Experimental determination of a demixtion curve

The principle of the measurements is as follows. Let us consider a polymer solution containing polymers of average molecular mass Mw the mass concentration of polymers is p and it is assumed that p is close to the overlap concentration 

The temperature of the solution is reduced to an arbitrary temperature T, at which demixtion may occur and is to be observed. Precautions have to be taken so that the system reaches the state of equilibrium at the end of the experiment. Thus, the cooling must be slow, and during this time, the solution must be kept continually stirred, until temperature T is reached. Gradually, a change in the appearance of the solution can be observed. It becomes milky, and finally after about 24 hours a meniscus appears, separating the solution into two different parts. This is a phase separation. The concentrations p (T) and p (T) p pl) in the phases are now obtained by measuring the refraction indices of the two phases (for more information concerning the relation between the index of refraction and the mass-concentration, see Chapter 6, Section 4). 

The whole process is repeated for various values of T. The set of points p T), p T) constitutes the demixtion curve. A characteristic example1 of such a series of measurements is given by Fig. 16.1. Here, the solution consists of polystyrene of molecular mass Mw = 1.1 x 105 and of cyclohexane. The concentrations are expressed with the help of the mass fraction 

In Fig. 16.1, the middle of the points (T) and was plotted for each value of T. These points define a curve which is nearly a straight line. This line cuts the demixtion curve at a point the coordinates c, TQ of which are the critical fraction and the critical temperature. The critical point is the top of the demixtion curve. 

The volume of solute is the product of its mass Jt by the (average) partial volume per unit mass Wj (see Chapter 5, Section 2.1). Thus, 

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