PIT Versus PIF for the Rational Formulation of Emulsions

Aug 1, 2012 | Contact Author | By: Steven Abbott, PhD, Steven Abbott TCNF Ltd. and University of Leeds
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Title: PIT Versus PIF for the Rational Formulation of Emulsions
hydrophilic lipophilic difference (HLD)x net average curvature (NAC)x phase inversion formulation (PIF)x
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Keywords: hydrophilic lipophilic difference (HLD) | net average curvature (NAC) | phase inversion formulation (PIF)

Abstract: This article deliberately pushes the boundaries for cosmetics scientists, showing how the much-used phase inversion temperature (PIT) technique is a limiting special case of a more versatile, rational approach to surfactant optimization: HLD-NAC. This simple way of understanding the basic interactions within emulsion formulations can be generalized to create totally new ways of formulating stable emulsions.

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S Abbott, PIT versus PIF for the rational formulation of emulsions, Cosm & Toil 127(8) 564-572 (Aug 2012)

Author's Note: I became involved in emulsion science by complete accident. My main expertise is in the coating/printing industry, as well as in web-handling, formulation chemistry, nanostructures, bio-mimetics and technical software applications. Two years ago, however, I had to re-formulate an emulsion by changing the oil in it, which required additional guidance as to which surfactant to then use; here, rather than the term emulsifier, surfactant is used, in its neutral scientific sense. Since this substitution process seemed fairly routine, one might assume it would be simple to find a scientific method to carry it out. However, in reviewing the literature, I found it surprisingly challenging.

Critical micelle concentration (CMC) and hydrophile-lipophile balance (HLB) were irrelevant and useless for my needs: CMC because like most cosmetic formulations, relatively high concentrations were being used; and HLB because it is largely discredited for anything other than ethoxylate surfactants at room temperature. Also, a new (to me) idea seemed promising: critical packing parameter (CPP), but also proved impractical for a real-world formulator, although it does provide insights into mesophases. Finally, my search led to the concept of hydrophilic lipophilic difference (HLD), and its recent extension, HLD-NAC, where NAC refers to the net average curvature. This concept will be described in greater detail in the present article.

It was obvious that HLD-NAC would easily meet my needs for rational formulation because it took account of all key parameters: surfactant blend, oil, salinity and temperature. However, since even easy theories can be tricky to grasp, I wrote a computer program that allowed me to “play” with all the parameters and make sense of them. To better understand these parameters, I contacted key people behind HLD-NAC, especially Jean-Louis Salager, the “father” of HLD, and Edgar Acosta, the “father” of NAC. It turned out that no one had attempted to put HLD-NAC into a user friendly format, so Acosta helped sort out the details and the resulting software was posted to the Internet, free to users.

As far as I was concerned, this was the end of the story. I had the theory I needed and using it, even a non-expert such as myself could formulate emulsions right the first time. Further, surfactant science could benefit from the theory, as it was published in the public domain. However, I suddenly found myself lecturing to expert surfactant scientists about how to formulate scientifically. These people had been working for decades on surfactants, and here was an ignorant outsider explaining to them that HLB and CPP were hopeless and useless, and that HLD-NAC was both simple and powerful. It is not a new or complicated theory but somehow over the decades, formulators seemed to consider surfactants as art rather than science. With this background out of the way, I can come to the point of the article. Time after time, I have met strong objection from surfactant experts who believe that HLD-NAC is not as good as the Phase Inversion Temperature (PIT) technique, so they are not interested in it. Even if you have not met PIT by name there is a good chance you have used it. It refers to formulations that are heated and stirred to enable the easy formation of an emulsion, then cooled rapidly to create a stable emulsion relying on phase inversion—provided they are based on ethoxylates, which are the only common class of surfactants that exhibit this behavior. Well, let me tell you something: HLD-NAC gives far more than the phase inversion temperature (PIT); it gives the phase inversion formulation (PIF).

—end Author's Note

Getting to the Himalayas

To climb Mt. Everest, explorers will find a map of the Himalayas instead of the Sahara rather useful. The map may not be perfect but once they are in the right region, they can refine it. In relation, this author’s experience finds that many individuals formulating emulsions have no map at all; or if they do, it is one based on HLB with large, uncharted areas saying, “Here be dragons.” HLD-NAC is a better way to find oneself on the complicated map of surfactant space. It is not a perfect or complete map but it reliably directs formulators at least to the foothills of Mt. Everest. Here’s how.

