Two sets of model compounds were spiked homogeneously during polystyrene sheet production. The first sheet was spiked with a mixture of n-alkanes n-octane, n-decane, n-dodecane, up to n-tetracosane. The second sheet was spiked with a mixture of the following substances: acetone, ethyl acetate, toluene, chlorobenzene, phenyl cyclohexane, benzophenone and methyl stearate. The concentrations of the model compounds were determined quantitatively in the PS sheets by extraction with acetone as solvent.
Subsequently, the solvent was removed and the sheets were extracted again in order to prove if the first extraction was exhaustive. Calibration was achieved by standard addition of the model compounds. The concentrations of the very volatile substances acetone and ethyl acetate were estimated from the headspace gas chromatograms GC—FID : Column: ZB 1;30 m length; 0. Concentrations were estimated compared to a neat standard of the substances.
The concentrations of the model compounds in the investigated PS sheets are summarized in Table 1. Experimentally determined concentrations of model compounds in the spiked polystyrene PS sheets. For each test, 1. Quantification of limonene was achieved by external calibration with standards of different concentrations.
Migrations into the gas phase of the spiked model compounds were determined according to [ 19 , 20 ] using an automated method that involved placing sheet samples of One sheet per temperature was analyzed. Subsequently, a new trapping cycle started.
By using this automated method, every 40 min a kinetic point was determined. The migrants were separated during the GC run and quantified during the chromatographic measurements. Calibration was achieved by injection of undiluted standard solutions of the migrants into the migration cell. Gas chromatograph: Column: Rxi ; 30 m length; 0. The diffusion coefficients D P were calculated from the area related migration into the gas phase according to Equation 1. The parameter t is the run time in s of the experiment.
The permeation rates were determined for 1-alcohols from methanol to 1-octanol. The homologous rows of substances with different polarities were chosen in order to establish correlations which might be useful to predict the diffusion behavior of other, non-tested substances.
The surface area of the tested films was cm 2. The permeation cell with the film was placed in a climate chamber. One film per temperature was analyzed. The cell has a lower and an upper space separated by the film. The lower space of the permeation cell had a volume of cm 3 and was spiked with the permeants.
The starting concentrations c gas phase of the investigated permeants 1-alcohols in the lower space of the permeation cell, their molecular weights and molecular volumes [ 21 ] are given in Table 2. The nitrogen stream went through a connected enrichment unit and the permeants were trapped on this unit. The enrichment unit was connected to a gas chromatograph with flame ionization detection GC—FID and the permeants were directly desorbed into the gas chromatograph.
By use of this technique, the permeated amount into the upper space of the permeation cell was analyzed for the applied permeants. During the GC run, the next sample was again trapped on the enrichment unit and subsequently injected into the GC.
By use of this method, kinetic points were measured every 45 min. Gas Chromatographic Conditions: Column: Rxi ; 30 m length; 0. Calibration was performed with injections of known amounts of the applied permeants. From the experimental data, the permeation rates as well as the lag times of the applied permeants are available.
The diffusion coefficient D P of the applied permeants in GPPS was calculated from the lag time t lag in s and the thickness l in cm 2 of the film according to Equation 2 [ 22 , 23 ]. This program calculates the van der Waals volume of organic molecules. The method for calculation of molecule volume developed is based on group contributions.
The applied desorption method determines the migration of spiked substances from PS sheets into the gas phase at elevated temperatures. Diffusion coefficients D P were determined from the slopes of the linear correlation between the square root of time and the area-dependent migration according to Equation 1. By use of this desorption method, several migrants can be determined simultaneously provided the model compounds are distributed homogenously in the spiked PS sheet and separation on the GC column is attained.
In order to obtain a homogenous distribution of the migrants in the sheet, the organic substances were spiked into the polymer melt during sheet production.
Notably, a proportion of the migrants evaporate during the thermal step of sheet production, especially in case of volatile substances. Thus, compounds of higher volatility are removed in greater amounts during sheet production, leading to lower concentrations in the final spiked PS sheet. It was therefore necessary to analyze the final PS sheets according to their residual concentration of the artificially spiked compounds Table 1. Styrene was not artificially added, but detectable in polystyrene polymers as residual monomer.
The diffusion coefficients D P derived from the desorption kinetics are summarized in Table 3 n -alkanes and Table 4 other substances with various functional groups and aromatic rings. Desorption kinetic curves all other applied substances had a similar shape. For all investigated migrant kinetic points, they were determined every 40 min. Therefore, several kinetic points are available for each diffusion coefficient. From this migration, it could be shown that the diffusion process is following Fickian laws of diffusion resulting in a linear correlation between the migrated amount and the square root of time [ 21 ].
However, it should be noted that the kinetic curves shown in Figure 1 do not go through the zero point. This is due to the fact that during sheet manufacturing, a portion of the spiked substances are lost from the hot surface of the sheets during sheet production, which reduces slightly the concentration at the surface of the sheets.
This leads to a slightly lower desorption at the beginning of the kinetics. Due to the high temperatures during the kinetic tests, the concentration is gradually replenished at the surface of the sheets. Therefore, the lower surface concentration at the beginning of the kinetics has no influence on the measured diffusion coefficients D P , because the slopes after this initial phase were taken into account.
