No works are known investigating surface energy vs pH (of the solution).
However, similar research is being accomplished.
Investigated are proton afinities (pKa) of acid/base centres (O-, OH, OH2+) on surfaces
of oxides. The research is done by people around Prof. Sprik.
Here are some references:
Redox potentials and acidity constants from density functional theory
based molecular dynamics
J Cheng, X Liu, J VandeVondele, M Sulpizi, M Sprik – Accounts of Chemical
Research (2014) 47, 3522
(DOI: 10.1021/ar500268y)
Surface acidity of 2:1-type dioctahedral clay minerals from first
principles molecular dynamics simulations
X Liu, J Cheng, M Sprik, X Lu, R Wang – Geochimica et Cosmochimica Acta
(2014) 140, 410
(DOI: 10.1016/j.gca.2014.05.044)
Acidity of edge surface sites of montmorillonite and kaolinite
X Liu, X Lu, M Sprik, J Cheng, EJ Meijer, R Wang – Geochimica et
Cosmochimica Acta (2013) 117, 180
(DOI: 10.1016/j.gca.2013.04.008)
Understanding surface acidity of gibbsite with first principles molecular
dynamics simulations
X Liu, J Cheng, M Sprik, X Lu, R Wang – Geochimica et Cosmochimica Acta
(2013) 120, 487
(DOI: 10.1016/j.gca.2013.06.043)
More complete list of papers:
http://www.ch.cam.ac.uk/publications/au ... 284?page=2