Energy Relations of the Surfaces of Solids II. Spreading Pressure as Related to the Work of Adhesion Between a Solid and a Liquid

Abstract

This is the second paper in a series which gives theoretical values for the free and total surface energy of the diamond, and experimental values for the total and free energy, the latent heat, and the entropy of adhesion between various crystalline solids and liquids. This second paper deals with the oldest part of the subject, but a part which has always been treated incorrectly. The total energy (ε_A(SL)) required to separate water from solids of the general type of BaSO₄, TiO₂, and ZrSiO₄, has been found by Harkins and Boyd to vary from 600 to 1000 erg cm⁻¹, while to separate octane from these solids requires only from 150 to 250 erg cm⁻². The free energy of separation, designated by W_A(SL), is smaller. It is generally believed that $$W_{\mathrm{A(SL)}}{\mathrm{=\gamma }}_L\text{(1+}\cos {\theta }_{\mathrm{SL}}\mathrm{),}$$ which gives values, for solids thus far investigated, from 47.5 to 144 erg cm⁻² at 25°C if the liquid is water, and much smaller values if organic liquids are used. Indeed the maximum value of the work of adhesion between water and any solid at this temperature is given by this equation as only 144 erg cm⁻². That the work of adhesion should be so small a fraction of the free surface energy of the solid itself as these numbers suggest, is, in the case of solids of high melting point, entirely incredible, since even polar solids of this type must have free surface energies in excess of 1000 erg cm⁻². For such a solid the work of adhesion toward water would be only ten or less percent of the free surface energy of the solid. The correct equation is $$W_{\mathrm{A(SL)}}{\mathrm{=f}}_{{\mathrm{E(SV}}^{\circ })}{\mathrm{+\phi }}_{{\mathrm{LV}}^{\circ }}^S.$$ Thus the work of adhesion is the sum of three terms which may be determined experimentally: (1) The solid, initially in a vacuum, is immersed in the vapor of the liquid with a decrease of free energy equal to f_I(SV°). The reversal of this process separates the solid from the vapor, with an increase of free energy of f_E(SV°), the free energy of emersion of the solid from the vapor. Equations of this type are in general written to correspond to a separation of phases, while the experimental processes take place in the opposite direction. (2) The free energy of transfer (φ^S_LV°) of the solid from the interior of the liquid to the interior of the saturated vapor, without a change in any other interfacial areas than that of the solid represented by the symbol S, and that of the solid‐liquid interface SL. It is shown that φ^S_LV°=φ_L/S′, where the term on the right is the spreading pressure of the liquid L over the surface of the solid S′, which is in equilibrium with the saturated vapor V° of the liquid. (3) The free surface energy of the liquid. The quantity listed in (2) above is defined by Eq. (17) as follows: $${\phi }_{{\mathrm{LV}}^{\circ }}^S{\mathrm{=\phi }}_{{\mathrm{L/S}}^{\prime }}{\mathrm{=\gamma }}_{{\mathrm{SV}}^{\circ }}{\mathrm{-\gamma }}_{\mathrm{SL}}.$$ It will be designated by either of the terms given in (2) but more commonly as the spreding pressure. This would be identical with what was defined by Freundlich as a Haftspannung, usually translated as the adhesion tension (A), but unfortunately the adhesion tension has never been defined nor used correctly (see Section 6), since it is designated by two equations which give magnitudes which are extremely different, and one of the two equations is incorrect. The term ``adhesion tension'' has also carried with it the unfortunate implication that it gives, through Eq. (A), which may be written W<sub>A(SL)</sub>=A+γ<sub>L</sub>, a measure of the free energy of emersion of a solid (f<sub>E(SL)</sub>), from which the work of adhesion may be obtained by merely adding the surface tension of the liquid. This is extremely erroneous, since the adhesion tension, if correctly defined, is equal to only the minor term φ<sub>L/S′</sub> in the expression $$f_{\mathrm{E(SL)}}{\mathrm{=f}}_{{\mathrm{E(SV}}^{\circ })}{\mathrm{+\phi }}_{{\mathrm{L/S}}^{\prime }}.$$ On account of the unfortunate implication of the term itself, and because it has always been defined and used incorrectly, it is recommended that the term ``adhesion tension'' should be discarded, and the correctly defined and more suitable term (spreading pressure) be substituted for it. If the angle between a liquid‐liquid (L₁‐L₂) interface meets the surface of a solid with the angle α, the displacement pressure (D) is defined by the equation $${\mathrm{D=\gamma }}_{L_1{L}_2}\cos \mathrm{\alpha .}$$ It is shown that the equations in the literature which relate the displacement pressure to the adhesion tension, are incorrect and entirely too simple. The true relation (that between D and φ_L/S′) is much more complicated.