Correlations between Gas Permeation and Free-Volume Hole Properties of Medical-Grade Polyesters

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Correlations between Gas Permeation and Free-Volume Hole Properties of Medical-Grade Polyesters

Medical Plastics and Biomaterials Magazine
MPB Article Index

Originally published January 1998


The gas permeation or barrier property of polymers is one of the important factors to be considered in the selection of materials for medical devices (e.g., blood-collection tubes) or packaging. Polyesters and copolyesters—in addition to having good chemical resistance, clarity, and biocompatibility—are known to exhibit very low gas permeation compared with most other polymers such as polycarbonate, polystyrene, ABS, polyethylene, and polypropylene.1 As a result, polyesters and copolyesters are often preferred materials for medical uses.2

It is of great interest to understand the correlations between the free-volume hole characteristics and the gas-permeation properties of polymers. The size and shape of the holes available in a polymer control its rate of gas diffusion as well as its permeation properties. The permeability, P, is a simple product of the average diffusivity, D, and the effective solubility, S, of the penetrant in the polymer matrix, such that P = D x S3,4 Until recently, free-volume hole properties have been thought of mainly as theoretical values. However, a technique known as positron annihilation spectroscopy (PAS) has been developed as a novel probe to determine free-volume hole properties directly.5—8 This article reports the results of a systematic PAS study on polyester and copolyester medical materials produced by Eastman Chemical Co. (Kingsport, TN) that investigated the direct correlations between gas permeation and free-volume properties.


Materials. The polymers used in this study were poly(ethylene terephthalate) (PET); copolyesters that were copolymerized by terephthalic acid and a mixture of ethylene glycol and 1,4 cyclohexanedimethanol (CHDM); and poly(ethylene-2,6-naphthalene-dicarboxylate) (PEN). The copolyesters are designated as PEC(x)T, where x represents the mole percentage of CHDM.

Mean Free-Volume Hole Size and Fraction. Positron annihilation lifetime (PAL) methods were used for the polymer analysis. Detailed descriptions of the PAL method can be found in the literature.9—11 All PAL spectra obtained were analyzed via finite-term lifetime analysis employing the PATFIT program.12 Finite-term lifetime analysis is a conventional method that decomposes a PAL spectrum into two to three terms of negative exponential. The longest lifetime (tau.gif3 = 1—3 nanoseconds) is due to orthopositronium (o-Ps) annihilation. In the current PAL method, we employed the results of o-Ps lifetime to obtain the mean free-volume hole radius by the following semiempirical equation 1:13

where tau.gif3 (o-Ps lifetime) and R (hole radius) are expressed in nanoseconds and angstroms, respectively. R 0 is equal to R  + R  where R is the fitted empirical electron-layer thickness (=1.66Å). The hole fraction is empirically determined by equation 2:

where I 3 is the intensity (in %) of o-Ps, and C is determined empirically to be ~0.0018.14


The experimental results of free-volume hole properties derived from PAL—hole radii (R ), hole volume (V f ), and fractional free volume (fv )—are listed in Table I. It can be seen that the free-volume hole radii, volume, and fractional free volume are linearly increased with increasing amounts of CHDM for the copolyesters shown in Figure 1, and that all the free-volume hole sizes and volumes for PEN are much smaller than the values for PET and the PEC(x)T copolyesters. It is worthwhile to mention that there is a lack of correlation between the observed free-volume hole fraction and the specific volume as obtained by a macroscopic density measurement. This emphasizes the importance of probing free-volume hole properties at the molecular level in order to understand the gas permeation properties of polymers.


3 (ns)





O2a Permeability

CO2b Permeability


1.67 ±0.01

21.9 ±0.3

2.53 ±0.02

67.8 ±1.0

2.66 ±0.04




1.75 ±0.01

21.3 ±0.3

2.61 ±0.02

74.5 ±1.0

2.84 ±0.04




1.78 ±0.01

19.9 ±0.2

2.64 ±0.01

76.8 ±0.8

2.75 ±0.06




1.82 ±0.01

23.7 ±0.2

2.68 ±0.01

80.6 ±1.0

3.44 ±0.04




1.87 ±0.01

24.5 ±0.2

2.72 ±0.01

84.3 ±1.0

3.73 ±0.04


2.10 ±0.01

32.7 ±0.2

2.94 ±0.02

105.9 ±3.2

6.23 ±0.07


aUnit of cm3 (STP)-mil/100 in.2-day-atm at 23°C and 75% RH.

