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Chin. Phys. B, 2021, Vol. 30(1): 016801    DOI: 10.1088/1674-1056/abb65a

Tolman length of simple droplet: Theoretical study and molecular dynamics simulation

Shu-Wen Cui(崔树稳)1,2, Jiu-An Wei(魏久安)3, Qiang Li(李强)1, Wei-Wei Liu(刘伟伟)1, Ping Qian(钱萍)4,†, and Xiao Song Wang(王小松)5
1 Department of Physics and Information Engineering, Cangzhou Normal University, Cangzhou 061001, China; 2 State Key Laboratory of Nonlinear Mechanics (LNM) and Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 3 Silfex, a Division of Lam Research, 950 South Franklin Street, Eaton, Ohio 45320, USA; 4 Department of Physics, University of Science and Technology Beijing, Beijing 100083, China; 5 Institute of Mechanics and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China
Abstract  In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension (R s) and found that they increase with the R s decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard-Jones (LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman's theory. These conclusions are significant for studying the size dependence of the surface tension.
Keywords:  Tolman length      surface tension radius of surface of tension      radius of equimolecular surface      molecular dynamics simulation  
Revised:  13 August 2020      Published:  30 December 2020
PACS:  68.03.Cd (Surface tension and related phenomena)  
  68.35.Md (Surface thermodynamics, surface energies)  
  68.08.Bc (Wetting)  
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0700500), the Scientific Research and Innovation Team of Cangzhou Normal University, China (Grant No. cxtdl1907), the Key Scientific Study Program of Hebei Provincial Higher Education Institution, China (Grant No. ZD2020410), the Cangzhou Natural Science Foundation, China (Grant No. 197000001), and the General Scientific Research Fund Project of Cangzhou Normal University, China (Grant No. xnjjl1906).
Corresponding Authors:  Corresponding author. E-mail:   

Cite this article: 

Shu-Wen Cui(崔树稳), Jiu-An Wei(魏久安), Qiang Li(李强), Wei-Wei Liu(刘伟伟), Ping Qian(钱萍), and Xiao Song Wang(王小松) Tolman length of simple droplet: Theoretical study and molecular dynamics simulation 2021 Chin. Phys. B 30 016801

1 Rowlinson J S and Widom B1982 Molecular Theory of Capillarity (Oxford: Clarendon Press)
2 de Gennes P G 1985 Rev. Mod. Phys. 57 827
3 Tolman R C 1949 J. Chem. Phys. 17 333
4 Lu H M and Jiang Q 2005 Langmuir 21 779
5 Lei Y A, Bykov T, Yoo S and Zeng X C 2005 J. Am. Chem. Soc. 127 15346
6 Pogosov V V 1994 Solid State Commun. 89 1017
7 Lee W T, Salje E K H and Dove M T 1999 J. Phys.: Condens. Matter 11 7385
8 Sergii B, Mykola I, Konstantinos T, Vladimir S and Leonid B 2017 Phys. Rev. E 95 062801
9 Nikolay V A 2018 Chem. Phys. 500 19
10 Blokhuis E M and Kuipers J 2006 J. Chem. Phys. 124 074701
11 Bykov T V and Zeng X C 2001 J. Phys. Chem. B 105 11586
12 Tovbin Y K2020 Russ. J. Phys. Chem. A 84 1717
13 Bykov T V and Zeng X C 1999 J. Chem. Phys. 111 10602
14 Napari I and Laaksonen A2001 J. Chem. Phys. 114 5796
15 Joswiak M N, Duff N, Doherty M F and Peters B 2013 J. Phys. Chem. Lett. 4 4267
16 Block B J, Das S K, Oettel M, Virnau P and Binder K 2010 J. Chem. Phys. 133 154702
17 Joswiak M N, Do R, Doherty M F and Peters B 2016 J. Chem. Phys. 145 204703
18 Ono S and Kondo S In Flugge (editor) 1960 Encyclopedia of Physics, Vol. 10 (Berlin: Springer-Verlag)
19 Yan H and Zhu R Z 2012 Chin. Phys. B 21 083103
20 Zhu R Z and Wang X S 2010 Chin. Phys. B 19 076801
21 Wang X S and Zhu R Z 2013 Chin. Phys. B 22 036801
22 McGraw R and Laaksonen A 1997 J. Chem. Phys. 106 5284
23 Buff F P 1955 J. Chem. Phys. 23 419
24 Koga K, Zeng X C and Shchekin A K 1998 J. Chem. Phys. 109 4063
25 Nijmeijer M J P, Bruin C, van Woerkom A B and Bakker A F 1992 J. Chem. Phys. 96 565
26 Haye M J and Bruin C 1994 J. Chem. Phys. 100 556
27 Rekhviashvili S Sh, Kishtikova E V, Karmokova R Yu and Karmokov A M 2007 Tech. Phys. Lett. 33 48
28 Cui S W, Zhu R Z, Wei J A, Wang X S, Yang H X, Xu S H and Sun Z W 2015 Acta Phys. Sin. 64 116802 (in Chinese)
29 Cui S W, Wei J A, Xu S H, Sun Z W and Zhu R Z 2015 J. Comput. Theor. Nanos 12 189
30 Thompson S M, Gubbins K E, Walton J P R B, Chantry R A R and Rowlinson J S 1984 J. Chem. Phys. 81 530
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