Emergent Active-Blob Length Scale Governs the Collapse Transition of Tangentially Driven Polymers

The coil-to-globule transition is a paradigmatic phenomenon in polymer physics and biophysics, in which polymer chains evolve from swollen to globular conformations upon decreasing solvent quality. At equilibrium, this transition can be rationalized in terms of a thermal blob length that diverges at the so-called $\mathrm{\Theta }$ condition, marking the crossover from self-avoiding to globular conformations. How activity modifies this conformational transition and affects the fundamental length scales at play remains poorly understood. Here, we address this question for tangentially driven polymers using Brownian dynamics simulations, systematically varying both intrachain attraction strength and activity. We find that polar activity smears out the crossover from swollen to globular conformations. Between self-avoiding and $\mathrm{\Theta }$ conditions, activity dominates by introducing an emergent folding length scale, which acts as an active blob length. In this regime, we demonstrate that the ratio of thermal to active length scales provides a new scaling variable that leads to a universal master curve for active polymer collapse.