2D classical density functional theory (CDFT) calculations are performed for three similarly or differently charged cylinder colloids immersed in a 1 : 1 electrolyte solution. Three-body potential is extracted from the calculated grand potential information and main conclusions reached for the three-body potential are summarized as follows: (i) It is indicated that even in the electrostatic systems only involved with the 1 : 1 electrolyte solution and characterized with coupling parameters less than 1.0, wherein the Poisson-Boltzmann equation (PBE) is generally believed to be reliable, the PBE predicts the three-body potential to be in partial conflict with those calculated by the CDFT, whereas the CDFT calculations are in qualitative agreement with computer simulations in similar situations; (ii) The CDFT three-body potential is characterized with a repulsion at short distances plus an attraction even in the 1 : 1 electrolyte solution or a repulsion at large distances (depending on solution conditions) and a continuous decay to zero at longer distances, and the attraction tends to become weaker with the counter-ion diameter; (iii) Given a constant total surface charge magnitude on the three cylinder rods, the three-body potential tends to become less repulsive when the three rods are similarly charged, and conversely, tends to be less attractive when the three rods are differently charged; and (iv) When the three-rod system is differently charged, the three-body potential is relatively insensitive to the counter-ion diameter. Based on analysis of the 3D density profiles of the salt ions calculated by the CDFT, the above findings are explained by a 'hydrogen-bond' type mechanism augmented by an aggregation repulsion effect.
