Estimating Preferred Alkane Carbon Numbers of Nonionic Surfactants in Normalized Hydrophilic−Lipophilic Deviation Theory from Dissipative Particle Dynamics Modeling

The preferred alkane carbon number (PACN) in the normalized hydrophilic−lipophilic deviation (HLD_N) theory is a numerical parameter and a transferable scale to characterize the amphiphilicity of surfactants, which is usually measured experimentally using the fish diagram or phase inversion temperature (PIT) methods, and the experimental measurement can only be applied to existing surfactants. Here, for the first time, we propose a procedure to estimate the PACN of C_iE_j nonionic surfactants directly from dissipative particle dynamics (DPD) simulation. The procedure leverages the method of moment concept to quantitatively evaluate the bending tendency of nonionic surfactant monolayers by calculating the torque density. Seven nonionic surfactants, C_iE_j (C₆E₂, C₆E₃, C₈E₃, C₈E₄, C₁₀E₄, C₁₂E₄, and C₁₂E₅), with known PACNs are modeled. Two surfactants, C₁₀E₄ and C₆E₂, were first selected to train and test the interaction parameters, and the relationship between interaction parameters and torque density was mapped for the C₁₀E₄−octane−water system using the artificial neural network (ANN) fitting approach to derive the interaction parameters giving zero torque density, then the interaction parameters were tested in the C₆E₂−dodecane−water system to get the final tuned interaction parameters for PACN estimation. With this procedure, we reproduce the PACN values and their trend of seven nonionic surfactants with reasonable accuracy, which opens the door for quantitative comparison of surfactant amphiphilicity and surfactant classification in silico using the PACN as a transferrable scale.