Non-draining polymer molecule

The frictional behavior of real polymer molecules is made of contributions of both free-draining and non-draining polymer molecules represented by Eqs. (3.136) and (3.139), respectively. The free-draining contribution dominates for very short chain or elongated rodlike molecules. 

A non-draining polymer molecule can be represented by an equivalent impermeable hydrodynamic particle, i.e. one which has the same frictional coefficient as the polymer molecule. Thus a non-draining random coil can be represented by an equivalent impermeable hydrodynamic sphere of radius Rh- From Stokes Law... 

A nondraining polymer molecule, also referred to as the impermeable coil, can be represented by an equivalent impermeable hydrodynamic sphere of radius R. The frictional coefficient of this sphere which represents the frictional coefficient of the non-draining polymer coil can thus be written,... 

As early as the 1930s Kuhn [101] had suggested that the solvent inside the polymer coil is immobilized, which means = 0. Flory [14] adopted it as a postulate in formulating his pioneering theory of polymer solutions summarized in his 1953 book [1]. However, unless the hydrodynamic mechanism responsible for this postulate is clarified, we cannot say that eq 3.2 has been explained by molecular theory. It is amazing that we are still unable to explain why actual polymer molecules behave as if non-draining for any chain length. 

Two extremes of the frictional behaviour of polymer molecules can be identified, namely free-draining and non-draining. A polymer molecule is said to be free-draining when solvent molecules are able to flow past each segment of the chain, and non-draining when solvent molecules within the coiled polymer chain move with it. These two extremes of behaviour lead to different dependences of the frictional coefficient, of a polymer molecule upon chain length. 

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