Lattice Model Simulation of Penetrant Diffusion along Hexagonally Packed Rods in a Barrier Matrix As Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

The structural influence on translational diffusion of 2,2,4-trimethylpentane (TMP) through SEBS triblock polymer (poly(styrene)-block-poly(ethene-co-but-1-ene)-block-poly(styrene)) was studied using pulse field gradient (PFG) NMR coupled with lattice model simulation. Two types of PFG experiments were performed: one observing the time-dependent apparent diffusion constant and another observing the diffusion-induced NMR signal attenuation. TMP is selectively sorbed into the rubbery ethylene/butylenes (EB) phase while the glassy poly(styrene) (PS) phase acts as a barrier to TMP diffusion. The observed apparent diffusion constant drops drastically at the grain boundary, in which the orientation of the minor EB cylinder phase changes from grain to grain. In the lattice model simulation, in order to match the large drop of diffusion constant, the diameter of the EB cylinder at the interface had to be reduced by a factor of about 0.7. This extra restriction in the size of the conductive phase indicates the important role of the grain boundary on diffusion in membrane applications of block copolymers. The simulation also shows that the grain boundary influence on diffusion becomes significant when the solubility and diffusivity of the penetrant are greatly different between the rubber and glass phases. In addition, we extended the lattice model to simulate the diffusion-induced PFG NMR signal attenuation. From the simulation and theoretical fitting, it is obvious that the EB phase at grain boundary is not connected well, which is in agreement with our observation of a drastic apparent diffusion constant drop at the grain boundaries in the PFG experiment.