Equilibrium melting temperature using

The equilibrium melting temperature T was determined on ECSCs using Wunderlich s method [26]. The Tm of ECSCs was estimated from a tem-... 

The equilibrium melting temperature, T°m, can be obtained from data for crystals of finite thickness using the Thompson-Gibbs equation. The melting point of crystalline polymers with a well-defined crystal thickness (/c) can be measured and the data extrapolated to 41 = 0 using the Thompson Gibbs equation (Gedde 1995) ... 

It is illuminating to rewrite this equation in terms of the degree of undercooling by substituting for Ag. To do that, however, we have to digress a little and define the equilibrium melting temperature. This will also be useful in our discussions of nucleation rates and the melting point, so bear with us ... 

Caffrey and Bilderback have made a similar study for natural rubber. Using a Vidicon camera they concluded that the amorphous halo disappears while the preferentially oriented powder pattern appears at the same time. Holl et all., have studied the reversibility of this process in more detail. Thus in Fig. 51 the variation of the modulus and the draw ration are compared with selected Vidicon patterns. corresponds to the onset of the crystallization, 3- to the maximum in crystallisation and 3-i to the melting of the last crystallites upon relaxation. Note that and Xj, occurr, at different draw ratios. This is obviously due to the nucleation process which demands a certain overdrawing while the melting occurs at the equilibrium melting temperature. 

The simple method based on Equation 10.13, however, is not commonly used because 100% pure crystalline samples for most polymers are not available. One alternative approach is to use the fusion enthalpy, the latent heat of melting, of chemical repeated units (A Hu) to replace A/fioo in the calculations. AHu can be calculated using the I dory relationship for the depression of the equilibrium melting temperature of a homopolymer due to the presence of low molecular mass diluents. The AHu values of some polymers are available in literature. 

Note The equilibrium melting temperature (tJJ,) of copolymers depends on the molecular weight, sequence distribution and counit content. The T, value is determined by two commonly used techniques the Hoffman-Weeks plot and the Thompson-Gibbs plot. Tire application of the Hoffman-Weeks method to determine the tJ, of a copolymer is unreliable (see reference 43). The more reliable method is to use the Tliompson-Gibbs relationship of Tm as a function of lamellar thickness, provided a large range of lamella thickness can be obtained. Considerable disagreement exists between different authors on the exact value of transition that can be identified for fhe copolymers. Consequently, values tabulated in this table must be used cautiously. See references (39, 43, and 44) for detailed discussions. 

We have seen that the experimental determination of the melting temperature of pol3nneric systems, suitable for use in thermodynamic analysis, possesses several inherent difficulties concerned with both concept and technique. Some of the main problems have been pointed out in this paper and the procedures by which they could be overcome has been indicated. Hence there are obvious difficulties in determining the equilibrium melting temperature from polymer data, even admitting the extrapolative procedure. A more detailed discussion of this aspect of the problem will be taken up in a subsequent publication (32). 

Thermal analysis data on lamellar crystals of polyethylene over a wide range of thicknesses are plotted in Fig. 2.90. The Gibbs-Thomson equation is a good mathematical description of the observed straight line and can be used to calculate the equilibrium melting temperature by setting C = (t ° = 414.2 K). Also, the ratio of the surface free energy to the heat of fusion can be obtained from the equation. 

The kinetic restraints that are placed on the crystallization of polymers make it difficult, if not impossible to directly determine their equilibrium melting temperatures. The directly observed melting temperatures are primarily a reflection of the structure and morphology of the actual crystalline systems. The primary factors involved are the crystallite thickness, the interfacial free energy, and the influence, if any, of the noncrystalline region. There are, however, indirect methods by which to estimate the value of T. One of these is a theoretical method. The others are based on extrapolative procedures. To properly use the T values that are tabulated, and to understand their limitations, the basic assumption involved and the problems in execution need to be recognized. 

There are obvious difficulties in obtaining T by either of these extrapolative methods. Therefore, caution must be used in accepting, and using, the values so obtained. Equilibrium melting temperatures listed in Tables 11.1 and 11.3 have been obtained by one or the other of these methods, except for the theoretical value for linear polyethylene. 

The other thermodynamic method that can be used to determine A// involves the variation of the equilibrium melting temperature with applied hydrostatic pressure, p. The ClapeyrOTi equatimi... 

Extrapolated equilibrium melting temperatures of the a and p forms are very close to one another. Depending on the method used they are close to 545 or 573 K [203]. 

If we remember om example of PE given in section (2.2), we would obtain a small value of gg. However, extended chain crystals can be observed rather close to the equilibrium melting temperature, where e can become only fractions of kT. Using Eq. (2.3), we obtain... 

For polymer blends in which one component is crystalline the melting behaviour depends on circumstances. For immiscible blends, where the components are phase separated (prior to crystallisation) and act independently, the crystal melting temperature will be that of the homopolymer. In miscible blends, where the amorphous phase contains both components, the melting temperature will be lower than the equilibrium melting temperature for the crystallisable homopolymer, i.e. the crystalline polymer exhibits a melting point depression as discussed above. The Nishi and Wang approach (Sect 3.2) has been used to estimate the magnitude of the interaction parameters in a niunber of blends (Sect. 7). Poly(e-caprolactone) blends are often semi-crystalline and the above considerations, therefore, apply to many PCL blends. 

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