-
由维里定理导出的适用于均匀系统的平衡态压力张量表达式可以分成两部分: 动压力张量和位形压力张量. 人们进而对平衡的非均匀系统进行物理分析得到了局部平均压力张量表达式. 本文用更为简洁的方法推导出这一表达式. 给出以原子直径为长度单位的局部平均尺寸L* > 8条件下均匀流体系统平均位形压力中的三部分贡献项(体贡献项、面贡献项和线贡献项)与L*的理论关系式(含有待定参数); 以氩原子气体为例, 在温度180 K、原子数密度0.8下, 对原子间采用林纳德-琼斯势进行了分子动力学模拟, 给出了0.4 ≤ L* ≤ 17条件下三项贡献及总位形压力的模拟曲线, 确定了L* > 8条件下理论关系式中的待定系数, 并得到在L* > 2时, 随着L*的增大, 体贡献项从正压单调下降并趋于负的总位形压力, 面贡献项和线贡献项都单调上升并趋于零, 但线贡献项趋向零最快. 从物理上解释了小尺寸L*下各项行为的复杂特点. 得出L*足够大, 才可以忽略面贡献项和线贡献项, 而在纳米尺度下, 忽略面贡献项和线贡献项, 也就是忽略边界效应会给计算带来明显的误差. 最后通过分子动力学模拟得出位形压力随着温度的升高而升高. 这些结论对于压力张量的分子动力学模拟计算时选项的最优化是有意义的.The expression of equilibrium pressure tensor for uniform systems derived from Virial theorem can be divided into two parts: dynamic pressure tensor and configuration pressure tensor. The local mean pressure tensor is obtained by physical analysis of the equilibrium non-uniform system. In this paper, this expression is derived in a more concise way. The theoretical relationship, with undetermined parameters, between the three parts (the volume contribution, the surface contribution and the line contribution) of the average configuration pressure of a homogeneous fluid system and the local average size L* with the atomic diameter as length unit greater than 8 is given. Taking argon as an example, molecular dynamics simulation is carried out by using the Lennard-Jones potential between atoms at temperature 180 K and density 0.8 (atomic diameter)–3. The simulation curves of configuration pressure and its three parts are given, and the undetermined coefficients in the theoretical relationship under the condition of L* > 8 are determined. It is found that for L* > 2, With the increase of L*, the volume contribution decreases monotonously from the positive pressure to the negative total configuration pressure, while the surface contribution and the line contribution both increase monotonously and tend to zero, but the line contribution tends to zero fastest. The complex characteristics of various behaviors are explained physically. It is concluded that the surface contribution and the line contribution can be neglected only if L* are large enough. In nanoscale, the neglect of the surface contribution and the line contribution, i.e., the neglect of the boundary effect, will bring obvious errors to the calculation. Finally, molecular dynamics simulation shows that the configuration pressure increases with the increase of temperature. These conclusions are significant for optimizing the selection of pressure tensor in molecular dynamics simulation.
-
Keywords:
- Virial theorem /
- molecular dynamics simulation /
- surface tension /
- local pressure tensor /
- configuration pressure
[1] Clausius R 1870 Philosoph. Magaz. 40 122
[2] Maxwell J C 1874 Nature 10 477
Google Scholar
[3] Kirkwood J G, Buff F P T 1949 J. Chem. Phys. 17 338
Google Scholar
[4] Irving J H, Kirkwood J G 1950 J. Chem. Phys. 18 817
Google Scholar
[5] Harasima A 1958 Adv. Chem. Phys. 1 203
[6] Schofield P, Hendersen J R 1982 Proc. R. Soc. London Ser. A 379 231
Google Scholar
[7] 毛志红, 包福兵, 余霞 2013 低温工程 3 47
Google Scholar
Mao Z H, Bao F B, Yu X 2013 Cryogenics 3 47
Google Scholar
[8] 周绍华, 黄永华 2018 低温物理学报 40 49
Zhou S H, Huang Y H 2018 Chin. J. Low. Temp. Phys. 40 49
[9] Cormier J, Rickman J M, Delph T J 2001 J. Appl. Phys. 89 99
Google Scholar
[10] Cheung K S, Yip S 1991 J. Appl. Phys. 70 5688
Google Scholar
[11] Sun Z H, Wang X X, Soh K A, Wu H A 2006 Model. Simul. Mater. Sci. Eng. 14 423
Google Scholar
[12] Xu R, Liu B 2009 Acta Mech. Solida Sin. 22 644
Google Scholar
[13] Li Y F, Cui M Q, Peng B, Qin M D 2018 J. Mol. Graph. Model. 83 84
Google Scholar
[14] Torres-Sánchez A, Vanegas J M, Arroyo M 2015 Phys. Rev. Lett. 114 258102
Google Scholar
[15] Chen Y 2016 Europhys. Lett. 116 34003
Google Scholar
[16] Yu Y X, Jin L 2008 J. Chem. Phys. 128 014901
Google Scholar
-
图 2 一个粒子在V内, 一个粒子在V外, 只有一个交点示意图
Fig. 2. Geometry for calculating the contribution to the pressure from a pair of molecules i and j with only one intersection.
