Mass transport through PDMS/clay nanocomposite membranes.

Liu, Quan ; De Kee, Daniel

INTRODUCTION

Polymer-clay nanocomposites are hybrid composite materials consisting of a polymer matrix with dispersed (exfoliated) clay nano-particles (Pinnavaia and Beall, 2001). There are two types of nanocomposites: (a) intercalated, in which extended polymer chains are intercalated between the host clay layers resulting in a well-ordered multilayer, and (b) exfoliated (delaminated), in which the clay layers (usually 1 nm thick) are dispersed in a continuous polymer matrix (Pinnavaia and Beall, 2001). Since many important chemical and physical interactions are governed by surface interactions, nano-structured materials can have properties that are substantially different from conventional composite materials (larger dimensional materials) of the same composition. Impressive improvements of mechanical (Lan and Pinnavaia, 1994; Lee and Wang, 1996; Okada et al., 1990), thermal (Okada et al., 1990; Kojima et al., 1993a), flame resistance (Gilman et al., 1997; Less et al., 1997), as well as barrier properties (Okada et al., 1990; Kojima et al., 1993b; Messersmith and Giannelis, 1995) at very low concentrations of the layered silicate have been reported. The improved barrier properties may find applications in protective clothing, gas separation, packaging, etc.

Polymer-clay composites have been produced using a broad range of polymers, such as polystyrene, polypropylene, poly(dimethylsiloxane), poly(ethylene oxide), polyamide, polycaprolactone, poly(L-lactide), liquid crystalline copolyesters, polyimide, epoxy, and poly(methylmetacrylate). The development of nanocomposites has typically involved intercalation of a suitable monomer followed by in situ polymerization. There is also a solution approach, in which the silicate clay and the polymer are intercalated in a solvent, and a melt intercalation approach, in which a molten thermoplastic is blended with silicate clay.

Industrial processes such as painting, solvent degreasing, printing, dry-cleaning, polymer synthesis and fibre spinning from solution involve the use of larger amounts of solvents such as toluene, xylene, dichloroethane, trichloroethane, dichloromethane and acetone, which contribute to the air pollution in the United States (Lahiere et al., 1993; Singh et al., 1998). Highly permeable and vapour selective polymeric membranes can be used to separate vapours from air streams and to recover such solvents from air or nitrogen streams. High permeability leads to low membrane area requirements, which reduces capital costs, while high selectivity results in high purity product streams. Poly(dimethylsiloxane) (PDMS) is used commercially for membrane-based vapour separation applications (Baker et al., 1987). This high free volume polymer is the most permeable rubber known and is among the most permeable polymers (Singh et al., 1998; Freeman and Pinnau, 1997). Here we use a melt intercalation approach to prepare silicate--poly(dimethylsiloxane) (PDMS) nanocomposites to test possible diffusion property changes due to the involvement of clay particles. The synthesis involves intercalation/delamination of the silicate particles in the PDMS matrix followed by cross-linking.

More importantly, we want to study the effect of mechanical deformation on the diffusion through polymer/clay nanocomposite membranes. We have shown earlier that mechanical deformation is an important factor affecting the diffusion process through polymers. We anticipate that it will still be important because the deformation may also lead to changes of orientation and delamination of the layered silicates in the polymer matrix. In this report, the transport properties of dichloromethane (DCM) through (deformed) PDMS (nanocomposite) are reported.

EXPERIMENTAL

Nanocomposite Synthesis

Silanol-terminated poly(dimethylsiloxane) (PDMS, PS342.5, United Chemical Technologies, Inc.) was used as received. The organosilicate is a commercial montmorillonite modified with a ternary ammonium salt (Cloisite[R] 30B, Southern Clay Products) with a cation-exchange capacity of 90 meq/100g. The specific gravity of the organosilicate is 1.98 g/[cm.sup.3], and the d-space is 18.5 [Angstrom]. Tetraethyl orthosilicate (TEOS, Aldrich Chemical) was used as a cross-linking agent, and tin 2-ethylhexanote (Aldrich Chemical) as catalyst.

