Active polymers under specific boundary constraints are a central topic in both biophysics and polymer physics. In this work, we perform a comparative study of polar active polymers with one end fixed, highlighting how the choice of the fixed point (tail vs head) leads to dramatically distinct conformational and dynamical behaviors. Tail fixation induces nonuniform stretching along the polymer and results in a nonmonotonic dependence of conformational relaxation on chain activity. In contrast, head fixation causes uniform chain compression, forming a yarn-ball-like structure and giving rise to a distinct conformational relaxation dynamics. We identify several scaling relations that have not been discussed previously, including the dependence of polymer size on chain length $R_{\mathrm{g}}\sim N^{-0.38}$, the conformational relaxation time on chain length ${\tau }_{\mathrm{r}}^{*}\sim N^{0.6}$ and on activity ${\tau }_{\mathrm{r}}^{*}\sim {\mathrm{Pe}}^{-1.35}$. These results provide fundamental insights into the interplay between activity and boundary conditions in determining the structural and dynamical behaviors of polar active polymers, offering potential implications for guiding the design of bioinspired active materials.

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• Polymer conformation changes
• Single polymer chains
• Polymer scaling theory