The Measurement of Polymer Crystallinity

A/7u = the enthalpy of melting of the unknown sample Xc = fraction crystallinity before heating. 

With the interpolation procediure, we are attempting to estimate the quantity Affvib = (1 -Xc(ri))/Cp,adr -t-Xc(7 )/Cp,xdr. when this is subtracted from the total signal (i.e. to calculate the non-reversing signal), this gives Xc(Ti)AH°(T2)f and so, provided AH(T2)f is known, the crystallinity at the start of the experiment. 

There are assumptions in this approach. Probably the most important is that the interpolation assumes the value for the heat capacity of the sample at the upper temperature is the same as the amorphous poljnner. For a 50% crystalline sample, for example, the vibrational heat capacity at T2 would not be the same as a 100% amorphous sample, which is, in effect, the assumption that is made in this method. When the level of crystallinity is low, then the error from this source will be small. As crystallinity increases the potential error increases, but the fact that, for most polymers, the liquid and crystalline vibrational heat capacities converge around the equilibrium melting temperature tends to reduce this problem. For PET at 48% crystallinity the error from this source has been estimated to be 1.5%. A fuller description of this method can be found in [37]. 

There are other approaches to measuring polymer crystallinity based on conventional DSC [31]. They use database values for the crystalline and amorphous heat capacity sometimes in combination with extrapolation procedures. Where they can be applied, these methods might be preferred as they make fewer assumptions than the MTDSC approach described above. However, industrially useful systems are often blends and/or contain fillers or other additives, so complex samples are frequently encountered. When this is the case, the more conventional approaches will either produce significant errors or will simply be inapplicable. Under these circumstances MTDSC can offer very real advantages. 

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Instrumentation used in the measurement of polymer crystallinity includes light scattering, positron annihilation lifetime spectroscopy, differential scanning calorimetry, differential thermal analysis, infrared spectroscopy, NMR spectroscopy and wide and small angle x-ray diffraction (Chapter 14). 

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