Design and mathematical modeling of polymeric phases to obtain controlled microporosity materials by 3D printing

A new method named implicit pseudo-spectral arrays (IPSA) was developed to obtain the numerical solution and plot it as a three-dimensional (3D) pattern. These results were used to elaborate the computational simulation of the spatio-temporal dynamics of the Swift–Hohenberg equation (SHE) of quintic order. Numerical solutions are employed as complex 3D computational models (computer-aided design files), which were studied and analyzed to generate a new method named "mathematical design process and 3D printing-assisted manufacturing (MDP-3DPAM)". This new technique is a new way to create porous polymeric materials through a controlled mathematical shape with pore size distribution and microstructure modulated by software parameters. Another advantage of this design process is its efficient computational computation time and various 3D printing methods available, such as: fused deposition modeling and UV-laser-assisted stereo-lithography. In this work, both techniques were used in the printing of porous materials. This work establishes a method for controlling pore size distribution through mathematical modeling and subsequent printing. Graphical abstract