As is well-known, emulsions typically are either Type I, oil-in-water or o/w; Type II, water-in-oil or w/o; or Type III, a phase where water and oil co-mix with low interfacial energy (see Figure 1). Very often, formulators want a stable Type I emulsion with small droplets, so a balance of water, oil, emulsifier, salinity and temperature are required to reach that “sweet spot” state of maximum stability with minimum surfactant; ideally that sweet spot is reached without the need for vast amounts of energy.

This is where PIT comes in; the system is heated to the inversion temperature, where it can flip from Type I to Type II or, more precisely, to a state where the interfacial energy becomes minimal. Relatively simple stirring at this low interfacial energy gives small emulsion drops and if the formulation can be cooled quickly enough, those small drops remain small and form a fine emulsion. PIT is a splendid technique and is used every day to generate cosmetics. So, why this author’s initial unimpressed opinion of PIT? Well, try using PIT to make an emulsion using alkyl polyglucoside (APG) surfactants. It does not work. Why? Because unlike the ethoxylates required for PIT, APGs do not change their surfactant property significantly with temperature. This is because the sugar group in the APGs happens to show neither the decrease in aqueous compatibility of ethoxylates, nor the increase of typical anionics. Also, creating a Type I emulsion using typical anionics is not possible; their temperature effect is the opposite of ethoxylates. In fact, PIT works fine for creating Type II emulsions with anionics but it is not an actual technique, rather, a trick that works brilliantly only for ethoxylates and Type I emulsions.

What PIT is doing with ethoxylates is making a Type I into a Type III, i.e., putting it in a low interfacial energy domain, then returning it to a Type I. Since HLD-NAC can calculate ways to go from Type I to Type III other than via temperature, replacing PIT with PIF allows a general formulation technique for emulsions: Find a way to get the formulation into the Type III or “phase inversion” region, create the emulsion with little energy, then quickly place the formulation in the correct portion of the Type I regime, for o/w, or Type II for w/o, to produce the final emulsion. If one uses ethoxylates for a Type I emulsion, the straightforward way to a PIF is to push the formula into Type III using temperature. To do anything else, however, one needs a map to explain how to get in and out of Type III territory with minimum effort. That’s where HLD comes in.

Equation 1 describing HLD balances the water and oil phases of an emulsion and is dependent upon four factors: salinity (S); temperature (T); oiliness, as described by the Effective Alkane Carbon Number (EACN); and a value that characterizes the surfactant, Cc. The constant α is a temperature coefficient—typically 0.1 for anionics, -0.6 for ethoxylates, and 0 for APGs. The functional dependency on salinity, f(S), is linear for nonionics and logarithmic for ionics. The factor of 0.17 for the dependency on “oiliness” has been determined experimentally across a broad range of oils and surfactants.

HLD = f(S) - α(T-25) - 0.17*EACN + Cc

Eq. 1

HLD: The name HLD captures some of what HLB was supposed to be, but the word difference makes all the difference. HLD is the calculated numerical hydrophilic/lipophilic difference at the interface, which depends on all aspects of the formulation: salinity, temperature, oil and surfactant—and, as an extension to the theory, alcohols. Unlike HLB, HLD can be used to carry out numerical calculations for all types of surfactants in all types of formulations. When HLD = 0, the perfect balance between hydrophilic and lipophilic tendencies is achieved and the emulsion is in a Type III domain, with very low interfacial tension.

EACN: The EACN is known, by definition, for simple alkanes. It is simply the number of carbon atoms in the chain, so octane is 8; decane is 10; and so forth. For other oils, the EACN value must be measured using “surfactant scans” and HLD theory. For example, isopropyl myristate (IPM), a common emollient, has 17 carbon atoms but its EACN is 13 because it behaves in emulsions as if it were tridecane.