The concentration of the organosilicate in the nanocomposites ranged from 0-10 wt. %. Montmorillonite was directly dispersed in the PDMS. The mixture was sonicated at room temperature for 60 min. Cross-linking was accomplished by adding TEOS and catalyst to the mixture, followed by sonication for an additional 2 min. The samples were then cast into Teflon moulds and cured at room temperature under vacuum for a minimum of 12 h (Burnside and Giannelis, 1995, 2000; Wang et al., 1998). Table 1 lists the compositions of all nanocomposites tested.

Characterization

In order to identify the montmorillonite gallery changes after intercalation, X-ray diffraction (XRD) data between 0.8[degrees] and 10[degrees] were collected at a rate of 1[degrees]/min on a Siemens D500 with Ni filtered Cu Ka radiation. The generator voltage was 40 kV and the generator current was 100 mA. Pellet samples with smooth surface were tested.

Transmission Electron Microscopy (TEM) (JEOL 2010 apparatus) operated at 200 KV was used to further characterize the samples.

Apparatus for Studying the Permeation Properties

A sketch of the apparatus used to quantify solvent permeation through polymer-clay nanocomposite membranes under uni-or biaxial deformation is shown in Figure 1. The major components of the apparatus are a modified ASTM F-739 permeation cell, a custom-build aluminum frame for stretching the membrane uni-or biaxially, a Shimadzu GC-17A connected to a personal computer for sample analysis.

A one inch diameter modified ASTM F-739 glass cell was used to expose one side of the membrane to a challenging organic liquid. The challenge chamber has a volume of approximately 10 ml and is equipped with a stoppered nozzle, allowing for liquid additions. The downstream (collection) chamber is equipped with inlet and outlet ports for nitrogen carrier gas flow. A Shimadzu GC-17A gas chromatograph (GC) with flame ionization detector (FID) and a 30 metre capillary column coated with Supelco Wax[R] 10 was used to identify the concentration of the permeating organic species

The aluminum apparatus to execute the uni-or biaxial deformations shown in Figures 2a and 2b has four mobile heads, four fixed heads. The movement of the heads was controlled with a screw system that allowed for a maximum elongation of 100% in two perpendicular directions. The degree of membrane deformation was monitored using a ruler attached to the sides of the frame. The lower chamber of the permeation cell was fixed to the centre of the frame, while the upper one was part of the clamping mechanism that allowed for the sealing between the two chambers and the membrane.

The GC operation parameters were optimized in order to analyze a sample within a minute. This fast detection was necessary to determine sudden changes in permeability. GC calibration was performed using 1 [micro]l penetrant sample.

Permeation Experimental Procedure

For tests under deformation, the membrane was clamped between the mobile heads of the stretching apparatus and elongated to the desired length. After the membrane was deformed, the upper and lower chambers of the permeation cell were aligned into place using a Teflon ring and the membrane itself as a seal. A liquid organic solvent was introduced into the upper (challenging) chamber of the permeation cell. The start (zero time) for a permeation experiment is the time at which the organic solvent makes contact with the membrane. The concentration of the permeant was analyzed using the GC and saved in the personal computer. Tests were performed at 298 [+ or -] 1 K.

[FIGURE 1 OMITTED]

The dry and wet (DCM soaked) thicknesses of membranes were measured using a digital micrometer. The wet membranes were soaked in the organic solvent for about 12 h and were surface-dried using Kimwipes before being measured at several locations. The dry and wet (DCM soaked) thicknesses of elongated membranes were also measured using a digital micrometer. In the case of a wet membrane, the lower chamber of the permeation cell was replaced by a flat plate with a circular cut out for the insertion of the micrometer. The upper chamber of the permeation cell was placed in contact with a stretched membrane and filled with acetone. After 2 h, the chamber was removed from the stretching apparatus and the membrane thickness was measured at several locations.

