Hansen Solubility Parameters in Practice (HSPiP) eBook Contents
(How to buy HSPiP)
Chapter 1
The Minimum Possible Theory (Simple Introduction)
Although we want HSP to be practical, we
don’t want you to think that they are magic or “just a bunch of correlations”.
At the same time, we don’t want to bog you down with unnecessary theory. So
here is the minimum possible theory necessary for a practical user of HSP.
Kinetics
versus Thermodynamics
Thermodynamics tells you if something is
possible nor not. You can dissolve sodium chloride in water because solvated
sodium and chloride ions are thermodynamically more stable (energy and entropy)
than crystalline sodium chloride. Barium sulphate crystals are
thermodynamically more stable than solvated barium and sulphate ions, so barium
sulphate is essentially insoluble.
Kinetics tells you how fast something will
happen if it is thermodynamically
possible. So kinetics have nothing much useful to say about dissolving
barium sulphate. But it’s entirely possible to have lots of salt and water in
close proximity without much of the salt dissolving if you don’t get the
kinetics right. One large lump of salt sitting in some very cold water will
dissolve far less quickly than a wellstirred fine salt powder in warm water.
Thermodynamics and kinetics are both
powerful. But ultimately it’s thermodynamics which is the more powerful.
Kinetics might suggest that you should try harder to dissolve the barium
sulphate, but thermodynamics tells you that you shouldn’t bother. The
observation of a slowdissolving lump of salt might suggest to you that it’s
going to be impossible, but thermodynamics encourages you to try.
So let’s make it clear. The strength of HSP
is that they are based on thermodynamics. They are all about whether something
is fundamentally possible or not. We won’t hide from you the fact that kinetics
can sometimes wreck even the best thermodynamic predictions of HSP. But the
fact that HSP are essentially a way for you to reach profound thermodynamic
conclusions is their prime strength.
It will become tedious to insert “thermodynamically”
into every sentence which says “HSP show that thermodynamically A will dissolve
in B”, so let’s take it that we now understand the difference between kinetics
and thermodynamics.
Note
to the sceptics: HSP really do come from deep thermodynamic insights. The fact
that most HSP have been determined by correlation experiments reflects a
limitation on our ability to do complex thermodynamic calculations rather than
a limitation of HSP themselves. The recent work of Panayiotou has at last
accurately derived HSP from first principles – with remarkable agreement
with the experimentally derived values. Similarly the molecular dynamics work
of Goddard’s group at CalTech has produced accurate numbers, showing that it is
possible for anyone to obtain HSP from first principles.
Doing
it the hard way
If you want to dissolve something in
something else then you have to compare two energy losses with one energy gain.
The first loss is the mutual interaction of the solvent with itself. You are
effectively making a hole in the solvent and that takes energy. The more the
solvent attracts itself, the more energy it takes. The second loss is from the
mutual interaction of the solute with itself – for the same reason. And
the gain is the interaction of the solvent with the solute. If this interaction
is greater than the sum of the losses, then the solute will dissolve.
So if you want to know if A dissolves in B,
“all” you have to do is to calculate the two losses and the one gain. For
simple systems this can be done, but it becomes impossibly hard for more
complex systems. And when you start trying to work out the best mixture of C, D
and E in which to dissolve A it’s even more impossible.
The glory of HSP is that in 3 numbers, all
those fussy thermodynamic calculations are done for you, with a high degree of
accuracy.
1,
2, 3 (or more?) energies
If we are going to shortcut the hard way,
we need to have numbers that characterise the internal energies (the energy
required to create the hole in the solvent and break up the solute) and also
the interactive energy.
You could imagine that if the chemicals
were all of one general type then one energy value could be sufficient to
enable the calculations. Hildebrand famously tried to do everything via just
one energy, but although that one energy is
fundamental, without partitioning it, its predictive value proved to be
limited. Indeed we are astonished that Hildebrand parameters still continue to
be used. There are many knockout arguments against using Hildebrand (see the
HansenSolubility website for a more detailed review) but one simple example
says it all. Epoxies aren’t generally soluble in nitromethane or in butanol
which, as it happens, have the same Hildebrand parameters. But a 50:50 mix of
these two solvents is a good solvent for epoxies. As we will shortly see, this
is easily explained by Hansen parameters and is inexplicable with Hildebrand.
As practical scientists we know that there
are at least 4 fairly distinctive forms of energy:
 Dispersion forces (atomic). These are the general van der Waals
interactions between just about everything. Put any molecule a few
Angstrom from another molecule and you get a powerful attractive force
between the atoms of the two molecules. Because they are everywhere, and
because they are unglamorous we tend to ignore them, but they are the
dominating force in most interactions! The famous gecko effect that allows
a gecko to walk upside down on a ceiling is due almost entirely to the
amazing strength of dispersion forces.
 Polar forces (molecular). These are the familiar “positive attracts
negative” electrical attractions arising from dipole moments. They are
important in just about every molecule except some hydrocarbons and
special chemicals consisting of only carbon and fluorine.
