Pseudo-ternary phase diagrams: reading, constructing and measuring the microemulsion region

Introduction

The composition of a three-component mixture is fixed by two numbers; the third follows of its own accord, because the percentages sum to 100. An equilateral triangle displays this constraint in the most natural way: each vertex represents a pure component, each edge the two-component mixtures, and each point in the interior a particular ratio of all three. In pharmaceutical technology this representation is used most often for microemulsions, self-emulsifying systems and topical vehicles (Lawrence & Rees, 2000; Karasulu, 2008). Because the surfactant and the cosurfactant are usually mixed at a fixed ratio (S_mix, K_m) and treated as a single component, the diagram is in fact a cross-section of a four-component system; hence the name pseudo-ternary (Aboofazeli & Lawrence, 1993; Shafiq-un-Nabi et al., 2007).

The diagram conveys two kinds of information: in which part of composition space a single-phase, clear, low-viscosity system forms, and how that region responds to variables such as the S_mix ratio, the type of oil or the cosurfactant chain. A wide region indicates high formulation tolerance; the region itself is the pool from which compositions are selected (Parmar et al., 2011; Berkman & Güleç, 2021).

Reading the diagram

In the tool's triangle the lower-left vertex is water, the lower-right vertex the surfactant mixture and the apex oil; the names can be changed. The percentage of a component at a point is read from the lines parallel to the opposite edge, running from that component's vertex towards the opposite edge: proximity to the vertex raises the percentage, and every point on the opposite edge contains zero percent of that component. The three percentages always sum to 100. The tool places a point from its oil and surfactant percentages and reads water as the remainder; rows whose total deviates from 100 by more than 0.5 points are shown in a yellow warning list after Calculate. The point is still plotted, but the remaining water, not the water entered, is used; correct these rows and recalculate.

A grid parallel to the edges (5, 10 or 20 units) makes reading easier. A straight line from a vertex to the opposite edge is a dilution line, along which the ratio of the other two components is held constant; measurement points obtained by water titration fall on such lines, because in the experiment the oil:S_mix ratio is kept fixed while water is added (Shafiq-un-Nabi et al., 2007). The tie lines and the lever rule of liquid–liquid equilibrium diagrams (the ratio of the amounts of two phases is inversely proportional to the distances from the composition point to the ends of the tie line) rest on the same geometry (Williamson, 2021); in microemulsion diagrams, however, the phase boundary is usually drawn and tie lines are not.

Brief history

The ternary composition triangle entered physical chemistry with Gibbs's work on the phase rule (1876) and took its present form with Roozeboom's equilateral-triangle representation. The concept of the microemulsion began in 1943, when Hoar and Schulman reported soap–oil–water mixtures that clarified spontaneously and remained transparent on addition of an alcohol, under the name "oleopathic hydro-micelle" (Hoar & Schulman, 1943). The term "microemulsion" was proposed by Schulman and co-workers in 1959, in the study that examined these systems by electron microscopy (Schulman et al., 1959). Winsor's 1948 division of surfactant–oil–water systems into four types (I: an oil-in-water micellar solution in the lower phase, II: reverse micelles in the upper phase, III: a middle phase, IV: a single-phase clear system) is still the standard for naming phase behaviour (Winsor, 1948; Salager et al., 2022). The definition of Danielsson and Lindman, "a single optically isotropic and thermodynamically stable liquid solution of water, oil and an amphiphile", became the common reference of the field (Danielsson & Lindman, 1981).

Pharmaceutical use accelerated in the 1990s: the pseudo-ternary diagrams of lecithin/alcohol/isopropyl myristate systems (Aboofazeli & Lawrence, 1993), the widely cited review by Lawrence and Rees (2000), Pouton's system for classifying lipid-based formulations (LFCS; Pouton, 2000, 2006) and Kreilgaard's survey of topical applications (2002). In the 2010s the frequently confused definitions of microemulsion and nanoemulsion were clarified (Anton & Vandamme, 2011; McClements, 2012). More recently, approaches that reduce the experimental workload of the phase diagram have come to the fore: the microplate dilution method (Schmidts et al., 2009) and machine-learning models that learn from thousands of formulations (Gao et al., 2021).

Phase regions and their recognition

During water titration the appearance of the mixture changes, and each state is marked as a separate region on the diagram. Typical regions and observation criteria (Syed & Peh, 2014; Boonme et al., 2006; Li et al., 2024):

• Microemulsion (Winsor IV): clear or transparent, fluid, isotropic; dark under polarised light (no birefringence). As the water content increases, the w/o → bicontinuous → o/w transition is most often followed through the percolation jump in conductivity (Boonme et al., 2006; Liu et al., 2022).
• Coarse emulsion (Winsor I/II): turbid, milky in appearance, may separate over time. The o/w and w/o types are distinguished with a water-soluble dye such as methylene blue (Syed & Peh, 2014).
• Gel / liquid crystal: viscous, often transparent but birefringent under polarised light (lamellar, hexagonal). Appears at high surfactant content and at certain S_mix ratios; confirmed by small-angle X-ray scattering and rheology (Sharma et al., 2025; Tartaro et al., 2020).
• Phase separation: two or three visible layers; in Winsor III the middle phase is a bicontinuous microemulsion (Salager et al., 2023).

