Experimental determination of crystallinity

It is easy to show (see problem 5.2) that, if is the density of the amorphous material, then 

With the assumption that the densities of crystalline and amorphous material are known, determination of the density of the sample easily provides a value for the crystallinity. 

The density of the crystalline material can be obtained from the chemical formula of the polymer and the lattice parameters, which can be found in the literature. A difficulty is that the lattice parameters of polymer crystals often depend on the precise conditions under which crystallisation took place, so a value obtained for a sample prepared in as similar a way as possible to the one whose crystallinity is to be determined should be chosen. The density of the amorphous material is quite difficult to determine because it too depends on the method of preparation. When fully amorphous material cannot be produced the densities of a series of samples whose crystallinities have been determined by another method ean be extrapolated to zero crystallinity. The density of the sample is usually obtained by means of a density-gradient column, the principles of which are explained in section 2.3. 

In principle the density method is readily applicable to oriented samples as well as random samples, although care must be taken in choosing appropriate values for Pc nd p. Another method that is applicable both to random and to oriented samples is the use of DSC. As explained in section 2.2, this method allows the change in enthalpy due to melting or crystallisation to be determined for any sample. If the change in enthalpy per unit mass of crystals is known from measurements on samples for which the crystallinity is known, the crystallinity of the sample can be determined. Care must be taken that the value used for the enthalpy per unit mass is appropriate for material crystallised in a similar way to the sample. 

The most obvious question that needs to be answered about polymer crystallites is question (i) of section 5.1, How can long molecules give rise to small crystallites . Two principal types of answer have been given they lead to the fringed-micelle model and the chain-folded model for polymer crystallites. A further type of crystallite, the chain-extended crystal, can also occur when samples are prepared in special ways. These three types of crystallite are considered in the following sections. 

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