波动力量, entropic 力量,源自热地激动的变化,和戏在在宾语的附近的表面之间的必要相互作用的一个关键角色。尽管波动力量的特征广泛地理论上并且试验性地被学习了,力量的距离依赖,组成它的很基本的特征,仍然保持糟糕理解。在这份报纸,首先,我们由采用弹性和统计力学为波动力量获得新奇表情并且证明它在对存在试验性的结果的好同意。第二,我们清楚地证明波动力量的二种代表性的形式由 Helfrich 求婚了, Freund 是分别地现在的表示的上面、更低的界限当在膜之间的分离是足够地小的时,它与波动力量的 Helfrichs 和 Freunds 形式对中间、小的分离仅仅合适的存在结果内在地不同。调查证明仅仅在足够地小的分离, Helfrichs 结果与一个大波浪数字和 Freunds 结果快车代表波动力量有一个小波浪数字的力量。最后,波动力量, entropic 力量将很快在以外腐烂接近零的批评代理距离,被介绍。
Undulation force, an entropic force, stems from thermally excited fluctuations, and plays a key role in the essential interactions between neighboring surfaces of objects. Although the characteristics of the undulation force have been widely studied theoretically and experimentally,the distance dependence of the force, which constitutes its most fundamental characteristic, remains poorly understood.In this paper, first, we obtain a novel expression for the undulation force by employing elasticity and statistical mechanics and prove it to be in good agreement with existing experimental results. Second, we clearly demonstrate that the two representative forms of the undulation force proposed by Helfrich and Freund were respectively the upper and lower bounds of the present expression when the separation between membranes is sufficiently small, which was intrinsically different from the existing results where Helfrich's and Freund's forms of the undulation force were only suitable for the intermediate and small separations. The investigations show that only in a sufficiently small separation does Helfrich's result stand for the undulation force with a large wave number and Freund's result express the force with a small wave number. Finally, a critical acting distance of the undulation force, beyond which the entropic force will rapidly decay approaching zero, is presented.