Solutions of Many Polymers

The overlap concentration C is an important dividing line in polymer solutions. Solutions much less concentrated than C, are effectively dilute and interactions between the polymers are unimportant. Solutions much more con- 

Naturally, chains in solvents close to the theta state must become very long in order to attain the asymptotic self-avoiding behavior. The chain size required for self-avoidance to become significant is called the thermal blob length [8.3]. Chains smaller than a thermal blob size are approximately random-walk chains. Even chains much larger than this size behave as simple random walk fractals with D = 2 on length scales r ft- This goes to infinity as theta-solvent conditions are approached. 

We may readily remove all the solvent from our solution and increase the volume fraction to unity. Sometimes removing the solvent causes crystallization of the polymers or it immobilizes them in a glassy structure. But at high enough temperature the chains in this solvent-free state remain in a liquid state called a melt. In this melt state the blob size has been reduced to a monomer size a. 

In this argument we ignored the interactions between the segments being joined. It is correct to ignore these, because the osmotic pressure and the work to compress the solution to the given concentration f are both expressed relative to the dilute state. In the dilute state the final chains have already been joined together. Thus it does not contribute to the work of compression and should not be counted. 

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An ample and systematic study was carried out by G. Schmid and O. Rommel, which followed the ultrasounds action on the diluted solutions of many polymers, such as poly(vinyl acetate), poly(methyl methacrylate), cellulose nitrate in organic solvents [1117-1122]. Analysing the behaviour of fractionated and unfractionated polystyrene solutions under ultrasonic field, in all cases they found the decrease of molecular weight in time and proved that, finally, all samples tend to the same limit value of the molecular weight. Figure 3.386, [1117]. The authors reported the same results for a series of polyacrylates. 

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