## 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 solution 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).

### Moisture Vapor and Oxygene Transmission Rates

Compound Vapor. (g 25μ/m2/24h) Oxygen. (g 25μ/m2/24h)
Polyvinylidene Dichloride (Saran) 0.9 - 3.4 1.2 - 2.3
Biaxial Oriented Polypropylene (PP) 5.9 2526
HD-Polyethylene 5.9 2325
Polypropylene (PP) 10.7 -
LD Polyethylene (LDPE) 17.7 8586
Biaxial oriented PET 18.6 35.6
Poly(ethylene terephthalate) (PET) 20.2 -
Ethylene-Vinyl Alcohol (EVAL G - L) 22 - 124 0.1 - 1.9
Rigid Polyvinyl Chloride (PVC) 46.5 -
Polystyrene (PS) 132 4030
Biaxially Oriented Nylon 6 (PA6) 158 25.6
Polycarbonate (PC) 170.5 -
aKuraray - Eval, Tachnical Bulletin No. 110

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).

## Summary

• The dissolution and permeation of gases, vapors, and liquids in and through thin layers of polymers (films) is of great importance for many industrial and biomedical applications.

• All polymers are permeable to fluids however, to very different extent depending on the nature of the polymer and the fluid.

• The transport of small molecules through polymers is caused by either a pressure, temperature or concentration gradient, or by an external force field.

• The permeability, solubility and diffusivity can be very different for different polymer-permeant systems and depends on many factors like chemical composition, degree of crystallinity, and molecular weight of the polymer. It also depends on the nature of the fluid (molecular size, and polarity).

• The transport of fluids through polymers consists of three steps: (1) solution (absorption) of small molecules into the membrane at the side of higher potential; (2) diffusion of the molecules in and through the membrane; and (3) release (desorption) of the diffused molecules at the opposite side into the liquid or gas phase at lower potential.

• ### Fick’s Law

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 is proportional to the concentration or pressure gradient.

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