 Hydrogen bond forces (molecular) are arguably a type of polar
force. But their predictive value in many different aspects of science
goes beyond simply thinking of them as polar forces so it seems worthwhile
to make them distinct. More generally they can be considered as a form of
electron exchange so that CO_{2} shows strong “hydrogen bonding”
forces that make it a good solvent for e.g. caffeine even though it
contains no hydrogen atoms.
 Ionic forces. These are what keep inorganic crystals together.
If you are going to describe molecular
interactions in simple numbers it’s clear that you would need at least 2 for
every molecule: Dispersion and Polar. By including the third parameter,
Hydrogen bonding, everything except strong ionic interactions became
thermodynamically predictable. It turns out that even for organic salts the
polar and hydrogen bonding contributions are sufficient. And as ionic
interactions are mostly the domain of aqueous environments dominated by the
extraordinary properties of water, it doesn’t seem to be useful to include a 4^{th}
descriptive parameter when you are trying to understand interactions that don’t
involve large amounts of water. There is a lot of progress being made, but the
division of energy types in the aqueous domain is still not fully understood.
So it seems reasonable that three parameters could be used to describe
solvent/solute interactions. But why should something as simple as 3 numbers be
sufficient to describe a process which, by our own admission, is far too complex
for the best computers to calculate?
Do 3
numbers give accurate predictions?
Yes. The data is overwhelming. We’ll come
back to that in a moment.
Aren’t
4 numbers even better?
Yes, and no. In principle, dividing the
Hydrogen Bonding parameter into Donar/Acceptor terms (as, for example, in
MOSCED) should give even better results. But the practical problems of creating
a large, selfconsistent database with 4 parameters, and of visualising issues
in 4D space mean that this has not proven to be a popular way forward.
Why
(in principle) does it work?
The strength of HSP is that they are based
on thermodynamics. And the key insight that led to the creation of
thermodynamics is that the law of large numbers lets you calculate things that
can’t be done by attending to individual details. It’s hard to calculate the
force on the wall of a container containing 1 trillion gas molecules if you try
to consider what’s happening to each of the trillion molecules, yet it’s easy,
and accurate, to calculate via simple thermodynamic gas laws.
The same applies to HSP. The dispersion,
polar and hydrogen bonding forces are impossibly hard to calculate via the interactions
of trillions of individual molecules, yet are easily encoded in the HSP
numbers.
We have to stress again, that if you can do the calculations (and it is
becoming increasingly routine to do them), then the calculated results confirm
the numbers you find listed in the tables of HSP.
Do 3
numbers give accurate predictions?
Let’s think of the most basic thermodynamic
situation. We are trying to mix solvent A with solute B. The claim is that you
will have to lose and gain energies. How can we calculate those?
A naïve approach would be to calculate
the sum of the (absolute) differences of the three HSP. By definition, if B is
so close to A that it’s the same molecule then these differences will be zero.
So the definition of a perfect solvent is a difference of 0. If A and B are
chemically fairly similar then you would expect their HSP to be similar, and
the differences to be small. And if they are utterly different, the difference
should be large.
So we might try:
Equ. 1‑1 Difference = [Dispersion_{A}Dispersion_{B}] +
[Polar_{A}Polar_{B}] + [Hydrogen Bonding_{A} –
Hydrogen bonding_{B}]
where the [square brackets] imply the
absolute value.
As it happens, you can’t add and subtract
energies quite like this. If we introduce δD, δP and δH for Dispersion, Polar
and Hydrogen bonding parameters then the true difference is:
Equ. 1‑2 Difference^{2}
=4 (δD_{A}δD_{B})^{2} + (δP_{A}δP_{B})^{2}
+ (δH_{A}δH_{B})^{2}
The squared terms mean that we don’t have
to worry about absolute values as (δD_{A}δD_{B})^{2}
is the same as (δD_{B}δD_{A})^{2}. The units of these
solubility parameters are (Joules/cm³)^{½ }or,
equivalently, MPa^{½}. In older papers you will see the units
expressed as (cal/cm³)^{ ½}. If you ever need to convert
between old units, simply multiply by a factor of 2 (or 2.046 if you want to be
precise). Throughout this book and in the software, all quoted values are in (Joules/cm³)^{½}
or, if you prefer, MPa^{½}. As Molar Volume (MVol) is commonly
used throughout the book it’s worth stating here that its units are cm^{3}/mole.
Note, too, that all quoted values are at the standard temperature of 25ºC.
You’ll have noticed that the famous factor
of four in front of the δD term has crept into the formula. Many have
questioned the justification for this factor. In the Handbook (pp3031), Hansen
provides some interesting possibilities based on Prigogine’s Corresponding
States Theory. At the heart of the issue is whether the “geometric mean” is the
best way to calculate the differential heat of mixing between components. For
nonpolar spherical molecules interacting via LennardJones potential there’s a
good case that this is a good approximation. But there is no reason to believe
that the same should apply to polar and hydrogenbonding interactions.
