2628
DONALD HOERNSCHEMEYER
The Relationship of Contact Angles to the Composition and Morphology of the Surface
by Donald Hoernschemeyer Research and Development Division Publication No. 397, Jackson Laboratory, Organic Chemicals Department, E. I . d u Pont de Nemours and Company, Wdmington, Delaware (Received November 89,1966)
The relationship of the contact angle of a liquid on a solid to the solid-liquid potential energy has been examined. A simple expression for the solid-liquid potential energy has been developed in terms of the structure of the bulk liquid and the surface of the solid. The differences in wettability of hydrocarbon and fluorocarbon monolayers and a fluorinated polymer are explained in terms of their surface morphology. It is shown that the water-alkane interfacial tensions are simply related to the respective surface tensions and the molar volume per CH2 group of the alkane.
Introduction
It is well known that the equilibrium contact angle of a liquid on a solid substrate is simply related to the liquid-v apor, solid-v apor, and solid-liquid int erf aci a1 tensions. However, in the case of solid substrate, the latter two tensions are not directly measurable. Moreover, as Gibbsl and Johnson and Dettre2 have pointed out, the surface tension of the solid is probably not a relevant parameter (see eq 4). The question of how the contact angle of a liquid on a solid is related to macroscopic properties of the solid and liquid phases then remains. I n addition to this thermodynamic question is that of how the contact angle is related to the molecular properties and the packing arrangement of the molecules at the solid-liquid interface. Why is it that most liquids have a greater contact angle on polytetrafluoroethylene (poly-TFE) than on polyethylene and paraffin? Is the contact angle only a function of certain properties of the substrate and of the surface tension of the liquid?
tangent to the drop surface, at the solid-liquid-vapor perimeter and measured in the liquid phase. The problem is to relate this deformation response, 8, to the liquid-solid perturbation, Uel, the potential energy per unit area between the two phases. It therefore behooves us to try to derive an expression for the solid-liquid perturbation in terms of molecular and structural properties of the components. However, before we do so we should examine the exact relationship between 8 and the molecular forces. Young’s equation, eq 1, relates the equilibrium contact angle to the various interfacial tensions.s Let us also relate the 7’s to free energies of adhesion 7’”= F1,
1
1
- -Fll - 2-F”, 2
Theory
where Fi, is the free energy change accompanying the process of bringing phases i and j into contact (e.g., see ref 4). If the liquid and solid phases are mutually insoluble, we obtain eq 3 and 4.
In free space a mass of liquid has a spherical shape but in the presence of an external force field, such as that presented by a solid planar surface, its shape will be altered. When the liquid is in contact with the solid surface we may easily measure the degree of deformation by the contact angle of the droplet. This angle is defined as that between the solid surface and the
(1) J. W. Gibbs, “Collected Works,” Vol. I, Yale University Press, New Haven, Conn., 1948, p 328. (2) R. E.Johnson, Jr., and R. H. Dettre, J . Colloid Sci., to be published. (3) R. E. Johnson, Jr., J.Phys. Chem., 63, 1655 (1959). (4) R. H. Fowler and E. A. Guggenheim, “Statistical Thermodynamics,” Cambridge University Press, London, 1939, pp 445-449.
The Journal of P h y 8 k d Chemistry
RELATIONSHIP OF CONTACT ANGLESTO SURFACE COMPOSITION AND MORPHOLOGY
ylv(1
+
COS
e)
= ylV
+ ysv - yd = -Fe1
lv COS
eN
+ F1v + Fev
1 - F ~ - ~F , ~ F., 2
+
(5)
(3) or a Kihara [12-61 core potential (4)
From the last equation we see that the contact angle is determined by properties of the liquid, through ylVand F11, and the differential free energy of “immersion” of the solid in the liquid and vapor phases. F,, is equal to the negative of the spreading pressure of the vapor on the solid, which commonly has a value of < 1 dyne/cm for alkanes on a fluorocarbon substrate.2 We will provisionally assume that F1, is also of the order of 1-2 dynes/cm and
