A General Thermodynamic Theory of the Spreading of Liquids to Form Duplex Films and of Liquids or Solids to Form Monolayers
Authors: Harkins William D. 
Published: January 2005

A comprehensive thermodynamic theory is developed for the spreading of any liquid or solid b over the surface of any liquid a. Spreading is considered to occur by two types of processes: (A) duplex film or D spreading, and (B) non-duplex or M spreading. A duplex film is always unstable, and transforms into a non-duplex film and a lens. Every non-duplex film of known structure is a monolayer (M). Either type of film may spread if its formation involves a decrease of free energy. The free surface energy of mercury at 20°C is 476 erg cm—2, and the spreading of water or any organic liquid on the surface as either a duplex film or a monolayer, gives a decrease of free surface energy, so all such liquids spread on mercury. On water all organic liquids spread as monolayers; an organic solid also spreads as a monolayer unless it is too non-volatile in the two-dimensional system. A liquid b will spread over the surface of a liquid a as a duplex film if the initial spreading coefficient Sb/a = WA — WCb is positive, that is if the work of adhesion WA between the two liquids is greater than the work of cohesion (WCb) in b. If b is saturated with a, then Sb′/a is designated as the semi-initial spreading coefficient, which has almost the value of the initial coefficient. If the liquids are mutually saturated the final spreading coefficient, Sb′/a′, is always negative. Thus a liquid b will never spread over its own monolayer, and if the whole surface of water in any vessel is covered by a duplex film, it is certain that a monolayer has not spread over any part of it. After a definite period, the length of which is dependent on many factors, a duplex film begins to segregate into a monolayer, patches of thicker duplex film, and lenses, and finally into a monolayer and a lens. The film pressure πe of a monolayer of b in equilibrium with a lens of b is equal to the difference between the semi-initial and the final spreading coefficient, or πe = Sb′/a — Sb′/a′. Since Sb′/a′ is always negative, the equilibrium film pressure is always greater than the semi-initial coefficient. Hydrocarbons of not too high molecular weight are found to spread on water as either duplex films or monolayers. Thus many nonpolar oils spread on water to form either type of film. Benzene, which according to one of the most prominent theories does not spread at all, spreads readily, and exhibits the following values, which are almost the same as those for isopentane: initial coefficient 8.94, semi-initial 8.90, and equilibrium film pressure 10.6, in erg cm—2. Carbon disulfide (nonpolar) and methylene iodide (highly polar) have initial coefficients —7.3 and —23.8, and therefore do not give duplex films, but they vaporize in the two-dimensional surface, and give equilibrium film pressures of 2.3 and 0.6 dyne cm—1, respectively. Presumably their monolayers are gaseous. In general for liquids which spread as duplex films, it takes less work (i.e., the increase of free energy is less) to pull a liquid away from its equilibrium monolayer than to pull it away from itself. For benzene the difference is 1.7 and for n-heptyl alcohol, 5.4 erg cm—2. An oil which is non-spreading in the sense of duplex film formation, may be caused to spread as a duplex film by the addition of an oil of sufficiently high initial spreading coefficient. This also increases the equilibrium film pressure of the monolayer. The oils added for this purpose are, in general, of the polar-nonpolar type, such as stearic acid. With such mixtures the values of the thermodynamic spreading coefficients, or the free energy levels, are highly dependent upon the nature and the concentration of the oil added. If the aqueous subphase is alkaline, stearic, or another similar acid is converted into a salt, and if the positive ions have a charge of two or higher, this has a pronounced effect upon the spreading coefficients and the film pressure.