Stable knotted phases in semiflexible polymers

在这个项目中，我们计划进行计算机模拟来研究线性聚合物链中结的发生。对于柔性聚合物，众所周知，各种类型的结以一定的概率形成。最近，我们发现在半柔性θ聚合物的相图中定义明确的区域，其中特定类型的结不仅偶然存在，而且是稳定的。这意味着几乎每种构象都具有相同的结类型。通过结合多通道算法和复制交换蒙特卡罗模拟方法，我们希望更详细地了解这些“打结”相的性质。例如，我们想阐明为什么在向打结相的过渡中有明显的相共存，尽管没有观察到潜热，为此，我们将采用自由能景观的分析。特别是，我们计划计算的自由能障碍和过渡到打结构象的途径。从初步的模拟，我们怀疑，打结的构象被抑制的情况下，键长是相同的非相邻单体之间的相互作用的平衡距离。为了更好地理解这一观察结果，我们将系统地改变键长，并研究其对稳定打结相的影响。接下来，我们将进行计算机模拟，研究吸附表面如何影响打结聚合物。在第一步中，我们计划模拟一个半柔性的粗颗粒聚合物，并调查哪些稳定的结生存的吸附过程。除此之外，我们还想更深入地了解半柔性聚合物吸附的一般方面。这项研究的粗粒度模型也作为一个准备更苛刻的模拟化学现实的聚合物与表面相互作用。在过去的几年中，在制备和检测吸附在表面上的单一聚合物方面取得了令人印象深刻的进展，因此现在可以检测由20个单体组成的聚合物。因此，我们的目标是设计这项工作中的模拟，使它们可以扩展到更现实的模型。

In this project, we plan to perform computer simulations to study the occurrence of knots in linear polymer chains. For flexible polymers it is well known that knots of various types form with a certain probability. Recently, we found in the phase diagram of semiflexible theta polymers well-defined regions, where knots of a specific type exist not only by chance but are thermodynamically stable. This means that almost every conformation is characterized by the same knot type. By combining the multicanoncial algorithm and the replica-exchange Monte Carlo simulation method, we want to understand the properties of these "knotted" phases in more detail. For example, we want to elucidate why there is a clear phase coexistence at the transition into the knotted phases, although no latent heat is observable.To this end we shall employ analyses of the free-energy landscape. In particular, we plan to calculate the free-energy barriers and the transition pathways into the knotted conformations. From preliminary simulations, we suspect that knotted conformations are suppressed in the case that the bond length is identical to the equilibrium distance of the interaction between non-adjacent monomers. For a better understanding of this observation, we will systematically vary the bond length and investigate its influence on the occurrence of stable knotted phases.Next we shall conduct computer simulations to investigate how an adsorbing surface influences the knotted polymers. In a first step, we plan to simulate a semiflexible coarse-grained polymer and investigate which thermodynamically stable knots survive the adsorption process. Besides that we want to get a deeper understanding of the generic aspects of adsorption of semiflexible polymers. This study of a coarse-grained model also serves as a preparation for more demanding simulations of chemically realistic polymers interacting with a surface. In the past few years quite impressive progress has been made in preparation and detection of single polymers adsorbed on surfaces, so that it is now possible to detect polymers consisting of down to 20 monomers. Therefore, we aim to design the simulations in this work such that they can be extended to more realistic models.