As expected, low molecular weight molecules show significantly higher diffusion coefficients D P than high molecular weight substances, especially at low temperatures. In case of sheet 1, it was possible to calculate the activation energies of diffusion below as well as above the glass transition temperature.
A similar situation was available for HIPS. Four sheet 1 and five sheet 2 kinetic points were available below, whereas two and three kinetic points, respectively, were available above the glass transition temperature. In the case of HIPS, the determination of the activation energies of diffusion was possible below and above the glass transition temperature. However, due to only a couple of kinetic points and the small temperature interval, the activation energies of diffusion above the glass transition temperature are less precise for HIPS compared to GPPS.
The diffusion coefficients were determined from the lag times of the permeation curves according to Equation 2. The lag time t lag is defined as the intercept of the asymptote to the permeation curve on the time-axis [ 22 ].
In previous studies, the same method was applied on thin films of oriented polyamide PA6 [ 24 ], polyethylene terephthalate PET [ 23 , 25 ], polyethylene naphthalate PEN [ 26 ] and ethylene vinyl alcohol copolymer EVOH [ 27 ]. The permeation curves of the other substances measured within this study follow a similar behavior.
The diffusion coefficients D P for the applied 1-alcohols are summarized in Table 5. Permeation tests with n -alkanes failed because the film became brittle and broke under the applied temperature and concentration conditions.
Diffusion coefficients increase significantly with molecular volume and therefore the lag time increases accordingly. For example, given a diffusion coefficient D P of 9. Thinner GPPS films, which will lead to significantly lower lag times for larger molecules, are not available on the market and also the handling with such thin and brittle films is difficult.
Therefore, higher temperatures need to be applied for 1-alcohols starting from 1-propanol. The diffusion coefficients of ethanol increase in the same temperature interval from 2.
In the permeation kinetic, the initial concentrations of the permeants in the lower cell Table 2 were chosen such that they are a factor of approx.
This avoids condensation of the permeants on the surface of the GPPS film. As a consequence, swelling of the polymer and the associated increase of the diffusion coefficients D P were minimized.
Without swelling of the polymer, the determined coefficients can be considered as pure diffusion coefficients in the GPPS polymer. In other trials, the permeation n -alkanes were also tested at similar low concentrations in the gas phase. However, after the contact of the GPPS film with the n -alkanes, the film becomes brittle and a breakthrough of the permeants increased significantly with a non-Fickian diffusion behavior. Therefore, the diffusion coefficients cannot reliably be derived.
Diffusion coefficients for n -alkanes are therefore not available from permeation tests on thin GPPS films. The activation energies of diffusion are calculated from the diffusion coefficients according to the Arrhenius approach [ 28 ]. In all cases, the Arrhenius plots show good linearity for the investigated substances. This indicates that the diffusion process follows Fickian laws and any swelling of the polymer by the permeants can be neglected under the experimental conditions applied within this study.
Activation energies are only calculated when a minimum of four kinetic points are available. This serves to ensure that the values determined are sufficiently precise for using in the parameterization of the prediction parameters.
The determined diffusion coefficients show a strong dependency on the size of the migrating substance, represented by the molecular volume, as well as on temperature. As expected, for larger molecules, the diffusion coefficients are significantly lower when compared to very small molecules like acetone of methanol.
In addition, lower temperatures result in lower diffusion coefficients for each individual permeant, which is in agreement with diffusion theory. From the slopes and the intercepts, the activation energies of diffusion E A as well as the pre-exponential factors D 0 were calculated.
The Arrhenius plots and the correlation of the reciprocal temperature versus diffusion coefficient are given in Figure 3. The activation energies of diffusion E A are lower above T g compared to the values below T g , which results in a lower slope of the Arrhenius plot above T g. The change in the diffusion behavior is more significant for larger molecules compared to smaller molecules. Relatively small sized molecules like styrene and n -octane show only a slight change in the diffusion behavior whereas n -octadecane shows a significant change of the diffusion behavior at the glass transition temperature.
The results indicate that that for larger molecules like phenyl cyclohexane and benzophenone, the activation energy of diffusion E A is also lower above T g compared to the slopes below T g , which is in agreement with the results of the n -alkane spiked sheet.
However, due to the fact that only one temperature is available, these findings are on a weak basis. However, the results are in agreement with the finding for HIPS Figure 3 d , where three temperatures were measured above T g. Benzophenone shows a lower activation energy of diffusion E A above T g. Here, I will demonstrate some important solubility and permeation highlights and anomalies with regard to the use of the Arrhenius equation in this context.
R: Universal gas constant 8. T: Temperature Kelvin. Physical Considerations The temperature dependence of the diffusion coefficient D of, for example, carbon dioxide in high density polyethylene can be obtained by using the formula based on the Van 't Hoff Equation or Arrhenius Law.
Realize that the temperature dependence of the solubility S of substance in materials is often also calculated by this Arrhenius Law. Moreover, as the steady state permeability P , follows from D times S, the permeation rate also follows an Arrhenius type of temperature behaviour.
Below we list some important consistencies with regard to the above: 1] From the general accepted picture of the mechanism of the activated diffusion process, it is known that larger holes need to be formed in the polymer for the diffusion of larger molecules.
These will require a larger energy for their formation and hence the activation energy will be larger for the diffusion of larger molecules, and the diffusivity will be smaller. Concerning polymers that have a low free volume, such as partly crystalline polyamide PA or polyimide PI , the change of activation energy is significant. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
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