Table I. Results of positron annihilation lifetime (PAL) spectroscopy showing free-volume hole and permeability properties of PEN, PET, PEC(x )T, and PC. 15,16

Figure 1. Mean free-volume size (circles) and fraction (triangles) of PEC(x)T as a function of CHDM composition.

Figure 2. Mean free-volume size versus oxygen permeability for all polyesters.

The free-volume sizes and gas-permeation data for all the polyesters as well as for bisphenol-A polycarbonate are listed in Table I. The relationship between oxygen permeability and mean free-volume hole size is plotted in Figure 2. As expected, all free-volume sizes and fractions have a direct correlation with the gas (O2 and CO2) permeabilities in all the polyesters; in other words, the larger the free-volume hole size and fraction in a polymer, the greater the gas permeation. The correlation between P and V f can be described by the following empirical equation 3:

where k 1 and k 2 are the fitting parameters, which may depend on the type of polymer and penetrant and on their solubility parameters and interactions. Figure 2 was fitted with equation 3, and k 1 = 2•10—5, k 2 = 0.175 were obtained.

As shown in Table I, polycarbonate has much bigger free-volume hole radii, volume, and fraction than do any of the polyesters.10 Therefore, polycarbonate has much higher gas permeation and offers very poor barrier properties compared with the polyesters.


Direct correlations have been observed in several polyesters between free-volume hole properties obtained by PAS and gas-permeation properties. Such free-volume hole information can be helpful in selecting the appropriate polymeric material for medical applications that specify gas-permeation and barrier properties. In the future, performing parallel experiments with PAS and gas-permeation procedures will doubtless lead to further insights into the detailed mechanisms and dynamics of gas or solvent separation.


1. Lee WM, Polymer Eng Sci, 20(1):65, 1980.

2. Stocksiefen H, Heijne B, and Minnick LA, Med Plast,  9:14.1—14.8, 1995.

3. Koros WJ, Coleman MR, and Walker DRB, Ann Rev Mater Sci, 22:47, 1992; and Koros WJ, Fleming GK, Jordon SM, et al., Prog Polym Sci, 13:339, 1988.

4. Hellums MW, Koros WJ, Paul DR, et al., AIChE Symp Ser, 85:6, 1989; J Membr Sci, 46:93, 1989.

5. Jean YC, Microchem J, 42:72, 1990.

6. Kluin J-E, Yu Z, Vleeshouwers S, et al., Macromol, 26:1853, 1993.

7. Zipper MD, Simon GP, Cherry AP, et al., J Polym Sci B: Polym Phy, 32:1237, 1992.

8. Xie L, Gidley DW, Hristov HA, et al., J Polym Sci B: Polym Phys, 33:77, 1995.

9. Jean YC, in Positron Spectroscopy of Solids, Dupasquier A, and Mills AP, Jr (eds), Amsterdam, IOS, p 563, 1995.

10. Jean YC, Yuan J-P, Liu J, et al., J Polym Sci B: Polym Phys,  33:2365, 1995.

11. Jean YC, Deng Q, and Nguyen TT, Macromol, 28:840, 1995.

12. The PATFIT program (1989 version) was purchased from the Riso National Laboratory, Denmark.

13. Nakanishi H, Wang SJ, and Jean YC, in Positron Annihilation Studies of Fluids, Sharma SC (ed), Singapore, World Scientific Publisher, p 292, 1988.

14. Wang YY, Nakanishi H, Jean YC, et al., J Polym Sci B: Polym Phys, 28:1431, 1990.

15. Salame MJ, J Plast Film Sheeting, 2:321, 1986.

16. Hoffman D, Weinhold S, and Stewart M, private communication, Eastman Chemical Co.

Hsinjin E. Yang, PhD, is a research associate at Eastman Chemical Co. (Kingsport, TN), where he is involved in polymer research and development for biomedical applications. He also specializes in polymer blends and imaging materials.

Y. C. Jean, PhD, is professor of chemistry and physics and chairman of the chemistry department at the University of Missouri (Kansas City). His major research interest is the characterization of material properties by positron annihilation spectroscopy.

Copyright ©1998 Medical Plastics and Biomaterials

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