A Mathematical Model for Estimating Molecular Compressibility of Fatty-Acid Methyl Ester and Biodiesel

In this study, the molecular compressibility (k_m) of a fatty-acid methyl ester (FAME) or a biodiesel is correlated with ΔG, (Formula presented.), via the Gibbs energy additivity method, where MW is the molecular weight of the FAME or the average MW of the biodiesel. The Gibbs energy associated with molecular compressibility ((Formula presented.)) is further correlated with the structure of FAME. Thus, the relationship between the structure (of a FAME or a biodiesel) and the physical property (k_m) is established. Thus, k_m of a FAME at different temperatures can be easily estimated from the carbon numbers of fatty acid (z) and the number of double bonds (n_d) with good accuracy. For biodiesel, k_m is calculated from the same equation with the average z (z_(ave)) and average n_d (n_d(ave)). k_m is not temperature independent and a slight change in k_m depends on the structure of the FAME and biodiesel. For FAME having 14 carbon atoms or less in the fatty acid, k_m decreases as temperature is increased. On the other hand, for FAME with a longer chain length (16 or higher), k_m increases as temperature is increased. Similarly, a double bond in the long-chain FAME is more sensitive to temperature than the saturated FAME.