柱状流体膜的静力学和动力学性质研究

【作者】 贾艳伟；

【导师】 刘全慧；

【作者基本信息】 湖南大学 ， 理论物理， 2002， 硕士

【摘要】 自20世纪80年代以来，软物质或称软凝聚态物质的奇异特性便引起了广大物理、化学、和生物科学家的广泛关注。软物质物理代表了21世纪凝聚态物理发展的重要趋势，膜和泡则是重要的软物质。 双亲分子所构成的膜泡，其行为和性质类似于向列相液晶。Helfrich通过与液晶的类比得出了流体膜的弹性能量以及膜泡的形状方程。本文在简要介绍了Helfrich的弹性理论及膜方程的基础上，开创性地引入Taylor级数法，在轴对称膜的边界条件下，对Helfrich膜方程以Taylor级数法求解，统一地得到了目前已知的两个特解：常平均曲率曲面和红血球形状解。 本文还研究了柱状膜的静力学方程。由于开口的柱状膜的不稳定性，对柱状膜的研究只能采取近似方法。利用环拓扑结构近似，我们得到了无限长柱状膜的方程，但此方程没有给出任何有用的信息；利用球拓扑近似，无论直接变分还是间接变分，都给出了一组条件，规定了参数的一个取值范围，所以，球拓扑近似比环拓扑近似更实用一些。同时，通过我们的分析，发现Helfrich方程中积分常数C为零的情况仅适用于具有球拓扑结构的膜泡。 在光镊的作用下，柱状膜表现出令人惊讶的动力学行为，即珠链状结构的形成及其发展后期的水珠运动现象。对于此动力学行为，本文从膜的微观结构出发，建立了一个简单的模型，解释了珠链状膜的形成以及光镊熄灭后水珠的运动。并且定量计算了水珠的运动速度，与实验结果吻合，从而说明了本模型的合理性。更多还原

【Abstract】 Since eighties of the 20th century, membranes and vesicles as main parts of soft matter or soft condensed matter have aroused many interests of scientists, such as physicists, chemists and biologists, because of their attractive characteristics. The development of soft matter physics indicates the progress of condensed matter physics in the 21st century.Recognizing that the vesicle consisting of amphiphiles bilayer membrane is just like a nematic liquid crystal cell, Helfrich gave the elastic energy of the fluid membrane and the shape equation. In this paper, we give a brief introduction to the Helfrich elastic theory. To solve the Helfrich equation under the physical conditions of vesicles, a Taylor series method is introduced, which offers a unified method to reproduce the exact solution including the famous axisymmetrical constant-curvature surfaces and the biconcave shape solution.The equilibrium condition for the cylindrical configuration in fluid membrane is re-examined in this paper, using the direct and the indirect variational method and taking account of possible influences of its topology. Since the pure cylindrical vesicles without ends are unstable even non-existence, approximations of torus and cylinder with spherical ends are utilized. The result from the former approximation means the condition of infinite long cylinder, which gives us no useful information. By spherically topological approximation, we get a set of conditions, all of which specify the range of parameters. Evidently, spherically topological approximation is more usable than the other. When our result is used to examine a debate related to the integral constant C, a clean conclusion is reached, that Helfrich shape equation with C=0 is only valid for spherical topology vesicles.Applying laser tweezers to cylindrical vesicles of lipid bilayers induces an instability, which propagates down the vesicle leaving behind it a peristaltic state, which appears under the microscope as pearls on a string. We make up a simple model based on the microscopic mechanism of the membrane to investigate this phenomenon. The model proves reasonable after we quantify the velocity of the pearls drift slowly towards the laser trap.更多还原