Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r(-6) interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r(-1) and the dispersion r(-6) potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r(-6) potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-wr)/r, to a power-law decay, r(-8), for large r. The pair distribution function acquire, at the same time, an r(-10) decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r(-6) interaction is switched on. When the Coulomb interaction is turned off but the dispersion r(-6) pair potential is kept, the decay of the pair distribution function for large r goes over from the r(-10) to an r(-6) behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.