Hoffman-Weeks extrapolation

A good straight line results when T of the L peak is plotted against Tc for i-PS materials crystallized between 150 - 180 C, see Figure 3. Extrapolation of this line to the T = Tc line, suggested by Hoffman-Weeks... 

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... 

It demonstrates that Gibbs-Thomson and Hoffman-Weeks approach are completely equivalent. The extrapolation of / - °o equals in thermodynamic terms extrapolation of T ° after Equation (28). Use of Equation (7) in Equation (28) results in ... 

In Fig. 3.25 Hoffman-Weeks plot for PCL/PBT blends is compared to pure PBT sample. A nonlinear extrapolation procedure was applied for the determination of the equilibrium melting temperature of the crystallizing phase. The linear extrapolation as proposed initially by Hoffman-Weeks neglects the contribution of the increment of the lamellar thickness. Note that the PCL is miscible with PBT only when the PCL molecular weight is equal or lower than MW = 1,250. The blend samples having a PCL molecular weight of 10,000 or 50,000 form immiscible mixture for which the crystallization behavior of pure PBT is recovered. The T ° of... 

Mackley MR, Waimaborwom S, Gao P, Zhao F (1999) The optical microscopy of sheared liquids using a newly developed optical stage. J Microsc Anal 69 25—27 Mall-Gleissle SE, Gleissle W, McKinley GH, Buggisch H (2002) The normal stress behavior of suspensions with viscoelastic matrix fluids. Rheol Aeta 41 61—76 Marand H, Xu J, Srinivas S (1998) Determination of the equilibrium melting temperatme of polymer erystals linear and non-linear Hoffman-Weeks extrapolation. Macromol 31 8219-8229... 

Crystal melting temperatures were also observed to increase with increasing T. for a given blend composition. Hoffman-Weeks type extrapolations gave values of equilibrium melting points (T ) for each composition which decreased with increasing SAN content (Fig. 32). 

Li et al. [81] and Nojima et al. [145] noted very small equilibrium melting point depressions for PCL. The former, using equilibrium values of T from Hoffman-Weeks extrapolations, found a melting point depression of about -0.14 K (wt %) PS. Tanaka and Nishi [146] showed that the depressions were consistent with the Nishi-Wang equation (Eq. 9). 

The crystallization of PEO was also unveiled at the level of individual lamellae in ultrathin films (278-280). It was observed that although lamellar growth rates were retarded in films thinner than 200 nm because of interfacial interactions, SFM provided the same qualitative and quantitative information as typically applied bulk characterization techniques on lamellar growth rates, lamellar thicknesses, and melting points. The Hoffman-Weeks extrapolation, the Gihhs-Thompson equation, and the Hoffman-Lauritzen theory were apphed and the results compared favorably to the corresponding hulk data. 

The melting temperatures of syndiotactic polypropylene were studied as a function of syndiotactic pentad content, rrrr (see Section 2.3.4) values determined via NMR spectra see Figure 14.3 (5). The upper figure utilizes the Hoffman-Weeks extrapolation procedure see Section 6.8.6. The lower figure shows a second extrapolation of the data to 100% rrr content, arriving at a melting temperature of nearly 182°C. By comparison, an isotactic polypropylene with >99% mmmm composition has a melting temperature of 170°C (6). 

Figure 14.3 Utilization of the Hoffman-Weeks plot to establish the theoretical melting temperature of rrrr syndiotactic polypropylene, (a) Melting temperatures Tf of melt-crystallized syn-polypropylene, taken from DSC scans at 2.5°C/min, as a function of the crystallization temperature, Tc, extrapolated to Tt= Tc. (b) Extrapolation of the Tt= Tc values in (a) to 100% pentad content, rrrr.

Sorrentino et al. [86], using a protocol similar to that proposed by Ho et al. [84], determined the thermodynamic melting temperature for both a and P phases from the Hoffman-Weeks extrapolation. From such a linear extrapolation, the equilibrium melting temperature of the a form was determined as 272 °C, whereas the equilibrium melting temperature of the p form was determined as 282 °C (Table 9.2). 

Figure 16.8 Phase diagram of i-PMMA/PEG blends. The filled circles are experimental cloud points obtained by fight scattering measurements. The open triangles and squares are equilibrium melting temperatures for single quench and double quench, respectively, obtained by extrapolation of the Hoffman-Weeks plots. Aral [122]. Reproduced with permission of Elsevier.

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]. 

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