Lesson 10: Polymer Solutions

Lesson 10: Polymer Solutions jls164 Wed, 02/26/2014 - 12:18

The links below provide an outline of the material for this lesson. Be sure to carefully read through the entire lesson before submitting your assignments.

Overview/Checklist

Overview/Checklist mjg8 Thu, 12/19/2019 - 11:53

Overview

In this Lesson, we continue to consider how polymers behave in solution, but more so focus on the thermodynamics of the mixing process. What are the driving forces for mixing, and how can we predict if a polymer and solvent will mix spontaneously? We will begin with ideal solution theory and build a framework for thinking about polymers in solution, and later move on to Flory Huggins theory, which is more accurate but slightly more complex. Keep in mind as you go through the lesson the situations in which these various parameters and theories are most accurate, and in which cases they may fail to accurately describe polymer solution behavior.

Learning Outcomes

By the end of this lesson, you should be able to:

Explain how and why polymer solutions differ from ideal solutions
Describe what the parameters in Flory Huggins represent
Define solubility parameters and use them to predict good and bad solvents for polymers
Discuss limitations of solubility parameters
Relate solubility parameters to the Flory parameter
Predict the behavior of a polyelectrolyte in solution with varying ionic strength

Lesson Checklist

Lesson 10 Checklist
Activity	Content	Access / Directions
To Read	Read all of the online material for Lesson 10.	Continue navigating the online material.
To Read	Chapter 10 - Theoretical Description of Polymers in Solution § 10.1 - 10.3.3 § 10.4.4	The chapter readings come from the textbook, Introduction to Polymers.
To Do	Homework Assignment 10 (Practice)	Registered students can access the homework assignment in the Lesson 10 module.

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

Thermodynamics and Mixing in Polymer Solutions

Thermodynamics and Mixing in Polymer Solutions jls164 Wed, 02/26/2014 - 12:24

Now that you have a sense of the various conformations that a polymer may assume in solution, let’s consider the thermodynamics of that mixing process. Will the polymer actually dissolve in the solvent? How do the solvent-polymer interactions affect the chain conformations? What about polymer-polymer interactions?

We begin to think about the thermodynamics of polymers in solution by starting with a far simpler solution, an ideal solution. This is a simplistic way of thinking of a solution, in which we mix a solute and solvent, but every molecule of solvent and solute is exactly the same in terms of size and intermolecular interactions. This is of course very idealistic and not representative of real solutions, but it’s a good place to start in terms of building a framework for thinking about enthalpy and entropy of mixing.

diagram of an ideal solution as described in the text

Figure 10.1: Ideal solutions

Source: Lauren Zarzar

Brief review of fundamental thermodynamics and free energy:

In previous courses, you have been introduced to the concepts of enthalpy (H) and entropy (S). Enthalpy is a measure of the potential to take up or give off energy in the form of heat, and entropy is a measure of disorder. Both properties are directly related to Gibbs free energy according to the following equation, in which $T$ is the temperature in Kelvin:

$G = H - T \cdot S$

Enthalpy and entropy, like Gibbs free energy, describe properties of a system at a given state. Like Gibbs free energy, the absolute amount of entropy or enthalpy in a system is not directly measurable; instead, we typically discuss changes in these values as a system moves from one state to another:

$Δ G = Δ H - T \cdot Δ S$

If a process is spontaneous, then $Δ G < 0$ and if it is non-spontaneous, then $Δ G > 0$ .

PROBLEM 1

What is true of the enthalpy of mixing, $Δ H_{m,}$ for an ideal solution?

$Δ H_{m} > 0$
$Δ H_{m} < 0$
$Δ H_{m} = 0$

Click here for the answer to Problem 1.

ANSWER 1

C. $Δ H_{m} = 0$

All intermolecular interactions are equivalent, thus there can be no change in enthalpy upon mixing.

PROBLEM 2

What is true of the entropy of mixing, $Δ S_{m,}$ for an ideal solution?

$Δ S_{m} > 0$
$Δ S_{m} < 0$
$Δ S_{m} = 0$

Click here for the answer to Problem 2.

ANSWER 2

A. $Δ S_{m} > 0$

Entropy is a measure of disorder. If we go from two pure substances (solvent and solute) and mix them together, there will be more disorder, as now we have to account for all of the different arrangements of the solvent and solute in space.

