of amorphous phase and also the chain lengths that connect the crystalline domains. Hence a higher material volume and flexibility of the network allow maximum uptake of the solvent. The equilibrium mol percentage uptake of the crosslinked samples for all solvents decrease in the order D 1 >D 2 >D 4 >D 6 >D 8. When the amount of DCP was increased, the extent of crosslinking goes up and this prevents the polymer matrix from swelling.

5 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 139 Q t (mol %) D 0 D 1 D 2 D 4 D 6 D Time 1/2 (min) 1/2 Figure 4.1 : Mol % heptane uptake of uncrosslinked and crosslinked EVA samples at 30 0 C This observation is complementary to the results using aromatic solvents. However, the Q values are significantly lower for aliphatic hydrocarbons compared to aromatic hydrocarbons. This can be attributed to the closer solubility parameter values of aromatic hydrocarbons with EVA samples Effect of penetrants Figure 4.2 shows the sorption curves of D 1 system for the three solvents. It is observed that the kinetic diffusion rate follows the order: n-heptane > n-pentane > n-hexane. Among the three aliphatic hydrocarbons, n-heptane shows the highest equilibrium uptake (Q ) values for all crosslinked samples. Figure 4.3 shows the variation of Q with the amount of crosslinker for the three solvents. The transport characteristics through a polymer matrix for a given liquid strongly depend upon the molecular size of the penetrant and its interaction with the matrix. Generally, for a

6 140 Chapter 4 given homologous series of penetrants, molecules of lower size diffuse faster than molecules of higher size through a matrix [14,15]. However, there are also reports, where the polymer-penetrant interaction overcomes the molecular size factor. The polymer-penetrant interactions in such cases can be described in terms of Flory-Huggins interaction parameter [16], as discussed later. Similar observations have been made by several researchers [17,18] Heptane Pentane Hexane Q t (mol %) Time 1/2 (min) 1/2 Figure 4.2 : Mol % uptake of D 1 sample at 30 0 C. 0.6 Q (mol%) Heptane Pentane Hexane Amount of the Crosslinker (phr) Figure 4.3 : Variation of Q with amount of crosslinker

7 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 141 It is noteworthy that the behaviour of n-alkanes through EVA samples is similar, in terms of crosslink density, to that of aromatic hydrocarbons. However, the Q values are significantly lower for aliphatic hydrocarbons compared to aromatic ones, for a given system. Figure 4.4 shows the Q values of differently crosslinked samples for benzene and heptane. For aromatic hydrocarbons, the Q values decrease regularly with increase in molecular mass. But for aliphatic hydrocarbons, there is a deviation in this trend as discussed above Heptane Benzene Q (mol%) Amount of the crosslinker (phr) Figure 4.4 : Variation of Q values for aliphatic and aromatic hydrocarbons Transport coefficients The diffusion coefficient is a kinetic parameter related to the polymer segmental mobility, penetrant nature and to the different crosslinks present in a polymer matrix. The diffusion coefficient present in a polymeric

8 142 Chapter 4 material immersed in an infinite amount of solvent can be calculated using the equation. ( ) π π ( ) (4.1) From this equation it is clear that a plot of Q t vs. t is linear at short time and diffusion coefficient, D can be calculated from the initial slope. Q t / Q = 4 [Dt/πh 2 ] ½ (4.2) The above equation on rearranging, gives the overall diffusion coefficient [19] D = π [hθ/4θ ] 2 (4.3) where, θ is the slope of the initial portion of the plots of Q t vs. t Since significant swelling was observed for the samples during sorption experiments in all solvents, corrections to diffusion coefficients under swollen conditions were essential. This was done by calculating the intrinsic diffusion coefficient D *, from the volume fraction of the samples using the relation [20]. D * = D/φ 7/3 ( 4.4 ) The volume fraction (φ) of the polymer in the fully swollen state is calculated using the equation [21].

9 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 143 w \ ρ w / ρ + w / ρ 1 1 f = (4.5) where, w 1 and ρ 1 are the weight and density of the polymer and w 2 and ρ 2 are the weight and density of the solvent respectively. D * values are given in Table 4.1. Table 4.1 : Values of intrinsic diffusion coefficient at 30 o C Samples D* x 10 7 m 2 s -1 Pentane Hexane Heptane D D D D D D It can be seen that the D* values decrease regularly with increase in crosslinking density in the polymer matrix, in a given solvent. The diffusion of solvent molecules depends on the availability of free volume in the polymer matrix. When the extent of crosslinking goes up, the free volume of the matrix decreases and hence accordingly D* value decreases. The permeation of a penetrant into a polymer depends on the diffusivity as well as on the sorption of the penetrant in the membrane. Hence, sorption coefficient, S which is the maximum saturation sorption value, has been calculated using the equation [22].

