Polymer solutions boiling point elevation

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... 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

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. ... 

The information in this section was taken fiiom Physiccd Chemistry by Castellan [21]. In a solution where the solute is not volatile (e.g., salts, polymers, and surfactants), the vapor pressure of the solvent is limited by the mole fraction of the solvent at the interface. Several other solution properties are also dependent on the mole fraction of the solute, x, only and not on the chemical nature of the solute. These properties are referred to as coUigative properties (fram the latin Un-gare, to bind, and co, together which include vapor pressure lowering, frezing point depression, boiling point elevation, and osmotic pressure. In each case, two phases are in equilibrium—one of which is the solution. 

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... 

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. 

Hence, any colligative method should yield the number average molar mass M of a polydisperse polymer. Polymer solutions do not behave in an ideal manner, and nonideal behavior can be eliminated by extrapolating the experimental (F/c) data to c = 0. For example, in the case of boiling point elevation measurements (ebullio-scopy) Equation 9.2 takes the form... 

The data reduction of vapor-pressure osmometry (VPO) follows to some extent the same relations as outlined above. However, from its basic principles, it is not an equilibrium method, since one measures the (very) small difference between the boiling point temperatures of the pure solvent drop and the polymer solution drop in a dynamic regime. This temperature difference is the starting point for determining solvent activities. There is an analogy to the boiling point elevation in thermodynamic equilibrium. Therefore, in the steady state period of the experiment, the following relation can be applied if one assumes that the steady state is sufficiently near the vapor-liquid equilibrium and linear non-equilibrium thermodynamics is valid ... 

Freezing-point depression, boiling-point elevation, and, a third technique, osmotic pressure, may be used to determine the number of moles of polymer per unit volume of solution and thereby establish the number-average molecular weight. The following are the relevant thermodynamic equations for the three techniques ... 

The SEC mechanism demands only an isocratic (constant composition) solvent system with normally a single solvent. The most frequently used organic solvents are THF, chloroform, toluene, esters, ketones, DMF, etc. The key solvent parameters of interest in SEC are (i) solubility parameter (ii) refractive index (iii) UV/IR absorbance (iv) viscosity and (v) boiling point. Sample solutions are typically prepared at concentrations in the region of 0.5-5 mg mL-1. In general an injection volume of 25-100p,L per 300 x 7.5 mm column should be employed. For SEC operation with polyolefins chlorinated solvents (for detector sensitivity and increased boiling point) and elevated temperatures (110 to 150 °C) are required to dissolve olefin polymer. HFIP is the preferred solvent for SEC analysis of polyesters and polyamides. 

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