Hamaker theory for atom–tip interactions of non-reactive surface in non-contact AFM

Hamaker summation method is used to approach the tip–surface interactions for rutile TiO2 surface with Si-tip in non-contact AFM. The calculated results show that the Hamaker summation method gives tip–surface force the periodical nature with the peak at O2 positions at the tip–surface distance of about 1.5 A ° , and abruptly at Ti4þ and O2 ion positions at the tip–surface distance of about 1 A ° on rutile TiO2(0 0 1) surface along [1 1 0] direction.