10 144 Chapter 4 S= M /M 0 (4.6) where M is the mass of the solvent at equilibrium swelling and M 0 is the mass of the polymer sample. The permeability coefficient can be computed from the following mathematical expression [23] P * = D * x S (4.7) The sorption coefficient is thermodynamic in nature and is related to the equilibrium sorption of the penetrant. The diffusion coefficient characterizes the average ability of the penetrant to move among the polymer segments. The permeability coefficient shows the net effect of sorption and diffusion processes. The values of S and P are given in the Table 4.2. It is found that the sorption coefficient is maximum for D 1 system and minimum for D 8 system. The maximum value for D 1 system is an indication of better accommodation of solvent molecules in the highly flexible polymer networks. The lowest value for D 8 system shows least capability to accommodate the solvent molecules in the less flexible C-C networks. It can also be seen that permeability coefficient value decreases with increase in crosslinks in the matrix. Table 4.2 : Values of sorption constant and permeation coefficient.

11 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes Temperature effects and thermodynamic parameters To examine the influence of temperature on transport process, the sorption experiments were conducted at 40º, 50º and 60ºC, in addition to those at 30ºC. Figure 4.5 illustrates the sorption curves of D 1 at different temperatures. The solvent used was hexane. The equilibrium uptake increases with the increase in temperature. It has been observed that the slope of linear portion of sorption curves increases with temperature indicating that transport process is temperature activated o C 40 o C 50 o C 60 o C Q t (mol %) Time 1/2 (min) 1/2 Figure 4.5 : Temperature dependence of mol % uptake of D 1 sample The computed values of the intrinsic diffusion coefficient (D * ), sorption coefficient(s) and permeability coefficient (P * ) at high temperatures are given in Table 4.3. The increase of D* with temperature invariably points out the activation of the diffusion process at higher temperatures.

12 146 Chapter 4 Table 4.3 : Values of intrinsic diffusion coefficient, sorption coefficient and permeability coefficient at higher temperatures. Solvents Temp o C Dx10 7 m 2 s -1 S P x 10 7 m 2 s -1 Hexane Heptane From the consideration of the temperature variation of transport coefficient (P, D and S), the energy of activation for the diffusion and permeation process can be estimated from Arrhenius relationship [23] X = X 0 e -E x /RT (4.8) where X is P, D or S and X 0 denotes P 0, D 0 or S 0 which is a constant. The values of activation energy for diffusion (E D ) and for permeation (E P ) were calculated and given in Table 4.4. Table 4.4 : Activation parameters of diffusion E D kj/mol E P kj/mol H kj/mol Solvent D 1 D 2 D 4 D 6 D 8 Hexane Heptane Hexane Heptane Hexane Heptane

13 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 147 A systematic variation in activation energies was observed. The D 8 system showed the highest activation energy. When the amount of DCP used for crosslinking was increased, more C-C crosslinks were introduced in the matrix. The higher activation energy of D 8 system indicates greater energy requirement for the transport of penetrants and this explains the lower equilibrium uptake of penetrants by these samples. E P is found to be greater than E D ; and from the differences between E P and E D, heat of sorption (ΔH)was estimated and placed in Table 4.4. The H values are positive, showing that sorption mechanism is mainly dominated by Henry s law, in which the molecules have to make room for themselves in the polymer matrix. From the amount of penetrant sorbed by given mass of the polymer the molar equilibrium sorption constant, K s has been computed as [24] K s = No. of mols of the solvent sorbed at equilibrium (4.9) Mass of the polymer From the values of K s, the change in entropy ( S) for the crosslinked EVA samples was calculated using Van t Hoff s equation [25] log K s = S _ H (4.10) R RT