PROBLEM 3

What is true of the Gibbs free energy of mixing, $Δ G_{m,}$ for an ideal solution?

$Δ G_{m} > 0$
$Δ G_{m} < 0$
$Δ G_{m} = 0$

Click here for the answer to Problem 3.

ANSWER 3

B. $Δ G_{m} < 0$

If $Δ H_{m} = 0$ and $Δ S_{m} > 0$ , then by using $Δ G = Δ H - T \cdot Δ S$ , we know $Δ G$ must be negative and mixing for an ideal solution will always be spontaneous.

So we know that entropy increases in an ideal solution, and this is what drives the spontaneous mixing. But what is the entropy exactly? In our simple model, imagine an array like that pictured (figure 10.2) in which you place the solvent and solute molecules in various spaces. How many different distinguishable arrangements of the solvent and solute molecules in this array can there be?

Enter image and alt text here. No sizes!

Figure 10.2: Simple model of an ideal solution

Source: Lauren Zarzar

Entropy is related to the “ $t o t a l # a r r a n g e m e n t s$ ”, where $N_{1}$ and $N_{2}$ are the numbers of solvent and solute molecules:

$t o t a l # a r r a n g e m e n t s = Ω = \frac{(n_{1} + n_{2})!}{N_{1}! N_{2}!}$

Entropy is related to $Ω$ through the Boltzmann equation, where $S$ is entropy and $k$ is the Boltzmann constant:

$S = k \ln Ω$

If we substitute the expression for $Ω$ into the Boltzmann equation, we get $Δ S_{m}$ :

$Δ S_{m} = R [n_{1} \ln X_{1} + n_{2} \ln X_{2}]$

…where have now switched from using “number of molecules” $N_{1}$ and $N_{2}$ to using mole fractions $X_{1}$ and $X_{2}$ (i.e. $X_{1} = N_{1} / (N_{1} + N_{2})$ and $X_{2} = N_{2} / (N_{1} + N_{2})$ ). Notice the switch from $k$ to $R$ (the gas constant) as well; the use of $k$ vs $R$ depends on whether you are dealing with individual molecules or moles of molecules, because $R = k N_{A}$ where $N_{A}$ is Avogadro’s number. (Usually we deal with moles, and we have introduced mole fractions into our expression for entropy, thus we are using $R$ ).

Because we know that $Δ H_{m} = 0$ in an ideal solution, we can also write an expression for the change in free energy:

$Δ G_{m} = R T [n_{1} \ln X_{1} + n_{2} \ln X_{2}]$

Now we have a good understanding of the thermodynamics of ideal solutions. Do polymer solutions behave like ideal solutions? Usually, they do not! In that case, what’s wrong with the theory of ideal solutions? There are two major flaws in the assumptions made for an ideal solution: 1) the assumption that all solvent and solute molecules are the same size is very wrong, especially in the case of polymer solutions because polymers are very large compared to solvent; 2) intermolecular interactions do occur, and they are usually different between solvent-solvent, solute-solute, and solute-solvent. After all, what if you choose a “bad” solvent for the polymer, like trying to dissolve polyethylene (a hydrophobic polymer) in water? Well, we know that won’t work. So intermolecular interactions are definitely important in determining whether two components will mix!

Flory-Huggins Solution Theory

Flory-Huggins Solution Theory jls164 Wed, 02/26/2014 - 12:24

Flory-Huggins solution theory attempts to describe the thermodynamics of polymer solutions in a more accurate way than ideal solution theory. We noted the two important flaws with ideal solution theory, namely the fact that polymers are large in comparison to solvent and that there are intermolecular interactions to account for. Let’s tackle the size issue first. How can we account for the fact that polymers are very large in comparison to the size of the solvent? We are going to imagine that a polymer has a bunch of segments, where each segment is the size of the solute. So in this picture (Figure 10.3) for example, each blue dot is a segment of a polymer, and all those blue dots are connected to make up one polymer molecule.

