Phase Behavior of Quinary Systems: The $$\tilde X$$ Surface

Abstract

Based on the features of the phase behavior of ternary and quaternary systems repoted on previously /1,2/, we have studied the phase behavior of quinary systems H2O — oil — nonionic amphiphile — ionic amphiphile — lyotropic salt. We have shown /3/, that the phase behavior of quinary systems evolves continously from the phase behavior of the corresponding ternary and quaternary systems. It can systematically be studied by tracing the point \(\tilde X\) /4/ as a function of the weight percentage δ of the ionic in the mixture of the two amphiphiles and the brine concentration ϵ. At constant weight percentage α of the oil in the mixture of oil and brine, \(\tilde X\), being that point at which the three-phase body touches the homogeneous solution of the five components, is unambiguously defined by its temperature \(\tilde T\) and the weight fraction \(\tilde \gamma\) of the two amphiphiles in the mixture. Furthermore, we suggested /5/ to represent \(\tilde T\) in T-δ-ϵ space, and \(\tilde \gamma \) in γ-δ-є space. The first representation gives the temperature at which to search for a three-phase body, the latter what efficiency of the amphiphile to expect. As an example, we show in the Figure (left) the \(\tilde T\)-surface created by uniform clockwise rotation of the \({\tilde T_\delta }\) trajectory from its position at δ=0, \({\tilde T_N}\), to that at δ=100, \({\tilde T_I }\), assuming the \({\tilde T_\delta }\) trajectories to be straight lines. For comparison, in the Figure (right) the actual \(\tilde T\) surface for the system H2O — n-decane — C12E4 — AOT — NaCl has been constructed from experimental \(\tilde X\) data/5/ in T-γ space as function of δ and ϵ at constant α=50 wt%.