14 148 Chapter 4 The value of S is given in Table 4.5. The standard entropy values are positive for all crosslinked samples. The standard entropy decreases gradually from D 1 to D 8 samples. Table 4.5 : Thermodynamic parameters Solvent Standard entropy S (J/mol) D 1 D 2 D 4 D 6 D 8 Hexane Heptane Interaction parameter The polymer solvent interaction parameter (χ) has been estimated from the equation [25] (dφ / dt) {[φ/ (1- φ) ] + N ln (1- φ) + N φ )} (4.11) χ = 2φ (dφ / dt) φ 2 N (dφ /dt) φ 2 /T where, φ is the volume fraction of the polymer in the solvent swollen sample and N is calculated using the equation N = [φ 2/3 /3 2/3] (4.12) [φ 1/3-2φ /3] The polymer- solvent interaction parameter is a dimensionless parameter, which characterizes the interaction between one polymer segment with the

15 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 149 solvent molecule. The polymer- solvent interaction parameter has been utilized to explain the interaction between the solvents and differently crosslinked EVA samples. A low value of χ indicates stronger interaction with the solvents. The calculated values are placed in Table 4.6. The values of χ decreases in the order D 8 >D 6 >D 4 >D 2 >D 1. These values also support the equilibrium uptake nature of crosslinked samples. All crosslinked samples showed lower χ values in heptane, indicating stronger polymer solvent interaction. This accounts for the higher equilibrium uptake of these samples in heptane (Figure 4.2). Table 4.6 : Values of interaction parameter Solvent D 1 D 2 D 4 D 6 D 8 Hexane Heptane Network analysis The molecular mass between crosslinks was estimated using the Flory- Rehner equation [26]. M c = - ρ p V φ 1/3 (4.13) ln (1- φ) + φ + χφ 2 where P is the density of the polymer, V is the molar volume of the solvent, φ is the volume fraction of the polymer in the fully swollen state and χ is the polymer solvent interaction parameter. The calculated M c values for two

16 150 Chapter 4 solvents are given in Table 4.7. The M c values decrease in the order D 1 >D 2 >D 4 >D 6 >D 8. When the value of M c increases, the spacing between crosslinks increases and hence more solvent molecules can be accommodated easily between the crosslinks. These values also support the maximum uptake of the solvent by D 1 system and minimum uptake by D 8 system. Flory-Rehner [27] relations were developed for a network deforming affinely, i.e., the components of each chain vector transform linearly with macroscopic deformation and the junction points are assumed to be embedded in the network without fluctuations. The molecular weight between crosslinks (M c ) for the affine limit of the model [M c (aff)] was calculated using the formula. M c (aff) = P V φ 2/3 φ 1/3 (1-µ/v φ 1/3 ) (4.14) 2c 2m 2m -[ln (1- φ 2m )+ φ 2m + χφ 2 2m ] where µ and v are the number of effective chains and junctions; φ 2m, the polymer volume fraction at swelling equilibrium; φ 2C, the polymer volume fraction during cross- linking. James and Guth [28] proposed the phantom network model where the chain 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 by

17 Sorption and Diffusion of Aliphatic Hydrocarbons Through EVA Membranes 151 M c (ph) = (1-2/x) P V φ 2/3 φ 1/3 (4.15) 2c 2m 2 [ln (1- φ 2m )+ φ 2m + χφ 2m ] where x is the junction functionality. The values are given in Table 4.7. It is seen that M c (chem) values are close to M c (aff). This suggests that in the highly swollen state of D 1, D 2, D 4, D 6 and D 8, the network deforms affinely. Table 4.7: Values of molecular weight between the cross links: M c (g/mol) M c Solvent D 1 D 2 D 4 D 6 D 8 M c (chem.) M c (aff.) M c (ph.) Hexane Heptane Hexane Heptane Hexane Heptane Conclusion The diffusion and transport through poly (ethylene-co-vinyl) acetate membranes have been studied using n-pentane, n-hexane and n-heptane as probe molecules in the temperature range of o C. The influence of crosslinking and nature of penetrants on the transport characteristics of EVA membranes were analysed. The crosslinked system with minimum

18 152 Chapter 4 dicumyl peroxide content (D 1 ) showed a higher solvent uptake. n-heptane has been found to show comparatively higher interaction with the samples than the other solvents. The values of polymer-solvent interaction parameter complement the above behaviour. Determination of network structure was done by calculating the molar mass between crosslinks (M c ). M c values were found to decrease with increase in dicumyl peroxide content. The phantom and affine models were used to analyse the deformations of the network during swelling. It was found that the affine model agrees well with the experiment.

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