[FIGURE 2 OMITTED]

RESULTS AND DISCUSSION

Characterization Results:

Figure 3 shows a series of XRD patterns of PDMS nanocomposite samples containing various silicate clay loadings. The XRD pattern of the Cloisite[R] 30B montmorillonite clay contained a strong peak at 2[theta]= 4.76[degrees]. The interlayer distance (d-space) of the montmorillonite was determined to be 18.56 [Angstrom], confirming Southern Clay's information. No strong peaks were observed for polymer-clay nanocomposites, indicating that the gallery spacings of the montmorillonite have been changed (increased) due to intercalation or exfoliation

Figure 4 shows the microstructure of PDMS with 5 wt.% montmorillonite. Layered structures of the clay can be observed. The structure of the nanocomposites was, in combination with XRD results, determined to be an intercalated structure, rather than an exfoliated structure.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

DCM/PDMS-Clay Nanocomposite Permeation

PDMS-clay nanocomposite membranes with five different concentrations of montmorillonite clay were used in the permeation experiments. The following notations are used to represent each category. PDMS00 refers to pure PDMS; PDMS01 is PDMS with 1 wt.% montmorillonite, etc. Three different elongations were performed on PDMS00 and four on PDMS01. Five different elongations were performed on the other samples.

Effect of Clay Concentration

Well-dispersed crystalline nano-clays could decrease the diffusion process by increasing the diffusion path. Figure 5 shows the effect of clay concentration on the diffusion of dichloromethane (DCM) through a PDMS (nanocomposite) membrane with zero extension. There are experimental difficulties associated with producing constant thickness membranes. Therefore, the reported flux is a thickness-modified flux calculated as the experimental flux times the thickness of the membrane.

The very small breakthrough time suggests that DCM easily diffuses through the PDMS membrane, even with a relatively high concentration of clay particles present in the matrix. The time for the systems to reach steady-state is also small, indicative of large permeabilities. One observes that the time to reach steady-state differs, especially for PDMS10, which had the smallest initial thickness. Recall that the diffusion characteristic time is defined as [L.sup.2]/D.

[FIGURE 5 OMITTED]

The thickness-modified steady-state permeation rate decreases with increasing clay concentration. Table 2 lists the thickness-modified steady-state permeation rates for deformed membranes. These were calculated as the experimental permeation flux times the original thickness of the membrane. A consistent decrease in steady-state permeation with increasing clay concentration is observed with or without external deformation. No significant difference in steady-state permeation rate was observed between PDMS01 and PDMS02 at any deformation.

With no external deformation, the steady-state permeation rate decreased about 27% from pure PDMS to PDMS with 10 wt.% montmorillonite clay; a 5% extension resulted in an 18% decrease from PDMS00 to PDMS10; a 10% extension was associated with a 10% decrease; a 15% extension with a 14% decrease from PDMS01 to PDMS10 and a 20% extension yielded an 8% decrease in steady-state permeation rate from PDMS02 to PDMS10. Thus, the effect of concentration of the silicate clays on the diffusion process became less crucial with external deformation. It has been reported that the external deformation could lead to packing of polymer chains, decreasing the free volume of the membrane and increasing the activation energy for diffusion (Williams, 1974). The membrane is then a better barrier, achieving an effect similar to that due to the presence of clay particles. The packed polymer chains interfere (decrease) the effect of the clay particles. The decrease/increase in values as one reads Table 2 horizontally (effect of mechanical deformation) is discussed in the next section.

Effect of Mechanical Deformation

Mechanical deformation can greatly influence the diffusion process (Hinestroza et al., 2001; Hinestroza, 2002; Li et al., 1999; Xiao et al., 1999). Enhanced permeation has been reported in the literature (Li et al., 1999; Xiao et al., 1999). The enhancement is in part due to the decrease of the membrane thickness (Hinestroza et al., 2001; Hinestroza, 2002), but is also associated with a change in diffusion coefficient. The DCM-PDMS system reported here was chosen for its distinctive behaviour.

