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Barrier Properties of Polymers
(Permeability, Solubility and Diffusivity)

The permeability or inverse barrier is an important physical property for many industrial and biomedical applications of polymers. For example, polymers with low permeability, i.e. high barrier properties, are required for food packaging applications to prevent loss of flavor, color and quality and to retard spoilage. But this is not the only important application; there are numerous other application for polymers with low, high or tailored permeability like protective coatings (e.g., paints and varnishes), filters and membranes for gas or liquid separation and water desalination, and polymer coatings for controlled drug release.

The transport of gases and liquids through polymer membranes (plastic films) is caused by either a pressure or temperature gradient, or by an external force field and/or a concentration gradient. The permeation of gases through polymer membranes is usually described in terms of a ‘‘solution-diffusion’’ mechanism. It consists of the following steps: (1) solution (absorption) of small molecules into the membrane at the side of higher potential (pressure, concentration, etc.); (2) molecular diffusion of the molecules in and through the membrane; and (3) release (desorption) of the diffused molecules from the membrane at the opposite side into the liquid or gas phase at lower potential. The term permeation describes the overall mass transport of the penetrant gas or liquid across the membrane, whereas the term diffusion describes the movement of the penetrant molecules inside the bulk of the polymer. Usually, the molecular diffusion through the polymer membrane is the slowest and, thus, the rate-determining step in the permeation process.

Diffusion can be described with Fick’s Law (1855). It states that at a steady state, the flux going through a unit area of polymer membrane (A) is proportional to the concentration (dc/dx) or pressure gradient (dp/dx) which is the “driving force” of the diffusion process:

Q = dm/dt = - D · A · dc/dx

The proportionality constant D is the so called diffusion coefficient which depends on the temperature and on the penetrant/polymer system and can also be a function of penetrant concentration. In the case of a gas (vapor), the equilibrium concentration, the so-called solubility c, of a penetrant gas dissolved in a polymer can be related to the (partial) pressure, p, of the penetrant gas by following relation:

c = S · p

where S is the solubility coefficient for the gas/polymer system which is the amount of gas per unit volume of solvent (polymer) in equilibrium with a unit (partial) pressure of gas. If this quantity is independent of the gas concentration, then the relation above reduces to Henry's law.

The overall process, i.e. the flux of permeant (Q) is proportional to the membrane are A, the potential difference (Δφ) between the two sides of the membrane, and inversely proportional to the thickness of the membrane (L):

Q = dm/dt = P · A · Δφ / L

or in th case of a gas with Δp the (partial) pressure difference:

Q = dm/dt = P · Δp · A/L

The proportionality constant P is the so-called permeability of the membrane (barrier) which depends on the temperature. Both the permeation of the gas and its diffusion through the polymer barrier is often a complex process, especially when plasticizers and other additives are present that might migrate to the interface. In this case, the diffusion coefficient is a function of position, and when the solute is highly soluble in the polymer (strong plasticizer), the diffusion coefficient is also a function of time and exposure history (non-Fickian diffusion).

 

The permeability and solubility of gases and liquids in a polymer can be very different for different polymers and permeants. In general, permeability and solubility  at a given temperature depend on the degree of crystallinity (morphology), the molecular weight, the type of permeant and its concentration or pressure, and in the case of copolymers, also on the composition. For example, butadiene-acrylonitrile copolymers with high acrylonitrile content have low permeability to gases of low polarity and high permeability to gases of high polarity. The explanation for this behavior is rather simple; the polarity of the polymer (acrylonitrile content) determines the gas solubility and, thus, the permeability. As the acrylonitrile content of the copolymer increases, the solubility of polar gases such as CO₂ and water vapor increases as well, whereas that of gases of low polarity (H₂, N₂, O₂) decreases.

 

Solubility of Gases in Butadiene-Acrylonitrile Copolymers

Similar trends are observed for other polymers and gases. For example, the permeability and solubility of vapor is high for polar polymers (PC, Nylon, EVOH) and low for nonpolar polymers (PE, PP, PIB, PVDC), whereas the opposite trend is observed for oxygen. The density of the polymer is also an important factor; for example, low density polyethylene (LDPE) has a much higher permeability to oxygen than high density polyethylene (HDPE). The effect of crystallinity follows the same trend. For example, oriented Nylon 6 with high crystallinity (and high density) has a lower permeability to oxygen than non-oriented Nylon 6 with lower crystallinity (density).