Characteristic curvature (Cc): During the development of the HLD theory, a number was needed to describe the tendency of a surfactant to curve inward (w/o) or outward (o/w), which is described by the term characteristic curvature (Cc). With the benefit of hindsight, this is unfortunate terminology as there is no such thing as a tendency to form a curvature because as HLD shows, it depends upon oil, temperature and salinity. Therefore, consider Cc simply as a number that defines a key property, or characteristic, of a surfactant. As a rough guide, a typical strongly hydrophilic surfactant has a negative Cc, e.g., -2.3 for SLS and +2.6 for AOT.

Equation 1 shows that, for nonionic surfactant formulations for decane at 25°C, without the use of salt, a perfect balance is achieved; i.e., HLD = 0 and 0.17*EACN = Cc. In other words, a surfactant of Cc = 1.7 is a perfect match for decane. Therefore, to create a Type I emulsion with decane, one would need an HLD < 0. That requires a Cc of, say, 1.1, giving an HLD of -0.6. If this were an ethoxylated surfactant, then the α value for the temperature equation is -0.06, so a temperature rise of 0.6/0.06 = 10°C would be sufficient to take the Type I emulsion into the Type III domain. However, this means that during transport or storage, if the temperature rises to 35°C, it could become unstable. So a surfactant with a Cc of say 0.5 would be necessary, giving an HLD of -1.2 at 25°C and requiring a temperature rise to 45°C for the PIT technique. This simple exploration of the surfactant map already explains a good deal. The further away from HLD = 0, the less suitable the surfactant is for creating an efficient Type I. In this example, however, the formulator is forced far away in order to create a stable system.

Mixed Surfactants

Why do formulators typically use surfactant mixtures, how do they know which ones to blend, and in what proportions? There are two answers to this question. The first is rather sad: most single surfactants are wildly inappropriate; i.e., their Cc values are much too large or too small, for the emulsions typically being created. The second is distressingly true: The mixtures were often arrived at by much expensive trial and error. Going back to the example above, using PIF, one can easily see a fix to this formulation dilemma. If, for example, the temperature constant α were -0.03 instead of -0.06, one could formulate at a Cc of 1.1 but still require a temperature rise to 45°C to reach the Type III domain.

Here is where HLD stars again. The Cc of a mixture of surfactants is simply the molar weighted average of the Cc of the individual surfactants, and the same applies to the temperature effect. So if, for example, an ethoxylate were mixed with Cc = 1.6 and an APG with Cc = 0.6, then assuming they are the same molecular weight, a 50:50 blend would give a Cc of (1.6 + 0.6)/2 = 1.1, and an α = (-0.06 + 0)/2 = -0.03. This would create a better Type I emulsion while still providing good thermal stability.

Now suppose that marketing announced decane was no longer acceptable for the formulation. If IPM were to be used instead, this creates a shift in the HLD of 0.17*(13-10) = 0.51, so the Cc must be changed to 1.61, and the ethoxylate:APG blend from 50:50 to ~100:0. Doing this would increase the temperature sensitivity, so instead the Cc = 1.6 ethoxylate were replaced with a Cc = 3.2, which is rather high; or a new blend could be created with a 50:50 Cc = 2.2:Cc = 1 EO:APG blend. Of course, this requires the availability of such surfactants. One of the important aspects of HLD-NAC is that it allows customers to say to suppliers, “I need an ethoxylate of Cc = 2.2 and an APG of Cc = 1.0,” which is better than asking, “Have you got some magic blend that gives me a nice PIT for IPM?”


As the above example shows, however wonderful it is to use temperature as a means of obtaining a fine dispersion, it has two crucial limitations in terms of choice of surfactant and emulsion stability: First, it only works for ethoxylates, and second, there is a constant battle between being too inefficient, i.e., HLD < 0, at room temperature; or too susceptible to temperature fluctuations, i.e., HLD close to 0. And even if techniques such as low energy emulsification1 are utilized, one must still apply a large amount of heat to the emulsion during production.

Now consider formulating a good emulsion at room temperature using APGs. First, one needs to be in a Type III domain. The use of IPM means an APG with a Cc = 0.17*13 = 2.21, which creates an excellent dispersion using little energy. But how can this be transformed into a Type I? Easy, by simply stirring in some APG with Cc = 0, then the average Cc comes down, the HLD is reduced, and the emulsion is in a Type I domain. The beauty of this is that a Cc such as 1.9 can be obtained, which gives an efficient Type I with no compromises on temperature stability. Also, the formulation of the emulsion is suddenly more sustainable as there is no need to heat large amounts of water and oil.