The effect of mechanical deformation on PDMS01 is shown in Figure 6. A decreased permeation rate was observed at a 5% membrane extension. The mechanical deformation has several effects on the physical properties of the membrane, and we suspect that mainly two can influence the permeation process. One obvious effect involves decreasing the membrane. The other, more implicit effect is associated with a possible change in structure of the membrane, which can alter the diffusion coefficient of solvent transport through the membrane. We assume that this is especially important for rubber-like substances with the presence of long polymer chains. In an unstrained state the polymer chains normally occur in a random coil arrangement, but they are also able to assume extended configurations. When the polymer is subjected to external mechanical forces, a large deformation can be accommodated merely through chains configuration rearrangements. Thus, in the process of extension, the uncoiling of the polymer chains likely results in a chain alignment parallel to the axis of elongation (Flory, 1953). PDMS is a high free volume silicon rubber (Singh et al., 1998; Merkel et al., 2003). When a small extension is applied, the thickness of the membrane decreases. At the same time, the polymer chains align, increasing the activation energy for diffusion, which leads to a decreasing in the diffusion coefficient (Williams, 1974). For nanocomposite membranes (such as PDMS01), a mechanical deformation might also lead to a reorientation of the clay particles in the polymer matrix, which could also contribute to a decrease in diffusion coefficient (Lan and Pinnavaia, 1994; Bharadwaj, 2001; Liu et al., 2003). The decreased permeation rates for PDMS00 and PDMS01 at 5% extension reflects the possibility that the effect of the deformation on the diffusion coefficient plays a dominant role.

[FIGURE 6 OMITTED]

When the mechanical deformation increases, the enhanced diffusion properties are recovered, indicating that the decrease of the membrane thickness gains importance. For nanocomposite membranes (such as PDMS01), an added extension may also lead to larger separation of clay particles, possibly providing a short-cut for solvent mobility, which may increase the diffusion coefficient (Falla et al., 1996). Thus, enhanced permeation is observed at high extensions.

Figure 7 illustrates the effect of mechanical deformation on the diffusion process of DCM through PDMS10. Enhanced permeation is observed for all extensions. It has been reported that the presence of clay particles in the polymer matrix leads to a decrease in the polymer chain mobility (Drozdov et al., 2003). The packing of the polymer chains intercalated between the clay particles becomes less important. Thus, at relatively high clay particle concentration (PDMS05 and PDMS10), the decrease of membrane thickness becomes more important, leading to an enhanced diffusion as quantified in Table 2.

[FIGURE 7 OMITTED]

Diffusion Coefficient

As mentioned previously, the membrane thickness is an important factor that influences the diffusion process. The diffusion coefficient can also be changed as a result of external factors. Three methods are widely used to compute the diffusion coefficient.

The first one is based on Fick's first law. Assuming that the concentration is linearly distributed in the thin membrane, the diffusion coefficient can be calculated as follows:

D = FL / [rho][c.sub.eq] (1)

where L is the membrane thickness, F is the permeation flux, ? is the penetrant density and [c.sub.eq], which can be determined via swelling experiments, is the solvent concentration at equilibrium on the challenging side of the membrane. Samples of known weight are immersed in DCM at room temperature and periodically weighed after blotting to remove excess solvent until no difference is observed between successive weight measurements. It is difficult to measure [c.sub.eq] under stress. Note that [c.sub.eq] may depend on the level of deformation of the membrane. Here, we use the same value of [c.sub.eq] for different deformations. The obtained value [c.sub.eq] (final weight--initial weight)/final weight for PDMS00, PDMS01, PDMS02, PDMS05 and PDMS10 are 0.72, 0.71, 0.70, 0.67, and 0.67, respectively. A high value for [c.sub.eq] indicates a strong interaction between DCM and PDMS and/or a high free-volume polymer matrix. DCM has a solubility parameter of 19.64 [(MPa).sup.0.5], while the solubility parameter of uncross-linked PDMS is 15.3 [(MPa).sup.0.5] (Kuwahara et al., 1968). The Flory-Huggins interaction parameter x is calculated to be relatively large (0.82)(Grulke, 1989):

x = 0.34 + [V.sub.1]/RT [([[delta].sub.1] - [[delta].sub.2]).sup.2] (2)

where [V.sub.1] is the DCM molar volume; R is the gas constant; T is the temperature and [[delta].sub.i] are the solubilities. Thus, "weak" interactions exist between DCM and PDMS. The high solvent concentration may also be due to the high free volume in the polymer matrix. It can be confirmed that only small volume changes (the thickness change is about 15%) occurs for all systems. The diffusion coefficients obtained using Equation (1) are listed in Table 3. This diffusion coefficient can be regarded as a steady-state diffusion coefficient.

