## Polar Oils

### Quick Start

For many years we have had the Polar Oil problem in formulation. Many oils are also surfactant-like and no simple variant of HLD was able to deal with them. The 2019 paper1 Characterizing the oil-like and surfactant-like behavior of polar oils from the Acosta group has given a way forward.

### Polar Oils

Ccpolar
EACNpolar
qmax
Km 1/M
Example
Other Input Data
Data source

For clarity, the explanation assumes an expert-level familiarity with HLD theory in general.

A polar oil does not fit neatly into HLD-NAC because, by hypothesis, at low concentrations it tends to go to the surfactant interface and influence curvature like a surfactant, and at higher concentrations it acts like a pure oil, albeit one with a very low EACN.

Taking this hypothesis seriously makes it possible to understand how a given polar oil interacts within a given system. The first thing to do is to measure the change of HLD as the % polar oil (with respect to the real oil) is increased. In the paper this is measured via changes in S* but the idea is general. That's what the Raw Data plot on the left is indicating

Now assume that the polar oil has migrated 100% to the surfactant at all concentrations and re-plot the S* data according to the mole fraction of the polar oil with respect to the real surfactant. By the Cc mixing rule, given an estimate of the Cc of the polar oil, we know the Cc of each mix so we can predict S* for each fraction of polar oil. If the results are a straight line then the assumption is correct; when it deviates (which it must do) we know that the polar oil isn't fully partitioning. From the slope of the linear part we can determine the Cc of the polar oil.

Now assume the opposite - that the polar oil partitions completely into the oil. The plot is now of the polar oil as volume fraction of total oil. From the volume mixing rule and an estimate of the EACN of the polar oil, we can estimate the EACN of that mix. The assumption is only valid for high concentrations of polar oil, so the fit is to the final part of the curve.

We now have (via your informal slider fitting) estimates for the effective "pure" Cc and "pure" EACN for the polar oil. To fit the whole dataset we need to know the actual concentrations of polar oil in the surfactant and oil for each of the overall polar oil concentrations. For this we need two more parameters. The first is qmax which tells us the saturated ratio of polar oil molecules to surfactant molecules at the interface. The second is Km where 1/Km is the concentration of polar oil at which the transition takes place from surfactant-like to oil-like. These extra parameters are used to create a Langmuir isotherm, from which we know the concentration of the polar oil in the surfactant and in the oil at any given concentration. Knowing these concentrations, and applying the respective mixing rules, we can fit the whole curve.

Although the app could have applied a fitting process, it is far more instructive to find how to fit the data by hand. In many cases, as pointed out in the paper, the data can be fitted adequately with a rather broad range of some of the parameters. At first this seems to be a problem. But in many cases, the dependency of one of the factors is rather low, which itself is an interesting fact.

### The datasets

I could not have created this app without considerable expert help from Amir Ghayour and Edgar Acosta, for which I am most grateful. All errors in the app are mine. The original paper uses the final datapoint as a pivot for fitting the EACN. I have chosen to keep the EACN curve floating because the app is not attempting to "fit", just to show us the influences of each of the parameters.

The 9 datasets in the paper are with Naphthenic Acid (C12-C16 fatty acids), NA, and Dodecanol, DD. The surfactants are sodium dihexyl sulfosuccinate, SDHS, sodium dodecyl sulfate, SDS, then three ethoxylates, C13E6, C9E5 and C9PhE which is a mix of E5-9, and an extended surfactant C10PO4S. The oils are Heptane, Toluene, Decalin and cyclohexane.

The fitted parameters in the paper are:

Polar OilSurfactantNon-Polar OilEACNCcqmaxKm
NASDHSHeptane-9-0.40.6500
NASDHSToluene-9-0.50.6410
NASDHSDecalin-9-0.50.416
NASDSCyclohexane-20-10.7205
NAC10PO4SHeptane-30-1.6168
NAC13E6Heptane-701.30.5286
NAC9PhEHeptane-681.70.5338
DDSDHSHeptane-801.40.7130
DDC9E5Heptane-101.50.9150

### So what?

Till now, polar oils have been coped with in many ways (fully described in the papers). This is the first time we have a theory simple enough to be usable and complex enough to be useful. This leaves the community with a choice

1. Hope that Acosta's group carry on getting more data and refining the theory till it's even better
2. Get involved by measuring, analysing and publishing the data so we have datasets beyond the 2 polar oils, 4 oils and 5 surfactants used in the paper.

If we start to get a lot of data then we can refine the theory and start to gain a wider understanding about which oils interact strongly with which surfactants in which ways.

Because the app allows you to load and analyse your own data, and because it is easy to add more examples to the combo box, we have no excuse in terms of data analysis. If you send a dataset in the simple, standard format, I will add it. Because the dataset automatically provides the reference to its source, all contributions are automatically acknowledged.