Case Study: poly(N-isopropylacrylamide)

Most of us have the intuition that if you want to get two things to mix better, we should heat them. For instance, if you want to be able to dissolve more salt or sugar in water, you heat the water. And usually this makes sense because when you mix two different pure substance together we normally expect the entropy term to be positive (more disorder), and therefore, increasing T just makes that term even more favorable. However, not all solutions behave in this way! Poly(N-isopropylacrylamide), or PNIPAAm, is an interesting example of a polymer in solution that actually shows the reverse behavior and is less soluble, and phase separates, upon heating. The temperature at which this phase separation occurs is called the lower critical solution temperature (LCST). In the video below, we can see when we reach the LCST because the solution turns white, which is indicative of the polymer phase separating out of the water.

Please watch the following (45 second) video. Note that the video has no sound. 

Can we understand this interesting behavior in terms of entropy and enthalpy?

PROBLEM 1

Which interactions occur when you dissolve PNIPAAm in water?

1. Dispersion forces
2. Hydrogen bonding
3. Ion-ion interactions (Coulombic forces)
4. A and B
5. A, B and C

Click here for the answer to Problem 1.

ANSWER 1

D. A (Dispersion forces) and B (Hydrogen bonding)

$\Delta H_m$ for dissolving PNIPAAm in water is negative.

Another consequence of polymers not “liking” to mix and giving rise to some unusual behavior– consider aqueous multiphase systems. Normally, we think that if two different solutes are soluble in a solvent, such as water, then those solutes should all be able to be mixed together in one solution. For example, salt and sugar both dissolve in water, so we can easily make a solution of salt and sugar together in water. But with some polymers, this is not the case! Even though several different polymers are soluble in water, they can phase separate from each other, even in an entirely aqueous system! The thermodynamics treatment is far more complicated – we need extra terms for the polymer interactions – but similar principles apply, and also gives some motivation for why we care which phases mix and which don’t.

Now that we have established the importance of intermolecular interactions, can we try to quantify, or estimate, the changes in enthalpy of mixing a bit more?  One framework to consider these interactions is the cohesive energy density (CED), which is the energy required to separate molecules from their nearest neighbors to infinite distance. If the interactions between molecules are strong, then we expect a high CED, whereas if interactions are weak, the CED will be lower. Keep in mind that this is defined as the CED for a pure substance (i.e., the solute or solvent). CED is equivalent to the solubility parameter squared:

$$CED={\delta }^2$$

For any compound, the solubility parameter can be determined experimentally, where $\Delta H_v=molarenthalpyofvaporization$ and $V=molarvolume$:

$$\delta ={\left[ \frac{\Delta H_v-RT}{V}\right]}^2$$

We build these solubility parameters into an expression for enthalpy of mixing, as shown, where $V_m=molarvolumeofmixture$:

$$\Delta H_m^{contact}=V_m{\varphi }_1{\varphi }_2{\left( {\delta }_1-{\delta }_2\right)}^2$$

This model predicts that mixing becomes more favorable (i.e., $\Delta H_m$ becomes less positive) as the difference between the solubility parameters of the two components decreases. We cannot get negative values of $\Delta H_m$ using this model because we square the difference in solubility parameters, and there are no negative terms. Thus, the most favorable $\Delta H_m$ we can ever predict is 0. In effect, we want to minimize the difference in the solubility parameters in order to try to get the most favorable $\Delta H_m$ possible. This is basically a way of saying “like dissolves like”. Polar solvents will have higher solubility parameters while nonpolar substances have lower solubility parameters. We will tend to mix polar and polar, nonpolar and nonpolar, in order to minimize the difference in solubility parameters. This falls in line with our intuition.

The fact that you cannot get negative values of $\Delta H_m$ highlights a shortcoming of this model, which is that it is unable to account for new, intermolecular interactions that occur as a result of mixing. For example, in the case of PNIPAAm that we considered, we formed strong hydrogen bonds between polymer and water, and $\Delta H_m$ was negative; those new hydrogen bonding interactions are not captured in this model. The solubility parameters come from separation of “like” molecules, but nowhere here do we account for new, different, interactions that may occur as a result of the specific choice of compounds to mix. Some example solubility parameters are given:

Looking at these example values of solubility parameters, we see some trends; water, a very polar solvent with strong intermolecular interactions, has a high solubility parameter, and hence a high CED. Non-polar substances, like hexane or polyethylene, have low solubility parameters and a low CED. This follows the trends as we expect.

The solubility parameters are also helpful in estimating the enthalpic contribution to the Flory-Huggins interaction parameter where $V_1$ is molar volume of solvent:

$${\chi }_H=\frac{V_1{\left( {\delta }_1-{\delta }_2\right)}^2}{RT}$$