A theoretical spinodal curve for the system water + chloroform + acetic acid at 25 °C is derived using a lattice model for ternary amphiphilic solutions: rod-like molecules covering the bonds of the honeycomb lattice with three-body interactions between the molecular ends associated to the same lattice site. The molecular model is equivalent to the standard Ising model on the same lattice; its mean-field solution is the most appropriate for reproducing, by local fitting, the experimental data for the binodal composition. The derived spinodal curve is in very good agreement with the spinodal composition determined also in the present work from the measured diffusion coefficients recently reported for the same system.

https://rd.springer.com/content/pdf/10.1007%2Fs10953-009-9384-5.pdf

Spinodal Composition of the System Water + Chloroform + Acetic Acid at 25 °C

A new method is presented to obtain a theoretical spinodal for ternary solutions with an amphiphile component. This method uses a generalized Wheeler-Widom model representing the ternary solution, and considers local fitting conditions with the experimental binodal, imposing that the theoretical binodal must pass through a point on the experimental binodal, and also that the slope of the theoretical binodal has to be as close as possible to the slope of the representative experimental binodal. Using the previously specified fitting conditions, the corresponding spinodal is derived. The results are in agreement with an older method of local fitting between the generalized Wheeler-Widom model and the experimental data, where the fitting condition implied the coincidence of the theoretical tie-line with the experimental tie-line.

New Method for Theoretical Spinodals Corresponding to Ternary Solutions with an Amphiphile Component

An exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types AA and BB cover the links of a honeycomb lattice, the neighboring molecular ends having three-body and orientation-dependent bonding interactions. At phase coexistence of AA-rich and BB-rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.

The four diffusion coefficients of the ternary system human serum albumin (HSA,1)–sodium cholate (NaC,2)–water (W,0) were determined at three average compositions with constant protein concentration, C
 1
 o
 , and variable bile salt concentration, C
 2. Various types of solute–solute interactions are present in this ternary system: electrostatic, co-ions–protein, and unspecific volume interactions due to the large difference in size of the two solutes. Each type of interaction has a different effect in determining the values and the sign of the experimental diffusion coefficients, exp
 D
 ij
 . To simplify the analysis of the dependence of the exp
 D
 ij
 s on C
 2, we considered three model systems where different types of solute–solute interaction are present individually. The overall analysis allows highlighting which kinds of solute–solute interaction predominates in determining the value of each diffusion coefficient.

Diffusion Properties of the Ternary System Human Serum Albumin–Sodium Cholate–Water

The liquid–liquid equilibrium data at 25 °C of the system water–1-pentanol–1-propanol, that present a I type solubility gap, have been used to calculate the spinodal curve of this system through the use of the Wheeler–Widom model. As in the case of the water–chloroform–acetic acid system, analyzed with the same model in the past, a local fitting method has been necessary. A procedure based on the experimental position of the plait point was used to obtain the single spinodal points. The relative positions of binodal and spinodal curves indicate the presence of a large metastable area in the alcoholic-rich region.

Spinodal Curve for the System Water + 1-Pentanol + 1-Propanol at 25 °C

A model is presented in which the bonds of a honeycomb lattice are covered by rodlike molecules of types AA and BB, molecular ends near a common site having both three-body interactions and orientation-dependent bonding between two A molecular ends and between an A and a B molecular end. Phase diagrams corresponding to the separation into AA-rich and BB-rich phases are calculated exactly. Depending on the relative strengths of the interactions, one of several qualitatively different types of phase diagrams can result, including diagrams containing phenomena such as a double critical point or two separate asymmetric closed loops. The model is essentially a limiting case of a previously considered ternary solution model, and it is equivalent to a two-component system of interacting A and B molecules on the sites of a kagome lattice.

Radu P. Lungu

Papers

Phase separation in an exactly solvable model binary solution with three-body interactions and intermolecular bonding.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.