Fundamental measure theory

In general, different approximations are invoked for the hard-core contribution and the attractive contribution to the free energy functional. For the hardcore contribution, two accurate approximations can be obtained from the fundamental measure theory [108] and the weighted density approximation... 

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A more versatile version of the DFT has been introduced by Rosenfeld (1989) and Rosenfeld et al. (1996) and is known as the fundamental measure theory (FMT). In this approach, only one integrand is required, and thus the excess free energy functional is expressed as ... 

Figure 16. The counterion density near a charged wall for the DFT scheme. Conditions as in Fig. 14. DFT denotes the density functional theory based on the fundamental measure theory [78], and WDA denotes the weighted density approximation based on the generalized Carnahan-Starling equation [75].

In Fig. 16 we plot the counterion density profiles for a symmetrical electrolyte 1 1 confined between two parallel hard walls. The conditions are the same as in Fig. 14. The WDA gives improvements over the dilute limit approximation, but the DFT fundamental measure theory results agree most closely with the simulation. 

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