Colligative properties of polymer solutions

The alternative value, which describes the polymer-solvent interaction is the second virial coefficient, A2 from the power series expressing the colligative properties of polymer solutions such as vapor pressure, conventional light scattering, osmotic pressure, etc. The second virial coefficient in [mL moH] assumes the small positive values for coiled macromolecules dissolved in the thermodynamically good solvents. Similar to %, also the tabulated A2 values for the same polymer-solvent systems are often rather different [37]. There exists a direct dependence between A2 and % values [37]. 

Rudin s aim was to predict the size of dissolved polymer molecules and the colligative properties of polymer solutions (hydrodynamic volume, second virial coefficient, interaction parameter, osmotic pressure, etc) from viscometric data (average molar mass, intrinsic viscosity, etc.). 

Membrane osmometry n. The pressure difference between a solution and the pure solvent is measured for the case where the solvent is separated from the solution by a semipermeable membrane, isothermally the measurement yields Ap (change in pressure) which corresponds to M number average molecular weight - a colligative property of polymer solutions ... 

Colligative properties are those properties of a solution of a non-volatile solute which in the limit of infinite dilution, depend only upon the number of solute species present in unit volume of the solution and not upon the nature or size of rtose species. Thus the colligative properties of polymer solutions enable Af to be measured for linear and branched homopolymers and copolymers with equal ease. The four important colligative effects are the osmotic pressure of the solution, the lowering of solvent vapour pressure, the elevation of solvent boiling point and the depression of... 

Table 6.2 Colligative properties of a solution of polymer of molar mass 20 000 at a concentration o/O.Ol g (from F. W. Billmeyer, Textbook of Polymer Science , John Wiley Sons, New York, 1962)...

Nagasawa, M. Kagawa, I. (1957). Colligative properties of polyelectrolyte solutions. IV. Activity coeflScient of sodium ion. Journal of Polymer Science, 25, 61-76. 

Originally x was stated to be independent of polymer concentration. The X-parameters determined by many investigators using one or another of the methods for measuring colligative properties of polymer-liquid solutions (mentioned below) show that this is not the case (see Tables 3-22 of Reference 43) nor does x vary linearly with 1/T as stated in Eq. 7. Later [44] a quantity Aws representing an entropic contribution from contact interaction was added to the Flory-Huggins definition of x to produce a relationship linear in 1/T. 

Z Alexandrawicz, A Katchalsky. Colligative properties of polyelectrolyte solutions in excess salt. J Polym Sci Pt A 1 3231-3260, 1963. 

Because chemical methods are rather limited, the most widely used techniques for measuring the molar mass of a polymer are physical. Methods that depend on the colligative properties of dilute solutions can be used to determine the molar mass of a substance. These include ... 

Osmotic Pressure The osmotic pressure counts the number of independently moving units per volume of the solution. It is one of the colligative properties of the solution. At low concentrations, the whole chain moves as a unit. The center-of-mass displacement is synonymons to a change in the position of the whole chain (in the small wave vector limit). The dilute polymer solution is an ideal solution of p/N = cNjM solute molecules in a nnit volume. The osmotic pressure nyeai of the solution is therefore... 

Alexanderowicz, A.,Katchalsky, A., Colligative Properties of Polyelectrolyte Solutions in Excess of Salt , Journal of Polymer Science, Vol. lA, pp3231-3260, 1963. 

The colligative properties of polymers. Show how a small molecule diluent can reduce the freezing point of a polymier solution. 

Colligative properties of dilute solutions—polymer solutions particularly—directly result from the variation of the chemical potential of the solvent into which a solute is added. Such properties can be assessed by measuring the osmotic pressure (membrane osmometry), the decrease of the vapor pressure (vapor phase osmometry) or of the freezing point (cryometry). Contrary to the titration of the terminal functional groups, colligative methods do not require a prior knowledge of the polymer structure and depend exclusively on the number of solute molecules. 

The knowledge of the distribution of molar mass of a polydisperse polymer is of extreme importance. Many of the physical properties of polymers depend upon this and a correct distribution is essential in any polymer which is used in a practical situation. One of the most important points in the distribution is the number average molar mass M , and there are several techniques which can be used to measure it. All of these methods involve determining the number of molecules in a given mass of polymer. The polymer is usually dissolved in a solution of known concentration and hence the mass of polymer per unit volume is defined. The most important methods involve the use of the colligative properties of dilute solutions although for a limited number of polymers it is possible to measure M by end-group analysis. 

Osmotic pressure is one of the colligative properties of solutions containing both low-Molecular weight compounds and high polymers. The major difficulty faced in the study of the behaviour of low Molecular weight compounds in solution by the Osmotic pressure measurement method is the selection of a suitable semi-permeable membrane. 

The changes in a colligative property of a polymer solution with concentration can be expressed by a virial expansional given below ... 

A measure of any of the colligative properties involves counting solute (polymer) molecules in a given amount of solvent. The most common technique for polymers is membrane osmometry. The technique is based on the use of a semipermeable membrane through which solvent molecules freely pass, but through which the large polymer molecules are unable... 

The number averageMn can, in principle, be determined by counting the molecules in a gramme of polymer. This is possible by measuring colligative properties of the polymer in solution these are properties which are strictly dependent on the number of molecules per unit volume of the solution, and independent of their nature or size. Colligative properties are ... 

Unless the nature and number of the liaisons in the initial and final states are known with certainty, the reliability of the x-Parameter (based on Eq. 7 and relationships derived therefrom) suffers accordingly, even with the most accurate thermodynamic methods for measuring colligative physical properties of polymer-liquid systems. It would be well, therefore, to develop methods for defining the mode of complexation at the initial and final states on a molecular basis. Elucidation of the molecular nature of these complexations at gel-saturation (or in true solution) is an end-objective of the work described in Sect. 3 of this review. 

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... 

Clearly then, if a colligative property of a polymer solution is measured this provides an estimate of of the solute. The choice of the solution property has determined the average molecular weight that the measurement yields. 

Equation (2-62) is the key to the application of colligative properties to polymer molecular weights. We started with Eq. (2-53), which defined an ideal solution in terms of the mole fractions of the components. Equation (2-62), which followed by simple arithmetic, expresses the difference in chemical potential of the solvent in the solution and in the pure state in terms of the mass concentrations of the solute. This difference in chemical potential is seen to be a power series in the solute concentration. Such equations are called virial equations and more is said about them on page 65. 

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... 

Table 4.1 A Comparison of Colligative Properties of a 1% (w/v) Polymer Solution with Molecular Weight 20,000...

In Chapter 12 you learned about the colligative properties of solutions. Which of the colligative properties is suitable for determining the molar mass of a polymer Why ... 

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