Schmitt Maurice P, Wettermann Sarah, Daoulas Kostas Ch, Meyer Hendrik, Virnau Peter
Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, 55099 Mainz, Germany.
Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
J Chem Phys. 2024 Oct 14;161(14). doi: 10.1063/5.0228826.
A central paradigm of polymer physics states that chains in melts behave like random walks as intra- and interchain interactions effectively cancel each other out. Likewise, θ-chains, i.e., chains at the transition from a swollen coil to a globular phase, are also thought to behave like ideal chains, as attractive forces are counterbalanced by repulsive entropic contributions. While the simple mapping to an equivalent Kuhn chain works rather well in most scenarios with corrections to scaling, random walks do not accurately capture the topology and knots, particularly for flexible chains. In this paper, we demonstrate with Monte Carlo and molecular dynamics simulations that chains in polymer melts and θ-chains not only agree on a structural level for a range of stiffnesses but also topologically. They exhibit similar knotting probabilities and knot sizes, both of which are not captured by ideal chain representations. This discrepancy comes from the suppression of small knots in real chains, which is strongest for very flexible chains because excluded volume effects are still active locally and become weaker with increasing semiflexibility. Our findings suggest that corrections to ideal behavior are indeed similar for the two scenarios of real chains and that the structure and topology of a chain in a melt can be approximately reproduced by a corresponding θ-chain.
高分子物理学的一个核心范式表明，熔体中的链表现得像随机行走，因为链内和链间相互作用有效地相互抵消。同样，θ链，即在从膨胀线团到球状相转变时的链，也被认为表现得像理想链，因为吸引力被排斥熵贡献所平衡。虽然在大多数情况下，简单地映射到等效的库恩链并对标度进行修正效果相当好，但随机行走并不能准确地捕捉拓扑结构和结，特别是对于柔性链。在本文中，我们通过蒙特卡罗和分子动力学模拟证明，聚合物熔体中的链和θ链不仅在一系列刚度的结构水平上一致，而且在拓扑结构上也一致。它们表现出相似的打结概率和结尺寸，而这两者都不能用理想链表示来捕捉。这种差异来自于真实链中小结的抑制，对于非常柔性的链来说，这种抑制最强，因为局部的排除体积效应仍然有效，并且随着半柔性的增加而减弱。我们的研究结果表明，对于真实链的两种情况，对理想行为的修正确实相似，并且熔体中链的结构和拓扑可以由相应的θ链近似再现。
