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This work explores interactions of functionalized nanoparticles (NP) with polymer brushes (PB) in a binary mixture of good and poor solvents. NP-PB systems are used in multiple applications, and we are particularly interested in the problem of chromatographic separation of NPs on polymer-grafted porous columns. This process involves NP flow through the pore channels with walls covered by PBs. NP-PB adhesion is governed by adsorption of polymer chains to NP surface and entropic repulsion caused by the polymer chain confinement between NP and the channel wall. Both factors depend on the solvent composition, variation of which causes contraction or expansion of PB. Using dissipative particle dynamics simulations in conjunction with the ghost tweezers free energy calculation technique, we examine the free energy landscapes of functionalized NPs within PB-grafted channels depending on the solvent composition at different PB grafting densities and polymer-solvent affinities. The free energy landscape determines the probability of NP location at a given distance to the surface, positions of equilibrium adhesion states, and the Henry constant that characterizes adsorption equilibrium and NP partitioning between the stationary phase of PB and mobile phase of flowing solvent. We analyze NP transport through a polymer-grafted channel and calculate the mean velocity and retention time of NP depending on the NP size and solvent composition. We find that, with the increase of the bad (poor) solvent fraction and respective PB contraction, NP separation exhibits a transition from the hydrodynamic size exclusion regime with larger NPs having shorter retention time to the adsorption regime with smaller NPs having shorter retention time. The observed reversal of the sequence of elution is reminiscent of the critical condition in polymer chromatography at which the retention time is molecular weight independent. This finding suggests the possibility of the existence of an analogous special regime in nanoparticle chromatography at which NPs with like surface properties elute together regardless of their size. The latter has important practical implications: NPs can be separated by surface chemistry rather than by their size employing the gradient mode of elution with controlled variation of solvent composition.