Because visual assessment on its own is subjective, conductivity, viscosity, dynamic light scattering, differential scanning calorimetry and polarised-light microscopy are used together; no single method proves the structure by itself (Li et al., 2024; Gradzielski et al., 2021). The tool does not make this distinction; the user decides from the experiment which points belong to which region and enters each region as a separate "group".

Experimental method: water titration

The most common route is water (aqueous-phase) titration. First the surfactant and the cosurfactant are mixed at fixed mass ratios (S_mix 1:1, 2:1, 3:1, 4:1 and so on; some authors write K_m). For each S_mix, nine separate oil:S_mix mixtures from 1:9 to 9:1 are prepared, and water is added drop by drop under stirring at constant temperature. The appearance is recorded after each addition; the compositions at which the system turns from clear to turbid or from turbid to clear are the phase-boundary points (Shafiq-un-Nabi et al., 2007; Syed & Peh, 2014). A diagram typically comprises 9 dilution lines × a few transition points; different S_mix ratios are drawn as separate diagrams and the region areas are compared (Parmar et al., 2011).

• Temperature must be held constant; with non-ionic surfactants the region boundaries are temperature-sensitive (Liu et al., 2022).
• Equilibration time. After each addition the system should be allowed to reach equilibrium; transient turbidity is not a phase boundary. A sample that appears kinetically stable may not be thermodynamically stable (Anton & Vandamme, 2011).
• Cosurfactant effect. Short-chain alcohols and glycols make the interfacial film more flexible and widen the single-phase region; the effect depends on chain length and on the S_mix ratio (Aboofazeli & Lawrence, 1993; Golwala et al., 2020).
• Active ingredient. Drug loading shifts the region; drug-loaded and drug-free diagrams may differ (Giang et al., 2020). The final formulation should be selected from the drug-loaded diagram.
• Alternative: the microplate dilution method examines a large number of compositions at once, saving time and material (Schmidts et al., 2009).

Region area, centroid and optimisation

The area of the microemulsion region is the standard measure for comparing S_mix ratios and excipient choices: the ratio that gives the widest region is selected, and formulations are then taken from within the region at that ratio (Parmar et al., 2011; Yadav et al., 2020). In most publications the area is estimated by eye or by counting squares on paper. Since 2001 this tool has instead computed the area and the centroid from the vertex coordinates of the polygon: the area and centroid of each group are given in the table, and the centroid is marked on the diagram. Berkman and Güleç (2021) published the same approach with explicit formulae and an Excel macro and showed how the centroid can be used as a "candidate optimum formulation"; the two approaches rest on the same geometry.

Is the centroid enough on its own? Generally not. Compositions within the region differ in droplet size, viscosity, drug loading and robustness to dilution; the range selected from the diagram is therefore screened in a second step by experimental design (Box–Behnken, central composite, simplex lattice) (Zhu et al., 2008; Yadav et al., 2020). The diagram narrows the range; the experimental design finds the optimum within it. Shafiq-un-Nabi and co-workers (2007) recommend selecting the composition that dissolves the most oil with the least surfactant and withstands dilution, and avoiding "metastable" points close to the boundary.

Microemulsion, nanoemulsion, SEDDS

These terms are often confused in the literature. The distinction lies not in size but in thermodynamics: a microemulsion is thermodynamically stable, forms spontaneously and persists indefinitely as long as the composition is unchanged; a nanoemulsion is only kinetically stable, is made with an energy input (high pressure, ultrasound) or by phase inversion, and breaks down over time (McClements, 2012; Anton & Vandamme, 2011; Gandhi et al., 2026). Size ranges are given differently from author to author; some reviews state 100–400 nm for microemulsions and 1–100 nm for nanoemulsions (Souto et al., 2022), whereas in the classical definition microemulsion droplets are 10–100 nm. This contradiction shows that size is not the defining criterion. Practical tests for the distinction: long-term stability, reversibility of temperature changes, and insensitivity of the result to the order in which the components are mixed (Gandhi et al., 2026).

SEDDS / SMEDDS / SNEDDS are anhydrous preconcentrates that spontaneously give an emulsion, microemulsion or nanoemulsion on contact with water (Pouton, 2000, 2006). For these systems the pseudo-ternary diagram maps the compositions of the anhydrous preconcentrate that form a clear dispersion after dilution; the "self-emulsification region" and the classical microemulsion region are not the same thing. For a comparison with Winsor terminology see Salager et al. (2022, 2023).

