An entropic equation to calculate contact angles of bulk water droplets on weakly-reactive solid surfaces

Abstract

Room temperature contact angle (θ25) of a water droplet on a weakly-reactive solid surface is directly calculated from an entropic equation: S25 = 335.86–0.65θ25 (J. unit-mass−1 k−1), where S25 is the entropy of the air/water/solid system and the unit-mass is defined as the sum of 1 mol air, 1 mol water and 1 mol cation solid. Two parameters in the equation are optimized based on thermodynamic calculations of air/water/ice systems and experimental contact angle of water on biotite. This entropy to contact angle linear equation reproduces well experimental contact angles of water on graphite, copper, sapphire, quartz, and calcite, ranging from 9 to 82°. It suggested that (1) contact angle is a direct measure of the state function entropy, and (2) for all solids one (1) J. unit-mass−1 k−1 increment in S25 results in about two (∼2) degrees reduction in θ25. In addition, a new semi-empirical equation is established for calculation of contact angle at high temperatures, by considering the effect of steam-solid reactions. This temperature-dependence equation reproduces well experimental data in water/graphite, water/sapphire, and water/quartz systems from 25 to 272° C. It further demonstrated that under an adiabatic approximation the popular semi-empirical Young's equation is consistent with this entropic equation. This simple and practical entropic equation will advance a wide range of applications from adhesion, coatings, corrosion, protein adsorption, blood compatibility, to cell-surface interactions. It also opens a new field in physics to understand and characterize contact angles from state entropy.