For small values of time, it has been shown that (Xiao et al., 1997a, b):

ln (F [t.sup.1/2]) = ln [[2c.sub.eq]([D.sub.0]/[pi] (3)

where D0 is the limiting diffusion coefficient at zero penetrant concentration and F is the permeation flux. A plot of 1n([Ft.sup.1/2]) versus [t.sup.-1] yields a straight line. The linear region is confined to a short time interval immediately following the breakthrough time. Here, the plot was observed to be linear in the region where F/[F.sub.s] <0.8, where [F.sub.s] is steady-state permeation flux. This diffusion coefficient ([D.sub.0]) is the so called zero concentration diffusion coefficient. The values of D0 are given in Table 4.

A third method of calculating the diffusion coefficient uses the following equation:

[D.sub.1/2] = [L.sup.2] / 7.119 [t.sub.1/2] (4)

[D.sub.1/2] is an average diffusion coefficient at time [t.sub.1/2] at which F/[F.sub.s] =0.5. Values of [D.sub.1/2] are listed in Table 5. This diffusion coefficient can be regarded as an average diffusion coefficient (Xiao et al., 1997a, b).

If the diffusion process is Fickian, D=[D.sub.1/2] = [D.sub.0]. For a concentration dependent diffusion coefficient, higher concentration always leads to higher diffusivity (D>[D.sub.1/2] > [D.sub.0]) (Li et al., 1999) because the region behind the diffusion front opens up and allows additional solvent to diffuse into the membrane at a faster rate. Comparing [D.sub.0] and [D.sub.1/2] values for PDMS10 under all deformation conditions (Tables 4 and 5), one notes that [D.sub.1/2] > [D.sub.0], indicative of a concentration dependent diffusion process.

However, for the PDMS00, PDMS01, PDMS02 and PDMS05 systems, the diffusion coefficients for [D.sub.1/2] were lower than those for [D.sub.0], suggesting that at higher solvent concentration, the diffusion coefficient decreased, which cannot be explained by plasticization of the membrane. Possible explanations are:

1. Due to the similar polarity of DCM and PDMS (a high free volume polymer), but weak interaction, DCM may be clustered in the polymer matrix. Dixon-Garrett et al. (2000) observed a similar trend involving poly(1-trimethylsilylpropyne) (PTMSP) polymer, also a high free volume polymer. They attributed this decrease in diffusion coefficient to an initial densification of the polymer as a result of penetrant absorption, reducing the transport of penetrant molecules. That is to say: the absorption process reduces the free volume.

2. The viscoelastic properties of polymeric materials are associated with non-Fickian diffusion. Initially, DCM has a high solubility in and a "high" diffusion coefficient through the PDMS matrix. Following membrane swelling, the polymer chains relax, indicating a negative convective flux (Vrentas et al., 1994). The diffusivity values of all systems were smaller than [D.sub.0] and [D.sub.1/2], indicative of a small diffusion coefficient at steady-state.

The effect of clay concentration on the diffusion coefficient is not consistent (see Tables 3-5), especially for [D.sub.0] and [D.sub.1/2]. For PDMS01, [D.sub.0] and [D.sub.1/2] were larger than for PDMS00. Though D0 and [D.sub.1/2] decreased with higher clay concentration, the values of PDMS02 and PDMS05 were still higher than PDMS00. Only PDMS10 showed lower [D.sub.0] and [D.sub.1/2] values, compared to PDMS00. The value of D, however, showed a decreasing trend with increasing clay concentration.

The effect of mechanical deformation on the diffusion coefficient can also be observed through Tables 3-5. The diffusivity values (D) for DCM through all polymers first decrease (at 5% extension), then increase (at 10%, or 15% extension), to remain constant. The initial decrease may be related to a reorientation of clay particles as well as to polymer chain packing. The decrease for PDMS00 is likely related to an extensive packing of this high free volume polymer, which greatly reduces the diffusion coefficient. For higher clay concentrations (reduced the polymer chain mobility, Drozdov et al., 2003), the packing of the polymer chains became more difficult, resulting in a smaller decrease. Higher extensions may lead to increased space between the nano-particles, which can increase the diffusivity (Falla et al., 1996). As the extension reached a certain degree, the movement of the nano-particles and of the polymer chains was restricted, resulting in a "constant" diffusion coefficient.

