Handbook of Solvents - George Wypych - ChemTech - Ventech!

494 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
to what we experience in our everyday life (petrol on the surface of water); however, it has
to be related to a finer classification of liquid interfaces we shall consider later.
Once again the potentials used for liquid/liquid surfaces are in general those used for
bulk liquids eventually with the introduction of a change in the numerical values of the parameters.
118 The difference from the bulk again regards the thermodynamical ensemble, the
boundary conditions for the calculations and the use of some additional concepts.
The liquid/solid surfaces may be of very different types. They can be classified according
to the electrical nature of the solid as:
• Liquid/conductor
• Liquid/dielectric
The presence of mobile electrons in metals and other solid substances (to which some
liquids may be added, like mercury 119 ), introduces in the modelling of the liquid interface
new features not present in the previously-quoted interfaces nor in the bulk liquids. For
many phenomena occurring at such interfaces there is the need for taking into explicit account
electrons flowing from one phase to the other, and of related electron transfers occurring
via redox mechanisms. The interaction potentials have to be modified and extended
accordingly. 120
The good electrical conductivity of the solid makes more sizeable and evident the occurrence
of phenomena related to the presence of electric potentials at the interface (similar
phenomena also occur at interfaces of different type, however 121 ). A well-known example is
the double layer at the liquid side of an electrolyte/electrode surface. For the double layer,
actually there is no need of interaction potentials of special type: the changes in the
modelling mainly regard the boundary conditions in the simulation or in the application of
other models, of continuum or integral equation type.
It is clear that attention must be paid to the electrostatic part of the interaction. Models
for the solid part similar to those used for bulk liquids play a marginal role. There are models
of LJ type, but they are mainly used to introduce in the solid component the counterpart of
the molecular motions of molecules, already present in the description of the liquid (vibrations
of the nuclei: phonons, etc.).
The electrostatic problem may be treated with techniques similar to those we have
shown for the continuum electrostatic model for solutions but with a new boundary condition
on the surface, e.g., V=constant. In this case, a larger use is made (especially for planar
surfaces) of the image method, 122 but more general and powerful methods (like the BEM)
are gaining importance.
An alternative description of the metal that can be profitably coupled to the continuum
electrostatic approach is given by the jellium model. In this model, the valence electrons of
the conductor are treated as an interacting electron gas in the neutralizing background of the
averaged distribution of the positive cores (some discreteness in this core distribution may
be introduced to describe atomic motions). The jellium is described at the quantum level by
the Density Functional Theory (DFT) and it represents a solid bridge between classical and
full QM descriptions of such interfaces: 123 further improvements of the jellium which introduce
a discrete nature of the lattice 124 are now often used. 125
The liquid/dielectric surfaces exhibit an even larger variety of types. The dielectric
may be a regular crystal, a microcrystalline solid, a glass, a polymer, an assembly of molecules
held together by forces of different type.