Pseudo ternary phase diagram, drawn from your own titration data.
A pseudo ternary phase diagram maps the oil, Smix and water compositions that form a clear single phase. Enter the water endpoint you recorded against each oil-to-Smix ratio, and this tool draws the boundary, overlays every Smix ratio on one triangle, and returns the area and centroid of each nanoemulsion region. So “the region was larger at 2:1” stops being an impression and becomes a number you can put in a table.
Titration data
MEASUREDFills the ratio column of a new dataset. You still type the water percentage you measured against each one.
The three must sum to 100. The marker is drawn on the diagram and tested against every region.
Phase diagram
—Direct answer
What is a pseudo ternary phase diagram?
A pseudo ternary phase diagram is a triangular plot that shows which combinations of oil, surfactant mixture and water form a single clear phase, and which separate. It is called pseudo ternary rather than ternary because one corner carries two components at a fixed ratio: the surfactant and the co-surfactant are combined into a single Smix apex, which collapses a four-component system onto a triangle that can be drawn on paper.
The boundary is measured, not calculated. Oil and Smix are mixed at a set of fixed ratios, each mixture is titrated with water, and the water content at which the mixture turns from clear to turbid is recorded. Those endpoints are the boundary of the nanoemulsion region. The plot itself follows the ordinary rules of a ternary plot, where the three components at any point sum to 100 percent.
How to construct a pseudo ternary phase diagram
The aqueous titration method, which is what almost every published nanoemulsion paper uses. Six steps, and the tool above handles the last two.
Fix the Smix ratio
Blend the surfactant and co-surfactant at a fixed weight ratio and treat that blend as one component. Ratios of 1:1, 1:2, 2:1, 3:1 and 4:1 are the usual set, so each one gives you a separate diagram to compare.
Mix oil with Smix across the range
Weigh oil and Smix at ratios from 1:9 through to 9:1 into separate vials, which gives nine points across the composition space. Some groups add 1:8, 1:7 and so on to sample the Smix-rich corner more densely, because that is where the boundary usually turns.
Titrate with water, drop by drop
Add the aqueous phase in small increments under constant stirring at a fixed temperature. Speed matters: a fast titration overshoots the true boundary, so equilibrate after each addition before you judge the appearance.
Record the endpoint
Note the water percentage at which the mixture first turns turbid. Visual clarity against a dark background is the classic criterion, but transmittance at 630 nm, a PDI below 0.30 or a droplet diameter below 200 nm are all defensible and all more reproducible between operators.
Convert endpoints to three-component percentages
At the endpoint, water is what you measured and the remainder is split between oil and Smix in the ratio you started with. The tool above does this conversion, so you enter the ratio and the water reading exactly as they appear in your lab notebook.
Plot the boundary and measure the region
Join the endpoints to enclose the region, then report its area. Most workflows stop at the picture, so this is the step that turns a pseudo ternary phase diagram into a result you can compare against another Smix ratio or against another paper.
How do you determine the endpoint in water titration?
This is the single most asked question about the method, and the honest answer is that clarity alone is operator dependent. Two people titrating the same vial can differ by several percent water, because “slightly hazy” is a judgement.
Three fixes, in increasing order of rigour. Titrate against a printed black and white grid and call the endpoint when the lines blur. Read transmittance at 630 nm and set a numerical threshold, usually 95 percent. Or take a DLS reading at each step and call the endpoint on PDI, which is slower but removes the judgement entirely. Whichever you choose, state it in the methods, because a region measured by clarity is not comparable with one measured by PDI.
How do you calculate the area of the microemulsion region?
Counting squares on graph paper is still common and it is neither accurate nor reproducible. The polygon area follows from the shoelace formula applied to the boundary vertices, and expressing it as a percentage of the whole triangle makes it independent of the size the figure was drawn at.
That percentage is what lets you write “the region at 2:1 was 1.34 times the region at 1:1” instead of “the region at 2:1 appeared larger”. The tool also returns the centroid, which is the composition at the area centre of the region and a reasonable starting point when nothing else constrains the choice.
Software people use to draw a pseudo ternary phase diagram
The tools named most often in the literature, and what each one leaves you to do by hand.
| Approach | Cost | Draws the triangle | Encloses the region | Reports area |
|---|---|---|---|---|
| Microsoft Excel, scatter on a transformed axis | Licence | Yes, by hand | No | No |
| OriginPro | Licence | Yes | Manual | No |
| CHEMIX School | Licence | Yes | Manual | No |
| Tri-plot spreadsheet | Free | Yes | No | No |
| ProSim Ternary Diagram | Free | Yes | No | No |
| Graph paper and square counting | Free | Yes | Yes | Approximate |
| This tool | Free | Yes | Automatic | Yes, with centroid |
Every general ternary plotter will place your points. What none of them does is close the boundary and measure what it encloses, which is the number the discussion section actually needs.
