contact angles

1. The Modern Theory of Contact
Angles and the Hydrogen Bond
Components of Surface Energies
Robert J. Good and Carel J. van Oss
1. INTRODUCTION
1
We owe a great debt to W. A. Zisman and his colleagues at the Naval Research
Laboratory for their extensive, pioneering work that opened up the field of contact
angles and made possible the development of the modern theory of wetting and
adhesion. Their data on the wetting of solids by apolar liquids and by hydrogen
bonding liquids pointed the way to the recent introduction of a theory of hydrogen
bond interactions across interfaces. We will devote this chapter to a review of this
new theory.
Hydrogen bonds have been recognized as chemical entities ever since 1920.0)
Their contribution to phenomena such as the mechanical strength of proteins, the
high boiling point and electric conductivity of water, the information-carrying
structure of DNA, and many other phenomena, have been known for several
decades. The fact that hydrogen bonds influence adsorbed films on water was men-
tioned by Harkins and Meyers(2) and Harkins,(3) and the influence of orientation
due to hydrogen bonds on surface entropy at liquid- vapor interfaces was noted by
Good(4) over 30 years ago. There is no question that hydrogen bonding is involved
in hydrophilic behavior of solid surfaces and that its absence is correlated strongly
with hydrophobic behavior. But, until recently, no quantitative theory has been
available by which these surface manifestations of hydrogen bonding could be
evaluated.
Pimentel and McClellan(5) have given the most authoritative discussion of
hydrogen bonds, saying (on p. 63) that "no really definitive paper connecting surface
Robert J. Good • Department of Chemical Engineering, State University of New York at Buffalo,
Buffalo, New York 14260. Carl J. van Oss • Department of Microbiology, State University of
New York at Buffalo, Buffalo, New York 14214.
1
M. E. Schrader et al. (eds.), Modern Approaches to Wettability
© Springer Science+Business Media New York 1992

2. 2 ROBERT J. GOOD AND CAREL J. VAN OSS
tension to hydrogen bonding has appeared." They mentioned, however, the corre-
lation found by Good and Girifalco(6) between the ratio rjJ of the free energy of
adhesion to the geometric mean of the free energies of cohesion of the separate
phases and the presence or absence of hydrogen bonding in one or both phases.
Jensen(7) has discussed the Lewis(8) and Bronsted-Lowry(9,10) theories of acids and
bases, but says little on hydrogen bonds. Coulson(ll) provided a theoretical basis
for hydrogen bonds in systems in which 11: electrons constitute the electron donor
system. Good and Elbing(l2) gave the first quantitative treatment of liquid-liquid
interfacial hydrogen bonds involving 11: electrons, showing that a bond energy of
about 2.4 kcal/mole would account for the difference between the water-benzene
interfacial tension and that between water and saturated hyrocarbons. See also
Ref. 13 in regard to polystyrene.
Hydrogen bonding is the most common type of molecular interacting that
leads to an acid-base component of the free energy of adhesion and of the inter-
facial tension between two phases. Hydrogen bonding can be well described in
terms of the Bronsted-Lowry acid-base (proton donor-proton acceptor) theory.
However, it is possible to describe hydrogen bonding via the (more general) Lewis
acid-base theory, in which an acid is an electron acceptor and a base is an electron
donor. Thus, we will use the terminology Lewis base, which is general, together
with Lewis acid, which means either an electron acceptor or the subclass of electron
acceptors that comprises proton donors. We may refer to the creation of an adduct
by hydrogen bond formation as an example of Lewis neutralization.
A quantitative theory has recently been developed(14-19) for estimating the
contribution due to the hydrogen bonding character of a single substance, to
surface and interfacial tension, and to free energy of adhesion at interfaces in
binary systems. The progenitor of this theory was Fowkes's(20,21) resolution of
surface free energy y into an apolar component and an acid-base component.
A treatment of the apolar component had been proposed earlier by Good and
Girifalco(4,12,13,22,23,24) and is by now well understood. The physical basis of that
treatment lies in the molecular theory of intermolecular forces between nonpolar
molecules in the gaseous state, due to Berthelot(25) and London(26) (the theory of
the dispersion force), and in the Scatchard-Hildebrand theory of the solubility
of nonelectrolytes.(27) (It was Berthelot who first proposed a geometric mean
combining rule for intermolecular interactions.)
Hildebrand and Scott have pointed out(27) that, in contrast to the London
dispersion force, hydrogen bonds cannot be fitted into the Berthelot-London-
Scatchard-Hildebrand formalism, with regard to the behavior of solutions. So, it
might be expected that the geometric mean combining rule would not be successful
for describing the hydrogen bond components of interfacial energy. This is indeed
the case.
The reason for this failure lies in the complementarity of functions in acid-base
interactions, which is in strong contrast to the symmetry of functions in the disper-
sion force field that acts between any two small molecules or molecular segments.
In the dispersion force interaction of two unlike molecules, i and j, the contri-
butions of i and of j are, formally, of the same kind as the interaction of two i
molecules with each other or of two j molecules with each other. The molecuhlr
polarizabilities !x, and !Xl' and the ionization energies I, and 11' enter the equations