Using the tool

The left column has three tabs: Data Entry, Diagram (title and vertex names) and Chart (grid, closing, smoothing, opacity). The diagram is on the right, with the group table below it.

1. Data entry. Each row is one measurement point: Group (region name, e.g. "ME 2:1"), Order (the order of traversal along the polygon edge), and the Oil, Sur/CoSur and Water percentages. Points in the same group are joined in Order to draw the polygon; the order must run consistently clockwise or anticlockwise along the boundary, otherwise the edges intersect. The grid works like a spreadsheet (copy and paste, add/delete rows); 4 sample data sets can be loaded from the menu.
2. Calculate. The points are converted to triangle coordinates, the groups are turned into polygons, and the area and centroid are computed. A group with one point is drawn as a point, a group with two points as a line. Rows whose total is not 100 (tolerance ±0.5) are listed in the warning list with their group and order number.
3. Closing. In a titration the boundary points often end on an edge (e.g. the water-rich corner where the oil percentage drops to zero). "Close Polygon" joins the first and last points directly; "Minimum-Value Closing" closes through the lowest values of the group; "Edge Closing" closes along the selected edge (Oil, Surfactant or Water). The closing points that are added sometimes coincide with the first or last measurement point; the tool removes these.
4. Smoothing. When "Smooth edges" is ticked, the boundary is drawn as a Catmull-Rom based Bezier curve passing through the measurement points; 60 % corresponds to the classical tension, and towards 100 % the curve becomes rounder. The curve does not leave the triangle. The area and centroid are computed from the smoothed outline. This is a visual interpretation: the true boundary between two measurements is unknown.
5. Style. Clicking a group on the diagram sets the fill colour, edge colour, opacity and edge width for that group alone; the sliders on the Chart tab are the defaults for all groups. Gradient fill is optional.
6. Saving. The work is stored automatically in this browser; "Save to file" writes the data, settings and styles to a single .json file, and "Open from file" restores them. "Download SVG" exports the diagram as a vector graphic that scales to publication quality.

Area unit. The area is computed in a triangle with sides of 100 units. The whole triangle is ≈ 4330 units²; the share of a region in the triangle is obtained as a percentage from area/43.3. Within one S_mix comparison the absolute value suffices; between different studies the percentage is safer.

Limitations and interpretation

• The boundary lies between the measurement points. The polygon passes through the measurement points; the true phase boundary lies somewhere between two points. The area estimate improves as the number of points increases; with sparse data, smoothing can give a misleading impression of precision.
• The choice of closing changes the area. With the same data, "Close Polygon" and "Edge Closing" give different areas. The closing used should be reported.
• Visual assessment is subjective. The "clear"–"turbid" threshold depends on the observer; support by conductivity, light transmittance or polarised-light microscopy is recommended (Li et al., 2024).
• The diagram is not thermodynamic proof. A region that looks clear may also be a kinetically stable nanoemulsion; time, temperature and mixing-order tests are needed to tell them apart (Anton & Vandamme, 2011; Gandhi et al., 2026).
• Temperature, drug loading and the dilution medium shift the region; for oral systems, what dilution does in gastrointestinal fluid and after digestion is tested separately (Pouton, 2006).
• Region width is not the only criterion. A wide region may mean a high surfactant content; toxicity and irritation limits (especially in topical and oral use) constrain the choice (Kreilgaard, 2002; Karasulu, 2008).

Contributions from Türkiye

The 2008 review by Karasulu of Ege University, which brings together the formation, stability, applications and toxicity of microemulsions within the framework of the pseudo-ternary diagram, is an internationally cited reference text (Karasulu, 2008). The pseudo-ternary diagrams and region areas in that review were prepared with the software that is the predecessor of the tool on this page.

The history of this tool. The first version of the software ("Micro") was written in Visual Basic 6 at the Faculty of Pharmacy of Ege University in the summer of 2001. The experiments were kept in an Access database (per experiment: date, formulation, surfactant:cosurfactant ratio and oil/surfactant/water/alcohol columns; the first records are ethanol-containing S_mix series from 3:1 to 6:1). The region boundary was drawn by converting the measurement points to triangle coordinates and closing through the edge parallel passing through the water value of the last point; the area was computed from the polygon vertices with the shoelace formula and the centroid with the classical polygon centroid formula, then converted back to percentages (Geometry.bas and Genel.bas, dated June 2001). The coordinate transformation, the area and centroid computation, the intersection point and the "closing through the lowest value" option of today's tool come from that code; they were later moved to the web, and the Blazor version added edge closing, the smoothed boundary, group styles, the total check and SVG export. The triangle favicon in use since 2012 also comes from this application. The diagrams and region areas in the Karasulu (2008) review were prepared with this program. Berkman and Güleç (2021) of Istanbul University published the same area and centroid computation with explicit formulae and an Excel macro, bringing the method into the literature.