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PEER-REVIEWED REVIEW ARTICLE
Several types of barrier properties are measured to determine the exposure of a package ’s contents to ambient conditions. The most common barrier measurements include gas transmission such as oxygen, liquid, and vapor transmission, such as water and water vapor, and oil transmission, followed in test conditions typically by castor oil. The properties of the permeating molecule, the properties of the film material, and ambient conditions all influence the barrier properties. For instance, the size and polarity of the molecule, the polarity and crystallinity of the film material, the temperature, and relative humidity conditions influence the amount and rate of permeating matter. In principle, transmission is non-existent when the permeant molecule and the film material are insoluble in each other, and vice versa . In this case, the cohesive energy is high between the permeating molecule and film material, whereas a high solubility, in turn, indicates low cohesive energy (Auvinen and Lahtinen 2008). Inside a polymer film, the molecular motion of permeating gas appears in small scale compared to the free space to another stochastically bouncing molecules. However, in the large scale there is a clear trend of molecular flow, which tends to equalize the difference in chemical potential between the sides of the film material. Thereafter, the large-scale motion of gas molecules from one side of a film material to the opposite side follows Fick’s first law of steady state diffusion, as indicated in Eqs. 1 (concentration difference between film edges) and 2 (pressure difference between film edges). In steady state conditions, the absorption of permeating matter into the film from one side is the same amount of matter as its desorption out of the film from the other side, thus resulting in steady diffusion of matter inside the film. Equation 2 is obtained when adding Eq. 3 (Henry’s law of solubility) to Eq. 1. Finally, Eq. 4 is a common permeation equation related to the relation of the gas coefficients (Paine and Paine 1992; Auvinen and Lahtinen 2008). In Eq. 4, J is the steady state diffusion [work/area], e.g. , [J/cm 2 ], P is the permeation coefficient [amount*material thickness/area*time*pressure difference], e.g. , [cm 3 cm/cm 2 s Pa], D is the dissolution coefficient [area 2 /time unit], e.g. , [cm 2 /s], S is the solubility coefficient, e.g. , [cm 3 (STP)/cm 3 polymer], l is the film thickness, e.g. , [cm], c is the concentration of dissolved gas , e.g. , mL/L or M, p is the partial pressure of a gaseous solute, e.g. , Pa, p 1 -p 0 is the partial pressure difference between the permeating gas on one side and the other side of the film , and c 1 -c 0 is the concentration difference between the permeating gas on one side and the other side of the film (Piringer 2000a; Auvinen and Lahtinen 2008). In steady state, given by Eqs. 1 to 4, the activation energy of diffusion is reached, thus allowing diffusion to occur. Equations 1 to 4 contain dimensionless coefficients, set by P , D , and S . The diffusion coefficient is a measure of the speed by which molecules pass through a given area of the film material, while the solubility coefficient is a measure of the molecules that pass through given area. Basically, the coefficients as such resemble ideal gas behavior, whereas for non-ideal gases, vapors, and liquids, the coefficients are corrected by applying to Eq. 4 the Arrhenius equation of activation energy (Paine and Paine1992; Auvinen and Lahtinen 2008). Moreover, Fick’s second law of diffusion is related to unsteady state conditions. Before reaching steady state and constant diffusion, the permeating gas exhibits an unsteady state, accelerating diffusion
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Helanto et al. (2019). “ Bio-based barriers ,” B io R esources 14(2), Pg #s to be added.
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