Furthermore, there is universal agreement amongst diverse luminaries such as
Prausnitz, Good, Beerbower and Gardon that the differential heat of mixing term
should be less for polar and hydrogen bonding than for dispersive forces. How
much less is a matter of debate, but values between 1/8 and 1/2 have received
support in a wide range of experiments, with the value of 1/4 providing the
best data fit for Hansens’s polymer/solvent data. So although we regret that
we, like everyone else, cannot provide a compelling argument that the factor
should be precisely four, we are confident that it should be at least a factor
of 2. Because the factor of 4 gives spherical plots, fits well with the largest
range of practical test correlations and has stood the test of time in such a
wide variety of realworld uses we feel that its continued use is more than
justified.
This famous difference equation is the core
of HSP. For any problem you just calculate the difference. If it’s small then
the thermodynamic chances are high that the two components will be mutually
soluble (or compatible or, well, “happy” together if you have some interaction
such as pigment dispersion where you know what “happy” means, even if it can’t
be defined precisely). If the distance is large then the chances are small.
For
those who are interested in the theory, for most cases, a distance greater than
0 means that mixing is enthalpically unfavourable. But of course mixing tends
to increase entropy so the total is energetically favourable. The smaller the
distance, the less you have to rely on entropy to help you. Large polymers have
less entropy gain when they are dissolved so you need a smaller distance from
the polymers’ HSP in order to dissolve them.
That would be fine, but rather limiting.
The true power of HSP is that because they are based on the thermodynamic law
of large numbers, a “solvent” can be a mixture of an arbitrary number of
components and the “solvent’s” HSP are simply the average (weighted for %
contribution) of the individual components.
Here are two examples to show the
principle. In both cases there happens to be a 50:50 mixture (so you can check
the answer by inspection). And in both cases you obtain effectively the same
solvent, even though they are created from very different starting solvents.

δD 
δP 
δH 
% 
Solvent X 
16 
8 
2 
50 
Solvent Y 
18 
10 
4 
50 
Mixture 
17 
9 
3 
100 

δD 
δP 
δH 
% 
Solvent X 
14 
0 
0 
50 
Solvent Y 
21 
18 
6 
50 
Mixture 
17 
9 
3 
100 
Table 1‑1 Creating the same solvent properties from very different solvent
blends
This is the real power of HSP. A striking
example is when you want the HSP of a particular solvent but can’t use that
solvent because it is toxic or too expensive. Simply mix together two (possibly
widely different) safe/cheap solvents in proportions that give you the correct HSP
and you have a fully functional solvent, indistinguishable (as far as the
solute is concerned) from the original solvent.
Note
that in this example we use the simple “linear mixing” rule that has been
successfully applied to HSP for more than 40 years. In the 3^{rd}
Edition a “squared mixing” option is available, as discussed in the chapter on
optimisation.
As we will often be referring to sets of δD,
δP, δH numbers always in that order we introduce the
convention that [17, 9, 3] means “δD=17, δP=9 and δH=3”. This shorthand makes
it easy for us to say that a 50:50 mix of [16, 8, 2] and [18, 10, 4] gives [17,
9, 3]. When, later on, we introduce a Radius, this will be the fourth element
so [17, 9, 3, 8] means [17, 9, 3] with a Radius of 8.
Let’s go back to the question: Do 3 numbers
give accurate predictions? The answer is overwhelming. Not only is it the case
that the 3 numbers do work, but in
fact they must work. This is
thermodynamics and one of the great rules of life is never to argue with the
laws of thermodynamics.
Do they work all the time? They can’t work outside their own thermodynamic area.
So they cannot work for ionic solids and they are not much of a guide for
anything to do with primarily aqueous solutions (though pioneers are doing good
work in this area). And of course there will be times when the HSP will say
that a given solvent blend will dissolve
a certain polymer but experiments show that it merely swells. This is because its excessively high molecular weight means
that it will take far too long to dissolve it and so only swells it. That’s the
limit of kinetics versus thermodynamics.
Even
here, the HSP can be deeply insightful. If the HSP for the polymer has been
determined using a low molecular weight, then it is entropically probable that
solvents which were just good enough for the low molecular weight version will
be inadequate for the high molecular weight. The need for a solvent closer to
the HSP of the polymer, or for a solvent with a lower molar volume, is
therefore predictable.
For some reason, HSP have irritated many
people over the years. There have been many attempts to overturn them, but
there is an overwhelming amount of theory and practical success in support. One
classic criticism was around “negative heats of mixing”. Both HSP and the
earlier Hildebrand parameter seemingly allowed “positive” heats of mixing only.
This situation was cleared up by some skilful thermodynamic calculations on
solubility parameters which showed that both positive and negative heats of
mixing were not only allowed, but were also required. Experiments by Patterson
and Delmas (see, for example, Patterson D., Delmas G., New Aspects of Polymer Solution Thermodynamics, Off. Dig. Fed. Soc.
Paint Technol., 34,677,1962) confirmed these calculations.
So for all practical purposes you can take
it that HSP do work and must work.
So all you have to do is to get to grips
with the Sphere in the next chapter.
Deeper
theory
The Sticking,
Flowing, Dissolving chapter contains some deeper theory about aspects of
polymer/solvent solubility. Once you’ve become comfortable with HSP and HSPiP
at this basic level of theory, you might want to dip into sections of that
chapter to find out more.