Ionomers and Associating Polymers

A rich variety of nano-scale structures and inhomogeneities is very typical of polymers. Fully uniform states are the exception rather than the rule. Now we shall explore yet another peculiarity of polymer structure, by looking at the so-called ionomers.

We have already discussed polyelectrolytes in Section 2.5. They are formed when small ions, called counterions, break o↵ from the chain. They leave behind monomer units of the opposite charge. If a counterion escapes and sets out on a “journey” on its own, the whole chain acquires an electrical charge, and becomes a polyelectrolyte (Figure 4.10 a). However, this is not the only scenario. Thermal motion may not be strong enough for the counterion to tear itself away from the ionized monomer. Instead, the two form an “ion pair”. The counterion stays in the vicinity of the charged monomer (at an average distance a), the two charges making a dipole (Figure 4.10 b). If all the counterions tend to stay in such pairs, the chain is called an ionomer.

Can we tell exactly when each of these two cases, a polyelectrolyte (Figure 4.10 a) and an ionomer (Figure 4.10 b), would occur? Assume that the charges of the dissociated monomer and the counterion are the same in magnitude, and equal to the electronic charge e. Suppose also the dielectric constant of the medium is ". Then the energy of the Coulomb interaction³ of the ions in a pair is e²/"a. If this energy is much less than the characteristic energy of thermal motion kBT , where kB is Boltzmann’s constant, and T is the absolute temperature (see Section 7.6 below for a more detailed discussion of characteristic thermal energy), i.e.

e²

"akBT 1 , (4.2)

then counterions break o↵ the chain. Thus we get the polyelectrolyte regime. Conversely, if

e²

"akBT 1 , (4.3)

3Throughout this book, we use the so-called Gauss system of units as far as electrical and magnetic quantities are concerned. These units are in fact the most convenient ones in all respects, except they do not agree with the tradition accepted in electrical engineering, such as the unit of Ampere for the current. Since we will not deal with any technical aspects anyway, we stick to the Gauss units, in which, for instance, the expression for Coulomb energy does not have the annoying coefficient 1/4⇡"0. If you, the reader, feel more comfortable with some unit system of your choice, we encourage you to repeat all our simple calculations using your preferred units and see for yourself that the results stay unchanged.

What Kinds of Polymer Substances are There? 47

2 Book Title

4 Book Title

Here, we have to digress and explain the signs⌧ and and their usage. Formally, they mean “much less” and “much greater”, respectively. Of course, one may ask — how much is “much”?

In other words, if x y , does it mean x should be twice larger than y , or ten times larger, or what? The general answer has to do not so much with the specific numerical values of x and y , but rather with dependencies of things on x and y when they change. Let’s illustrate this rather abstract point with the specific example of Equations (4.2) and (4.3). Formula (4.2) says that we have polyelectrolyte regime if the ionization energy is much smaller than thermal energy kBT ; the meaning of it is as follows:

the smaller the value of dimensionless parameter e²/("akBT ), the more complete ionization, and the more accurate polyelectrolyte concept. Similarly, formula (4.3) states that ionomer regime occurs if the ionization energy is much larger than thermal energy kBT , which means: the larger the ratio of energies e²/("akBT ), the more accurate the ionomer model. Qualitatively then, portraying the situation in imprecise impressionists strokes, we can say we deal with either a polyelectrolyte or an ionomer regime.

Quite similarly, we discussed in Section 4.6 the regimes of dilute and semi-dilute solutions, realized at concentrations c such that c⌧ c^? (Figure 4.7 a) and c c^? (Figure 4.7 c), respectively.

Of course, such a description leaves a “gray zone”, an inter-mediate regime, or a cross-over, when parameter is neither big nor small. However, when parameters, such as concentration or ioniza-tion energy, change by many orders of magnitude, the “gray zone”

is in many cases insignificant: yes, it is possible that a system is neither really a polyelectrolyte nor an ionomer, neither dilute nor semi-dilute, but something in between, but if we understand well both limits, we are usually not scared by the intermediates, too.

This is why, in this book, as it is customary everywhere in modern physics, we will consider the limiting regimes, delineated by “strong inequalities”,⌧ and ; moreover, we shall frequently simply write

< instead of⌧ and > instead of , pretending silently that the cross-over “gray zone” is rather narrow and not interesting to us.

