Permeability of N2, Ar, He, O2 and CO2 through biaxially oriented polyester films — dependence on free volume
Introduction
Drawing or stretching of an amorphous polymer film is known to lead to reorientation and closer chain packing, and restriction of chain mobility [1]. Since sorption and diffusion may be assumed to occur in the amorphous regions, these processes can be altered due to changes in the spatial distribution of the amorphous phase during drawing. At present there are simple models which describe the gas permeability in biaxially oriented semi-crystalline polymers such as poly(ethylene terephthalate) (PET). Early works by Michaels and Brixler [2] revealed that sorption and diffusion take place exclusively through the amorphous phase. It is accepted that the stretching process can break up the initial structure of the polymer and transform it into a new structure [3], [4], [5], [6]. Any areas of crystallinity — resulting from the stretching process — either lengthen the diffusion pathway or reduce the amorphous chain mobility. Other mechanisms proposed are associated with lengthening of crystallites or tautening of tie molecules in the structure. All these changes will increase the tortuousity of the pathway for a permeant molecule.
When polymers such as PET are stretched, substantial improvements in gas barrier properties are obtained due to changes in shape, extent and perfection of the non-permeable crystalline regions as well as a result of the ordering effects imparted in the amorphous regions. During the orientation process the chains become aligned in the direction of the applied stress, whilst the aromatic rings and crystal planes are thought to become parallel with the film surface [3], [4], [5]. Stretching in a second direction then redistributes the structure toward the new direction of stress, and a balanced structure with the aromatic rings and crystal planes almost parallel to the two orthogonal stretch directions is obtained. Obviously, this will be a function of the fabrication variables used. The chain alignment increases the tautness or rigidity, and decreases the mobility within the remaining amorphous regions of the polymer [6]. Indeed, uniaxial orientation in PET has been found to decrease the diffusion rate of CO2 through a combination of an increased tautness of the chains and a decrease in the mobility of the oriented segments, coupled with an increase in the tortuousity of the diffusion pathway [7]. Biaxial orientation causes a further decrease by constraining the amorphous chain segments, which bridge between the more ordered regions. One would expect that increasing the orientation would improve the barrier properties; but this need not be the case if fibrillation occurs.
Poly(ethylene naphthalate) (PEN), is a semi-crystalline polymer akin to PET. Its unique properties lie in its higher melt viscosity and polymorphism [8]. With PEN, uniaxial stretching produces a highly localised alignment of naphthalene planes parallel to the surface of the film [9], [10], [11]. Biaxially oriented PEN shows bimodal orientation of the chain axes in the draw directions [9]. The net effect of the stretching process is to constrain the surrounding amorphous regions and/or lengthen the diffusion pathway. Necking is a common problem when orienting (uniaxial or biaxial) PEN films and high draw areas have to be employed to produce films of uniform thickness. Therefore, it has been found necessary in practice to incorporate a second component in the polymer, such as poly(ether imide), that will disrupt the co-operative alignment of naphthalene groups parallel to the surface [9], [10]. For the PETN copolymer systems studied in this paper it may be envisaged that at certain compositions the effect of the co-monomer is to disrupt the alignment of aromatic planes.
The microstructures of PET and PEN are relatively well defined and two distinctive conformers exist in completely amorphous samples: gauche and trans ethylene glycol moieties. Stretching of the PET or PEN causes an alignment of molecules in the stretch direction, with individual segments becoming extended (gauche to trans) [12]. This is generally accompanied by an increase in crystallinity, an increase in rigidity of the intervening amorphous phase and a decrease in gas permeability. Upon stretching, one would perhaps expect to see a reduction in the free volume due to closer chain packing and restricted mobility in the amorphous regions [1].
The model commonly used to describe the permeation process of a gas through a polymer film is the solution-diffusion model [7], [13]. This model assumes that the permeation of a gas through a polymer film occurs in three stages; first, sorption of the gas into the polymer; second, diffusion of the gas through the bulk polymer; and third, desorption from the opposite face of the film. Permeability, P, can thus be defined as a combination of the diffusivity, D, of the gas dissolved in the polymer, and the gas solubility, K:At a molecular level it is important to understand the effect that polymer chain packing has on the free volume and free volume distribution, since physical, mechanical and transport properties are sensitive to the amount of free volume available [14].
The molecular free volume is defined as the difference between the total volume and the volume occupied by the polymer molecules. Free volume theories assume that both the mobility of a polymer segment and movement of a diffusing species are determined by the amount of free volume in the system. The diffusing molecule can only move from one place to another when the local free volume exceeds a critical value [7], [13].
Light and Seymour [15] looked at the gas transport properties of copolyesters based on PET and poly(1,4-cyclohexamethylene terephthalate) and concluded that modifications which restricted local molecular motions in the β-relaxation region in turn decreased the permeability to oxygen and carbon dioxide. Similar explanations have been proposed by Weinkauf and Paul [16] for thermotropic liquid-crystalline copolyesters, and by Kim et al. [17] in a study encompassing gas transport properties and dynamic mechanical properties of blends and random copolymers of bisphenol-A polycarbonate and tetramethyl-bisphenol-A polycarbonate. The incorporation of naphthalate in the structure of PET will effectively diminish the local chain motions associated with the β-relaxation [18].
