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HSP Application note #65

Intrinsic Viscosity of polymer Solution and Hansen Solubility Parameters (HSP)


HSPiP Team Senior Developer, Dr. Hiroshi Yamamoto


I compiled Mark-Houwink parameters(WikiPedia) and make database.

You can calculate Intrinsic Viscosity with this scheme.
[η] = KMa
I compiled K and a values for many polymers with a lot of solvents.

For solvents, a value of a = 0.5 is indicative of a theta solvent.
A value of a = 0.8 is typical for good solvents.
For most flexible polymers, 0.5< a <0.8.
For semi-flexible polymers, a>0.8.
For polymers with an absolute rigid rod, such as Tobacco mosaic virus, a = 2.0. (WikiPedia)

I studied this K and “a” value.
Do you know the relationship of K and “a” value?
I show the example of PolyStyrene.
I had 121 data point of K and “a” value of polystyrene with 33 kinds of solvent.
(The temperature and MW range are very different.)
And plot them.

There is very beautiful relationship like above chart.
If you have “a” value, you can predict K value.

This is not peculiar to polystyrene.

Ethylcellulose Poly(methyl acrylate)

Polycarbonate Poly(methylphenylsiloxane)

Poly(vinyl acetate) Polyacrylamide

Then how can we get “a” value for certain polymer with specific solvents?

Temperature effect is not so large, but higher temperature make “a” value large.

Solvents Temperature C MW 10^-4 MW 10^-4 K 10^3 a
Carbon tetrachloride 10 1.8 180 12.6 0.717
Carbon tetrachloride 20 1.8 180 12 0.72
Carbon tetrachloride 30 1.8 180 11.4 0.724
Carbon tetrachloride 40 1.8 180 11.2 0.725
Carbon tetrachloride 50 1.8 180 11 0.726

And the HSP distance from polystyrene to solvents have relationship of “a” value.

Let's see the result in Hansen Space.

Drag=Rotate, Drag+Shift=Larger/Smaller, Drag+Alt or Command(Window key)=Translate.

If you are using HTML5 enable browser such as Chrome, Safari or FireFox (IE9 is out of support), you will see the Canvas. If you pick solvent, solvent name will appear.

Red small sphere mean the solvents that dissolve PSt good. Blue small spheres are poor solvents. Large sphere means PSt. The Green(R=8), Cyan(R=6), Yellow(R=4).

The solvents located near center of PSt sphere, the viscosity become larger.


Hansen Solubility Parameters (HSP)

Hansen Solubility Parameters(HSP) were developed by Charles M. Hansen as a way of predicting if one material will dissolve in another and form a solution. They are based on the idea that "like dissolves like" where one molecule is defined as being 'like' another if it bonds to itself in a similar way.
Specifically, each molecule is given three Hansen parameters, each generally measured in MPa0.5:
dD:The energy from dispersion bonds between molecules
dP:The energy from dipolar intermolecular force between molecules
dH:The energy from hydrogen bonds between molecules.
These three parameters can be treated as Vector for a point in three dimensions also known as the Hansen space. The nearer two molecules HSP Vector are in this three dimensional space, the more likely they are to dissolve into each other.

What can perhaps be surprising is that one can assign HSP to so many different things. Gases like carbon dioxide, solids like carbon-60, sugar, and biological materials like human skin, depot fat, DNA, and even some proteins all have HSP. The list can be continued with drugs, polymers, plasticizers, and in fact any organic material and even many inorganic materials like salts. The only requirement for an experimental confirmation is that the material must behave differently in a sufficient number of test solvents upon contact.

Pirika JAVA Demo Applet calculate HSP. HSPLight is available here.
Please refer to e-Book of HSPiP if you want know more about HSP.
About the Power Tools that handle HSP more effectively.

HSP Distance

To calculate the distance (Ra) between Hansen parameters in Hansen space the following formula is used:

HSP distance(Ra)={4*(dD1-dD2)2 + (dP1-dP2)2 +(dH1-dH2)2 }0.5

The theta solvent (“a” =0.5) HSP distance is long. And for this polystyrene, HSP Sphere radius is 8. And at Sphere radius 8, we think it will become theta solvent.

If the HSP distance become shorter than 8, the solvent become good solvents.
According to become shorter distance, “a” value become larger.

So, We can predict “a” value from HSP distance.

That means,
From HSP distance, we can predict, “a” value.
From “a” value, we can get K value.
And we can get Intrinsic Viscosity for any molecular weight of polystyrene with every kinds of solvents and mixture solvewnts.

HSPiP ver. 3.1.x, we have new sphere algorithm.
With Quantitative Sphere algorithm, in ordinal case, you input real solubility data like g/100ml solvents. But you can enter this “a” value.

HSPiP(Hansen Solubility Parameters in Practice)

The first edition of HSPiP that appeared in November, 2008, greatly enhanced the usefulness of the Hansen solubility parameters (HSP).

The HSP values of over 1200++ chemicals and 500 polymers are provided in convenient electronic format and have been revised and updated using the latest data sources in the second edition (March, 2009).

A third edition of the HSPiP appeared in March, 2010. There are now 10,000 compounds in the HSP file which also includes data on density, melting point, boiling point, critical parameters, Antoine constants and much more. The user is able to carry out many different sorts of optimisations of solubility, evaporation, diffusion, adhesion, create their own datasets (automatically if required) and explore the huge range of applications for HSP in coatings, paints, nanoparticles, cosmetics, pharma, organic photovoltaics and much more.

The 3rd Edition v3.1 was released on 12 December 2010. Current users can upgrade free (now v3.1.09) by downloading the latest .msi installer from http://hansen-solubility.com

The 4th Edition v4.0.x was released on 2 Jan. 2013. The Current users can upgrade with free charge.

2013.1.28 The Visual How to manual of HSPiP. You can understand what HSPiP can do.
Please check the Functional Group List whether your targets are available with HSPiP.
How to purchase HSPiP
2013..1.2 The HSPiP ver. 4 include Power Tools for HSPiP power user.

In that case, program determine polymer HSP so as to get highest correlation “a” with HSP distance. I tried for polystyrene and get [18.1, 3.8, 4.0].
If you want to get “a” value from HSP of polymer, you’d better use this Quantitative Sphere function.