Theoretical estimation of the critical packing parameter of amphiphilic self-assembled aggregates

The estimating of critical packing parameter (p) of amphiphilic compounds is considered as a hypothetical rather than an empirical. Consequently, an attempt has been made for determining such a dimensionless parameter for homologous series of sodium p-n-alkyl benzoates (n = 0–8) hydrotropes using quantum mechanical calculations that depend on density functional theory (DFT). The calculations were based on the following well-defined model, p = v/a0lc, where v is the volume of the hydrotrope tail, a0 is the effective head group area and lc is the length of the extended hydrotrope tail. It was found that the magnitude of both v and lc parameters can be estimated directly from quantum mechanical calculations. While the investigations found that the a0 parameter is parallel to the Connolly solvent accessible surface area (Csa) which could also be determined through theoretical computations. The obtained results were in good agreement with published data using small angle neutron scattering (SANS) technique. Hence, the theoretical model for predicting p of amphiphilic at critical micelle- or aggregation-concentration (cmc or cac) is p = v/Csalc. An apparent success was observed through applying this simple model to some randomly selected surfactants. It has been concluded that the theoretical calculations that based on quantum mechanical (DFT) method can be considered as a powerful tool for estimating the critical packing parameter of amphiphilic molecules. Finally, the results strongly suggest the employment of the presented model for estimating p of amphiphilic molecules at cmc or cac by computational chemistry software.