Charged amphiphiles in solution usually self-assemble into flat nanoribbons that spontaneously twist into different shapes. The role of electrostatics in this process is still under strong debate. This work studies the electrostatic free energy of twisting a nanoribbon at the level of the nonlinear Poisson–Boltzmann approximation. It is shown that helicoid-shaped ribbons are more stable than flat ribbons, while other shapes under consideration (cylindrical helixes and bent ribbons) are always less stable than the flat ribbon. The unexpected electrostatics-driven twisting of the ribbon into a helicoid is ascribed to the increase in its perimeter with increasing degree of twisting, as charges near the edge of the ribbon are electrostatically more stable than those near its center. This argument successfully explains the effects of salt concentration and the width of the ribbon on the optimal twisting period and allows us to approximately describe the problem of ribbon twisting in terms of two dimensionless variables that combine the helicoid twisting period, the Debye length of the solution, and the width of the ribbon. The magnitude of the electrostatic twisting energy predicted by our calculations is comparable to that of restoring elastic forces for typical ribbons of self-assembled amphiphiles, which indicates that electrostatics plays an important role in determining the equilibrium shape of charged nanoribbons.

中文翻译：

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静电将带电纳米带扭曲成螺旋体

溶液中带电的两亲物通常自组装成扁平的纳米带，纳米带会自发地扭曲成不同的形状。静电在此过程中的作用仍在激烈辩论中。这项工作研究了在非线性Poisson–Boltzmann逼近水平下扭曲纳米带的静电自由能。结果表明，螺旋形带比扁平带更稳定，而所考虑的其他形状（圆柱螺旋形和弯曲带）总是比扁平带更不稳定。由于带的边缘附近的电荷比其中心附近的电荷在静电上更稳定，因此带子意外地由静电驱动的带状扭曲变成螺旋状归因于其周边随着扭曲程度的增加而增加。该论点成功地解释了盐浓度和色带宽度对最佳加捻时间的影响，并允许我们用两个无量纲变量来近似地描述色带加捻问题，该变量结合了螺旋形加捻时间，溶液的德拜长度。 ，以及功能区的宽度。通过我们的计算预测，静电扭曲能量的大小可与恢复典型自组装两亲物带的弹力相媲美，这表明静电在确定带电纳米带的平衡形状方面起着重要作用。