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纳观接触角的确定方法
The method for determining nano-contact angle

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崔树稳 1   朱如曾 2 *   魏久安 3   王小松 4   杨洪秀 5   徐升华 6   孙祉伟 6  
文摘 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 = (1-2E_(PS)/E_(PL)π (其中E_(PL)和E_(PS)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E_(PL)/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+kE_(PS)/E_(PL)α E_(PL)/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(1-2xE_(PS)/E_(PL)/(1+kE_(PS)/E_(PL).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E_(PS)/E_(PL)=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.
其他语种文摘 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 difficult to improve them. Among these approaches, both the conclusions of nano-contact angle sure being 0° and 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 (College 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 angle α = (1-2E_(PS)/E_(PL)π,where E_(PL) is the potential of a liquid molecule in the internal liquid and E_(PS) is the interact potential between a liquid molecule and the solid on which it locats. Both E_(PS) and E_(PL) 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 E_(PL)/2x and that of a liquid molecule on the three-phase contact line is (1+kE_(PS)/E_(PL)α E_(PL)/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(1-2xE_(PS)/E_(PL)/(1+kE_(PS)/E_(PL) is obtained.To obtain the value of x and k, MD simulations are carried on argon liquid cylinders placed on the solid surface under the temperature 90 K, by using the lennard-Jones (LJ) potentials for the interaction between liquid molecules and for that between a liquid molecule and a solid molecule with the variable coefficient of strength a. Eight values of a between 0.650 and 0.825 are used. The Gibss surfaces of tension are obtained by simulations and their bottom angles are treated as the approximate nano-contact angles. Combining these data with the physical conditions (when E_(PS)/E_(PL)=0, α = π), the optimized parameter values x=0.7141, k=1.6051 with the correlation coefficient 0.9997 are obtained by least square method. This correlation coefficient close enough to 1 indicates that for nano liquid solid contact system with different interaction strength, the parameter of optimization x and k really can be viewed as constants, so that our using MD simulation to determine of the optimized parameters is feasible and our approximate formula is of general applicability.
来源 物理学报 ,2015,64(11):116802-01-116802-09 【核心库】
DOI 10.7498/aps.64.116802
关键词 纳观接触角 ; 分子动力学模拟 ; 表面张力 ; 实用公式
地址

1. 沧州师范学院物理与电子信息系, 沧州, 061001  

2. 中国科学院力学研究所, 非线性力学国家重点实验室;;微重力国家实验室, 北京, 100190  

3. Silfex, a Division of Lam Research, America, Ohio, 45320  

4. 河南理工大学机械与动力学院, 焦作, 454003  

5. 沧州师范学院图书馆, 沧州, 061001  

6. 中国科学院力学研究所, 微重力国家实验室, 北京, 100190

语种 中文
文献类型 研究性论文
ISSN 1000-3290
学科 力学
基金 河南理工大学博士基金 ;  河南省教育厅科学技术研究重点项目 ;  国家自然科学基金
文献收藏号 CSCD:5439496

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引证文献 1 篇

1 徐威 微液滴在不同能量表面上润湿状态的分子动力学模拟 物理学报,2015,64(21):216801-1-216801-8
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