Studies of internal pressure in aqueous solutions of a surfactant (decyltrimethylammonium bromide) at 298.15 K: Understanding and use of Gibson−Tait equation

•Isothermal compressibility variations with molality of C10TAB in aqueous solutions are studied.•Internal pressures of solutions are studied and intrinsic volume of monomer is estimated.•Tammann−Tait−Gibson model is applied to the data.•C10TAB forms spherical micelle of radius equal to 15.51 Å and Nagg = 36 in water.•Volume changes due to transfer of monomer to micelle has been found positive. Recently reported literature density (ρ), thermal coefficient of expansion (α) data for aqueous solutions of decyltrimethylammonium bromide (C10TAB) in limiting concentration range (0.01 to 0.15 mol kg−1 comprising both pre-micellar and post-micellar regions) have been used and combined with literature density, adiabatic compressibility (βS) and specific heat capacity data (Cp), to calculate isothermal compressibility (βT) and internal pressure (Pi) properties of solutions. The variations of apparent molar adiabatic compressibility (Kϕs) of solute, apparent molar isothermal compressibility (KϕT) of solute and internal pressure (Pi) of solutions are studied and used to obtain infinite dilution parameters such as limiting apparent molar adiabatic compressibility (KϕS0) of C10TAB. The Tammann−Tait−Gibson (TTG) model is applied to calculate the excess volume change for the electrolyte (ΔV¯2E) and intrinsic volume (Vint.) of the cationic surfactant both in pre-micellar and post-micellar regions of concentration. A new method based on internal pressure of solutions and an approach by Tanford incorporating alkyl chain volume, length and head group is developed and used to obtain radius of the micelle and aggregation number. From these data, it is concluded that the micelles are small, spherical and incorporating the surface area of the head group. Our proposed method provides a framework for examining the thermodynamic properties of surfactant in terms of equilibria of the monomer (in limiting range of concentration) and the micelle aggregates after critical micelle formation (cmc) (post-micellar region). In pre-micellar region, water structural changes are important and the hydration of the cations is determined by hydrophobic van der Waal's forces, of which extent increases after cmc, resulting in self-assembly in the form of micelle. Volume changes due to transfer of an electrolyte C10TAB from a liquid hydrocarbon like environment to aqueous solutions and to interior of micelle are also estimated and found to be of positive magnitude. [Display omitted]