25564 | Phys. Chem. Chem. Phys., 2014, 16, 25564--25572 This journal is © the Owner Societies 2014 Cite this: Phys. Chem. Chem. Phys., 2014, 16, 25564 Prediction of the wetting condition from the Zeta adsorption isotherm Chunmei Wu, ab Seyed Hadi Zandavi a and C. A. Ward* a We use the Zeta adsorption isotherm and propose a method for determining the conditions at which an adsorbed vapour becomes an adsorbed liquid. This isotherm does not have a singularity when vapour phase pressure, P V , is equal to the saturation-vapour pressure, P s , and is empirically supported by earlier studies for P V o P s . We illustrate the method using water and three hydrocarbon vapours adsorbing on silica. When the Zeta isotherm is combined with Gibbsian thermodynamics, an expression for g SV , the surface tension of the solid– vapour interface as a function of x V ( P V /P s ) is obtained, and it is predicted that adsorption lowers g SV from the surface tension of the substrate in the absence of adsorption, g S0 , to that at the wetting condition. The wetting hypothesis indicates that g SV at wetting, x V w , is equal g LV , the surface tension of the liquid–vapour interface. For water vapour adsorbing on silica, adsorption lowers g SV to g LV at x V w equal unity, but for the hydrocarbons heptane, octane and toluene adsorbing on silica x V w is found to be 1.40, 1.30 and 1.32 respectively. 1 Background When a smooth, rigid, homogeneous solid surface is exposed to a vapour at a P V that is small compared to P s , the Zeta isotherm 1–3 indicates the adsorbate consists of single, adsorbed molecules, but as x V is increased, molecular clusters form in the adsorbate and then an adsorbed vapour film forms. We propose a method to determine the value of x V at which a nascent liquid phase forms with a contact angle of zero, denoted x V w . Since the Zeta adsorption isotherm has been shown to give an accurate description of 21 different vapour–solid systems, 1–5 we use it to propose a method for determining the value of x V w , the pressure ratio at which the wetting transition occurs. When a solid surface is exposed to a vapour at x V less than x V w , there is no liquid phase present, only the adsorbed vapour. But at wetting, we suppose a nascent liquid phase is present, and that thermodynamic equilibrium exists between the phases: the liquid, the vapour, the liquid–vapour, the solid–vapour, and the solid–liquid phases, denoted L, V, LV, SV, SL respectively. This requires the chemical potentials of these phases to satisfy 6 m j + Wgz = l, j = L, V, LV, SV, SL, (1) where l is a constant; g is the acceleration of gravity; W is the molecular weight of the fluid; and the height in the field is denoted z. In terms of the surface tensions, the Young equation and the wetting hypothesis 1,4 indicate the wetting condition is reached when g SV (x V w ) is equal the surface tension of the liquid–vapour interface, g LV : g SV (x V w )= g LV . (2) When the wetting transition is complete, the SV interface is converted to an SL interface. For a soild–vapour system, the Zeta isotherm expression for the amount adsorbed, n SV (x V ), as function of x V contains four isotherm constants. These constants can be determined from adsorption measurements made at x V less than unity, and used to predict the isotherm for x V greater than unity. 3 We combine the Zeta isotherm with the Gibbs adsorption equations 7 at the solid–vapour interface, and integrate the result to obtain an expression for g SV (x V ). This integration can be performed with the Zeta isotherm because it does not have a singularity at x V equal unity, as do many other isotherms. 8 By measuring the value of x V w independently and using it in the expression for g SV (x V w ) for one solid–fluid system, we show that g S0 of that solid can be determined. This value of g S0 can then be used to determine the wetting condition of any other fluid on that solid. When x V is increased from zero to x V w , the surface tension of the solid–vapour interface is decreased from g S0 to g SV (x V w ). Historically, the wetting condition has been taken to be the condition at which a sessile droplet of a hypothetical liquid forms an equilibrium contact angle of zero on the solid surface. 9 We use that definition of the wetting condition, but the ‘‘critical surface approach’’, assumes adsorption is negligible. Our study does not support that assumption. a Thermodynamics and Kinetics Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, M5S 3G8, Canada. E-mail: charles.ward@utoronto.ca; Fax: +1 416-978-7753; Tel: +1 416-978-4807 b College of Power Engineering, Chongqing University, Chongqing, 400044, China Received 11th August 2014, Accepted 21st October 2014 DOI: 10.1039/c4cp03585b www.rsc.org/pccp PCCP PAPER