Gas diffusion coefficients have been successfully fitted to the following equation predicted by the free volume theory [13], [19], [20]:where A and B are constants for a given gas. A is related to the size and shape of the permeant and B is related to the minimum hole size of the polymer matrix required for a diffusional jump. A drawback of this free volume approach is that the permeant is assumed to be approximately spherical and its interactions with the matrix purely van der Waals.
There have been numerous studies of the possible correlation between positron annihilation and gas transport [19], [21], [22], [23], [24], [25], [26], [27]. In polymers, PALS gives rise to a long-lived component, which is a consequence of ortho-positronium (o-Ps) annihilation in amorphous regions. The o-Ps species localises itself in free volume cavities of radius 0.2–0.6 nm, a range which correlates to the non-bonded interatomic distances in polymers, and the molecular radii of diffusing substances [26]. Analysis of the PALS data is usually carried out in terms of three lifetime components in polymers: τ1 which is attributed to para-positronium (p-Ps) annihilation; τ2 which is attributed to free positron and positron-molecular species annihilation; and τ3 which is attributed to o-Ps annihilation. In molecular systems the o-Ps localised in a cavity annihilates through an exchange process with an electron of opposite spin from molecules forming the cavity wall. Each lifetime has a corresponding intensity (I) relating to the number of annihilations occurring at a particular lifetime. The long lifetime component is the important quantity for polymers (τ3, I3). The free volume cavity size is related to τ3. It follows that PALS can provide valuable information on both mean size and relative number of free volume cavities probed by o-Ps.
The average free volume size (VF) for spherical cavities can be calculated [28], [29], [30]:where the cavity radius, R is calculated from the o-Ps lifetime results:where, ΔR represents an electron layer thickness and is estimated as 0.166 nm by fitting τ3 to known vacancy sizes of molecular crystals. Eq. (4) can be used to calculate R from experimentally measured values of τ3.
Furthermore, the fractional free volume, f, can be found from the empirical equation:where, VF is in nm3, I3 in %, and C is an arbitrarily chosen scaling factor for a spherical cavity and is typically assigned [26] a value of 1.5.
Successful correlations of gas diffusivity and permeability with free volume measured using PALS have been obtained for polyimides [19], PEEK [21], [24], epoxies [22], [23] and polycarbonates [25], [27]. Hill et al. [26] studied the effect of copolymer composition on free volume and related the results to gas permeability in PET/PCT copolyesters. It was found that increasing the concentration of PCT in the polyester copolymer series increased the gas permeability and free volume. The PALS results were subjected to the , to calculate VF and f. These results were found to follow the Cohen–Turnbull theory [31] which is defined below:where, C and γ are constants, v∗ the critical free volume cavity size necessary for diffusive displacements. The best fit to the Cohen–Turnbull theory was provided by τ33I3. The study showed the usefulness of PALS for relating free volume and transport properties. Similarly, Tanaka et al. [19] found a clear correlation between log D and VF calculated from Eq. (3).
In this paper we report gas transport measurements for a series of biaxially oriented PET, PEN and PETN copolymers. The effects of orientation on the gas transport parameters are discussed with reference to crystallinity, chain orientation and free volume. The role of segmental mobility will be discussed in a subsequent paper [32].
Section snippets
Materials
Cast amorphous sheets approximately 230 μm thick-provided by ICI Polyester (Table 1), were cut into 6 cm squares and stretched on a T. M. Long Stretcher at the Wilton Research Centre. Operation of the film stretcher is based on the movement of two bars at right angles to each other using hydraulically driven rods [33]. Samples were drawn simultaneously in the machine direction (MD) and transverse direction (TD) above Tg using a draw rate of 425% s−1. Two draw areas were obtained for each film as
Differential scanning calorimetry and density measurements
The DSC and density results on the oriented films are presented in Table 3. The density measurements provided a measurement of the crystalline content of the films. An increase in density was observed on going from a cast amorphous film to a biaxially oriented film. The apparent degree of crystallinity (Xρ), expressed as a volume fraction was calculated using the following relationship:where, ρ is the density of the semi-crystalline sample, ρc is the density of the perfect polymer
Differential scanning calorimetry and density measurements
The study of gas transport in polymer films requires an understanding of the polymer morphology of the films. Differential scanning calorimetry can be used to determine the transition temperatures and enthalpies of crystallisation and fusion of polymer films. Crystallinity plays an important role in barrier properties and chain organisation can determine the path and extent of diffusion. Crystallinity not only reduces permeability by reducing the free volume of the amorphous phase, but also
Conclusions
The PALS experiments have shown that rather than static theories like free volume being used as the main explanation for differences in gas transport in these PET, PETN and PEN systems, dynamic theories such as those proposed by Light and Seymour [15] may be more appropriate. These polymers exhibit to a greater or lesser extent microcrystalline organisation and, therefore, a percolation element to the diffusion process would be expected. The data presented here indicates that whilst changes in
Acknowledgements
The authors thank ICI Polyester (now Du Pont) and the EPSRC for funding the work. Special thanks to Paul Davis (Du Pont Polyester) for preparing the amorphous PET samples, performing the density measurements and oxygen permeability measurements.
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