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Polymer molecular weight, or chain length distributions, are a core characteristic of a polymer system, with the distribution being intimately tied to the properties and performance of the polymer material. A model is developed for the ideal distribution of polymers made using reversible activation/deactivation of chain ends, with monomer added to the active form of the chain end. The ideal distribution focuses on living chains, with the system having minimal impact from irreversible termination or transfer. This model was applied to ATRP, RAFT, and cationic polymerizations, and was also used to describe complex systems such as blended polymers and block copolymers. The model can easily and accurately be fitted to molecular weight distributions, giving information on the ratio of propagation to deactivation, as well as the mean number of times a chain is activated/deactivated under the polymerization conditions. The mean number of activation cycles per chain is otherwise difficult to assess from conversion data or molecular weight distributions. Since this model can be applied to wide range of polymerizations, giving useful information on the underlying polymerization process, it can be used to give fundamental insights into macromolecular synthesis and reaction outcomes. 

Protein‐polymer bioconjugates present a way to make enzymes more efficient and robust for industrial and medicinal applications. While much work has focused on mono‐functional conjugates, that is, conjugates with one type of polymer attached such as poly(ethylene glycol) or poly(N‐isopropylacrylamide), there is a practical interest in gaining additional functionality by synthesizing well‐defined bifunctional conjugates in a hetero‐arm star copolymer architecture with protein as the core. Using ubiquitin as a model protein, a synthetic scheme is developed to attach two different polymers (oligo(ethylene oxide) methacrylate and N,N‐dimethylacrylamide) directly to the protein surface, using orthogonal conjugation chemistries and grafting‐from by photochemical living radical polymerization techniques. The additional complexity arising from attempts to selectively modify multiple sites led to decreased polymerization performance and indicates that initiators for continuous activator regeneration atom transfer radical polymerization and reversible addition‐fragmentation chain transfer polymerization are not well‐suited to bifunctional bioconjugates applications under the studied conditions. Nonetheless, the polymerization conditions preserve the native fold of the ubiquitin and enable production of a hetero‐arm star protein‐polymer bioconjugate.