手性聚合物与生物聚合物螺旋的手性选择理论
Theory of Handedness Selection in Helices of Chiral Polymers and Biopolymers
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中文总结 AI 辅助
该研究针对手性聚合物与生物聚合物的螺旋结构，建立三态类伊辛转移矩阵理论，分离螺旋-线团协同性与手性持久性，推导特征长度公式，发现局部手性偏差可在有限螺旋域放大。
中文摘要 AI 辅助
螺旋是生物与合成聚合物中最常见的有序结构之一，但其形成不仅涉及局部构象偏好。有限长度的螺旋必须成核、生长、抵抗断裂，并在热涨落下维持选定的手性。我们建立了一种三态类伊辛转移矩阵理论，其中每个链段可呈无规线团状、右手螺旋或左手螺旋。该公式将普通的螺旋-线团协同性与手性的持久性分离开来。左右对称问题可分解为对称与反对称扇区，给出两个特征长度：螺旋相关长度ξ_H和手性持久长度ξ_χ。在强螺旋的稀有壁极限下，ξ_χ≈(1/2)exp[β(K+J)]。受拉氏图（Ramachandran landscape）启发的局部手性偏差，会在有限螺旋域内被放大。
英文摘要
Helices are among the most common ordered structures in biological and synthetic polymers, but their formation involves more than local conformational preference. A finite helix must nucleate, grow, resist breaking, and maintain a selected handedness against thermal fluctuations. We develop a three-state Ising-like transfer-matrix theory in which each segment is coil-like, right-handed helical, or left-handed helical. This formulation separates ordinary helix--coil cooperativity from the persistence of handedness. The right--left symmetric problem decomposes into symmetric and antisymmetric sectors, giving two characteristic lengths: the helical correlation length $ξ_H$ and the chiral persistence length $ξ_χ$. In the strongly helical rare-wall limit, $ξ_χ\simeq (1/2)\exp[β(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.
