Polynomial functions for direct calculation of the surface free energy developed from the Neumann equation of state method

SCHUSTER, JONATHAN M.; SCHVEZOV, CARLOS E.; ROSENBERGER, MARIO R.

INTERNATIONAL JOURNAL OF ADHESION AND ADHESIVES

ELSEVIER SCI LTD

Año: 2023

0143-7496

The Neumann Equation of State (EQS) allows obtaining the value of the surface free energy of a solid (γ_SV) from the contact angle (θ) of a probe liquid with known surface tension (γ_LV). The value of γ_SV is obtained by numerical methods solving the corresponding EQS. In this work, we analyzed the discrepancies between the values of γ_SV obtained using the three versions of the EQS reported in the literature. The condition number of the different EQS was used to analyze their sensitivity to the uncertainty in the θ values. Polynomials fit to one of these versions of EQS are proposed to obtain values of γ_SV directly from contact angles (γ_SV (θ)) of particular probe liquids. Finally, a general adjusted polynomial is presented to obtain the values of γ_SV not restricted to a particular probe liquid (γ_SV (θ,γ_LV)). Results showed that the three versions of EQS present non-negligible discrepancies, especially at high values of θ. The sensitivity of the EQS to the uncertainty in the values of θ is very similar in the three versions and depends on the probe liquid used (greater sensitivity at higher γ_LV) and on the value of γ_SV of the solid (greater sensitivity at lower γ_SV). The discrepancy of the values obtained by numerical resolution of both the fifth-order fit polynomials and the general fit polynomial was low, no larger than ±0.40 mJ/m2. The polynomials obtained allow the analysis and propagation of the uncertainty of the input variables in the determination of γ_SV in a simple and fast way.