There is more, however—production is not the same as the lab environment. Sometimes oil must be added before water, or water before oil, or the surfactant pre-dissolved, or some oil pre-heated in order to dissolve/ melt components such as cetyl alcohol, etc. These differences often lead to catastrophes during scale-up because at some point in the production process, a w/o emulsion is produced that can be very difficult to “flip” to the desired o/w emulsion. See Reference 1 for a good discussion of these factors; it is interesting to read the examples given through the eyes of HLD-NAC. The author’s intuitions regarding low surfactant emulsification, in addition to the idea of low energy emulsification, match the predictions of HLD-NAC very closely.

The point about HLD-NAC is that it provides a map for producing the emulsion. If at some stage there is a large amount of one of the surfactants, it can be calculated whether the emulsion is at risk of being in the wrong w/o state. If so, a plan can be developed to do something about it; e.g., adding the surfactant at a later stage. Therefore, the lab and production teams can predict in advance what scale-up problems are likely, and therefore work through the compromises necessary to get a robust, low-cost production process.

All Too Simple?

A confession: So far, all the calculations shown work perfectly for 50:50 o:w but this is generally not what most applications require, which is where NAC comes in. Building on the basic physics of HLD, Acosta has shown2 that with NAC, one can calculate what happens at any o:w ratio. In particular, it allows the construction of what can be referred to as a Cc fishtail diagram. Personally, this author finds this to be the most powerful map in the whole of emulsion formulation.

Many formulators have heard of a fish diagram, which plots the Type I, II and III phases as both the temperature and percent surfactant change. Although it is helpful in working out PIT formulations, it is merely one slice through the complex map of surfactant space. A Cc fish is another slice through space—keeping temperature constant but varying the surfactant blend to see how one might move in and out of Types I, II and III. Just like the classic temperature fish diagram, the default version of the diagram shows what happens at 50:50 o:w blends.

Using HLD-NAC, however, one can calculate a Cc fish at any o:w ratio; importantly, the tail point, i.e., the moment when all three phases coexist, can be plotted for all o:w ratios (see Figure 2). This makes it possible to know that, for a 20:80 o:w blend, a full, homogeneous, Type III emulsion can be obtained at a 2.1% surfactant blend, with starting surfactants Cc = 1.6 and 0.6, with a Cc of 1.077, and with a surfactant ratio of 54:46. For a PIF technique, this is the starting point from which changes can be made to the Cc value to 0.9 in order to create a stable Type I.

Sharp readers will see a problem with this. Although the Cc is decreased by adding extra surfactant, the overall percentage of surfactant is then increased—something that is not necessarily desirable. Fortunately, PIF can again help formulators with this problem. One need not be at the tail to formulate Type III; this is generally over-the-top in terms of surfactant percentage. The map shows where the emulsion is safely in a Type III domain as well as where a little extra surfactant will shift the emulsion to the desired Type I. This example is based on a real formulation challenge and in fact, by starting at 1.8% of the surfactant blend and increasing to 2.5% total by addition of another 0.7% of the low Cc surfactant, changing the ratio from 60:40 to 43:57, the formulation flipped from Type III to Type I as predicted.3 There’s more. Smart formulators know that a Type III can be shifted to a Type I by changing the ratio of oil to water.

Sometimes this shift is a dramatic and rather risky catastrophic phase inversion that deliberately goes from too much oil and a w/o emulsion to the correct oil ratio with a “hopedfor” inversion. With PIF, however, one does not need to be so dramatic. By knowing where the emulsion is in the Cc space, one can have a nice Type III with too much oil, then add a bit more water to take the emulsion comfortably into the Type I domain. A glance at the screen shots from the software calculations and plots (see Figure 3 and Figure 4) will show that there is a lot more to this than has been described so far but the point of this article is not to bore readers with the niceties of HLD-NAC, rather to give good reasons why formulators might explore this theory.

Too Good to be True?

From the start, this author claimed no expertise at formulating emulsions. Yet here it is stated that anyone can rationally and efficiently formulate an emulsion on the basis of a simple equation, HLD, supplemented with a slightly more complicated one, NAC. Also, the software to make these calculations is provided free. Is there not something wrong with this equation? Of course there is.

