 # Fick's First Law Of Diffusion And The Penetration Of Polymers

Where P is the permeability coefficient, Q is the amount of permeant passing through the material, x is the thickness of the plastic film, A is the surface area available for mass transfer, t is the time, and ∆p is the change in permeant partial pressure across the film.
Hence the permeability coefficient (P) is the proportionality constant between the flow of the penetrant gas per unit film area per unit time and the driving force (partial pressure difference) per unit film thickness. The amount of gas penetrating through the film is expressed in terms of either moles per unit time (flux) or weight or volume of the gas at STP. Commonly, it is expressed in terms of volume.
The permeability coefficient (P), as defined by Eq. 2.24, is equal
Fick’s first law of diffusion is applicable only under steady state conditions, that when the concentration is not changing with time (Mangaraj et al., 2009). The transfer of gases and vapors in polymers is realized by mechanisms of diffusion. Diffusion is defined as a flow of matter which originates as difference in chemical potential of migrant material in different locations of the system (Zeman and Kubik, 2007). Whereas, the solubility, S, can be defined as the amount of gas dissolved into the polymer divided by the volume of sample for 1 atm of gas on the sample surface. (2.26)
When, , , then the above equation can be rewritten as and when p1 = 1 atm (2.27)
Where, c1 is the concentration in the sample when the equilibrium is reached. The solubility S is expressed in cm3 of gas at STP per cm3 of the solid at a pressure of 1 atm. (cm3 STP/cm3 atm). Equation (permeability) obeys Henry’s law when S is independent of p (Mangaraj et al., 2009).

Effect of temperature on permeability
The permeability of the packaging films with respect to oxygen and carbon dioxide is temperature dependent and its dependence is usually described by an exponential equation, i.e. Arrhenius equation (2.28) which is represented as follows: (2.28)
and,