A Self‐Consistent Model for Sorption and Transport in Polyimide‐Derived Carbon Molecular Sieve Gas Separation Membranes

Abstract

Demand for energy-efficient gas separations exists across many industrial processes, and membranes can aid in meeting this demand. Carbon molecular sieve (CMS) membranes show exceptional separation performance and scalable processing attributes attractive for important, similar-sized gas pairs. Herein, we outline a mathematical and physical framework to understand these attributes. This framework shares features with dual-mode transport theory for glassy polymers; however, physical connections to CMS model parameters differ from glassy polymer cases. We present evidence in CMS membranes for a large volume fraction of microporous domains characterized by Langmuir sorption in local equilibrium with a minority continuous phase described by Henrys law sorption. Using this framework, expressions are provided to relate measurable parameters for sorption and transport in CMS materials. We also outline a mechanism for formation of these environments and suggest future model refinements.

Effects on Carbon Molecular Sieve Membrane Properties for a Precursor Polyimide with Simultaneous Flatness and Contortion in the Repeat Unit

“…Finally, in the thermal soaking and cooling process, an amorphous structure is formed containing ultra‐micropores, micropores, and orphan strands in the final CMS membrane as revealed in a recently published model . The micropores resulting from imperfect packing of plates creates the dispersed Langmuir phase (L), while orphan strands around microporous Langmuir domains constitute the continuous phase (C), which jointly contributes to the dual‐model behavior of transport and sorption in CMS . Due to the vigorous decomposition of precursor and complexity of CMS structure, no direct and clear connection has been established so far between the performance of the precursor membrane and that of CMS membranes.…”

Key Features of Polyimide‐Derived Carbon Molecular Sieves

“…Differences in sorption, diffusion and permeability properties of the two CMS types are quite interesting to compare and understand. As will be discussed below, such key performance properties differ dramatically, but can be understood using the dual mode sorption and transport models developed for CMS derived from random coil precursors [5] . First we consider the standard characterizations, and then focus on sorption, diffusion and permeability properties.…”

“…Such ac ellular structure is consistent with amathematical model of sorption and transport within CMS materials derived from conventional random coil polyimide precursors. [5] Additional components of graphene-like CMS plates might be mainly composed of such structures,t ogether with fragments containing other possible structures represented in Scheme 2b.D uring pyrolysis process,h ighly aromatic rigid strands,t hat is,t he isolated strands (Scheme 2a)a nd fused fragments with analogous structures (Scheme 2b)c an align and organize into the main plates.T hese plates may organize into imperfect cells containing micropores,with adjacent cells coalescing to yield the final cellular structure typical of conventional CMS materials. [4] Such amorphous CMS membranes contain micropores connected via ultramicropores, providing intrinsic molecular sieve characteristics with attractive gas permeabilities.G raphene-like CMS plates are envisioned to be composed of isolated strands with pyridinic and/or pyrrolic rings at low pyrolysis temperature.S uch feature,with few cross-linked fragments containing pyridinic, pyrrolic,g raphitic structures,p yridonic, and few pyridine oxide structures provide high diffusion coefficients.T he chemical structures of strands in Scheme 2depend on avariety of factors,n amely precursor polymer structure,p yrolysis temperature,p yrolysis atmosphere,a nd inert purge gas flow rate.The diverse functional groups present can affect sorption affinity for specific gas molecules,but this is beyond the scope of the current study.T he chemical structures of strands in Scheme 2d epend on av ariety of factors,n amely precursor polymer structure,p yrolysis temperature,p yrolysis atmosphere,and inert purge gas flow rate.Physically organized wall structures in Figure 1c based on Scheme 2a strand elements should be most prevalent at low pyrolysis temperatures.O n the other hand, more fused structures in plate walls illustrated in Figure 1c similar to Scheme 2b should become more prevalent at higher pyrolysis temperatures.A ni solated strand, even derived from the simplest PMDA/pPDAP I, contains pyrrolic moieties (Scheme 2a), preventing truly straight strands from the original precursor.T his fortunate fact creates useful ultramicropores between strands for molecular sieving in CMS plates formed from such strands during low temperature pyrolysis of any polyimide.Aslateral connections develop between strands,the Scheme 2bfeatures can become more prevalent in CMS formed from conventional random coil polyimide or PMDA/pPDA.…”

“…Evidence indicates that such strands can organize into imperfect plates, and neighboring plates further organize to form imperfect cell structures. Adjacent cells can coalesce to form a larger cellular structure with 7–20 Å internal micropore volumes having ultramicropore cell walls, [4] with orphan strands randomly packed between cells to form a continuous phase around cells in the cellular structure, [5] as illustrated in Figure 1. Besides small normal ultramicropores (<7 Å) between strands in individual plates, imperfections at the plate joints can create slit bypass pores [6] .…”

“…Carbon molecular sieve (CMS) membranes [1] have gained attention owing to their excellent thermal, chemical, and plasticization stability,a nd particularly attractive gas separation properties, [1e,i, 2] which surpass the permeability versus selectivity polymer upper bound trade-off. [3] CMS membranes can be created by pyrolysis of polyimide precursor membranes under controlled conditions to produce relatively pure carbon materials.D uring pyrolysis random coil precursor polymers become aromatized by releasing small molecules to form rigid highly aromatic strands.E vidence indicates that such strands can organize into imperfect plates,a nd neighboring plates further organize to form imperfect cell structures.A djacent cells can coalesce to form al arger cellular structure with 7-20 internal micropore volumes having ultramicropore cell walls, [4] with orphan strands randomly packed between cells to form acontinuous phase around cells in the cellular structure, [5] as illustrated in Figure 1. Besides small normal ultramicropores (< 7 )b etween strands in individual plates,i mperfections at the plate joints can create slit bypass pores.…”