The computed [D.sub.0] and [D.sub.1/2] values showed a different dependence on mechanical deformation. For pure polymer and polymers with low clay particle concentration, the initial extension results in a very small increase in diffusion coefficient. When the extension becomes larger, the packing of polymer chains and the reorientation of clay particles affects the diffusion process. The combined effect of clay concentration and elongation on the nanocomposite structure leading to these results is not know as yet and will require further study.

The diffusion coefficient D and the average diffusion coefficient ([D.sub.1/2]) are used to calculate the diffusion characteristic times [tau] = [L.sup.2.sub.0]/D and [[tau].sub.1/2] = [L.sup.2.sub.0]/D1/2. Figure 8 shows the computed normalized flux versus normalized time for the permeation of DCM through PDMS00 at zero extension. Clearly, Fick's laws cannot represent the experimental data. The initial stage of the diffusion can be assumed to be Fickian, and the normalization involving [D.sub.1/2] provides quantitative agreement between Fick's laws and the data. However, as 0.2 < t/[tau]<0.6, strong deviations can be observed. At this stage, the normalization involving D starts to show agreement with the data. Thus, the diffusion process can be characterized by a decreasing diffusivity. This cannot be explained by Fick's laws or by concentration-enhanced diffusion properties.

[FIGURE 8 OMITTED]

As the clay particle concentration increases, the diffusion process of DCM through PDMS nanocomposites becomes more Fickian. The normalized flux versus normalized time for permeation of DCM through PDMS10 is shown in Figure 9. Fick's laws shows good agreement with the normalization based on [D.sub.1/2].

Modelling of Diffusion through Nanocomposite Membrane

We have derived a set of governing equations for diffusion through viscoelastic membranes (Liu and De Kee, 2005). The Figure 8. Normalized flux versus normalized time for the permeation of DCM through PDMS00 at zero extension governing equations for a one-dimensional diffusion process through polymer-clay nanocomposite membranes under small deformation are given by:

[rho] [partial derivative]c/[partial derivative]t = - [partial derivative]F/partial derivative x (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

-[[lambda].sup.m][G.sub.0] (1-c) [((1-c(2-[c.sub.eg]))[m.sub.11]/[k.sub.B]T/K)-1] (7)

[partial derivative][A.sub.11]/[partial derivative]t = [partial derivative]/partial derivative]x (F/[rho](1- c)[A.sub.11])-[[lambda].sup.A.sub.1111] c [[GAMMA].sub.1] (8)

[FIGURE 9 OMITTED]

Equation (5) is the equation for mass conservation. Equation (6) is an extension of Fick's first law. It includes a convective flux due to the relaxation of the viscoelastic polymer (characterized by a conformation tensor m) and another convective flux due to the relaxation of the complex interfaces between clay particles and polymer matrix (characterized by an area tensor A). The quantities [m.sub.11] and [A.sub.11] are the (1,1) components of m and A. Parameters E and [LAMBDA] are two tensors that represent the importance of the polymer and the complex interface relaxation. Again, [E.sub.11] and [LAMBDA]11 are the (1,1) components of tensors E and [LAMBDA]. [[lambda].sup.m] and [[lambda].sup.A.sub.1111] are two non-negative parameters. [G.sub.0] is the modulus of elasticity of the polymer, [k.sub.B] is the Boltzman constant, K is the characteristic elastic constant and T is the temperature. The interaction between the clay particles and the penetrant is characterized by an interaction parameter [[GAMMA].sub.1]. The dimensionless forms of Equations (5) to (8) yield four dimensionless parameters: [product], [De.sub.m], [THETA] and [De.sub.A]. [product] relates the polymer elasticity to the mixing properties of the polymer and the solvent. [De.sub.m] is a Deborah number related to polymer relaxation. [THETA] is a quantity that relates the complex interface to the mixing properties and [De.sub.A] is a Deborah number that associates the interface relaxation to the diffusion. Detailed derivations and some applications of the governing equations have been presented in Liu and De Kee (2005). Extreme values for [De.sub.m] and [De.sub.A], (too small or too large) are indicative of Fickian diffusion. Here we applied Equations (5) to (8) to model the diffusion through PDMS01, as shown in Figure 10. Clearly, there is a deviation from Fick's laws prediction. Parameters leading to a good fit are [product] = -0.4, [D.sub.em] = 0.1, [THETA] = 1 and [De.sub.A] = 500. The value of [D.sub.em] indicates a relatively important role for the polymer relaxation effect, but the large value of [De.sub.A] suggests that the effect of interface relaxation is less important for the diffusion process.

