“…Here in our revised formulae, the thickness of the alkyl layer no longer needs to be calculated because the product of thickness and density is found in all the equations, which is equal to φ × nSi × Nchain, as per Eq.10; the substitution levels will be calculated directly from the revised formulae (vide infra). Within the continuum model as shown in Figure 5, the total Si 2p signal intensity at the alkyl chain-modified surface is given by 14If we assume , and , Eq 14 can be written as (15) Substituting Eq 10, , Eq 15 becomes (16) The carbon signal from the alkyl group is given by (17) where the same assumptions and substitutions are made when deriving Eq 16. The signal from the fluorine layer is given by (18) We can assume that , Eq 18 becomes Given that , the signal from the fluorine layer is given by (19) The intensity of adventitious carbon signal is given by (20) Combining Eq 17 and 20, the total intensity of the carbon signal is given by (21) After obtaining the intensity of the silicon signal, ISi (Eq 16), the intensity of fluorine signal, IF (Eq 19), and the total intensity of carbon signal, IC total (Eq 21), two quantification methods for the substitution level, using the ratio of C to Si, IC total /ISi, or the ratio of F to Si, IF/ISi, respectively, will be derived as shown below.…”