Beauty of Explicit Dispersity (Đ) Equations in Controlled Polymerizations

Dispersity (Đ) as a critical parameter indicates the level of uniformity of the polymer molar mass or chain length. In the past several decades, the development of explicit equations for calculating Đ experiences a continual revolution. This viewpoint tracks the historical evolution of the explicit equations from living to reversible-deactivation polymerization systems. Emphasis is laid on displaying the charm of explicit Đ equations in batch reversible-deactivation radical polymerization (RDRP), with highlights of the relevant elegant mathematical manipulations. Some representative emerging applications enabled by the existing explicit equations are shown, involving nitroxide-mediated polymerization (NMP), atom transfer radical polymerization (ATRP), and reversible addition-fragmentation chain transfer (RAFT) polymerization systems. Stemming from the several outlined challenges and outlooks, sustained concerns about the explicit Đ equations are still highly deserved. It is expected that these equations will continue to play an important role not only in traditional polymerization kinetic simulation and design of experiments but also in modern intelligent manufacturing of precision polymers and classroom education.