The cluster isolated chemical reaction (CICR) technique was applied to neon clusters (Ne-approximate to 7000) on which barium atoms and methane molecules were deposited. Clusters carrying barium only were studied first. Qualitatively, the present results on neon clusters are in line with our previous results on argon clusters. In particular, surface location of barium was observed. The central part of the present work concerns neon clusters carrying both one barium atom and one to ten methane molecules. Several types of spectroscopy were performed in the region of the resonance transition (6s(2))S-1 --> (6s6p)P-1 of barium (excitation spectrum of the total fluorescence, emission spectrum, action spectrum for forming (6s6p)P-3), and experiments where the number of methane molecules per cluster, which was strictly controlled, was varied systematically. The corresponding results were interpreted on the ground of a model, which transposes both chemical thermodynamics of equilibria and reaction kinetics to CICR experiments. Such an approach has a strong relationship, although it is more simple, with the thermodynamical approach to reactions in micellar solutions. The present thermodynamical model helped us to determine the origin of the action spectrum for forming Ba(6s6p)P-3 in clusters carrying both one barium atom and an average of 2.5 methane molecules. This action spectrum was assigned to direct excitation of the Ba(CH4) and Ba(CH4)(2) complexes. The present thermodynamical model was also applied to our former results on argon clusters. This allowed us to derive a consistent picture of the association reaction of barium with methane and of the quenching of electronic excitation of barium by methane in both environments.