Unusual swelling and anomalous block diffusion of di- and tri-block coploymers made of active and passive monomers

Block copolymers exhibit rich morphological and dynamic properties. Motivated by that and considering the recent interest in designs of polymers with self-propelled monomers, here using Brownian dynamics simulations we study a model copolymer consisting of blocks of passive (P) and active (A) Brownian monomers. Identifying with the popular arrangements of blocks in copolymers, we consider a di-block copolymer PnAm and two tri-block copolymers PmAnPm and AmPnAm, where m and n denote respective block lengths. The results for symmetric compositions of P and A monomers show that when the active blocks are at the end, the polymer conformation gets unusually swelled, even larger than what is observed for a fully active polymer (FAP) of the same length. Although the dynamics of the center-of-mass of all the copolymers show enhanced diffusion and Rouse-like scaling behavior, individual passive and active blocks show anomalous transient super- and sub-diffusive dynamics, respectively. We characterize this anomaly in terms of the dependence of a generalized diffusion constant with the polymer length and activity strength. Furthermore, we explore the effect of variation in the relative compositions of P and A monomers. If the active block is at the center, we find that as the passive monomer fraction xp increases, the copolymer approaches the behavior of the corresponding passive polymer. Surprisingly, when the active blocks are at the end, for xp > 0.5, the size of the copolymer becomes even larger than the size of an FAP of the same length. We rationalize this observation using phenomenological arguments and by probing the individual conformation and dynamics of the blocks. Our results shall encourage design of novel passive-active block copolymers with tunable conformations and block dynamics.