图 3 两个粒子都在V外有两个交点示意图
Fig. 3. Geometry for calculating the contribution to the pressure from a pair of molecules i and j with two intersections.
图 4
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ ,$\overline {p_{\rm{c}}^*} $ 与${L^*}$ 的关系Fig. 4. Relation between
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ ,$\overline {p_{\rm{c}}^*} $ and${L^*}$ .
图 7
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ ,$\overline {p_{\rm{c}}^*} $ 与${T^*}$ 的关系Fig. 7. Relation between
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ ,$\overline {p_{\rm{c}}^*} $ and${T^*}$ .表 1
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ 和$\overline {p_{\rm{c}}^*} $ 的模拟值Table 1. Values of
$\overline {p_1^*} $ ,$\overline {p_2^*} $ ,$\overline {p_3^*} $ and$\overline {p_{\rm{c}}^*} $ given by simulation.${L^*}$ $\overline {p_1^*} $ $\overline {p_2^*} $ $\overline {p_3^*} $ $\overline {p_c^*} $ 0.4 0 0.014 –0.082 –0.069 0.8 0 0.00814 –0.0773 –0.069 1.2 0.035 –0.04 –0.067 –0.0705 1.6 0.039 –0.071 –0.038 –0.07 2 0.034 –0.072 –0.031 –0.069 2.4 0.024 –0.072 –0.021 –0.069 2.8 0.018 –0.07 –0.015 –0.069 3.2 0.011 –0.068 –0.012 –0.069 3.6 0.0053 –0.067 –0.0089 –0.069 4 –3 × 10–4 –0.064 –0.007 –0.07 5 –0.01 –0.06 –0.0054 –0.07 6 –0.02 –0.05 –0.0038 –0.073 8 –0.035 –0.034 –0.0021 –0.071 10 –0.045 –0.024 –0.0014 –0.07 12 –0.051 –0.02 –9 × 10–4 –0.071 14 –0.055 –0.015 –5 × 10–4 –0.07 16 –0.06 –0.012 –2.6 × 10–4 –0.072 17 –0.06 –0.01 –1 × 10–4 –0.07 
下载: 导出CSV
-
[1] Clausius R 1870 Philosoph. Magaz. 40 122
[2] Maxwell J C 1874 Nature 10 477
Google Scholar
[3] Kirkwood J G, Buff F P T 1949 J. Chem. Phys. 17 338
Google Scholar
[4] Irving J H, Kirkwood J G 1950 J. Chem. Phys. 18 817
Google Scholar
[5] Harasima A 1958 Adv. Chem. Phys. 1 203
[6] Schofield P, Hendersen J R 1982 Proc. R. Soc. London Ser. A 379 231
Google Scholar
[7] 毛志红, 包福兵, 余霞 2013 低温工程 3 47
Google Scholar
Mao Z H, Bao F B, Yu X 2013 Cryogenics 3 47
Google Scholar
[8] 周绍华, 黄永华 2018 低温物理学报 40 49
Zhou S H, Huang Y H 2018 Chin. J. Low. Temp. Phys. 40 49
[9] Cormier J, Rickman J M, Delph T J 2001 J. Appl. Phys. 89 99
Google Scholar
[10] Cheung K S, Yip S 1991 J. Appl. Phys. 70 5688
Google Scholar
[11] Sun Z H, Wang X X, Soh K A, Wu H A 2006 Model. Simul. Mater. Sci. Eng. 14 423
Google Scholar
[12] Xu R, Liu B 2009 Acta Mech. Solida Sin. 22 644
Google Scholar
[13] Li Y F, Cui M Q, Peng B, Qin M D 2018 J. Mol. Graph. Model. 83 84
