MOTION OF A CYLINDRICAL DIELECTRIC BOUNDARY
MOTION OF A CYLINDRICAL DIELECTRIC BOUNDARY
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DOI：
10.1137/120867986
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发表时间：
2013-01-01
影响因子：
1.9
通讯作者：
Zhou, Shenggao
中科院分区：
文献类型：
--
作者：
Cheng, Li-Tien;Li, Bo;Zhou, Shenggao
几何形状和静电之间的相互作用对生物分子在水溶液中的疏水相互作用有重要贡献。对于隐式溶剂，这样的系统可以通过将高介电溶剂与低介电溶质分开的介电边界来宏观地描述。这项工作涉及的模型圆柱形介电边界的自由能泛函，包括表面能和静电能的最陡下降的运动。定义了有效介质边界力，并得到了该力的显式表达式。发现这种力总是从溶剂区指向溶质区。在一个圆柱体的内部是一个较低的介电介质的情况下，介电边界的运动最初主要由表面力驱动，但随后被迅速向内驱动到圆柱轴的表面力和静电力。在圆柱体内部具有较高介电常数的情况下，几何贡献和静电贡献之间的竞争导致圆柱体平衡边界的存在。线性稳定性分析表明，这样的平衡是稳定的波数大于一个临界值的扰动。数值模拟报告的情况下，确认的驱动力的每个组件的作用上的分析。数学研究结果的带电分子系统的理解的影响进行了讨论。
The interplay between geometry and electrostatics contributes significantly to hydrophobic interactions of biomolecules in an aqueous solution. With an implicit solvent, such a system can be described macroscopically by the dielectric boundary that separates the high-dielectric solvent from low-dielectric solutes. This work concerns the motion of a model cylindrical dielectric boundary as the steepest descent of a free-energy functional that consists of both the surface and electrostatic energies. The effective dielectric boundary force is defined, and an explicit formula of the force is obtained. It is found that such a force always points from the solvent region to the solute region. In the case that the interior of a cylinder is of a lower dielectric, the motion of the dielectric boundary is initially driven dominantly by the surface force but is then driven inward quickly to the cylindrical axis by both the surface and electrostatic forces. In the case that the interior of a cylinder is of a higher dielectric, the competition between the geometrical and electrostatic contributions leads to the existence of equilibrium boundaries that are circular cylinders. Linear stability analysis is presented to show that such an equilibrium is only stable for a perturbation with a wavenumber larger than a critical value. Numerical simulations are reported for both of the cases, confirming the analysis on the role of each component of the driving force. Implications of the mathematical findings to the understanding of charged molecular systems are discussed.