Mathematical modeling and numerical simulation for nucleated solution flow through slit die in foam extrusion

Calculating diffusion coefficients from molecular dynamics simulations for foam extrusion modelling of polypropylene with CO2, N2 and ethanol

In foaming processes, the blowing agent has a significant influence on the material behaviour and the necessary processing parameters. Low-density polypropylene foam sheets are usually produced with aliphatic hydrocarbons or alkanes as physical blowing agent. Due to the necessary safety precautions and the environmental impact, there is great interest in using alternative blowing agents such as CO2. The sole use of CO2 often leads to corrugation, open cells or surface defects on the foam sheet and therefore requires modifications to the process technology. For this reason, blowing agent mixtures based on CO2 and organic solvents are used for the production of foam sheets. For developing a process model describing the melt flow in the extrusion die and the formation of cells, specific material data like diffusion coefficients are necessary. For CO2 and N2 as sole blowing agent, experimental data exist in the literature. Since no experimental data are available for co-blowing agents such as ethanol at elevated temperatures as they occur in the foam process, these data were calculated using molecular dynamics (MD) simulations. The benefit of MD simulations lies in their ability to reduce the experimental effort and, in particular, to provide data in cases where this data is not available through experimental measurements. The calculated diffusion coefficient values are compared to experimental data from the literature and presented for CO2, N2 and ethanol in polypropylene. The calculated diffusion coefficients of CO2 and N2 are compared with literature results and agree well with them. For the ethanol molecules, the diffusion coefficient is compared relative to the both aforementioned ones considered the larger size of the ethanol molecule compared to N2 and CO2. The results of the diffusion coefficients for ethanol are reasonable compared to the values found for the other two molecules.