Free-energy landscapes of semiflexible theta-polymer aggregation with and without external force

这个项目的主要目标是探索有外力和没有外力的半柔性聚合物聚集的普遍方面。重点将集中在植根于统计物理的类属结构特性和接枝的半柔性聚合物在外力作用下的自由能景观。分析将依赖于通过精心定制的多正则计算机模拟获得的数值数据。我们的目标是研究周期性边界条件下半柔性聚合物聚集的有限尺寸效应，并应用有限尺寸标度理论得出普遍的结论。重点将放在自由能格局上，特别是表征自由能势垒与链数的比例，取决于聚合物的刚性。在介观范围内，这种方法应该允许我们区分不同的聚集体形态，通常可以用作混合相相变的协议。由于聚集转变将能量主导的致密结构与熵主导的可溶区域分开，这需要低密度的系统和复杂的模拟方法，允许对能量和熵贡献进行有效采样，以及复杂的分析工具来分离它们。受受力作用下聚合物束的实验实现的推动，我们计划研究接枝的半柔性聚合物在有拉力和没有拉力的情况下的构象性质。确定自由能格局和相关的自由能势垒将允许描述从无序到无定形或束(塔)相的相关转变。在外力作用下，我们将重点放在相当灵活的聚合物上，在这种情况下，我们预计会有一个中等作用力区域，在该区域中，自吸引、相互吸引和拉力之间的竞争应该会产生具有螺旋扭曲的束状物。在这种情况下，我们想测试蠕虫链近似(适用于相当坚硬的聚合物束)是否适用于受外力作用的柔性聚合物束。这将扩展到一些接枝聚合物到一个有外场的装置，在那里我们的目标是研究自由能景观作为温度和场的函数。考虑交替场也可以让我们一瞥稳态属性，其中我们希望通过有限大小缩放来确定相关的长度尺度。将延伸的几何物体附着到未接枝的聚合物末端会带来额外的限制，并可能导致有趣和有前景的实验设置。

The main objective of this project is to explore universal aspects of semiflexible polymer aggregation with and without external force. The focus will be on generic structural properties rooted in statistical physics and free-energy landscapes of grafted semiflexible polymers subject to an external force. The analysis will rely on numerical data obtained with carefully tailored multicanonical computer simulations.We aim to investigate finite-size effects of semiflexible polymer aggregation in periodic boundary conditions and apply finite-size scaling theory to draw universal conclusions. Emphasis will be laid on the free-energy landscape, especially characterizing the scaling of the free-energy barrier with chain number, in dependence on the stiffness of the polymers. This approach in the mesoscopic range should allow us to distinguish different aggregate morphologies and may be used as a protocol for phase transitions with mixed phases, in general. Since the aggregation transition separatesenergy-dominated compact structures from an entropy-dominated soluble regime, this demands systems at low density and sophisticated simulation methods that allow efficient sampling of both energy and entropy contributions as well as sophisticated analysis tools to disentangle them.Motivated by experimental realizations of polymer bundles under force, we plan to study the conformational properties of grafted semiflexible polymers with and without pulling force. Determining the free-energy landscape and the associated free-energy barrier will allow the characterization of the involved transitions from disordered to amorphous or bundle (tower) phases. With an external force, wewill focus on rather flexible polymers where we expect an intermediate force regime in which the competition between self-attraction, mutual attraction and pulling force should give rise to bundles with a helical twist. In this case, we want to test if the worm-like chain approximation (which is well-applicable to rather stiff polymer bundles) becomes valid for flexible polymer bundles underexternal force.This will be extended for a few grafted polymers to a setup with an external field where we aim to study the free-energy landscape as a function of both temperature and field. Considering also alternating fields allows a glimpse at steady-state properties, where we want to identify relevant length scalesthrough finite-size scaling. Attaching extended geometric objects to the non-grafted polymer ends introduces additional constraints and may lead to interesting and promising experimental setups.