How the region is built
Each oil-to-Smix ratio is a straight path across the triangle. Adding water moves the composition along that path towards the water apex, so the titration endpoint marks one point on the boundary. The region is the band enclosed by the anhydrous edge and the curve joining those endpoints, walked in ratio order rather than wrapped in a convex hull, because the boundary of a nanoemulsion region is usually concave and a hull would swallow it.
oil % at endpoint = f × (100 − water %)
Smix % at endpoint = (1 − f) × (100 − water %)
How the area is computed
The polygon area comes from the shoelace formula, taken in oil-water coordinates where the whole simplex has area 5000. Reporting it as a percentage of the triangle makes it independent of how the figure is drawn, so two diagrams from different papers can be compared directly. The mapping to an equilateral triangle is affine, which preserves area ratios exactly.
region area % = 100 × A ÷ 5000
What the number does and does not mean
The area is the fraction of the composition space that met your endpoint criterion, over the ratios you actually titrated. It is not a quality score. A large region at high Smix may still be unusable if the surfactant load is above what the route of administration tolerates, and two regions are only comparable when the endpoint criterion, temperature and titration rate were the same.
Coverage and interpolation
Only the ratios you enter are measured. Between two adjacent endpoints the boundary is a straight segment, so it is interpolated rather than observed, and the area therefore depends in part on how densely you sampled. Nine ratios and five ratios across the same system will not give quite the same number, which is why the endpoint count sits next to every area in the table.
Outside the range you titrated nothing is claimed at all. Titrate 1:9 through 9:1 and the span runs from 10 to 90 percent oil on the anhydrous edge; the tool reports that span instead of extrapolating to the corners, because the corners are where a fitted curve is least trustworthy and where a reviewer looks first.
The assumption behind the closed region
Each region is closed along the water-free edge, which assumes that for every ratio you titrated, all compositions from the anhydrous mixture up to the recorded endpoint met your criterion. For a clear-to-turbid water titration that is the standard construction and it is defensible, because the mixture was watched continuously as water went in.
It is weaker for criteria read at intervals. If the endpoint was called on PDI below 0.30, on droplet diameter, or on separation after standing, then the compositions below the endpoint were only assessed at the points you actually measured. Say which criterion you used in the methods, and if the criterion was intermittent, say at what intervals it was applied.
Frequently asked questions
Pseudo ternary phase diagram questions.
The questions researchers ask most often on this method, answered plainly.
What does pseudo mean in a pseudo ternary phase diagram?+
It means one apex is not a single component. The surfactant and co-surfactant are pre-mixed at a fixed ratio and treated as one pseudo-component called Smix, so a four-component system can be drawn on a three-cornered plot. Change the surfactant to co-surfactant ratio and you get a different diagram, which is why several are usually built and compared.
How many oil to Smix ratios should be titrated?+
Nine, running 1:9 through 9:1, is the convention and it is what most published diagrams use, as in this clove and olive oil nanoemulsion study. Add intermediate ratios wherever the boundary turns sharply, because that is where nine points can miss the shape. Fewer than five leaves the boundary under-defined and a reviewer will say so.
Which Smix ratio gives the largest nanoemulsion region?+
There is no general answer, which is exactly why the diagram is built. Increasing the surfactant share usually widens the region up to a point, then a very high surfactant fraction pushes the system towards a gel or liquid crystalline phase and the region shrinks again. Measure the area for each ratio and let the numbers decide rather than the appearance.
What is the difference between a microemulsion and a nanoemulsion region?+
The diagram is the same and the distinction is thermodynamic. A microemulsion forms spontaneously and is thermodynamically stable, while a nanoemulsion is kinetically stabilised and will separate eventually. Titration alone cannot tell them apart, so if the label matters, support it with stability data rather than with the phase diagram.
Can a formulation outside the region still work?+
Sometimes, because the boundary was measured at one temperature and one titration rate and applies to a blank system. Adding a drug shifts the boundary, often inward. Treat a point just outside as worth titrating rather than as ruled out, and treat a point deep outside as a reason to change the ratio.
Does the drug change the pseudo ternary phase diagram?+
Usually yes. A lipophilic drug partitions into the oil and interfacial film and commonly narrows the region. The safe practice is to build the blank diagram to choose a working ratio, then confirm the selected composition with the drug loaded rather than assuming the blank boundary still holds.
What temperature should the titration be run at?+
Whatever temperature the product will sit at, held constant and stated. Non-ionic surfactants are strongly temperature sensitive near their cloud point, so a diagram built at 25 degrees and a diagram built at 37 degrees can look quite different for the same system. Two diagrams are only comparable when the temperature matches.
Is anything uploaded when I use this tool?+
No. The calculation is JavaScript running inside this page, so your titration readings never leave the browser and nothing is stored or logged. It keeps working offline once the page has loaded.
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