[FIGURE 10 OMITTED]

CONCLUSIONS

Mass transport properties through PDMS (nanocomposite) membranes are presented. An apparatus for studying the permeation of organic solvents through mechanically deformed polymer (nanocomposite) membranes was built. This equipment was used to monitor the permeation of DCM through PDMS (nanocomposite) membranes at several elongations. A number of PDMS (nanocomposite) membranes with different clay particle loading were prepared and characterized (TEM, SEM, XRD) for testing.

The diffusion of DCM through pure PDMS was determined to be non-Fickian. The diffusion process became slower (diffusion coefficient was smaller) with time, in contrast to plasticization, which involves an increase in diffusion coefficient for higher solvent concentrations. This non-Fickian diffusion was explained via the viscoelastic properties of the polymer matrix. The polymer chains relax and introduce a negative convective flux, thus decreasing the permeation flux.

With the introduction of clay particles into the polymer matrix, the diffusion path for the solvent becomes longer, slowing the diffusion process. With increasing concentration of clay particles, the diffusion process became more Fickian-like.

The imposed external deformation has important effects on the diffusion process of DCM through PDMS (nanocomposite) membranes. The extension of the membrane will not only decrease the thickness of the membrane, which will enhance the diffusion process, but also pack the polymer chains (decreasing the free volume), which can decrease the diffusion coefficient. At small deformation, the decrease of free volume resulted in a decrease in permeation flux. At high deformation, the decrease in thickness of the membrane enhanced the diffusion process. However, as the clay particle concentration increased, the effect of external deformation on the free volume change was reduced, resulting in an enhanced diffusion.

ACKNOWLEDGEMENTS

The authors thank Jibao He for assistance with the TEM and SEM studies. DDK also gratefully acknowledges financial support through NASA grants NAG 1002070 and NCC 3-946.

NOMENCLATURES

A area tensor, [A.sub.11] is the (1,1)
 components of A ([m.sup.2]/[m.sup.3])
C solvent concentration (kg/kg)
[c.sub.eq] solvent concentration at equilibrium on the
 challenging side (kg/kg)
D diffusion coefficient ([m.sup.2]
 [s.sup.-1])
[D.sub.0] limiting diffusion coefficient at zero
 penetrant concentration ([m.sup.2]
 [s.sup.-1])
[D.sub.1/2] average diffusion coefficient at time
 [t.sub.1/2] ([m.sup.2] [s.sup.-1])
[De.sub.A] Deborah number that associates the
 interface relaxation to the diffusion
 (dimensionless)
[De.sub.m] Deborah number related to polymer
 relaxation (dimensionless)
F permeation flux (kg [m.sup.-2] [s.sup.-1])
[F.sub.s] steady-state permeation flux (kg [m.sup.-2]
 [s.sup.-1])
[F.sup.*] modified flux (kg [m.sup.-1] [s.sup.-1])
[G.sub.0] modulus of elasticity of the polymer (Pa)
K characteristic elastic constant (Pa)
[k.sub.B] the Boltzman constant (J [K.sup.-1])
L membrane thickness (m)
m conformation tensor ([m.sup.3])
R gas constant (J [mol.sup.-1] [K.sup.-1])
t time (s)
T temperature (K)
[V.sub.1] DCM molar volume ([m.sup.3]/mol)
x position (m)

