Nishiyama Yoshihiro
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 1):031901. doi: 10.1103/PhysRevE.68.031901. Epub 2003 Sep 3.
Effective bending moduli of a fluid membrane are investigated by means of the transfer-matrix method developed in our preceding paper. This method allows us to survey various statistical measures for the partition sum. The role of the statistical measures is arousing much attention, since Pinnow and Helfrich claimed that under a suitable statistical measure, that is, the local mean curvature, the fluid membranes are stiffened, rather than softened, by thermal undulations. In this paper, we propose an efficient method to observe the effective bending moduli directly: We subjected a fluid membrane to a curved reference plane, and from the free-energy cost due to the reference-plane deformations, we read off the effective bending moduli. Accepting the mean-curvature measure, we found that the effective bending rigidity gains even in the case of very flexible membrane (small bare rigidity); it has been rather controversial that for such a nonperturbative regime, the analytical prediction does apply. We also incorporate the Gaussian-curvature modulus and calculated its effective rigidity. Thereby, we found that the effective Gaussian-curvature modulus stays almost scale invariant. All these features are contrasted with the results under the normal-displacement measure.
通过我们前文所发展的转移矩阵方法，研究了流体膜的有效弯曲模量。该方法使我们能够考察配分函数的各种统计量度。统计量度的作用引起了广泛关注，因为平诺和赫尔弗里希声称，在合适的统计量度下，即局部平均曲率，流体膜会因热涨落而变硬，而非变软。在本文中，我们提出了一种直接观测有效弯曲模量的有效方法：使流体膜与一个弯曲的参考平面接触，并根据参考平面变形所产生的自由能代价，读出有效弯曲模量。采用平均曲率量度时，我们发现即使对于非常柔性的膜（裸刚度小），有效弯曲刚度也会增加；对于这样一个非微扰区域，解析预测是否适用一直颇具争议。我们还纳入了高斯曲率模量并计算了其有效刚度。由此，我们发现有效高斯曲率模量几乎保持尺度不变。所有这些特征都与法向位移量度下的结果形成对比。
