Analogy with the Boyle point

Analogy with the Boyle point Flory (1953) has pointed out a far-reaching analogy between the 0-point for polymer molecules in solution and the Boyle point for nonideal gas molecules. This is useful in understanding the nature of the 0-point, which is crucial to much that is to follow on steric stabilization. 

Noninteracting point molecules, if they existed, would obey the ideal equation of state  

The compressibility factor z, defined as pV/RT, is clearly unity for an ideal gas. Deviations from unity are a measure of the nonideality of a gas negative deviations arise if the intermolecular attraction is dominant whereas positive deviations appear if the finite volume effects are paramount By way of specific example, we present in Fig. 3.2 the compressibility factor of methane as a function of pressure at several temperatures. At low temperatures, the attractive deviations are dominant and negative deviations from ideality result. At high temperatures, the excluded volume repulsion is paramount and 

The solution analogue of the compressibility factor of a gas is the reduced osmotic pressure (I7/C2). This quantity is shown sch aticaOy in Fig. 3.3 for polymer molecules under different solvency conditions. In a poor solvent for the polymer, negative deviations from ideality are apparent. This can be envisag as arising because the polymer molecules are in dynamic association under such solvency conditions. Since osmotic pressure is a coUigative 

By way of contrast, the segments are mutually repulsive in a good solvent since, by definition, contacts with solvent molecules are enthalpically favoured. This tends to cause the polymer chains to swell, a process that is counteracted by the loss in configurational entropy as the chains expand. Nonetheless, the polymer molecules are mutually repulsive so that the volume available in the polymer solution is effectively reduced below the nominal volume. This causes the effective polymer concentration to be greater than that expected for an ideal system and results in positive deviations from ideality. 

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