Trapping macromolecules is important for the study of their conformations, interactions, dynamics, and kinetic processes. Here, we develop a new theory using a Gaussian variational approach to confine the center-of-mass of polymers. It self-consistently introduces a mean force that controls the average position of the center-of-mass and a self-adjustable harmonic potential that counters the fluctuation of the center-of-mass position. The effectiveness and versatility of our theory are verified in three classical yet not fully understood problems in polymer science: (1) single-chain conformation in the whole regime of solvent quality, (2) globule-pearl necklace-coil transition of a polyelectrolyte, and (3) interchain interaction by simultaneously confining two polymers. The scaling relationships and θ behaviors are well captured. Conformations with large shape anisotropies appearing in charged polymers are clearly depicted. Being a field theoretical framework, our theory also facilitates visualization of the conformational response and kinetic process. Our theoretical prediction of the radius of gyration of poly(N-isopropylacrylamide) (PNIPAM) is in quantitative agreement with experimental results reported in the literature.

中文翻译：

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一种控制大分子质心的变分场论方法


捕获大分子对于研究它们的构象、相互作用、动力学和动力学过程非常重要。在这里，我们开发了一种新理论，使用高斯变分方法来限制聚合物的质心。它自洽地引入了一个控制质心平均位置的平均力和一个自可调的谐波电位，以抵消质心位置的波动。我们理论的有效性和多功能性在聚合物科学中的三个经典但尚未完全理解的问题中得到了验证：（1） 整个溶剂质量范围内的单链构象，（2） 聚电解质的小球-珍珠项链-线圈转变，以及 （3） 通过同时限制两种聚合物的链间相互作用。缩放关系和 θ 行为被很好地捕获。在带电聚合物中出现的大形状各向异性的构象被清楚地描绘出来。作为一个场论框架，我们的理论还有助于构象响应和动力学过程的可视化。我们对聚（N-异丙基丙烯酰胺）（PNIPAM）回转半径的理论预测与文献中报道的实验结果在定量上是一致的。