With this in mind, let’s return to ionomers and polyelectrolytes.

then the thermal motion cannot break up the ion pairs, and the chain is an ionomer.

We have already said that proteins, DNA, and polyacrylic and poly-methacrylic acids are all polyelectrolytes when dissolved in water (see Sec-tion 2.5). We emphasize that the solvent should be water. Why is this so essential? The dielectric constant of water is extremely high (" 80).

Therefore, the ratio e²/("akBT ) is relatively small, and inequality (4.2) holds. However, if you use other solvents, with much smaller values of "

(usually between 2 and 20), then inequality (4.3) holds instead, and the polymer is an ionomer rather than a polyelectrolyte. This is why poly-electrolyte regime is typical for polymers dissolved in water, including the biopolymers, while ionomer regime is typical for polymers dissolved in or-ganic solvents.

Ion-containing polymer chains in a melt (in the absence of a solvent) are also typically in the ionomer regime. This is because the dielectric constant of a pure polymer tends to be rather low. What is the structure of such an “ionomer” melt? Ionomer chains contain some (usually small) proportion of monomers in the form of ion pairs (see Figure 4.10 b). They interact strongly with each other, since they are electric dipoles. The other monomers have no electrical charge. Dipoles always arrange themselves in such a way that the interaction between them is attractive (see inset in the Figure 4.10). This is why ion pairs are strongly attracted to each other.

Fig. 4.10 A polyelectrolyte (a): all the counterions are free and not attached to the polymer chain; an ionomer (b): counterions are “condensed” on the charges of the chain and form ion pairs. Inset: Dipoles (ion pairs) are free to choose any orientation with respect to each other. The one they prefer is (B), since it gives the lower energy than (A). It corresponds to attraction.

What Kinds of Polymer Substances are There? 49

Fig. 4.11 (a): A cartoon of multiplet structure in a melt of ionomers. Strongly interacting ion pairs are shown explicitly. Multiplets are circled and shaded. (b): A sketch of a solution of an associating polymer. Strongly interacting monomers are depicted as big empty circles.

Associates are circled and shaded. In contrast to Figure (a), the space between associates is mainly taken up by the solvent molecules — the volume fraction occupied by monomer units of the chains is rather small.

However, they are part of a polymer chain, so they cannot be separated into a distinct phase. As a result, small islands emerge in a sea of neutral monomers (Figure 4.11 a). Such aggregates are called ionomer multiplets.

Compare Figure 4.11 a and Figure 4.8 b. You may notice that the multiplets in a polymer melt somewhat resemble the spherical domains in a block-copolymer melt that form when one of the blocks is much longer than the other. This similarity is not surprising. The structure in Figure 4.11 a can be obtained from Figure 4.8 b by letting the shorter block tend to one monomer, and increasing the attractive force between the monomers.

As a matter of fact, it is quite a common pattern in polymer structure when small spherical multiplets (“associates”) are formed by strongly attracting monomers, whatever the nature of their attraction. Such polymers are called associating.

Associating polymers have many practical uses. Let’s give the simplest example. Suppose we wanted to increase the viscosity of a liquid substan-tially. Can we do it by adding just a little bit of some other substance?

If yes, then how to choose the substance? As you might have guessed, an associating polymer consisting of two di↵erent types of monomers (Figure 4.11 b) can play this role. Let’s see how it works. The greater part of the

monomers easily dissolve in the liquid. However, a small fraction of the monomers try to avoid the solvent. Any contact with the liquid molecules is extremely energetically unfavorable for them. Such strongly associat-ing monomers join together to form aggregates (multiplets). The structure of the resulting solution is shown in Figure 4.11 b. It looks like a polymer network (a gel). The special thing about it is that the role of covalent cross-links is played by associates of strongly interacting monomers. This is not a real network (like the ones described in Section 2.5). The associates can dissociate from time to time, as well as appear in a new place. Therefore, if we apply shear stress to such liquid, it will start flowing, together with the associating polymer that is dissolved in it. Nevertheless, the viscosity of the liquid is substantially increased because dissociation of such associates is relatively rare. Even a very small amount of an associating polymer is enough to increase the viscosity of the liquid substantially.