中文摘要：

对纳观接触角的确定曾有过许多研究工作,本文对各种理论进行分析评论,指出其各自的优缺点甚至错误,认为最为简单实用的理论是朱如曾于1995年在《大学物理》（（Vol.14（2）））的文章中对前人的宏观接触角的错误理论采用澄清接触角概念的方法所得到的纳观接触角的近似理论及近似公式α=（1？2EPS/EPL）π（其中EPL和EPS分别表示液体内部一个液体分子的势能和固体表面一个液态分子与固体的相互作用势能,并可用分子动力学（MD）模拟得到）,此理论属于纳观接触角的分子动力学理论的近似简化形式,值得进一步发展.为此,本文根据物理分析假设Gibbs张力表面上位于非三相接触区的一个液体分子的势能为EPL/2x,三相接触线上一个液体分子与其余液体的相互作用势能为（1＋kEPS/EPL）αEPL/2xπ,其中x和k 为优化参数.根据Gibbs分界面上处处势能相等条件,得到改进的纳观接触角的近似公式α=π（1？2xEPS/EPL）/（1＋kEPS/EPL）．对固体表面的氩纳米液柱,在温度90K下对液体分子之间采用林纳德－琼斯（L-J）势,液体分子与固体原子间采用带有可变强度参数a的 L-J 势,对0.650〈a〈0.825范围内的8种a值进行了MD模拟．得到了相应的Gibbs 张力面．将其纳观底角视为近似纳观接触角,结合物理条件（当EPS/EPL =0时,α=π）用最小二乘法得到优化参数值x=0.7141, k=1.6051和相关系数0.9997.这一充分接近于1的相关系数表明,对于不同相互作用强度的纳米液固接触系统,优化参数x和k确实可近似视为常数,由此确认我们提出的利用MD模拟来确定纳观接触角近似公式中优化参数的可行性和该近似公式的一般适用性.

英文摘要：

Theoretical analyses are given to the known approaches of nano-contact angle and arrive at the conclusions： 1） All the approaches based on the assumptions of Qusi-uniform liquid film, or uniform liquid molecular density, or uniform liquid molecular densities respectively inside and outside the interface layer cannot give the correct nano-contact angle, and it is dicult to improve them. Among these approaches, both the conclusions of nano-contact angle sure being 0and sure being 180 are false. 2） Density functional theory （DFT）approach and Molecular Dynamics （MD） approach are capable to treat of nano-contact angle, however, the work is very heavy for using the DFT approach. 3） In 1995, Ruzeng Zhu （Col lege Physic [Vol. 14 （2）, p1–4 （in Chinese）], corrected the concept of contact angle in a earlier false theory for macro contact angle and obtained the most simple and convenient approximate formula of nano-contact angleα=（12EPS/EPL）π,where EPL is the potential of a liquid molecule in the internal liquid and EPS is the interact potential between a liquid molecule and the solid on which it locats. Both EPS and EPL can be obtained by MD, therefore this theory as a approximate simplified form belongs to Molecular Dynamics approach of nano-contact angle. The results of 0 and 180 for complete wetting and complete non-wetting given by this formula are correct under the assumption of incompressible fluid, therefore, this theory is worthy of further development. For this end, based on the physical analysis, we assume that the potential energy of a liquid molecule on the Gibss surface of tension outside the three-phase contact area is EPL/2x and that of a liquid molecule on the three-phase contact line is （1＋kEPS/EPL）αEPL/2xπ, where x and k are optimal parameters. According to the condition that the potential energy is the same everywhere on the Gibss surface of tension, an improved approximate formula for nano-contact angle α = π（12xEPS/EPL）/（1＋kEPS/EPL） is obtained.To ob