Case Studies

Gas Solubility Coefficient and Free Volume

The permeability coefficient P derived from the gas permeability (gas barrier properties) of polymer material are evaluated by multiplying the solubility coefficient S by the diffusion coefficient D. When using MD (molecular dynamics) to calculate the diffusion behavior of gas molecules within the polymer, using the solubility coefficient and system free volume, at the same time setting the number of gas molecules and default installation site will produce results closer to actual phenomena.

By using EVMS (Evaluated Volume Map Sampling), the solubility coefficient can be estimated ([1]-[3]). Make sure to create the matrix component structure via NPT ensemble MD beforehand. Compartmentalize the region, then arrange the test particles into each compartment of the given size. By evaluating changes in the energy of this system, the candidate installation site for the gas molecules can be selected (where ΔE < 0). Lastly, evaluate the solubility coefficient S using the in energy changes by placing the actual gas molecules into the candidate position.

Using the J-OCTA COGNAC modeler, create the cis-polyisoprene molecular structure (100 for the degree of polymerization). An amorphous structure was created using VSOP under 1 atm at 100°C. Figure 1 shows the distribution of where ΔE < 0 after inserting test particles with a diameter of 2.75 Å. This location will be the candidate installation site for the gas molecules. Furthermore, by adjusting the size of the test particles, the free volume can be evaluated.

The solubility coefficient S obtained from the energy changes when placing carbon dioxide molecules into all candidate positions is 4.23E-06 [cm^3 (STP)/(cm^3 Pa)] (STP stands for standard temperature). These are reasonable values when compared to the experimental data values.

We created a solver for EVMS method. It is possible to consider the LJ potential and electrostatic interactions when making these energy calculations. Please contact us for details.



Figure 1 Candidate Installation Site of Gas Molecules Within Polyisoprene (Projection on XY Plane)
Actuality, only limited positions can be used where the energy changes for the placed gas molecules becomes negative (the position where solubility coefficient can be properly evaluated).




Reference
[1] Mitsuhiro Fukuda, Journal of Chemical Physics, 112, 478, (2000)
[2] Yoshinori Tamai et al, Macromolecules , 28, 2544, (1995)
[3] Florian Muller-Plathe, Macromolecules , 24, 6375, (1991)





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