[BF4] or C4, dotted curves) and 1-octyl-3-methyl-imidazolium tetrafluoroborate ([OMIM][BF4] or C8, solid curves). The pmf corresponds to the reversible work involved when two NPs approach each other, hence, the difference between the value of the pmf at two given distances r 1 and r 2 corresponds to the free energy variation in changing the distance from r 1 to r 2 . Therefore, local minima correspond to thermodynamically favorable distances and the maxima to activation barriers. From the pmf gradient (Equation ), we can also derive the average force acting along the reaction coordinate at each distance r between NPs centers of mass (Figure bottom), which would be the result obtained in an atomic force microscopy experiment if the two NPs were pulled apart from each other inside the solution with a rate slow enough to guarantee that the process is nearly reversible. The force profiles obtained for C8 are qualitatively similar to the atomic force microscopy profiles reported between mica surfaces separated by ILs films, but a quantitative comparison is not possible because the ILs used are not the same and here we are studying small spherical NPs instead of surfaces. Notice that the force profile is noisier than the pmf because the numerical calculation of derivatives increases the effect of random noise, thus, we will focus the discussion mostly on the free energy profile rather than the average force.