Macromolecular interactions in solutions are behind many processes in living organisms. Organization — Physical Chemistry — Thermodynamics Chemistry Question
Cooperative interactions in polymer solutions
Macromolecular interactions in solutions are behind many processes in living organisms. Organization of DNA into a double helix can serve as a well-known example. Formation of such intermolecular complexes is often driven by significant entropy gain. In laboratory this phenomena can be studied by using a simple model system, a mixture of poly(methacrylic acid) and poly(ethylene glycol).
Chemicals and reagents
* (C4H6O2)n, poly(methacrylic acid) (PMAA, molecular weight of 30000) aqueous solution, 2 g dm-3, 50 cm3
* C2nH4n+2On+1, poly(ethylene glycol) (PEG, molecular weights of 1000, 2000, 3000, 6000) aqueous solutions, 1 g dm-3, 10 cm3 of each solution
* Deionized water
Apparatus and glassware
* Ubbelohde viscometer or other capillary viscometer with thermostat
* Graduated cylinder, 10 cm3
* 10 glass vials, 20 cm3
* Volumetric pipette, 5 cm3
* Stopwatch
Procedure
a) Prepare a solution of PMAA with a concentration of 1 g dm-3 in water by diluting the initial solution of PMMA.
b) Prepare mixtures of the initial solution of PMMA with the initial solutions of PEG of different molecular weights, each in volume ratio of 1 : 1 (4 mixtures in total).
c) Measure the flow time of water at 25°С using the Ubbelohde viscometer (repeat three times)
d) Measure the flow time of the prepared PMAA solution and of all mixtures at 25°С (repeat each three times).
e) Fill in the table below.
[VISUAL]
f) Repeat ii. c) - e) at 40°С.
Calculate the specific viscosity (see the explanation in Problem 34) for each of the measured samples.
Model Answer
Experimental flow times and the calculated specific viscosities are given in the hereunder table.
Note 1. The molar masses of the repeating units of PMMA and PEG are of 86.06 and 44.05 g mol-1, respectively. Mixing of equal volumes of a 2 g dm-3 PMMA and a 1 g dm-3 PEG (of any molecular mass) solutions results in a reaction mixture with the molar ratio of the PMMA and PEG units of approximately 1 : 1.
Note 2. The final concentration of PMMA in the resulting mixtures and its aqueous solutions is of 1 g dm-3.
[VISUAL]
| Composition | Temperature, °С | Flow time t, s | Specific viscosity of the solution ηsp |
| --- | --- | --- | --- |
| Water | 25 | 44.0 | - |
| PMAA, 1 g/L | 25 | 60.2 | 0.368 |
| PMAA+PEG-1000 | 25 | 60.0 | 0.364 |
| PMAA+PEG-2000 | 25 | 58.3 | 0.325 |
| PMAA+PEG-3000 | 25 | 49.6 | 0.127 |
| PMAA+PEG-6000 | 25 | 46.3 | 0.052 |
| Water | 40 | 31.2 | - |
| PMAA, 1 g/L | 40 | 41.8 | 0.340 |
| PMAA+PEG-1000 | 40 | 40.2 | 0.288 |
| PMAA+PEG-2000 | 40 | 35.6 | 0.141 |
| PMAA+PEG-3000 | 40 | 31.8 | 0.019 |
| PMAA+PEG-6000 | 40 | 31.6 | 0.013 |
Plot specific viscosity against molecular weight of PEG for each temperature.
Model Answer
[VISUAL]
Explain the dependences of the viscosity on temperature and molecular weight of PEG.
Model Answer
The reaction scheme of the complex formation is given below. A decrease of the specific viscosity of the PMАA solution upon addition of the equimolar amount of PEG is observed, which reflects that that polymer coils in the interpolymer complex are more compact than those in the initial solution. The compaction is due to hydrophobizsation of the PMAA chain with PEG.
[VISUAL]
Dramatic changes in the density of the complexes are observed within a rather narrow range of PEG molar masses (of about 1500 g mol-1 at 40°C and 2500 g mol -1 at 25 °C). Such processes are often referred to as cooperative.
The enthalpy change in PMAA-PEG complex formation being negligible, the entropy gain due to the release of water molecules is the driving force of the reaction.
As positions of the repeating units in a polymer chains are constrained, the total entropy of the polymer coil is less than that of the same number of unbound monomer units. For longer polymer chains such entropy loss is more significant. Consequently, the entropy gain as a result of PMAA-PEG complex formation (∆S = S(complex) + S(water) – S(PMAA) – S(PEG)) is increasing with an increase of the PEG chain length (total entropies of released water molecules, the complex, and the initial PMAA molecules are nearly the same). This is why the PMAA-PEG interaction proceeds efficiently only starting with a certain molar mass of PEG (<1000 g mol-1 at 40°C and of about 1000 - 2000 g mol -1 at 25 °C).
Higher efficiency of the complex formation at elevated temperatures (PEG with a lower molecular weight is needed to provide for a noticeable viscosity drop) contributes to the consideration that the entropy gain is behind the process.