Emergent Isotropic-Nematic Transition in 3D Semiflexible Active Polymers

TL;DR

This work investigates how activity and semiflexibility govern the isotropic–nematic transition of 3D active polymers. Using large-scale Brownian dynamics simulations with tangential activity across a range of densities and bending stiffness, the authors map non-equilibrium state diagrams and measure global/local nematic order and confinement effects. They find that activity shifts the I–N transition to higher densities and qualitatively changes its character—from a discontinuous, first-order-like transition at low activity to a continuous, instability-driven transition at moderate activity, with high activity eventually suppressing nematic order. The mechanism involves activity-enhanced bending fluctuations that enlarge the effective confinement tube, causing chain shrinkage and delayed nematic alignment; for moderate activity, stochastic switching between nematic and isotropic states emerges, revealing activity-induced nematic-field instabilities. These results establish a framework for understanding active nematics in 3D semiflexible systems and suggest new directions for theory and design of active polymer-based materials.

Abstract

Active semiflexible filament collectives, ranging from motor-driven cytoskeletal filaments to slender organisms such as cyanobacteria and worm aggregates, abound in nature. Yet how activity and flexibility jointly govern their organization, especially Isotropic-Nematic (I-N) transition, remains poorly understood. Performing large-scale Brownian dynamics simulations of 3D active semiflexible polymers with varying flexibility degrees, we show that tangential active forces systematically shift the I-N transition to higher densities, with the shift controlled by the flexibility degree and activity strength. Strikingly, activity alters the nature of the transition: discontinuous at low strengths, continuous at moderate strengths, and ultimately suppressed at high activity levels. The delayed I-N transition originates from enhanced collective bending fluctuations, resulting in chain shrinkage and enlargement of effective confinement tube. At moderate activity levels, these fluctuations can trigger large-scale excitations that stochastically drive temporal transitions between nematic and isotropic states, indicating an activity-induced instability of the nematic field. We summarize this behavior in non-equilibrium state diagrams of density and activity for different flexibility degrees.

Figures (10)

• Figure 1: (a) Time-averaged global nematic order parameter of bond vectors, $\langle S_B \rangle$ (solid symbols) and (b) Mean end-to-end distance $R_E = \sqrt{\langle \mathbf{R}_e^2 \rangle}$ normalized by the contour length $L = 31\sigma$ as a function of density at fixed bending stiffness $\kappa/k_B T = 16$ for different active forces as shown in the legend. Open symbols in panel (a) (colored according to the same active-force code) represent estimates of $\langle S_B \rangle$ obtained from the mean end-to-end distance using $\langle S_B \rangle (R_E) = 3R_E/L - 2$.
• Figure 2: (a) Radius of effective confinement tube $r_{\text{eff}}$ for $\kappa/k_BT = 16$ as a function of density for varying active forces. (b) Mean end-to-end distance $R_E$ of a tangentially driven polymer confined in a cylindrical channel of radius $R$, normalized by the passive unconfined single-chain value $R_E^0$. The dashed line indicates $R_E/R_E^0 = 1$, and its intersections with $R_E/R_E^0$ curves mark the crossover from compressed to stretched conformations under confinement.
• Figure 3: (a) Instantaneous global nematic order parameter $S_B$ (blue) and director angle $\theta$ (red) for $\kappa/k_BT = 16$, $\rho\sigma^{3} = 1.0$, and $f^{a} = 0.5$ as functions of time. The angle $\theta$ is measured relative to the $z$-axis, with $\theta = 0$ indicating alignment along $z$ and $\theta = \pi/2$ alignment in the $x$–$y$ plane. Time is normalized by the passive polymer center-of-mass diffusion time $\tau_D = \gamma N L^2 / 6k_B T$. Snapshots in panels (b)–(d) correspond to the black markers in (a), illustrating (b) alignment along $x$, (c) loss of global order due to instabilities, and (d) realignment along $y$. (e) Orientational pair correlation function $g_{\mathrm{or}}(r)$ of bond vectors at selected times marked by squares of the same color in panel (a).
• Figure 4: (a) State diagram for $\kappa/k_BT=16$ as a function of density and activity, with isotropic (disks), nematic (triangles), and unstable (diamond) regimes. Colors denote the time-averaged global nematic order parameter $\langle S_B \rangle$. Representative snapshots of (b) isotropic ($\rho\sigma^{3}=0.5$, $f^{a}=0.1$), (c) nematic ($\rho\sigma^{3}=0.8$, $f^{a}=0.1$), and (d) unstable ($\rho\sigma^{3}=0.9$, $f^{a}=0.5$) states, where polymers are colored by their local nematic order $S_B^{\text{loc}}$ using the same color code as panel (a).
• Figure 5: (a) State diagram for larger bending stiffness $\kappa/k_BT=32$, covering the same range of activities and densities as in Fig. \ref{['fig:Phase_Diagram']}(a) with identical symbol representation. (b) The I--N transition density $\rho_{\text{I--N}}$ as a function of active force for different bending stiffness values.