Figure 10.3: Simple model of a polymer molecule in a solvent

Source: Lauren Zarzar

Flory’s result for the combinatorial entropy of mixing is then:

$Δ S_{m} = - R [n_{1} \ln ϕ_{1} + n_{2} \ln ϕ_{2}]$

where $ϕ_{1}$ and $ϕ_{2}$ are the volume fractions (not mole fractions) of the two components (i.e., solvent and polymer), respectively.

EXAMPLE

In the picture above (Figure 10.3), what is the mole fraction (or number fraction) of polymer?

$\to$ There is 1 molecule of polymer and 75 molecules of solvent, thus the total number of molecules is 76. $Χ_{p o l y m e r} = 1 / 76$ .

What is the volume fraction of polymer in the picture above?

→ The volume of the polymer is 25 times larger than the volume of the solvent. The total volume is 100. Thus the volume fraction of polymer is $ϕ_{p o l y m e r} = 25 / 100$ .

What is $Δ S_{m}$ for the above picture using ideal solution theory?

$Δ S_{m} = - k [n_{1} \ln X_{1} + n_{2} \ln X_{2}]$

$Δ S_{m} = - k [1 * \ln (1/76) + 75 * \ln (75/76)]$

What is $Δ S_{m}$ for the above picture using Flory-Huggins theory?

$Δ S_{m} = - k [n_{1} \ln ϕ_{1} + n_{2} \ln ϕ_{2}]$

$Δ S_{m} = - k [1 * \ln (0.25) + 75 * \ln (0.75)]$

PROBLEM

Determine the entropy change that takes place when mixing 10 g of toluene with 10 g of a polystyrene sample with M_n = 100 000 g/mol. Assume the volume of a monomer is approximately the same as a solvent molecule. Molar mass of toluene = 92 g/mol, molar mass of styrene = 104 g/mol. R = 8.314 J/(K mol)

Click here for the answer.

ANSWER

First, let’s solve for the number of moles of solvent and polymer:

$n_{1}_{(s o l v e n t)} = \frac{10 g}{92 \frac{g}{m o l}} = 0.109 m o l$

$n_{2}_{(p o l y m e r)} = \frac{10 g}{100, 000 \frac{g}{m o l}} = 0.0001 m o l$

We need to find the degree of polymerization of the polystyrene so we can figure out the “volume” of the polymer in relation to the solvent:

$x_{n} = \frac{\frac{100, 000 g}{m o l}}{104 \frac{g}{m o l}} = 962$

$(1 m o l e c u l e o f p o l y m e r i s 962 t i m e s b i g g e r i n v o l u m e t h a n t h e s o l v e n t)$

$ϕ_{1 (s o l v e n t)} = \frac{0.109}{0.0001 m o l * 962 + 0.109 m o l} = 0.531$

$ϕ_{2 (p o l y m e r)} = \frac{(0.0001 m o l) * 962}{0.0001 m o l * 962 + 0.109 m o l} = 0.469$

$Δ S_{m} = - 8.314 J / (K m o l) [0.109 * \ln (0.531) + 0.0001 m o l * (0.469)]$

$Δ S_{m} = 0.574 J$

Next, we will tackle the intermolecular interactions and their contribution to mixing. We are going to first make a “nearest neighbor” assumption, which is to say that we are going to neglect long range interactions and only consider the interactions between molecules that are closest to each other. In the pure solvent before mixing, we have solvent-solvent interactions, and let’s call the free energy of this interaction g₁₁. In the pure polymer before mixing, we have polymer-polymer interactions, which we will call g₂₂. When we mix the solvent and polymer, we must break the solvent-solvent interaction, and break the polymer-polymer interaction, before forming a new solvent-polymer interaction, g₁₂. The change in energy per each new solvent-polymer pair formed is thus:

$Δ g_{12} = g_{12} - \frac{1}{2} (g_{11} + g_{22})$

Flory defined the following interaction parameter, which he made dimensionless by dividing by $k T$ , and it represents polymer-solvent interactions using this value of ∆g₁₂ and “ $z$ ”, which is the number of surrounding “sites” or “cells” around each position in our matrix:

$F l o r y - H u g g i n s i n t e r a c t i o n p a r a m e t e r = χ = \frac{(z - 2) Δ g_{12}}{k T}$

We use this interaction parameter as a contribution to the free energy of mixing. It is a way of trying to account for the change in enthalpy that can occur when the polymer and solvent mix:

$Δ G_{m} = R T [n_{1} \ln ϕ_{1} + n_{2} \ln ϕ_{2} + n_{1} ϕ_{2} χ]$

Now even though this model is still relatively simplistic – after all, we are still considering that the molecules are organized in this matrix which is of course unrealistic – it is still much better than ideal solution theory.

