HSP Examples: Measuring Nanoparticles

The Nanoparticles example discusses the HSP values measured by the classical technique. Here we discuss an alternative methodology using a centrifugal technique.

The general centrifugal technique has been around for some time, but an excellent paper that uses the LUMiSizer, refines the technique and introduces an objective methodology for scoring "good" and "bad" solvents. The paper (it is Open Access so freely downloadable) is Sebastian Süß, Titus Sobisch, Wolfgang Peukert, Dietmar Lerche, Doris Segets Determination of Hansen parameters for particles: A standardized routine based on analytical centrifugation, Advanced Powder Technology 29 (2018) 1550–1561

The LUMiSizer is an analytical centrifuge that measures the light transmission, %T, or Optical Density, OD, along the whole length of the centrifuge tube. You start with a dispersion with a uniform high OD along the tube (shown in orange) then follow, via the OD profile along the tube, how due to centrifugation, particles move to the bottom of the tube (towards the right in the images of the tubes). For "good" solvents (left image) the movement is slow and the OD curve shows a small degree of clarification after a certain centrifugation time (green line) with a slightly higher OD at the bottom of the tube. For "bad" solvents (right image) the particles settle rapidly to the bottom of the tube, giving a big reduction in OD along most of the tube and a large rise in OD at the bottom.

Note that the graphics show lots of particles crowding together. In reality the concentration is kept low so that sedimentation is not strongly affected by crowding effects.

From the data (and by adding corrections for viscosities and densities of the solvents) you calculate the RST - Relative Sedimentation Time. The key is that a good HSP determination needs a balanced set of "good" (large RST) and "bad" (low RST) solvents. But how do you objectively define the cutoff RST value?

This raises another question. What change of % transmission (or Integrated Extinction, IE, calculated along the tube) tells us when the particles have settled?

Their technique makes an intelligent guess for the IE change, defines the fastest RST as 0, the slowest as 1 and creates a bad/good cutoff at RST=0.5. Via the standard HSP procedure, a value for the HSP of the nanoparticle is calculated. But this is based on a guess of the relevant IE value and the 50% cutoff point from the RST. Another more automatic approach is preferred. Start with the 2 heighest RST values, define these solvents as good, and calculate HSP. Then, in decreasing RST values, classify more and more solvents as good. The calculated HSP at first changes rapidly, then there is a plateau, followed by a rapid deterioration as obviously bad solvents are included. The start of that plateau region is the objective criterion for good/bad solvent classification.

Our experience with HSP measurements in general is that people are sometimes unhappy that the judgement of good versus bad is subjective. With this approach, the subjectivity is removed.

A friendly disagreement

Clearly this objective methodology has a lot of potential and the HSPiP team are delighted that such a capability has been added to the world of HSP. However, we disagree (as scientists are allowed to do politely!) with another aspect of the paper. The authors believe that "dispersions" are different from "solutions". So they want to call the values they measure "Hansen Dispersibility Parameters", HDP. There is a very clear benefit to this new terminology: it makes it much easier to talk to nanoparticle scientists who think that a "Solubility Parameter" cannot be relevant to a dispersed particle.

However, this advantage comes with the disadvantage of raising difficult questions. Why is the "Dispersibility" obtainable from the "Solubility" parameters of the solvents? If you have a polymer with an HSP, how do we know how it should interact with a particle with an HDP if HDP is something significantly different? If it is valid to blend HSP with HDP, why not keep a single phrase HSP? And as Steven has noted in his Solubility Science book, there are good thermodynamic arguments saying that "soluble" and "dispersed" are the same thing.

A friendly proposal

It is not just those who work with particles who are uncomfortable with the word "Solubility". For example, many crosslinked polymers are merely swellable. So we have suggested on the Similarity page that HSP can be considered, informally, as Hansen Similarity Parameters. This means that one concept (captured in terms of HSP Distance) can apply to soluble and swellable polymers and also to particle systems.