Polymer solutions freezing point depression

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

Since the pioneering work of Kuhn, the solvent freezing point depression observed in swollen crosslinked rubbers has been the subject of many works. The observed AT can be attributed to two origins. A sizable AT is accounted for by the lowering of the thermodynamic potential of solvent molecules in a polymer solution derived from the Flory theory, and the additional AT observed for crosslinked rubbers has been attributed to confinement effects, fn 1991, Jackson and McKenna [32] studied... 

Barton [41] has assembled a well-referenced source book for the derivation and use of x and cohesion parameters for various polymer solvent pairs. There are many ways to measure solvent activity, the simplest being boiling point elevation, freezing point depression, and osmotic pressure discussed in Section 11.5, Solution and Suspension Colligative Properties. ... 

Suppo.se that a colligative property of the polymer solution is measured. These are properties that depend on the number of dissolved solute molecules and not on their sizes (see also Section 2.10). Osmotic pressure, vapor pressure lowering, and freezing point depression are some examples of colligative properties. If the value of the property measured is P, then by definition... 

Colligative properties reflect the chemical potential of the solvent in solution. Alternatively, a colligative property is a measure of the depression of the activity of the solvent in solution, compared to the pure state. Colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and membrane osmometry. The latter property is considered here, since it is the most important of the group as far as synthetic polymers are concerned. 

An alternative approach is based on the theoretical foundation described earlier for the colligative properties. If the solution is isotonic with blood, its osmotic pressure, vapor pressure, boiling-point elevation, and freezing-point depression should also be identical to those of blood. Thus, to measure isotonicity, one has to measure the osmotic pressure of the solution and compare it with the known value for blood. However, the accurate measurement of osmotic pressure is difficult and cumbersome. If a solution is separated from blood by a true semipermeable membrane, the resulting pressure due to solvent flow (the head) is accurately measurable, but the solvent flow dilutes the solution, thus not allowing one to know the concentration of the dissolved solute. An alternative is to apply pressure to the solution side of the membrane to prevent osmotic solvent flow. In 1877, Pfeffer used this method to measure osmotic pressure of sugar solutions. With the advances in the technology, sensitive pressure transducers, and synthetic polymer membranes, this method can be improved. However, results of the search for a true semipermeable membrane are still... 

In other instances, the values did not correlate with those provided from other sources and in at least one instance no freezing point depression was noted. These effects have not been well explained, although similar anomalies have been observed with other high polymers. For example, in the case of cellulose derivatives, Freudenberg has shown that the freezing point method is very susceptible to error, due both to a tendency of the solute to crystallize and to the probable presence of small amounts of impurities of low molecular weight. 

A solution containing 4.22 g of a nonelectrolyte polymer per hter of benzene solution has an osmotic pressure of 0.646 torr at 20.0°C. (a) Calculate the molecular weight of the polymer, (b) Assume that the density of the dilute solution is the same as that of benzene, 0.879 g/mL. What would be the freezing point depression for this solution (c) Why are boiling point elevations and freezing point depressions difficult to use to measure molecular weights of polymers ... 

In a similar fashion, solubility measurements (of a gas in a liquid, a liquid in a liquid, or a solid in a liquid) can be used to determine the activity coefficient of a solute in a solvent at saturation. Also, measurements of the solubility of a solid solute in two liquid phases can be used to relate the activity coefficient of the solute in one liquid to a known activity coefficient in another liquid, and freezing-point depression or boiling-point elevation measurements are frequently used to determine the activity of the solvent in a solute-solvent mixture. We have also showed that osmotic-pressure measurements can be used to determine solvent activity coefficients, or to determine the molecular weight of a large polymer or protein. 

The number average molecular weight determines the colligative properties (i.e., those which depend only on the number of dissolved molecules) of polymer solutions. Measurements of freezing point depression (cryoscopy) or... 

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