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The recent, didactically relevant and experimentally sophisticated article by J.-Y. Lee et al. (1), “Applying Chemical Potential and Partial Pressure Concepts To Understand the Spontaneous Mixing of Helium and Air in a Helium-Inflated Balloon”, shows two nonnegligible drawbacks, insofar as it (i) proposes a model of permeation (designated as “diffusion”) untenable and in contradiction with correct statements present in the same text and consequently (ii) does not consider the material of which the investigated balloon(s) is(are) made. As to the first point, if the gases external and internal to the balloon were in contact only through tiny holes1 (how tiny? if of diameter comparable to molecular sizes,2 they could act as a semipermeable membrane,3 so that not all the chemical potentials would tend to equalize) the driving force for the transport of material would be the total pressure, rather than the partial pressures (or fugacities) related to the chemical potentials of individual substances, as correctly stated a few lines before. A realistic approach to permeation of gases through (nonporous) polymeric films is taken from a time-honored textbook on polymers (2): “A [partial] pressure or concentration difference, or, more accurately, a fugacity difference serves as the driving force for the isothermal diffusion of molecules through polymers. Molecules at the higher fugacity sorb into the solid polymer film and move through the matrix of polymer chains, with subsequent desorption at a lower fugacity from the downstream film face.” Concerning the second point, the permeation of gases through the polymeric films of which the balloons (toy, advertising, meteorological, or gas reservoir bags, or glove bags4) are made is strongly dependent on the nature of the films (single or multiple, in the case of composites), and each layer is characterized by a permeability coefficient P = SD, where S is the solubility of the gas (typically in STP [standard temperature and pressure] mL × atm) in 1 mL of the polymer, and D is the diffusion coefficient (cm2 s–1) within the polymer appearing in Fick’s first law. Frequently P determines the use of the film as a packing or protective means for chemicals, for chemicals handling, for foods or else (3), and in some cases is so selective to make the film to approximate the behavior of a semipermeable membrane. For instance, the permeability for oxygen is around 0.220 mL(STP) cm2 s–1 atm–1 for low density polyethylene and 0.003 mL cm2 s–1 atm–1 for polyethylene terephthalate (4). Notes- Some films are known as porous, that is having tiny (large with respect to, say, van der Waals molecular diameters) holes, but such materials are generally avoided as single films because they are unsuitable for maintaining the balloon contents for a reasonable time at the initial composition. They may be a layer of a composite film, as in foil balloons.
- For instance gas kinetic diameters from viscosity measurements or van der Waals (or effective) diameters from critical parameters: See Hanle, W.; Franck, E. U. In Landolt Börnstein Zahlenwerte und Funktionen, 6th ed.; Springer-Verlag, Berlin 1950, I Band, 1ster Teil, p 325.
- Defined as a rigid, fixed membrane permeable in both directions only to the specified compounds. See also ref 2, p 265.
- For instance, see Aldrich Catalog 2005–2006 pp E229–231, 239.
Literature Cited- Lee, J.-Y.; Yoo, H.-S.; Park, J. S.; Hwang, K.-J.; Kim, J. S. J. Chem. Educ. 2005, 82, 288.
- Stancell, A. F. In Polymer Science and Materials; Tobolsky, A. V.,
Mark, H. F., Eds. Wiley-Interscience: New York 1971; p 259.
- Stancell, A. F. In Polymer Science and Materials; Tobolsky, A. V.,
Mark, H. F., Eds. Wiley-Interscience: New York 1971; p 247.
- Stancell, A. F. In Polymer Science and Materials; Tobolsky, A. V.,
Mark, H. F., Eds. Wiley-Interscience: New York 1971; p 260.
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