We study by computer simulations the interaction between two similarly charged colloidal particles confined between parallel planes, in salt free conditions. Both the colloids and ions are simulated explicitly, in a fine-mesh lattice, and the electrostatic interaction is calculated using Ewald summation in two dimensions. The internal energy is measured by setting the colloidal particles at a given position and equilibrating the ions, whereas the free energy is obtained introducing a bias (attractive) potential between the colloids. Our results show that upon confining the system, the internal energy decreases, resulting in an attractive contribution to the interaction potential for large charges and strong confinement. However, the loss of entropy of the ions is the dominant mechanism in the interaction, irrespective of the confinement of the system. The interaction potential is therefore repulsive in all cases, and is well described by the DLVO functional form, but effective values have to be used for the interaction strength and Debye length.
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