Huang Wenjun, Huang Ming, Lei Qi, Larson Ronald G
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136, USA.
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China.
Polymers (Basel). 2016 Jul 16;8(7):264. doi: 10.3390/polym8070264.
We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy ( γ s ), energy of bundle end folds ( γ e ), and bending energy per unit length in a torus ( γ b ). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain.
我们开发了一个分析模型，用于预测溶液中单个半柔性聚合物链的塌缩构象，该模型考虑了链的长度、直径、刚度和自吸引力。我们构建了构象相图，该相图包含三种塌缩状态，即环面、束状和球状，其涵盖了三个能量参数的一系列无量纲比值，这三个能量参数分别为溶剂 - 水表面能（γs）、束状末端折叠能（γe）以及环面中单位长度的弯曲能（γb）。我们的相图捕捉了单个长链（>10个库恩长度）在中等偏高（约为1）的无量纲温度下的一般相行为，无量纲温度是热能与相邻单体间吸引相互作用的比值。我们发现，当无量纲链长与直径之比（L*）超过300时，相行为趋近于一个渐近极限。我们通过布朗动力学（BD）模拟成功验证了我们的分析结果，方法是将模拟参数映射到相图中使用的参数。我们评估了在中等偏高无量纲温度范围内三种不同弯曲势的影响，这是一个此前模拟未探索过的区域，并且发现模型与模拟结果之间存在定性的一致性。因此，我们证明了一个相当简化的分析模型可用于定性预测给定聚合物链的最终塌缩状态。
