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ION–ION INTERACTIONS 319

Review
1. H. L. Friedman, E. O. Raineri, and O. M. D. Wodd, “Ion-Ion Interactions,” Chemica Scripta
29A: 49 (1989).
2. J. C. Rasaiah, “A Model for Weak Electrolytes,” Int. J. Thermodyn. 11: 1 (1990).
3. L. M. Schwartz, “Ion Pair Complexation in Moderately Strong Aqueous Acids,” J. Chem.
Ed. 72: 823 (1995).

Papers
1. J.-L. Dandurand and J. Schott, J. Phys. Chem. 96: 7770 (1992).
2. E. H. Oelkers and H. C. Helgeson, Science 261: 888 (1993).
3. J. Gao, J. Phys. Chem. 98: 6049 (1994).
4. J. Wang and A. J. Haymet, J. Chem. Phys. 100: 3767 (1994).
5. M. Madhusoodana and B. L. Tembe, J. Phys. Chem. 99: 44 (1995).
6. G. Sese, E. Guardia, and J. A. Padro, J. Phys. Chem. 99: 12647 (1995).
7. M. Ue and S. Mori, J. Electrochem. Soc. 142: 2577 (1995).

3.10. COMPUTER SIMULATION IN THE THEORY OF IONIC
SOLUTIONS
All parts of the physical sciences are now served by calculation techniques that
would not have been possible without the speed of electronic computers. Such
approaches are creative in the sense that, given the law of the energy of interaction
between the particles, the software allows one to predict experimental quantities. If
agreement with experiment is obtained, it tells us that the energy of interaction law
assumed is correct. Sometimes this approach can be used to calculate properties that
are difficult to determine experimentally. Such calculations may allow increased
insight into what is really happening in the system concerned or they may be used
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simply as rapid methods of obtaining the numerical value of a quantity. There are
two main computational approaches and these will be discussed next.

3.10.1. The Monte Carlo Approach
The Monte Carlo approach was invented by Metropolis (Metropolis, 1953). The
system concerned is considered in terms of a small number of particles—a few
hundred. The basic decision that has to be made is: What law are the particles i and j
going to follow in expressing the interaction energy between them as a function of
their distance apart? For example, a useful law might be the well-known Lennard-
Jones equation:

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The major attraction of such computer simulation approaches is that they often result in lower costs.
However, a prerequisite to their use is an experimental value on some related system, so that the As and
Bs of equations such as Eq. (3.166) can be calibrated.