The modelling results of gas diffusion in polyethylene

To calculate the time required for placing the polyethylene film rolls in hydrocarbon gas atmosphere, Fick’s second law is used [6]. Assuming the homogeneousness of the polyethylene film roll, three-dimensional geometry could be simplified to a one-dimensional problem (1) due to the cylindrical symmetry:

                                                                                                           (1)

where  is the gas concentration in the polyethylene film roll,  is the diffusion coefficient. The boundary conditions are those of the first kind. Gas concentration on the surface layers is equal to the limit concentration of this gas in polyethylene.

The limit gas concentration in the material and diffusion coefficient could be determined both by using experimental data [7, 8] and by using mathematical modelling methods such as molecular dynamics [9].

In this work, the time, required for polyethylene film roll to absorb ethylene until it reaches the limit concentration at normal temperature and pressure (NTP, 1 atmosphere and 300 K), is calculated. The time, required for to the preliminary deoxygenation of polyethylene film roll in the vacuum chamber, is also calculated.

Table 1 Parameter values that were used in calculations [7-9]

Gas	Diffusion coefficient, cm2/sec	Limit concentration at NTP, mol/cm3
Oxygen (O2)	4.7 * 10-7	2.389 * 10-5
Ethylene (C2H4)	3.3 * 10-8	0.83 * 10-5

We assume that the polyethylene film roll is homogeneous, 1.5 mm thick with fraction crystallinity of 0.69 and the density of amorphous region equal to 0.86 g/cm³ [7]. The diffusion coefficients and limit concentrations of oxygen and ethylene are shown in Table 1. The results of the modelling of the preliminary deoxygenation process are shown in Figure 1.

Figure 1 . Distribution of oxygen concentration inside the polyethylene film roll

According to the modelling results, it can be seen that oxygen concentration in the polyethylene film roll is significantly reduced two hours after the start of the degasification process. This concentration is almost equal to zero eight hours after the degasification process begins. The results of the ethylene absorption process are shown in Figure 2.

Figure 2 Distribution of ethylene concentration inside the polyethylene film roll

It is shown that the ethylene concentration inside the polyethylene film roll becomes close to the limit concentration 50 hours after the absorption process begins at NTP.

Conclusion

In this paper, the way of increasing the speed of crosslinking process by means of placing the samples in the ethylene atmosphere at NTP before the crosslinking process with preliminary deoxygenation was studied. The results show that the absorption process at NTP occurs too slowly, so it does not actually accelerate the crosslinking process. Nevertheless, the absorption process will go faster at higher pressure and temperature. Hence, it is necessary to set the required ethylene concentration and determine the conditions for the absorption process acceleration.

Reference list

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