PROBLEM 2

Which is more favorable for mixing, a high or low Flory-Huggins parameter?

Click here for the answer.

ANSWER 2

Low. For favorable, spontaneous mixing, we need ∆G_m to be negative. We thus want χ to be small.

Case Study: poly(N-isopropylacrylamide)

Case Study: poly(N-isopropylacrylamide) jls164 Wed, 02/26/2014 - 12:25

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.

Source: The Chemistry Lounge - Lower Critical Solution Temperature (LCST) of PNIPAAm

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

PROBLEM 1

Which interactions occur when you dissolve PNIPAAm in water?

Dispersion forces
Hydrogen bonding
Ion-ion interactions (Coulombic forces)
A and B
A, B and C

Click here for the answer to Problem 1.

ANSWER 1

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

$Δ H_{m}$ for dissolving PNIPAAm in water is negative.

PROBLEM 2

Given that $Δ H_{m}$ is negative, and the observation that phase separation occurs upon heating, what does this tell you about $Δ S_{m}$ of mixing? $(Δ G = Δ H - T \cdot Δ S)$ ?

$Δ S_{m}$ is positive
$Δ S_{m}$ is negative
Not enough information

Click here for the answer to Problem 2.

ANSWER 2

B. $Δ S_{m}$ is negative

If we know that $Δ H_{m}$ is negative (favorable), but we observe phase separation upon heating $(Δ G_{m} > 0)$ , then what can be said about $Δ S_{m}$ ? How does temperature play a role in all this? Well, $Δ S_{m}$ must be negative! As $T$ increases, the entropy term starts to dominate over the enthalpy term. Given the observation that mixing becomes less favorable, the entropy upon mixing must be unfavorable, and therefore negative. WHY? This mixing of polymer and solvent actually gives rise to a more ordered system, in part because of the hydrogen bonding and ordered interacts of the water around the polymer. This is great example of a mixture that does not follow ideal mixing behavior.

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:

$C E D = δ^{2}$

For any compound, the solubility parameter can be determined experimentally, where $Δ H_{v} = m o l a r e n t h a l p y o f v a p o r i z a t i o n$ and $V = m o l a r v o l u m e$ :

$δ = {[\frac{Δ H_{v} - R T}{V}]}^{2}$

We build these solubility parameters into an expression for enthalpy of mixing, as shown, where $V_{m} = m o l a r v o l u m e o f m i x t u r e$ :

$Δ H_{m}^{c o n t a c t} = V_{m} ϕ_{1} ϕ_{2} {(δ_{1} - δ_{2})}^{2}$

This model predicts that mixing becomes more favorable (i.e., $Δ H_{m}$ becomes less positive) as the difference between the solubility parameters of the two components decreases. We cannot get negative values of $Δ H_{m}$ using this model because we square the difference in solubility parameters, and there are no negative terms. Thus, the most favorable $Δ H_{m}$ 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 $Δ H_{m}$ 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 $Δ H_{m}$ 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 $Δ H_{m}$ 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:

Table 10.1: Solubility Parameters
Polymer	δ (cal/cm³)^1/2	Solvent	δ (cal/cm³)^1/2
Poly(tetraflouroethylene)	6.2	n-Hexane	7.3
Poly(dimethylsiloxane)	7.4	Cyclohexane	8.2
Polyisobutylene	7.9	Carbon tetrachloride	8.6
Polyethylene	7.9	Toluene	8.9
Polyisoprene	8.1	Ethyl acetate	9.1
1,4-Polybutadiene	8.3	Tetrahydrofuran	9.1
Polystyrene	9.1	Chloroform	9.3
Atactic polypropylene	9.2	Cadbon disulfide	10.0
Poly(methyl methacrylate)	9.2	Dioxane	10.0
Poly(vinyl acetate)	9.4	Ethanol	12.7
Poly(vinyl chloride)	9.7	Methanol	14.5
Poly(ethylene oxide)	9.9	Water	23.4

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.

