# Barriers and Chemistry in a Bottle: Mechanisms in Today's Oxygen Barriers for Tomorrow's Materials
## 2 Background
### Measuring Oxygen in Packaging  
In order to determine whether a package can provide sufficient protection from oxygen, several quality parameters have been defined [51; 52; 53]. * Oxygen transmission rate (OTR). The most common definition of OTR is the volume of O\({}_{2}\) per package per day. The exact conditions need to be specified and preferably resemble the real storage environment of the packaging. Usually, the partial oxygen pressure is regulated to 0.21 atm, but temperature may vary between 20 \({}^{\circ}\)C and 25 \({}^{\circ}\)C and humidity between 0% and 100% RH [54; 55]. * Permeability. This is usually defined in terms of Equation (3) [52]. \[\mathbf{P}=\frac{\mathbf{V}\,\mathbf{L}}{\mathbf{A}\,\mathbf{t}\,\mathbf{A} \mathbf{p}}\] (3) With P the permeability (most commonly expressed in units of cm\({}^{3}\) mm m\({}^{-2}\) day\({}^{-1}\) atm\({}^{-1}\)). Herein, V is the volume of the gas permeating in time t (cm\({}^{3}\) day\({}^{-1}\)), L is the thickness of the film or bottle wall (mm), A the surface area of the film over which permeation is measured (m\({}^{2}\)) and \(\Delta\)p the difference in partial pressure of the gas inside and outside the packaging (atm). The effect of temperature can then be quantified by a conventional Arrhenius equation, as shown in Equation (4) [52]. \[\mathbf{P}=\mathbf{P}_{0}\,\mathbf{e}^{-\frac{\mathbf{E}_{\mathbf{P}}}{\mathrm{RT }}}\] (4)With P the permeability at temperature T (K), P\({}_{0}\) a pre-exponential factor (cm\({}^{3}\) mm m\({}^{-2}\) day\({}^{-1}\) atm\({}^{-1}\)), E\({}_{\text{p}}\) the activation energy for the permeability action (J mol\({}^{-1}\)) and R the ideal gas constant (J mol\({}^{-1}\) K\({}^{-1}\)). The activation energy of oxygen in amorphous PET has been determined to be 37.7 \(\times\) 10\({}^{3}\) J mol\({}^{-1}\)[52]. * Barrier improvement factor (BIF). This is a unitless factor, usually used in a commercial setting, defined as the ratio between either OTR or permeability of the given barrier composition and a standard packaging [53]. A common mistake is that OTR is often inputted as V/t in Equation (3) to calculate permeability. However, whereas permeability is a measure for the material at a given humidity and crystallinity, OTR is very specific for the examined package design and is not a representation for the material used or the packing size (200 mL bottles versus 1 L bottles). After all, packaging, especially bottles, usually consists of several areas with different permeabilities (e.g., the thin, stretched body versus the thick, amorphous bottom of a bottle). The material distribution of a bottle may influence the ratio of crystalline to amorphous wall surface, thickness gradients and possibly the multilayer position [56]. OTR can therefore be different for two bottles of the same material but in different shapes. As stated, humidity and crystallinity will also have an effect on oxygen permeation and this is often harder to control than wall distribution. These effects can be explained by separating permeability into a diffusive and solubility factor according to Equation (5). \[\mathbf{P}=\mathbf{D}\;\mathbf{S} \tag{5}\]  
While solubility S (cm\({}^{3}\) cm\({}^{-3}\) atm\({}^{-1}\)), expressed as the volume of permeant dissolved per volume of polymer (cm\({}^{3}\) cm\({}^{-3}\)) at a determined partial pressure (atm), is an indication to the free volume in the matrix, diffusivity (D) (in m\({}^{2}\) s\({}^{-1}\)) is a measure of channel formation, enabling the gas molecule to move through this free volume [55]. Specified for oxygen through a PET-wall, studies have shown that high crystallinity reduces both factors since the free volume in crystallites is lower. This affects solubility, but also creates obstacles that will increase the diffusion path length. High humidity will increase diffusion due to swelling, but will also lower the free gaseous volume and thus decreasing solubility by a factor relating to the dissolution of oxygen in water.