Entropic force between biomembranes

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.