Universality in the Dependence of the Drop Contact Angle on Liquid-Solid Interactions and Temperature Obtained by the Density Functional Theory *

A nonlocal density functional theory is employed to calculate the contact angles of nano- and macrodrops on smooth solid surfaces in wide ranges of temperature and parameters of the Lennard-Jones potentials representing the fluid-fluid and fluid-solid interactions. For both types of drops, simple linear dependencies of the contact angle on the fluid-solid energy parameter ϵ_fs was found for various temperatures and hard core fluid-solid parameters σ_fs . Expressions are suggested that relate the contact angle θ to the parameters of the interaction potentials and temperature. The most intriguing feature was that for each considered σ_fs there is a value https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ4_2_0001.tif"/> of https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ4_2_0002.tif"/> for which the contact angle θ = θ ₀ becomes independent of temperature and of σ_fs . It is shown that https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ4_2_0003.tif"/> divides the materials for which θ increases from those for which θ decreases with increasing temperature.