HLD-NAC is not perfect, although key experts such as Salager and Acosta continue to work hard to refine it. The software certainly is not perfect, although user feedback has helped improve it tremendously over the past year. Also, surfactants and oils are not perfect—not to mention the issue of alcohol co-surfactants where there is currently too little data to accurately predict the effects of alcohols such as propanol and butanol, and where the distinction between an “alcohol” and a “surfactant” for, say octanol, is unclear. The example given is a simplification of the real complexities of the formulation with which formulators are working, and it still was not trivial to create a fully functional formulation. However, without HLD-NAC, there would have been little chance of creating such a novel formulation from scratch.

The fact of the matter is that basically, the HLD-NAC approach is sound, and in one area where huge fortunes are at stake—i.e., extended oil recovery, it has been used routinely for years.4 The biggest limitation for cosmetics is that there are not enough published Cc values for surfactants, or enough EACN values for oils. Suppliers are urged to give customers tools that build on the power of HLD-NAC, including good Cc and EACN values and, importantly, sets of surfactants that are properly tuned for the intended applications.


If this author had to choose a slogan for HLD-NAC it would be something like, “so easy and powerful that even Steven Abbott can formulate emulsions with it.” To smart, experienced emulsion formulators, however: Imagine how much more powerful HLD-NAC will be in your hands. For many years this general, validated technique to understand the effects of oils, salinity, temperature and surfactant blends on the behavior of a surfactant formulation has been available and applied to other large industries such as oil recovery. The technique works well for microemulsions, for which it was originally developed, but applies equally well to classical emulsions as well as provides alternative routes to nanoemulsions, which currently tend to rely on PIT approaches. The tragedy is that the technique is so little known to this industry. Perhaps this article, the free software and additional information referenced here will help bring this important theory to life.

Acknowledgements: The advice and help from Jean-Louis Salager, PhD, Universidad de los Andes, Mérida, Venezuela; and from Edgar Acosta, PhD, University of Toronto, Canada, is warmly acknowledged. Any faults in interpretation and implementation of their theories are the author’s own.


  1. TJ Lin, Manufacturing Cosmetic Emulsions: Pragmatic Troubleshooting and Energy Conservation, Allured Business Media, Carol Stream, IL, USA (2009)
  2. EJ Acosta, The HLD–NAC equation of state for microemulsions formulated with nonionic alcohol ethoxylate and alkylphenol ethoxylate surfactants, Colloids and Surfaces A: Physi-cochem Eng Aspects 320 (2008) pp 193–204
  3. S van Loon, VLCI, Amsterdam, private communication (2012)
  4. F-H Haegel, JC Lopez, J-L Salager and S Engelskirchen, Microemulsions in large-scale applications, ch 10 in C Stubenrauch, ed, Microemulsions, Background, New Concepts, Applications, Perspectives, Wiley, NY (2009)


Figure 1. Navigating around surfactant space with HLD

Figure 1. Navigating around surfactant space with HLD

As is well-known, emulsions typically are either Type I, oil-in-water or o/w; Type II, water-in-oil or w/o; or Type III, a phase where water and oil co-mix with low interfacial energy.

Figure 2. The Cc fish diagram

Figure 2. The Cc fish diagram

The Cc fish diagram (green and red lines); the plot in magenta shows where the fishtails cross at different o:w ratios.

Figure 3. A 50:50 blend of this ethoxylate and APG

Figure 3. A 50:50 blend of this ethoxylate and APG

A 50:50 blend of this ethoxylate and APG gives a Type I at 25°C but has a T* of 45°C.

Figure 4. Results of changing the temperature and blend

Figure 4. Results of changing the temperature and blend

Changing the temperature to 45°C and the blend to 49:51 shows that the maximum solubility, o/w and w/o, occurs for EACN = 10, i.e., the decane oil.

Additional Information

More information, including free software, slides and reference papers about HLD-NAC can be found at www.stevenabbott.co.uk/HLD-NAC.html. Many aspects of this article are also brought to life in the second lesson of Allured's Optimization for Cosmetics course, available at http://learn.cosmeticsandtoiletries.com/optimization-for-cosmetics.html.

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