Evolution of Micropores in Polymer-Polymer Composite Thin Films
Research Background
The simulation of micropore structure evolution in LBL film starts from defining the initial nodes and elements. The generation of nanopres is caused by removing one polymeric component which results in serpentine shape with rough interface. Thus, we set up the initial nodes with 4 types of variations.
Following the finite element method which are described in Ref. (1), elemental H and f matrix are calculated and combined to global H and f matrix. From the global F matrix, the V (velocity at nodes) matrix is extracted. Because the nanopores are growing during the process by removing one LBL component, the constant increment term of the pore size is integrated to the V matrix. This increment term is added till the pore size being 60% of total system size because the volume ratio of pores, porosity, in the LBL film is usually below 60%. Adjusting the speed of enlargement of the pore can be controlled by changing the evaporation variable which is added to the V matrix. Physically this speed variance is affected by the pH of dipping solution during pore generation.
The mobility of the material can adjust the speed of shape changing like the evaporation variable in surface migration process. Although the concept of the mobility in ref. (1) is for one atomic molecule, it is also safely adopted for polymer materials which are the main constitution component in the LBL film. This surface diffusion process continuously proceeds even after the surface migration process stops and the shape change of the pore is mainly following the surface diffusion process. Figure 1. shows the shape change from the initial set-up to stabilized result.
Figure 1. The shape change of pores from the wrinkled nanopore to the round micropore.
Numerical calculation is done by adaptive time-step Runge-Kutta method in order to achieve higher accuracy. The classical fourth order Runge-Kutta formula is in Figure 2.