General Equation to Express Changes in the Physicochemical Properties of Organic Homologues

Changes in various physicochemical properties (P ₍) of organic compounds with the number of carbon atoms (n) can be roughly divided into linear and nonlinear changes. To date, there has been no general equation to express nonlinear changes in the properties of organic homologues. This study proposes a general equation expressing nonlinear changes in the physicochemical properties of organic homologues, including boiling point, viscosity, ionization potential, and vapor pressure, named the "NPOH equation", as follows: P _(n) = P ₍₁₎ α e ^∑ where α and β are adjustable parameters, and P ₍₁₎ represents the property of the starting compound (pseudo-value at n = 1) of each homologue. The results show that various nonlinear changes in the properties of homologues can be expressed by the NPOH equation. Linear and nonlinear changes in the properties of homologues can all be correlated with n and the "sum of carbon number effects", ∑_i=2 ⁿ(1/i - 1). Using these two parameters, a quantitative correlation equation can be established between any two properties of each homologue, providing convenient mutual estimation of the properties of a homologue series. The NPOH equation can also be used in property correlation for structures with functionality located elsewhere along a linear alkyl chain as well as for branched organic compounds. This work can provide new perspectives for studying quantitative structure-property relationships.