Introduction
Polyelectrolyte Expansion - General Evidence
Experimental
Measurement of Intrinsic Viscosity
Appendix
For extra background information, visit these fun-filled Macrogalleria pages:

Introduction

Polyelectrolytes - "substances containing macromolecules carrying a large number of ionic charges -- the polyions -- with the small counterions which render the system electroneutral".

In English this means a polyelectrolyte is a polymer with ionizable groups along it's backbone chain. A typical polyelectrolyte is the sodium salt of polyacrylic acid:

Usually when we're studying polyelectrolytes we study them in aqueous solution. Often times we will study them in the presence of low molecular weight electrolytes such as NaCl.

There two variables which we can easily control to alter the properties of a polyelectrolyte. These have a large effect on polyelectorlyte properties, and they are the counterion and the byion. In the case of an aqueous solution of the sodium salt of acrylic acid with NaCl, Na+ is the counterion and Cl- is the byion. To simplify things we usually use a low molecular weight salt that has the same counterion as the polyelectrolyte, sodium in this case.

For a system like poly(acrylic acid) and NaCl in aqueous solution, the polymer is weakly acidic, and the byions, chloride ions in this case, are weakly basic.

In the case of weakly acidic groups such as acrylic acid groups or for instance, methacrylic acid groups, these are weak bases whose charge density along the chain can be greatly altered by changing the neutralization. Typical polyelectrolytes are given in the table below:

Other types of polyelectrolytes other than polyacids are:

Polymultibasic Acids, e.g., copolymers of acrylic acid maleic anhydride, hydrolyzed to convert the anhydrides into acid groups.

    Polybases, e.g., poly(ethylene imine), poly(4-vinylpyridine)

    Amphoteric (both acid and base groups inthe same polymer), e.g., copolymer of methacrylic acid and vinyl pyridine.

    Proteins which contain charged amino acids. The charged groups greatly effect polymer structure and function. Here are the charge-containing amino acids which are found in proteins:

When we study polyelectrolytes it is important to remember while they behave like low molecular weight elecrtrolytes, there are different in a lot of ways, too. Here are some of the differences:
1. Polyions have high charges. This is because a single polyelectolyte molecule may have many thousands of ionizable groups, whereas a low moleuclar weight electrolye may have only one or two ionizable groups.

2. Polyions have high values of electrostatic potential, because of the high charge, of course.

3. The like ions on the chain can only separate to a certain extent because they are connected to each other by the polymer backbone chain.

4. Effects produced by ionic charge interaction will not vanish as concentration decreases to infinite dilution as in the case of low molecular weight electrolytes. In low molecular weight electrolytes, if the solution is dilute enough, the charged groups will be too far apart to interact. But with polyelectrolytes, even if there is only one polyelectrolyte molecule in the solution, the charges on that molecule will interact with each other. (Remember from #3 that the charges can only separate a short distance from each other.)

5. In a highly dilute solution, the individual polyelectolyte molecule is an area of increased charges density. Counterions are attracted to these pockets of charge density. Out in the bulk solvent, far away from the polyelectrolyte molecule, counterion concetration will be very low.

Far all of these reasons, it is hard to really speak of the "ionic strength" of a polyelectrolyte solution. The ionic strength may be different in some regions than in others. It will be high in and around the polyelectrolyte coils, but lower in the bulk phase far from the polyelectrolyte molecules.

The unusual nature of polyelectrolytes affects the properties of the system in two ways:

    1) Coil expansion

    A polyelectrolye molecule expands in aqueous solution instead of being bundled up tightly. This is because the like charges on the polymer chain repel each other. Expansion allows these charges to be as far apart as possible. In today's experiment we're going to learn how expansion affects the macroscopic properties of a polyelectrolyte solution, and we're also going to try to measure the coil expansion itself.

    2) Electrochemistry

    ionic activity coefficients, ion-pair formation, electrophoretic phenomena.

Polyelectrolyte Expansion - General Evidence

Both light scattering and viscosity studies provide direct evidence for expansion of polyelectrolytes in solution. In Figure IX-1, the polymer radius of gyration of polymethacrylic acid is plotted as a function of the degree of dissociation of the carboxyl groups (a).

Note that in general (`Rg2 )1/2 increases as a increases.

Now, we can also use light scattering to measure increases in (`r2 )1/2 or (`Rg2 )1/2 as salt is added to an aqueous polyelectrolyte solution as is shown in Figure IX-2. Obviously as counterions are added (Na+) which can diffuse into the polymer matrix or domain, they greatly effect the repulsion between negatively charged carboxylic acid groups. The result is to decrease (`Rg2 )1/2 as [Na+ Cl-] increases.

The radius of gyration or (`Rg2)1/2 is readily calculated from the slope of each plot.

Finally, as can be seen in the Figure IX-3 below, an increase in the counterion concentration greatly decreases hsp /C in very dilute solutions.

In considering viscometric analysis of aqueous solutions of polyelectrolytes we can consider extrapolation of hsp /C vs. C to very dilute solutions where the counterions diffuse into the bulk of the solution at more dilute concentrations. This leaves the fixed charges on the polyion with lower shielding and the polyion expands. Thus, we see the dramatic results in Figure IX-4. Now we can add (or rather consider) one other complication in viscosity measurements due to shear dependence:

Region I - [h] varies as salt concentration changes

Region II - reflects decreasing interaction between chains as you get more dilute.

Region III - as yet more dilute counterions diffuse into solution and polyion expands thus hsp increases C.

Experimental

This experiment will be conducted with poly(acrylic acid).
1. Prepare at least four dilutions of poly(diallyldimethylammonium chloride) in 100 ml of deionized water.

2. Neutralize the dissolved poly(diallyldimethylammonium chloride) to a pH of 7 with 3M NaOH solution.

3. Fill a viscometer with an aliquot of the solution. Leave enough volume to allow for dilution in the viscometer.

4. Measure the apparent viscosity as a function of concentration while diluting in the viscometer. Plot the reduced specific viscosity (hsp/c) as a function of concentration. Continue to measure viscosities until the plot of reduced specific viscosity against concentration goes through a maximum upon dilution.

5. Determine the slope of the line in region 1. For a rigid rod the Mark-Houwink constant should theoretically be 2. For a free-draining coil, the Mark-Houwink constant should be 1.

6. Conduct the same set of viscosity measurements as above, but now in 1M NaCl. Draw a plot of reduced specific viscosity against concentration and extrapolate to zero concentration to obtain the intrinsic viscosity.

Question

How would you check if the molecules were fully extended rigid rods, using viscosity data alone?

Measurement Of Intrinsic Viscosity

For polyelectrolytes, the intrinsic viscosity is measured in an excess of salt solution. The salt shields the polyions from intramolecular expansion-- and a linear plot should be obtained.

Find the appropriate Mark-Houwink constants from the Polymer Handbook and calculate the molecular weight of your sample of poly(acrylic acid).

Appendix

Aqueous Sodium Poly(acrylate) in 0.01M NaBr

As the solution is diluted, chemical potential forces counterions to diffuse away from the polygon. Thus at low polymer concentrations many unshielded charged groups exist on the polyion chain, and the polyion expands due to intrachain charge repulsion.

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