Influence of the dividing surface notion on the formulation of Tolman’s law

  • M T Horsch STFC Daresbury Laboratory, United Kingdom American University of Iraq, Sulaimani (AUIS), Iraq
Keywords: Nucleation theory; surface tension; nanodroplets; Tolman’s law; interfacial thermodynamics


The influence of the surface curvature 1/R on the surface tension γ of small droplets at equilibrium with a surrounding vapour, or small bubbles at equilibrium with a surrounding liquid, can be expanded as γ(R) = γ0 –2δ0/R + O(1/R2), where R = RL is the Laplace radius and γ0 is the surface tension of the planar interface, with zero curvature. According to Tolman's law, the first-order coefficient in this expansion is obtained from the planar limit δ0 of the Tolman length, i.e., the deviation δ = Re – RL between the equimolar radius Re and RL. Here, Tolman’s law is generalized such that it can be applied to any notion of the dividing surface, beside the Laplace radius, on the basis of a generalization of the Gibbs adsorption equation which consistently takes the size dependence of interfacial properties into account.


D Bedeaux and S Kjelstrup (2018), Chem. Phys. Lett., 707, pp. 40-43.
K V Cherevko, L A Bulavin, L L Jenkovszky, V M Sysoev and F S Zhang (2015), Phys. Rev. C, 92, p. 014308.
S K Das and K Binder (2011), Phys. Rev. Lett., 107, p. 235702.
R L Davidchack and B B Laird (2018), J. Chem. Phys., 149, p. 174706.
J Feder, K C Russell, J Lothe and G M Pound (1966), Adv. Phys., 15, pp. 111-178.
J W Gibbs (1878), Transact. CT Acad. Arts Sci., 3, pp. 108-248, 343-524.
T L Hill (1964), Thermodynamics of Small Systems, Benjamin, New York.
A A Homman, E Bourasseau, G Stoltz, P Malfreyt, L Strafella and A Ghoufi (2014), J. Chem. Phys., 140, p. 034110.
M T Horsch (2019), Chem. Eng. Transact., accepted.
M T Horsch, S Becker, M Heier, J K Singh, F Diewald, R Müller, G Jackson, J Vrabec and H Hasse (2019), in preparation.
A Malijevský and G Jackson (2012), J. Phys.: Cond. Mat., 24, p. 464121.
A V Mokshin and B M Galimzyanov (2012), J. Phys. Chem. B, 116, 39, pp. 11959-11967.
S H Min and M L Berkowitz (2019), J. Chem. Phys., 150, p. 054501.
X Mu, F Frank, B Riviere, F O Alpak and W G Chapman (2018), Ind. Eng. Chem. Res., 57, pp. 16476-16485.
P Rehner and J Gross (2018), J. Chem. Phys., 148, p. 164703.
J S Rowlinson and B Widom (1982), Molecular Theory of Capillarity, Clarendon, Oxford.
B A Strøm, J M Simon, S K Schnell, S Kjelstrup, J He and D Bedeaux (2017), Phys. Chem. Chem. Phys., 19, 13, pp. 9016-9027.
S Sumardiono and J Fischer (2007), Microfluid. Nanofluid., 3, 2, pp. 127-140.
R C Tolman (1949), J. Chem. Phys., 17, 3, pp. 333-337.
Ø Wilhelmsen, D Bedeaux and D Reguera (2015), J. Chem. Phys., 142, p. 064706.
How to Cite
T Horsch, M. (2019) “Influence of the dividing surface notion on the formulation of Tolman’s law”, Zanco Journal of Pure and Applied Sciences, 31(s3), pp. 199-203. doi: 10.21271/ZJPAS.31.s3.27.