“…where Ф is the volume fraction of coating within the brush layer (d) (1.31 nm, 10 nm, and 3.2 nm respectively for TX-100, SDBS, and CTAB were taken for calculation according to other studies (Liang et al, 2009;Muller et al, 1998;Yuan et al, 2002)), Г max is the maximum attained surface excess concentration (1.0 mg m −2 , 10.0 mg m −2 and 1.5 mg m − 2 for TX-100, SDBS and CTAB, respectively) (Tkachenko et al, 2006;Li and Tripp, 2004), χ is the Flory-Huggins solvency parameter (a value of 0.45 was taken for calculation), M w is the molecular weight of the surfactant (628 g mol − 1 , 348.48 g mol − 1 , and 364.45 g mol −1 for TX-100, SDBS, and CTAB, respectively), ρ is the density of adsorbed surfactant layer (0.98 g cm − 3 , 1.1 g cm − 3 , and 0.95 g cm −3 for TX-100, SDBS, and CTAB, respectively), and v is the volume of a solvent molecule (0.03 nm 3 ) (Wang et al, 2012). The estimation of osmotic and elastic repulsive potentials (defined in the range of d ≥ h N 0) between coated-nTiO 2 and an uncoated flat surface is given in the following expression as (Song et al, 2011):…”