Google Scholar
[14] Torres-Sánchez A, Vanegas J M, Arroyo M 2015 Phys. Rev. Lett. 114 258102
Google Scholar
[15] Chen Y 2016 Europhys. Lett. 116 34003
Google Scholar
[16] Yu Y X, Jin L 2008 J. Chem. Phys. 128 014901
Google Scholar
-
[1] 秦梦飞, 王英敏, 张红玉, 孙继忠. 〈100〉 间隙型位错环在纯钨及含氦杂质钨(010)表面下运动行为的分子动力学模拟. 物理学报, 2023, 72(24): 245204. doi: 10.7498/aps.72.20230651[2] 张超, 布龙祥, 张智超, 樊朝霞, 凡凤仙. 丁二酸-水纳米气溶胶液滴表面张力的分子动力学研究. 物理学报, 2023, 72(11): 114701. doi: 10.7498/aps.72.20222371 [3] 张博佳, 安敏荣, 胡腾, 韩腊. 镁中位错和非晶作用机制的分子动力学模拟. 物理学报, 2022, 71(14): 143101. doi: 10.7498/aps.71.20212318 [4] 潘伶, 张昊, 林国斌. 纳米液滴撞击柱状固体表面动态行为的分子动力学模拟. 物理学报, 2021, 70(13): 134704. doi: 10.7498/aps.70.20210094 [5] 周浩, 李毅, 刘海, 陈鸿, 任磊生. 最优输运无网格方法及其在液滴表面张力效应模拟中的应用. 物理学报, 2021, 70(24): 240203. doi: 10.7498/aps.70.20211078 [6] 史超, 林晨森, 陈硕, 朱军. 石墨烯表面的特征水分子排布及其湿润透明特性的分子动力学模拟. 物理学报, 2019, 68(8): 086801. doi: 10.7498/aps.68.20182307 [7] 林文强, 徐斌, 陈亮, 周峰, 陈均朗. 双酚A在氧化石墨烯表面吸附的分子动力学模拟. 物理学报, 2016, 65(13): 133102. doi: 10.7498/aps.65.133102 [8] 徐威, 兰忠, 彭本利, 温荣福, 马学虎. 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. doi: 10.7498/aps.64.216801 [9] 喻晓, 沈杰, 钟昊玟, 张洁, 张高龙, 张小富, 颜莎, 乐小云. 强脉冲电子束辐照材料表面形貌演化的模拟. 物理学报, 2015, 64(21): 216102. doi: 10.7498/aps.64.216102 [10] 崔树稳, 朱如曾, 魏久安, 王小松, 杨洪秀, 徐升华, 孙祉伟. 纳观接触角的确定方法. 物理学报, 2015, 64(11): 116802. doi: 10.7498/aps.64.116802 [11] 司丽娜, 王晓力. 纳米沟槽表面黏着接触过程的分子动力学模拟研究. 物理学报, 2014, 63(23): 234601. doi: 10.7498/aps.63.234601 [12] 颜超, 段军红, 何兴道. Ni原子倾斜轰击Pt(111)表面低能溅射现象的分子动力学模拟. 物理学报, 2011, 60(8): 088301. doi: 10.7498/aps.60.088301 [13] 李瑞, 胡元中, 王慧. Si表面间水平碳纳米管束的分子动力学模拟研究. 物理学报, 2011, 60(1): 016106. doi: 10.7498/aps.60.016106 [14] 贺平逆, 宁建平, 秦尤敏, 赵成利, 苟富均. 低能Cl原子刻蚀Si(100)表面的分子动力学模拟. 物理学报, 2011, 60(4): 045209. doi: 10.7498/aps.60.045209 [15] 颜超, 段军红, 何兴道. 低能原子沉积在Pt(111)表面的分子动力学模拟. 物理学报, 2010, 59(12): 8807-8813. doi: 10.7498/aps.59.8807 [16] 孟丽娟, 李融武, 刘绍军, 孙俊东. 异质原子在Cu（001）表面扩散的分子动力学模拟. 物理学报, 2009, 58(4): 2637-2643. doi: 10.7498/aps.58.2637 [17] 孟利军, 张凯旺, 钟建新. 硅纳米颗粒在碳纳米管表面生长的分子动力学模拟. 物理学报, 2007, 56(2): 1009-1013. doi: 10.7498/aps.56.1009 [18] 赵九洲, 刘 俊, 赵 毅, 胡壮麒. 压力对非晶铜形成影响的分子动力学模拟. 物理学报, 2007, 56(1): 443-445. doi: 10.7498/aps.56.443 [19] 王昶清, 贾 瑜, 马丙现, 王松有, 秦 臻, 王 飞, 武乐可, 李新建. 不同温度下Si(001)表面各种亚稳态结构的分子动力学模拟. 物理学报, 2005, 54(9): 4313-4318. doi: 10.7498/aps.54.4313 [20] 唐 鑫, 张 超, 张庆瑜. Cu(111)三维表面岛对表面原子扩散影响的分子动力学研究. 物理学报, 2005, 54(12): 5797-5803. doi: 10.7498/aps.54.5797
下载:
计量
- 文章访问数: 7559
- PDF下载量: 44
- 被引次数: 0
