Spontaneous Chiral Symmetry Breaking in Polydisperse Achiral Near-Rigid Nematogens

Understanding chirality transfer from the molecular to the macroscopic scale poses a significant challenge in soft and biological condensed matter physics. Many nanorods of biological origin not only have chiral molecular features but also exhibit a spread in contour length leading to considerable size dispersity. On top of this, random backbone fluctuations are ubiquitous for non-rigid particles but their role in chirality transfer remains difficult to disentangle from that of their native chirality imparted by their effective shape or surface architecture. We report spontaneous entropy-driven chiral symmetry breaking from molecular simulations of cholesteric liquid-crystals formed from achiral bead-spring rods with a continuous spread in contour length and marginal chain bending. The symmetry-breaking is caused by long-lived chiral conformations of long rods undergoing chiral synchronization leading to a homochiral twisted nematic. A simple theory demonstrates that even without chiral synchronization, the presence of shape-persistent configurational fluctuations along with length-dispersity can be harnessed to generate non-zero chirality at moderate polydispersity.

💡 Research Summary

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This paper investigates how achiral, near‑rigid rod‑like particles can spontaneously break mirror symmetry and form a cholesteric (twisted nematic) phase when they possess both backbone flexibility and a polydisperse distribution of contour lengths. Using a minimal bead‑spring model, each rod is represented by a chain of spherical beads (diameter d₀) linked by stiff harmonic bonds (k_bond = 1000 k_BT/d₀²) and angular potentials (k_angle = 120 k_BT) applied every three beads, giving the particles a “floppy cylinder” character. The persistence length Lₚ ≈ 240 d₀, so the rods are marginally flexible (L < Lₚ < ∞). Non‑bonded interactions are purely repulsive (WCA), ensuring that all phase behavior is entropy‑driven.

Rod lengths are drawn from a log‑normal distribution with mean aspect ratio (\bar L/d₀ = 15) and polydispersity σ = 0.2, 0.3, 0.38, 0.5, spanning realistic values for biological nanorods. Simulations start from a dilute isotropic state (c ≈ 1.15) in NVT, then the system is compressed at a constant rate into the dense nematic regime, followed by NPT runs at various pressures to map the isotropic‑nematic (I‑N) coexistence and any intermediate phases. Each run lasts 10⁶ τ (10⁷ τ for selected states) with a total of ≈ 5 × 10⁵ beads (≈ 3.3 × 10⁴ rods).

The phase diagram reveals that the I‑N biphasic region widens with increasing σ, as expected for polydisperse hard rods. Strikingly, only at intermediate polydispersity σ = 0.38 does a cholesteric phase appear, characterized by a uniform helical twist of the nematic director with pitch (P ≈ 16 \bar L). The global nematic order parameter S drops sharply at this σ, indicating that the twist is not a weak perturbation but a genuine symmetry‑breaking transition.

To quantify local chirality, the authors introduce a pseudo‑scalar order parameter
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