Hoffman-Weeks method

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. 

The Hoffman-Weeks Method. Lauritzen and Hoffman (Lauritzen and Hoffman 1960 Hoffman and Weeks 1962) observed a linear relationship between the melting points and the crystallization temperatures of a polymer crystallized isothermally at various temperatures. Hoffman and Weeks (1962) then realized that the lamellar thickness and the crystal perfection increases with increasing crystallization temperature, and they proved that the T =f(T ) curves must intercept the curve at the... 

Figure 2.46. Determination of equilibrium melting point for poly(2-methylpenta-methylene terephthalamide) by the Hoffman-Weeks method. Heating rate = 10 °C/ min. Melting point data obtained on samples isothermally crystallized at 252.5 °C, 260 °C, 267.5 °C and 275 °C were used to determine the equihbrium melting point. [From Menczel et al. (1996) reprinted with permission of Springer-Verlag.]...

The Hoffman-Weeks method is one of the most common approaches in the literature [1, 3, 39, 40] for estimating the equilibrium melting temperature from the experimental data. This frequently used method was often critically assessed as by Hoffman and Miller in Reference [41] and modified as proposed by Phillips and coworkers [39] for iPP to avoid thickening of lamellae. 

A plot of the observed melting point of both melting endotherms as function of the crystallization temperature (Hoffman-Weeks plot) is another method to detect whether recrystalhzation occurs. The melting point of recrystallized material is independent of T thus a horizontal line is observed in the T vs. T plot. 

Figure 9.17 shows the results of the extrapolation of the equilibrium melting temperature T° based on the Floffman-Weeks extrapolation [38], in which the melting temperature is plotted for various crystallization temperatures for semicrystalline PLA. Data for this method were collected only from calorimetric measurements, and the final result of the value of the T° for PLA is close to 480 K, as obtained from different methods [22, 36]. It should be noted that the above corrected result of the for PLA using the Hoffman-Weeks extrapolation was obtained from data for samples crystallized at small supercooUngs, at high crystallization temperatures, similar to what was reported for many cases in the literature [3,39,40]. 

A method was described for measuring the heat and rate of crystallisation following partial melting. The method uses a specific sequence of temperatures with a differential scanning calorimeter, and the melting and recrystallisation processes were confirmed by optical observations. The method was applied to poly(butylene terephthalate). The melting temperatures obtained from recrystallisation were used in the Hoffman-Weeks equation to deduce 236 C as the equilibrium melting temperature for PBTP. 22 refs. 

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