Effect of Copolymerization on Tg

The glass transition behavior of copolymers can also be analyzed using the free volume concept. Block and graft copolymers usually have multiple glass transition temperatures that are near to the values of Tg for each constituent homopolymers. In contrast, random or statistical copolymers usually have a single Tg between that of the corresponding homopolymers. If a series of such copolymers are produced from two monomers by varying their relative 

The dependence of the Tg of a random or statistical copolymer upon composition can be predicted if it is assumed that each type of monomer unit has a characteristic free volume and that it is the same in a copolymer or homopolymer. Denoting the two types of monomer units in a copolymer by subscripts 1 and 2, Eq. (2.33) can be written as 

If the thermal expansion coefficients of the free volume also add in a similar manner, then 

By assuming, as above, that each type of monomer unit retains its characteristic free volume in the copolymer above Tg and using the iso-free-volurae criterion for the glass transition, the following relationship has been derived [48] 

Here 5 is a constant for the pair of monomers. It is specified by theory but is difficult to predict numerically it is however never far from unity. When 

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