PROBLEM 3

Which would you predict is a better solvent for poly(ethylene oxide)? Use solubility parameters in Table 10.1 above.

n-hexane
dioxane
water

Click here for the answer to Problem 3.

ANSWER 3

B. dioxane

Using solubility parameters, we would choose dioxane (δ=10(cal/cm³)^1/2), because it would minimize the difference in solubility parameters (for<PEO,  (δ=9.9(cal/cm³)^1/2)). However, in reality, the best solvent for PEO is water, because it can participate in hydrogen bonding with the polymer and has much more favorable enthalpy of mixing. You would never choose water as the solvent based on solubility parameters however, which highlights a significant shortcoming of this method – which is that it cannot account for any new interactions, like hydrogen bonds, that occur between the polymer and solvent because the solubility parameters are only for the pure substances.

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:

$χ_{H} = \frac{V_{1} {(δ_{1} - δ_{2})}^{2}}{R T}$

PROBLEM 4

If the difference in solubility parameters increases (i.e the solvent is not as good for your polymer) then what can be said about ΔGm? Recall,

$Δ G_{m} = R T [n_{1} \ln ϕ_{1} + n_{2} l n ϕ_{2} + n_{1} ϕ_{2} χ]$

$Δ G_{m}$ increases
$Δ G_{m}$ decreases
We can't tell from this information

Click here for the answer to Problem 4.

ANSWER 4

A. $Δ G_{m}$ increases

The Flory parameter will increase. This means mixing is less favorable. And that’s certainly the quantitative way to think about this problem…..But does this make sense conceptually to you? If we increase the difference between the solubility parameters then this means the solvent is increasingly not very good for the polymer. We expect mixing to become less favorable, and therefore we expect $Δ G_{m}$ to become less favorable as well. Hence, we expect $Δ G_{m}$ to go up!

PROBLEM 5

If we increase the difference in solubility parameters, how would we expect the conformation of the polymer to change?

The polymer becomes more coiled, favoring polymer-polymer interactions
The polymer elongates, favoring solvent-polymer interactions
The polymer conformation isn’t affected by $Δ G_{m}$

Click here for the answer to Problem 5.

ANSWER 5

A. The polymer becomes more coiled, favoring polymer-polymer interactions

As the difference in solubility parameters increases, this means the solvent is becoming “worse” for the polymer. Eventually, if the solubility is different enough, you may not be able to have spontaneous mixing and would instead get phase separation.

Recall when we talked about polymer conformations that there are the two extremes: a coiled up, spherical polymer globule, and the fully elongated polymer. Well, each of these have very different surface contact area with the solvent; the coiled polymer reduces contact area between polymer and solvent, while the elongated polymer has increased contact area with the solvent. If solvent-polymer interactions are favorable, then the polymer would elongate to maximize those favorable interactions. But if the interactions are not good, such as between a polymer and poor solvent, then probably polymer-polymer interactions are going to more favorable. This would induce the polymer to coil.

Polyelectrolytes

Polyelectrolytes jls164 Wed, 02/26/2014 - 13:08

Polyelectrolytes are a class of polymers that have rather special and useful properties when dissolved in solution. Polyelectrolytes are characterized by having a charged backbone. A few considerations:

There are counter ions – how do they affect things?
The polymer backbone is charged, what does that do?

What about osmotic pressure? (Remember what it is??)

Recall that osmosis is the movement of molecules through a semi-permeable membrane from a region of low solute concentration to a region of high solute concentration. Osmotic pressure is then the minimum pressure that is required to prevent the flow of solvent across the membrane, and in effect is a measure of the tendency of the solution to take up solvent.

PROBLEM

Which of these polymers would be a polyelectrolyte when dissolved in water?

molecular diagrams of A-sodium polyacrylate, B-polyacrylic acid, and C-poly(methyl acrylate)

sodium polyacroylate
polyacrylic acid
poly(methyl acrylate)

Click here for the answer.

ANSWER

A and B

molecular diagrams of A-sodium polyacrylate, B-polyacrylic acid

A is a salt and B is an acid that would be dissociated in water.

