Permeability

{{active_language_id_uc}} {{settings.doi}}

5.5.1. Definitions and General Principles

        Permeability is a measure of how easily gases or liquids can pass through a material. A low permeability means that the gases or liquids pass through with difficulty, usually requiring a long period of time and/or high pressures. Hence, the material is said to be a barrier to the passage of gases or liquids and permeability is often called a barrier property. Many plastics applications, especially in packaging, require that the plastic material be a barrier to the passage of gases and liquids. These plastic materials would, therefore, have low permeabilities. 

       The permeability of a plastic material is governed by many of the same properties that determine the susceptibility of the plastic material to solvents. For instance, just as a polymer with many polar groups is sensitive to a polar solvent, that same polymer would be permeable to a polar gas or liquid. Conversely, a nonpolar polymer would be a barrier to polar gases and liquids. Hence, "like is permeable to like." As with solvents, the openness of the plastic material structure is also a factor. If the structure is largely amorphous with few areas of dense packing of the atoms, gas and liquid molecules can move more easily into and through the plastic structure and the material will have a high permeability. Therefore, in two plastic materials with similar polarities, the higher-density, more crystalline material would be the better barrier resin. 

       In comparisons of the openness or permeability of plastic materials an assumption is logically made that the permeating gas or liquid is the same for the materials compared. The nature of the permeating gas or liquid will obviously have an effect, as already mentioned, with respect to the polarity of the permeating material relative to the polarity of the polymer. The size of the gas or liquid molecule is also extremely important. Small molecules can work their way through the polymeric structure much more easily than can large molecules. This size effect is so strong that the permeation rate of a small molecule (helium) can be 10¹⁶ greater than that of a large gaseous molecule (pentane). Size effects can, therefore, outweigh all other permeation effects.

5.5.2. Diffusion Coefficient

        These permeability characteristics of a material (plastic, metal, or ceramic) can be expressed by a quantity called the diffusion coefficient or diffusivity constant, D. Diffusion or diffusivity is the susceptibility of a material to permeation in relation to a particular gas or liquid. For instance, if the plastic material is solvent-sensitive to a particular gas or liquid, the D for that system will be large. If the plastic material has an open structure, D will be larger than for a dense, crystalline plastic, assuming the same diffusing gas. Therefore, a plastic material with a high diffusion coefficient will have high permeability. 

        The environment under which the diffusivity is measured can also affect D. Any condition that will cause the plastic structure to swell will significantly increase D. One critical environmental effect is temperature. Raising the temperature will impart flexibility to the plastic system, which will make it more open and thus allow the gas or liquid to permeate more easily. Therefore, the temperature at which the diffusivity was determined must be specified. Tables of diffusion constants for many plastic materials with various common gases or liquids are available in several plastic materials handbooks. The diffusivity is given for a standard temperature (usually room temperature, 73°F or 23°C). Conversion to another temperature is done using Equation (5.3), which is one form of the Arrhenius equation.

$ D = D_oe^{-(\dfrac{A}{RT})} $

D is the diffusivity at the environmental temperature, D_o is the diffusivity under standard temperature conditions, A is the activation constant and measures the energy required for the gas or liquid to pass through the molecules of the plastic material, R is the gas constant, and T is the absolute temperature (usually measured in Kelvin). A useful rule of thumb is that a temperature increase of approximately 5 K can double the diffusivity. 

        Other environmental effects, such as the presence of a second gas or liquid, can also affect the permeability. For instance, a plasticizer will significantly increase diffusivity because the polymeric structure has been swelled and softened, thus allowing the permeating agent to pass more easily. These combinations of factors are, however, so numerous that diffusivities for all these conditions would be impractical to list. Therefore, for conditions such as these, specific diffusivities would be measured in each case.

5.5.3. Fick's Laws of Diffusion

        The permeability of a particular gas or liquid through a barrier material depends not only on the diffusion coefficient of the barrier material but also upon the difference in concentrations of the diffusing material from point to point within the material and inversely upon the thickness of the material. If a steady-state condition exists, such as when the concentrations on either side of the barrier material are not allowed to change with time, this relationship can be expressed as in Equation (5.4), which is called Fick's first law of diffusion:

where J is the flow of gas or liquid through the material expressed as a flux (flow per unit area), D is the diffusion coefficient of the material, dC is the change in concentration of the gas or liquid from one side of the plastic part to the point of measurement, and dx is the distance from one edge of the material to the point of measurement. The negative sign is introduced because dx is usually chosen to be opposite in sign to the direction of flow. These relationships are illustrated in Figure 5.3. 

