Crystalline and porous 2D poly(arylene vinylene)s (2D PAVs), i.e. vinylene-linked 2D conjugated covalent organic frameworks, represent promising materials for electronic and electrochemical applications. Chemically robust 2D PAVs with strong electron affinity are highly desirable for effective host-guest charge transfer to achieve enhanced device performance. Herein, we report the efficient synthesis and host-guest interaction of two novel 2D PAVs incorporating electron-deficient bipyrazine units with a N-free 2D PAV as a reference. They are crystalline and chemically robust. Various spectroscopies coupled with theoretical calculations indicate that the abundant N sites boost the electron affinity of 2D PAVs. We test their efficiency in hosting guest sulfur species and find that the electron-deficient materials help to physically confine and stabilize sulfur/polysulfide (e.g., Li₂S₆) molecules with facilitated intermolecular charge transfer in the porous channels. As a result, using sulfur encapsulated by 2D PAVs as electrode materials, we achieve high specific capacities with excellent capacity retention after 200 charge-discharge cycles for Li-sulfur batteries.