Abstract
<jats:p> Since the establishment of Carothers’ step-growth gelation theory in 1936, it has been widely accepted that an average functionality greater than two ( <jats:italic toggle="yes">f</jats:italic> <jats:sub>avg</jats:sub> > 2) is a prerequisite for polymer network formation, thereby precluding the direct construction of polymer networks from difunctional monomers. Herein, we introduce the concept of improbable polymer networks (iNETs), whose design is guided by an extended Carothers equation and realized through mechanical bond-mediated step-growth polymerization of difunctional monomers. By employing topological entanglement rather than chemical affinity as the governing design principle, difunctional figure-of-eight rings and linear chains undergo entropy-driven transient threading and are subsequently locked via hydroxy-yne click chemistry, yielding a mechanically interlocked network. The resulting iNET exhibits decent mechanical performance, underpinned by synergistic topological and dynamic mechanisms: sliding of interlocked junctions enables stress redistribution, dissociation of the metal coordination bonds contributes to energy dissipation, and release of latent chain segments affords enhanced extensibility. Meanwhile, mechanically interlocked junctions act as permanent topological anchors, while the entropy-enthalpy co-regulated recovery pathway of the figure-of-eight topology enables rapid and efficient structural restoration after large deformation. This work redefines the conceptual boundaries of gelation theory and establishes a general strategy for constructing polymer networks from difunctional building blocks. It opens new avenues for the rational design of mechanically interlocked materials, in which the classical requirement of <jats:italic toggle="yes">f</jats:italic> <jats:sub>avg</jats:sub> > 2 no longer stands as an insurmountable barrier. </jats:p>