        The application of Fick's first law (equilibrium conditions) can be envisioned in the case where a plastic panel serves as a window in a wall separating a vacuum chamber from the rest of a laboratory. We assume that the wall is so thick that no air will pass through it. Air will diffuse through the plastic panel and, because the supply of air on the laboratory side is constant and the vacuum system is running inside the vacuum chamber, steady-state conditions can be assumed to exist. Hence, Fick's first law will apply. The flow (or flux) of gas, J, is found by multiplying the diffusion constant for the plastic, D (which has been adjusted to the proper temperature using Equation (5.3)), by the difference in concentrations of air between the room and the vacuum chamber and then dividing by the thickness of the plastic panel. 

        The much more common and interesting case is when the permeability of materials varies with time. This case has been shown to follow a law called Fick's second law of diffusion. This law can be written as given in Equation (5.5):

$ \dfrac{\delta C}{\delta t} = D \dfrac{\delta ^2 C}{\delta x^2} $

5.5.4. Barrier Properties of Plastic Materials

        In practice, most applications require plastic parts with low diffusivity, which are, therefore, barrier plastics. For instance, food packaging would normally try to exclude the permeation of air or water. The permeation of oxygen and of water through various plastic materials is illustrated in Table 5.2, where the dependence of permeation on the properties of the plastic material and the gas or liquid that is permeating through can be seen. The relative humidity (RH) is noted in the conditions because it affects the concentration gradient of water. 

        The differences in permeabilities of various plastics as seen in Table 5.2 can be readily understood from a basic understanding of the natures of the polymers. For instance, ethylene vinyl alcohol has polar groups along the chain and has, therefore, a relatively high permeation rate for water (which is polar) and a low permeation rate for oxygen (which is nonpolar). Other polymers with polar groups along the chain are nitrile barrier resin and nylon, which also have high permeation rates for water. Polyethylene, on the other hand, has no polar groups along the chain and has, therefore, a low permeation rate for water but a much higher permeation rate for nonpolar oxygen than do the polar polymers. Note also that high-density polyethylene has a lower permeation rate than does low-density polyethylene, illustrating the more compact structure (higher crystallinity) of the high-density material. 

Polymer	Permeability of Oxygen at 25°C. 65% RH (cc, mil/100 in2/24h)	Permeability of Water at 40°C, 90% RH (cc, mil/100 in2/24h)
Ethylene vinyl alcohol	0.05-0.18	1.4-5.4
Nitrile-barrier resin	0.80	5.0
High-barrier PVDC	0.15	0.1
Good-barrier PVDC	0.90	0.2
Oriented PET	2.60	1.2
Oriented nylon	2.10	10.2
Low-density polyethylene	420	1.0-1.5
High-density polyethylene	150	0.3-0.4
Polypropylene	150	0.69
Rigid PVC	5-20	0.9-5.1
Polystyrene	350	7-10

Table 5.2 Barrier Properties of Selected Commercially Available Plastics (from Designing with Plastics and Composites by D. V. Rosato and D. P. DiMatta, Van Nostrand Reinhold, 1991, page 280).

        A difficulty arises when a barrier to both polar and nonpolar gases or liquids is desired, because most plastics materials are either one or the other. The packaging industry has solved this problem by coating one material with another or by combining two or more materials into a multilayered film wherein each of the layers is a barrier to a type of gas or liquid to be excluded. Layers can also be added for improving other properties, such as strength or ability to heat-seal. Seven-layer barrier films of this type are currently available and are used chiefly for wrapping meat. Some common coated plastic materials are cellophane coated with polyethylene or PET coated with metal, which is widely used for helium-filled balloons. Metals generally have much lower permeabilities than plastics because of the highly dense, crystalline nature of metals in comparison to plastics. Therefore, the metal-coated PET material will resist the permeation of helium, even though helium has the highest permeation rate of any material since it is the smallest of all atoms. (These metal-coated balloons are sometimes known by the PET trade name, as Mylar™ balloons.)

        Another method that has been employed to modify the permeability of plastic materials is to chemically bind polar groups onto the chain of an otherwise nonpolar polymer. By careful regulation of the conditions under which the chemical reaction is conducted, the polarity of the polymer can be chosen and its permeability controlled. An example of this procedure is the creation of DuPont's Nafion®, which is a modified Teflon® to which polar groups have been added. Nafion is used for membranes in chemical cells that require the passage of water and some ions to work but still require the overall chemical resistance of Teflon®. Unmodified Teflon® would not permit the passage of the molecules. 

        Tightening the structure of a plastic material is another method of improving barrier properties. As indicated previously, one way this can be done is by increasing the density (crystallinity) of a material. Also, thermosetting plastics can be crosslinked to tighten their structure and thus increase their barrier properties. This crosslinking not only tightens the structure (higher density and less open), it also makes the molecules less mobile and, therefore, more resistant to the passage of a penetrating molecule.