Quantities derived from osmotic pressure

The measurement of the osmotic pressure at various fixed concentrations p, immediately gives the basic quantity II(p). We observed in Chapter 5 that the molecular mass and the higher virial coefficients are derived from the function II(p), determined in the range of weak concentrations (dilute solutions). We must write the development (5.1.107) of the osmotic pressure in the 

Note that this relation also reads 

The average A 2 of the second virial coefficient is defined by the relation [see (9.4.19)] 

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Osmotic pressure, as indicated earlier, is one of the quantities that can be obtained experimentally from the Flory-Huggins and Flory-Krigbaum theories. Before we illustrate how thermodynamic parameters characteristic of polymers can be derived from osmotic pressure measurements, let us first explain very briefly the basis of these measurements. ... 

From this expression, one can derive many useful relations involving experimentally obtainable quantities, such as osmotic pressure. We will use it to develop a phase diagram for a polymer solution. 

These basic quantities are derived from the results of two fundamental experiments the measure of the osmotic pressure II of the solution, at membrane equilibrium with the solvent, and the measure of the intensity scattered by the solution at constant pressure. 

To check the theoretical prediction for the nonequilibrium enhancement of the concentration fluctuations, as given by Eq. (4), we need in addition to D and ST also values for the kinematic viscosity v and for (d/ i/dw)p.T. The latter quantity is related to the concentration derivative of the osmotic pressure [22] which can be deduced from information provided by Noda et al. [31,32]. To obtain the kinematic viscosity v = rj/p the concentration dependence of the shear viscosity t can be represented by the Huggins relation... 

A typical thermodynamic quantity to be derived from the calculation is the osmotic pressure 11 (divided by the polymer temperature 7). A general thermodynamic theorem relates II to the grand partition function... 

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