Designing and modeling doubly porous polymeric materials
1 Laboratoire Modélisation et Simulation Multi-Echelle, UMR 8208 CNRS, Université Paris-Est Marne la Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex, France
2 Institut de Chimie et des Matériaux Paris-Est, UMR 7182 CNRS, Université Paris-Est Créteil, 2 rue Henri Dunant, 94320 Thiais, France
Received: 8 December 2014
Revised: 21 May 2015
Published online: 30 July 2015
Doubly porous organic materials based on poly(2-hydroxyethyl methacrylate) are synthetized through the use of two distinct types of porogen templates, namely a macroporogen and a nanoporogen. Two complementary strategies are implemented by using either sodium chloride particles or fused poly(methyl methacrylate) beads as macroporogens, in conjunction with ethanol as a porogenic solvent. The porogen removal respectively allows for the generation of either non-interconnected or interconnected macropores with an average diameter of about 100–200 μm and nanopores with sizes lying within the 100 nm order of magnitude, as evidenced by mercury intrusion porosimetry and scanning electron microscopy. Nitrogen sorption measurements evidence the formation of materials with rather high specific surface areas, i.e. higher than 140 m2.g−1. This paper also addresses the development of numerical tools for computing the permeability of such doubly porous materials. Due to the coexistence of well separated scales between nanopores and macropores, a consecutive double homogenization approach is proposed. A nanoscopic scale and a mesoscopic scale are introduced, and the flow is evaluated by means of the Finite Element Method to determine the macroscopic permeability. At the nanoscopic scale, the flow is described by the Stokes equations with an adherence condition at the solid surface. At the mesoscopic scale, the flow obeys the Stokes equations in the macropores and the Darcy equation in the permeable polymer in order to account for the presence of the nanopores.
© EDP Sciences, Springer-Verlag, 2015