Hoffman-Weeks plot, polymer crystal

The equilibrium temperature of a polymer (blend) can experimentally be determined by a Hoffman-Weeks plot, which is a plot of the experimental melting point versus the crystallization temperature T vs. T) as presented in Figure 3.18. Extrapolation from experimental data to the r =T line results in the value of T... 

The same polymer blend was studied by Stein et al. (1981), Morra and Stein (1984). Since PVDF crystallizes into several types of morphologies, different lines are shown in the Hoffman-Weeks plot (Fig. 3.24). The curve representing the melting point of PVDF as a function of the crystallization temperature for the a modification shows a break that was associated with defect exclusion from the crystal (Stein et al. 1981) and by entrapment of head-to-head defects of the PVDF chains into the crystals during rapid crystallization at large undercooling (Morra and Stein 1984). 

According to Hoffman nucleation theory (see Sect. 1.6.1), if chains in a polymer crystal stayed as they were laid down, the crystal would melt almost immediately above its crystallization temperature (solid black line at 45 in Fig. 2.1) however, following subsequent processes the lamellar thickness increases by a thickening factor p (2 in the case of polyethylene) giving a slope with its reciprocal y (here 1/2) in a Hoffman-Weeks plot. The theory of this is quite complicated, and the simple linear plot has been called into question (Marand et al. 1998). Nevertheless, it suffices as a very practical guide to the use of DSC in relating thermal history of a polymer specimen to lamellar morphology. 

Fig. 2.1 Hoffman-Weeks plot for polyethylene crystallized in a fast DSC. The symbol open circle represents melting by fast scan DSC after isothermal crystallization, filled circle represents melting after a constant cooling rate and filled diamond represents the melting of a conventional DSC after isothermal crystallization. The solid black line plots Tm — T c (Part of Figure 6 reprinted from Polymer, 55(14), 3186-3194 Toda et al. Copyright 2014 with permission from Elsevier)...

FIGURE 2.4 Left) Hoffman-Weeks plots of neat polymers and their nanocomposites the of the pol3mers is not affected by the nanocomposite formation. Right) Half-time of crystallization for the same neat polymers and their nanocomposites the overall crystallization rate is reduced for PET and PEO upon incorporation of an inorganic nanofiller, and is not affected for PP-g-MA. When accounting for changes in the nuclei density with filler incorporation, the linear growth rates Gr are slowed down in all systems shown. For both panels PP-g-MA top), PET middle), PEO bottom). 

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