# Hands-on Theory of Micelles, Di-blocks and Host/Guest Solubilization

**TAGS:** Science-based Formulation

**two user-friendly tools** for exploring the **Scheutjens-Fleer (SF) or Self-Consistent Field (SCF) theory of polymers** on and around particles. This is the first time that this **powerful theory** has been made generally available, even though it has been around and used with considerable success by the academic community for decades.

Briefly, it places polymers, particles and solvents into a box and calculates all the interactions between neighboring elements within the box. It moves components around till there is a **self-consistent balance** and from that, we can work out where all the components are with respect to each other, and what happens if you try to bring particles together – telling you if they **attract (unstable)** or **repel (stable)**.

The interactions between components are calculated via the Flory-Huggins** **χ (chi) parameter between them.

- When χ is 0, there are no penalties for elements to be next to each other.
- When χ=0.5, the elements are on the borderline of compatibility, and higher values mean that the components will try to be apart from each other.

Fortunately for us, these χ parameters can be estimated via

**Hansen Solubility Parameters**, which are one of the core elements of

**SpecialChem’s Science-Based Formulation strategy**,

**with values known or estimated for many thousands of chemicals and polymers**.

The SF calculations are immensely complicated, but thanks to the generosity of

**Prof. Frans Leermakers**of Wageningen U, his

**SFBox**, which does all the calculations, is available to the formulation community. “All” we need is a front end to pose the questions and read the answers, and that’s what I have provided.

In this article, I show how the complex world of (non-ionic) surfactants, di-block (in the examples, I use a 50-50 A-B di-block, as illustrated) and tri-block polymers can be modeled easily using the widely-available commercial package, HSPiP, Hansen Solubility Parameters in Practice.

**Structure of 50-50 A-B Di-block**

*Let's begin with an example.*

## Complex Calculations Made Easier Via SF Approach

Let us assume we need to solubilize a

**water-soluble ingredient**in a formulation (e.g. cosmetics), which might contain some co-solvents, such as

**propylene glycol**or a

**greener alternative**. The presence of these components might:

- Slightly increase the solubility of the solute
- Decrease the water compatibility of the surfactant head, and
- Reduce the effective hydrophobicity of the tail.

Overall, the relative effects will depend on many factors.

For conventional

**oil/water emulsions**, the

**newer HLD-NAC tool**is now becoming commonly accepted, but there is nothing much available for micellar systems.

It is also imperative to note that

**Critical Micelle Concentration (CMC)**is OK for a pure surfactant in pure water, but that is not true for formulations with multiple components and generally does not interest formulators, as multiple ingredients play multiple roles. Therefore, going with trial and error can be a very tedious strategy, but can be easily understood using a rational, science-based approach to complex systems. The SF approach that we are going to discuss here, allows a systematic exploration of all three effects, giving us a clearer picture of what is going on.

Indeed, the new approach takes us out of our comfort zone but having powerful tools can help us to formulate better with a clearer understanding of our micelles. At first, it is tricky and confusing, but after a while, it becomes clear. Each calculation is either instant or takes just a few seconds, so it is easy to play around. Make all your mistakes in the software – it’s far easier than making your mistakes in a set of test tubes.

» Readers will know that I am co-author of the package, and therefore biased. Although I like to make

**science available via free apps**, these simulations require the infrastructure of a proper software package, with the added bonus that estimation of the χ parameters can be done via the HSP infrastructure of the package itself.

In what follows, we will assume that the solvent is water, but the calculations are general and can adapt to different

**solvents**by changing the various χ parameters.

## A Single Di-block Polymer

The figure below shows the basic graphical representation of a single 50-50 A-B di-block polymer. If you have a 50-unit A block (say 20nm long) with χ=2 (very unhappy in water) and a 50-unit B block with χ=0.4 (OK in water), this is what you would find from the graph below.

- The
**A-block (red)**is curled up on itself and only extends by ~1.5nm. - The
**B-block (green)**starts to appear in the outer 1nm and then extends out to 4nm. - Their combination is the
**“All” curve (blue)**.

**A Single 50-50 A-B Di-block, with A Being Insoluble in Water**

If you change the χ values of A-Solvent, B-Solvent, and A-B, you see modest changes, but it’s not very exciting.

