If you add a plasticiser, another polymer, a nanoparticle, or a drug molecule to a polymer, for ease of blending and for long-term compatibility you need to know that the components are mutually compatible. Doing this via HSP is a tried-and-tested methodology used across a wide range of industries.
To get started, choose polyethylene, and start with δD=16, δP=1, δH=1 for a compatible molecule, then increase δP and δH to see how incompatibility (a large Flory-Huggins χ value) develops.
A second app discussing Flory-Huggins theory appears later on in the page.
The HSP Distance has a profound effect on the behaviour of things blended into polymers. These might be:
- Other polymers
- Drugs (APIs)
Take, for example, a polymer and plasticiser. If the Distance is too large then the plasticiser will tend to want to separate from the polymer and come to the surface - the fate of far too many poorly-chosen plasticisers
Or it might be two polymers. It is very difficult to completely blend two polymers (even PMMA and PEMA are immiscible!) but in terms of adhesion, it is possible for two polymers to intermingle if their HSP Distance is reasonably small.
And for those who want to get pigments, drugs/APIs, nanoparticles or nanoclays into a polymer, the smaller the Distance between them, the easier they are to blend and the more integrated they are into the overall structure.
For those who are used to the Flory-Huggins χ parameter for thinking about polymer solubility/miscibility, it is calculated via:
where MVol is the molar volume and RT is the usual gas constant times temperature term. For polymer-polymer intermingling (rather than complete mutual solubility which is hard to achieve) the χ parameter can be used to calculate the distance two polymers can reach across the interface, with a lower χ value giving a greater possibility of intermingling. In other words, the HSP Distance is a good guide to polymer intermingling even if (for those who know Painter-Coleman) they are a less good guide to polymer miscibility.
The app lets you calculate the HSP distances between a polymer and the HSP values of the blend ingredient (plasticiser, polymer, API...) of your choice. Simply select a polymer and the HSP distance is calculated. The χ parameter is also calculated and, for reasons discussed below, highlighted in red when it becomes greater than 0.5.
So far the discussion has been about blending things (plasticisers, polymers, nanoparticles, APIs) with polymers. The solubility behaviour of a polymer in a solvent depends on a balance of entropic and enthalpic effects. These are captured in the Flory-Huggins free energy equation showing dependence of ΔG on the solvent and polymer volume fractions φ1, φ2:
The factor x is the ratio of the MWts of the polymer and the solvent and is large as the polymer MWt becomes very large so that 1-1/x approaches 0, reducing entropic effect to a minimum. The graph shows how a nicely negative ΔG suddenly switches to a positive value as you approach χ~0.5. In the calculation the input is the HSP Distance, and the solvent is assumed to have a MVol=100.
This shows the classic Flory-Huggins behaviour.
- Low MWt polymers are more easily solubilised
- Not much happens as Distance (or χ) increases from 0 to 7 (0.4)
- The ΔG curve becomes flat near the start, i.e. borderline solubility, but still a dip at higher φ2
- A catastrophic flip of behaviour for a small increase in Distance or χ value.