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Gas Garrier Seminar

Gas Barriers: An Introduction Basic Reference 6

Gas transmission coefficient and free volume

Chain molecules of high molecular weight make up a plastic. Fig. 6-1 shows the frame format of the chain molecules clustered in an amorphous area. Gaps are created when molecules gather as shown by the red ellipses in the figure.
These gaps are called free volume. Free volume is always changing because the molecular chains undergo thermal oscillation.

In recent years, it has become possible to measure the free volume in polymer materials directly using the positron annihilation method.

Ordinary electrons are particles with a negative charge, and positrons have a positive charge. If they enter into the plastic, they are annihilated due to the interaction with the electrons in the plastic. The fading time and the size of the free volume are related. Therefore the size of the free volume can be calculated from the fading time.

Fig. 6-1 Clustered polymer chains
Fig. 6-1 Clustered polymer chains

Fig. 6-2 shows free volumes of various types of plastic. You can see that the free volume varies widely depending on the type of polymer. Fig. 6-3 is a comparison of the free volume and size of the oxygen molecules for PE and PVA2). The free volume of PE is about the size of three oxygen molecules.

You can see from Fig. 6-2 that the lower the oxygen transmission coefficient of plastic, the smaller the free volume will be. Now let us look at the relationship between the oxygen transmission coefficient and free volume. Based on the free volume theory of diffusion as well as on the hypothesis that solubility does not change greatly by the type of polymer, it is found that there is a linear relationship between the inverse of the free volume and the logarithm of the gas transmission coefficient.


Fig. 6-2 Free volume of various types of plastic


Fig. 6-3 Free volume of PE and PVA, and size of the oxygen molecules
The diameters are the figures shown here.
The size of the oxygen molecules are measured from the viscosity.

Fig. 6-4 shows the relationship between the inverse of the free volume and the oxygen transmission coefficient3-7). Although it is somewhat inconsistent, there is a linear relationship between the inverse of the free volume and the logarithm of the oxygen transmission coefficient.

Although the free volume is the size of the gap, it is easier to understand the quantity as a parameter that reflects the molecular mobility. In other words, the stronger the intermolecular cohesion is, the stronger the intermolecular interaction becomes and this lowers the mobility, resulting in a decrease in free volume. Also if the intermolecular cohesion is strong, when the gas molecules diffuse, it makes it difficult to push open the polymer chains and lowers the gas transmission coefficient. From this perspective, it is possible to understand the connection between intermolecular cohesion, and free volume and gas permeability.

Fig. 6-4 Relationship between the inverse of the free volume and the oxygen transmission coefficient

Fig. 6-4 Relationship between the inverse of the free volume and the oxygen transmission coefficient

EVOH-29 : Ethylene composition 29mol% Ethylene-vinylalcohol copolymer
EVOH-44 : Ethylene composition 44mol% Ethylene-vinylalcohol copolymer
LDPE : Low-density polyethylene
NY6 : Nylon6
PDMS : Polydimethylsiloxane
PMP : Polymethylpentene
PSF : Polysulfone
PVAc Polyvinyl acetate

The next article in this series will focus on how temperature changes the gas permeability.

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