Let’s say we start with a polyelectrolyte that is a salt, like sodium polyacrylate. When the polymer not in water, the counter ion is electrostatically attracted and tightly associated with the ion on the polymer backbone. In this picture (figure 10.3), the blue negative charge is on the polymer and the red positive charge is the counter ion. When we add water – pure water, with limited ions in it – we have now created an environment in which there is osmotic pressure. We have lots of ions around the polymer, no ions in the surrounding water. The water diffuses near the polymer and the counter ions diffuse away from the polymer some distance due to the osmotic pressure. As the counter ions drift further away, the charge on the polymer backbone is less shielded and so the charges repel each other and the coil expands. This is called the polyeletrolyte effect.

diagrams showing the polyelectrolyte effect

Figure 10.3: Polyelectrolyte effect

Source: Lauren Zarzar

Polyelectrolytes are very important commercially. Some of them, such as the sodium polyacrylate that is pictured below, can absorb and “trap” hundreds of times their weight in water. This is how diapers work! Other great examples of where superabsorbent polymers like sodium polyacrylate are used include “instant snow” and “moisture control” potting soil.

molecular diagram of sodium polyacrylate

Figure 10.4: sodium polyacroylate

Source: Lauren Zarzar

If the polyelectrolyte is a linear polymer, when you keep adding water to it, it will eventually become completely diluted. Imagine dumping a bowl of spaghetti into the ocean – the noodles will all float away from each other. But if you have a network – where all the polymers are connected – then this network will retain its shape and can’t get infinitely diluted. If you throw a net into the ocean, it remains a net! If the polymer is swollen in water and it is crosslinked, we refer to this as a hydrogel. Some examples of hydrogels are those water beads that you put in candles which are popular at weddings – they look like solid beads when you buy them, but after soaking in water, they swell up into large hydrogel spheres. Even if you left them in water forever, they would never get any larger than their equilibrium swelling volume because the polymer is crosslinked. Another example is contact lenses; obviously, you don’t want your contacts to dissolve into your eye, so it has to be crosslinked!

Figure 10.5: Schematic of a crosslinked polymer, a hydrogel, swelling in water.

Source: Lauren Zarzar

PROBLEM 2

If you added NaCl to an aqueous solution of sodium polyacrylate, how would the polymer conformation change?

molecular diagram of an aqueous solution of sodium polycarbonate plus NaCL

Nothing would change
The polymer would be more extended (swell)
The polymer would become more coiled (shrink)

Click here for the answer.

ANSWER 2

C. The polymer would become more coiled (shrink)

The added salt ions will reduce the osmotic pressure and will help shield the charges on the polymer backbone from each other, both will drive the polymer to “shrink”.

We can use polyelectrolytes to make pH-responsive polymers. Consider the polyacrylic acid, shown below. Here, we are basically switching between a polyelectrolyte and non-polyelectrolyte; in base, the backbone of the polymer is charged, and this polymer would then swell in water as we expect. But when acid is added, and the polymer is fully protonated and has no charge, then it is not a polyelectrolyte, it is not affected by the osmotic pressure, and shrinks in volume.

molecular diagram showing how the polymer shrinks in low pH and swells in high pH

Figure 10.6: Effect of pH on a crosslinked polyacrylic acid hydrogel.

Source: Lauren Zarzar

Summary and Final Tasks

Summary and Final Tasks jls164 Wed, 02/26/2014 - 12:25

Summary

In this lesson, we began to think in depth about how a polymer behaves when it is mixed with a solvent to make a solution and have described the entropy, enthalpy, and free energy of mixing. We started with ideal solution theory, and discussed in what instances and why polymer solutions are not well described by this theory. We then introduced Flory-Huggins theory to try to address some of those false assumptions. We covered cohesive energy density and solubility parameters and how these can be used to predict which solvents might be best for which polymers, but also realize the limitations of that model as well! Specifically for polymers in water, we saw some examples of polyelectrolytes which have some very useful and interesting properties due to the charged polymer backbone.

Reminder - Complete all of the Lesson 10 tasks!

You have reached the end of Lesson 10! Review the checklist on the Lesson 10 Overview / Checklist page to make sure you have completed all of the activities listed there before you begin Lesson 11.