**Polymers**like to coil-up on themselves, and that’s about it.

## A Di-block Micelle

Things are much more interesting when we take the

**same di-block and simulate a micelle**.

**The Same 50-50 A-B Di-block as a Spherical Micelle. The Inset Shows Some Calculated Values.**

The figure above shows the following results.

- The A-block core of the micelle is about 7nm radius. It is made from ~360 di-blocks aggregated together and contains a surprising amount (~8%) water (magenta line).
- Then there is a fairly sharp transition to the B-block, which extends out to about 14nm, though the effective hydrodynamic radius is 12nm.

The

**Critical Micelle Concentration (CMC)**is estimated as a volume fraction, and as mentioned, there is an estimate of the number of molecules aggregated into the micelle. All this takes about 5s to calculate on my laptop.

You can repeat the calculations imposing either a

**cylindrical or bilayer (laminar) geometry**. Depending on which gives the lowest CMC, you then know which is the stable configuration. Within a few minutes after doing a few calculations, you get to know just about everything you need to know about your micellar system, with the ability to play “what ifs” with different lengths of the blocks and with different blocks – capturing their different solubility characteristics in their χ parameters.

## Solubilization of Guest Molecules

- The first three of these are the
**χ values of the guest**with respect to A, B and the solvent. The guest is happy in A, doesn’t like B and (not surprisingly when we are trying guest solubilization) really hates water. - The
**φ G-bulk parameter**forces that amount of guest into the system so we can see what happens. - The Layer* is discussed below.
- The
**G Type**is S9, which means a star-shaped molecule with 9 lattice segments.

**The Full Screenshot with the Guest Solubilization**

Although real molecules aren’t made of star-shaped or linear blobs, this sort of approximation is surprisingly successful in producing the main effects observed experimentally. Other options are:

**S5**– A 5-element star**L2 to L6**– Linear molecules.

It is interesting seeing the effect of shape and size on the guest interactions.

The graph output shows that in this case the

**guest (orange line)**is mostly sitting in the core though with a little peak towards the core-corona interface. It’s well known (and easily shown with different sets of χ values) that the guest often accumulates at this interface. The output boxes tell us that the guest is

**88% in the core and 12% in the interface**, with, effectively, none in the corona or solution.

## Guest Emulsion Calculation

All these calculations are carried out using SFBox scripts developed by

**Dr. Alessandro Ianiro**during his Ph.D., available

**online**. I was checking with him that my implementation was correct (it was!) but had a question about one part of his thesis which I did not understand. His answer opened a whole new aspect of the simulation.

**The Same as Previous But With Layer* Set to 3, Giving an Emulsion Calculation**

Thanks to a numerical trick, we have tripled the amount of guest. Now there is almost no A in the core – we have mostly guest. In other words, we are well on the way to an emulsion drop. So not only can we calculate

**guest solubilization**, but also we can explore

**guest emulsification**too.

There are plenty of assumptions behind all this (e.g. the guest is assumed to be a liquid!), and we can’t take the results too literally. But the point is that we have never had the sort of power to explore issues like this before and we all have to learn what to do with the power.

## The Future of SF Di-blocks

This article is based on the first version of the di-block calculations in HSPiP.

**What will future versions bring?**No one knows. The emulsion calculations are very much an unexplored area. And although this version handles tri-blocks, it cannot simulate the viscosity effects of tri-block associative thickeners, such as

**Hydrophobically-modified Ethoxylated Urethane Resins (HEURs)**.

The future is, therefore, open. If the user community gets in the habit of working with

**SF theory**, then we will be in a better place to understand the limitations and ask for improvements. Although academics often publish work that speaks only to other academics, my experience is that there are those who are keen to work with the formulation community to open up new real-world possibilities.

As with other aspects of Science-Based Formulation, we progress one step at a time. With SF theory now available to the formulation community, the first step is for the community to get to know its strengths and limitations. That’s what this article and the

**previous one**are for. Then we can start thinking of what happens next.

*I could not have reached this stage without the generous help of Prof. Terence Cosgrove, Prof. Frans Leermakers, Dr. Nicholas Tito, Dr. Álvaro García and Dr. Alessandro Ianiro and I send them my thanks.*

The next steps are up to you, the formulation community.

### Simplify Your Calculations Using SFBox – Formulators Stay Alert!

Optimize complex particle systems much faster using a new science tool known as

**SFBox based on Hansen Solubility Parameters (HSP)**that simplifies complex calculations of SF lattice theory.

**» Discover More About Science-based Formulations!**

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