ATTRACTION AND REPULSION

Two surfaces coming close together may repel each other for a variety of causes. The corresponding Gibbs energy of repulsion is indicated by $G_r$ or $G_$el if the repulsion is due to electric effects ($g_r$ or $g_$el is taken for unit area of each of two flat and parallel surfaces). $G_r$ (or $G_$el) is defined as

$$G_r($$or $$G_$$el$$)=\left[{\int}_\text{final distance}^{\infty}\text{Force. d(distance)}\right]_{T,p}.$$

It is in general not equal to the difference in surface Gibbs energy between the final distance and infinite separation. The Gibbs energy of attraction ($G_a$ or $g_a$ for unit area) is similarly defined.

Van der Waals attraction constants are valid for small separations. Between molecules the van der Waals-London constant ${\lambda}= -{\phi}r^6$, where $r$ is the distance between the centre of the molecules and ${\phi}$ the energy of attraction.

Between semi-infinite flat plates the van der Waals-Hamaker constant (Hamaker constant)²⁴ $A_H = -g_a{\cdot}12{\pi}h^2$ where $h$ is the distance between the surfaces of the semi-infinite plates and $g_a$ is the Gibbs energy of attraction per unit cross-sectional area of the two plates. If the van der Waals forces between molecules are strictly additive, $A_H = {\pi}^2n^2{\lambda}$ where $n$ is the number of molecules per unit volume.

Retarded van der Waals constants are valid for large separations. Between molecules, the retarded van der Waals constant is ${\beta}= -{\phi}r^7$.

Between semi-infinite flat plates, the Gibbs energy of the retarded van der Waals attraction per unit cross-sectional area is given by $g_a = -B/3h^3$. With strict additivity of retarded van der Waals forces, $B = \frac{1}{10}{\pi}n^2{\beta}$.

The total Gibbs energy of interaction is indicated by $G_t$ ($g_t$ if taken per unit area of each of two flat and parallel plates). It is composed of the electrostatic, the van der Waals and possibly other components.

The curve representing the total Gibbs energy of interaction against the distance between the interacting surfaces frequently shows two minima. If this is the case, the minimum at the shorter distance is called the primary minimum, that at the larger separation the secondary minimum.

The total Gibbs energy of interaction is in general not equal to the difference in surface Gibbs energy between the final distance and infinite separation but it is equal to the change of Gibbs energy of the whole system as the separation changes.

Current usage often describes the Gibbs energies defined above as `potentials' but this usage is to be discouraged.

The force per unit area which can be obtained as the derivative of $-g_t$ with respect to the distance is called the disjoining pressure, symbol ${\Pi}_d$.