Greek Symbols

[[GAMMA].sub.1] interaction parameter (J/[m.sup.3])
E tensor ([m.sup.-3])
[THETA] quantity that relates the complex interface
 to the mixing properties (dimensionless)
[product] parameter relating the polymer elasticity
 to the mixing properties of the polymer and
 the solvent(dimensionless)
[[delta].sub.i] solubility for i-th components
 ([(MPa).sup.0.5])
[[lambda].sup.A.sub.1111] non-negative parameter ([m.sup.3]/(s Pa))
[[lambda].sup.m] non-negative parameter ([m.sup.2] /(s J))
[rho] penetrant density (kg/[m.sup.3])
[tau] diffusion characteristic time
 (dimensionless)
[chi] Flory-Huggins interaction parameter
 (dimensionless)
[LAMBDA] tensor (m)

Manuscript received January 17, 2006; revised manuscript received September 5, 2006; accepted for publication September 11, 2006

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Quan Liu and Daniel De Kee *

Department of Chemical and Biomolecular Engineering and Tulane Institute for Macromolecular Engineering and Science (TIMES), Tulane University, New Orleans, LA, 70118 U.S.A.

* Author to whom correspondence may be addressed. E-mail address: ddekee@tulane.edu

Table 1. Compositions of the nanocomposites tested

PDMS Clay Wt.% TEOS Tin(II)
(g) (g) clay ([micro]L) ethylhexanoae
 ([micro]L)
40 0 0 1200 300

39.6 0.4 1 1200 300

39.2 0.8 2 1200 300

38 2 5 1140 300

36 4 10 1080 300

Table 2. Thickness-modified steady-state permeation rate
([micro]g [cm.sup.-2][s.sup.-1] mm) of DCM through PDMS
(nanocomposite) membranes at 298 K under uniaxial elongation

 Elongation (%)

 0 5 10 15 20

PDMS00 34.01 30.94 32.63 N/A N/A

PDMS01 30.47 29.46 32.69 34.44 N/A

PDMS02 30.18 29.66 32.21 33.27 32.92

PDMS05 27.64 28.51 31.5 31.72 31.84

PDMS10 24.94 25.33 29.43 29.67 30.27

N/A = Not Applicable

Table 3. Diffusion coefficient (D x [10.sup.6] [cm.sup.2]
[s.sup.-1] of DCM through PDMS (nanocomposite) membranes under
uniaxial elongation

 Elongation (%)
 0 5 10 15 20

PDMS00 3.565 3.165 3.26 N/A N/A

PDMS01 3.239 3.056 3.313 3.415 N/A

PDMS02 3.254 3.121 3.312 3.343 3.240

PDMS05 3.113 3.134 3.385 3.322 3.273

PDMS10 2.809 2.786 3.163 3.118 3.113

N/A = Not Applicable

Table 4. Diffusion coefficient ([D.sub.0 x [10.sup.6]
[cm.sup.2] [s.sup.-1] of DCM through PDMS (nanocomposite)
membranes under uniaxial elongation

 Elongation (%)

 0 5 10 15 20

PDMS00 5.5 5.49 5.25 N/A N/A

PDMS01 6.39 6.47 6.09 6.01 N/A

PDMS02 6.38 6.40 6.24 5.91 5.69

PDMS05 5.90 5.80 5.62 5.61 5.52

PDMS10 4.59 4.17 4.08 3.92 3.78

N/A = Not Applicable

Table 5. Diffusion coefficient ([D.sub.1/2] x [10.sup.6]
[cm.sup.2] [s.sup.-1] of DCM through PDMS (nanocomposite)
membranes under uniaxial elongation

 Elongation (%)

 0 5 10 15 20

PDMS00 5.08 5.21 4.96 N/A N/A

PDMS01 6.05 6.31 5.69 5.55 N/A

PDMS02 5.68 6.10 5.64 5.39 5.22

PDMS05 5.85 5.58 5.26 5.28 5.08

PDMS10 5.03 4.73 4.38 4.22 4.06

N/A = Not Applicable