Hoffman-Weeks plots

Table 20.3 Results obtained for the equilibrium melting temperatures from the Hoffman-Weeks plots of the P(HB60-ET40)/ PET and P(HB80-ET20)/PET blends...

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... 

Figure 3.18. Hoffman-Weeks plot for PCL rich PCL/PC blends (the data are displaced by 5°C to discern the different blend compositions) [Jonza and Porter, 1986],...

Hoffman-Weeks plots have also been drawn for several other amorphous/crystalhne miscible blends, such as PVDF/PEMA [Eshuis et al., 1982], PEG/PMMA [Martuscelh, 1984], PCL/SARAN [Zhang and Prud homme, 1987], as well as for some miscible blends containing two semicrystalline components, PCL/PC [Jonza and Porter, 1986] and PCL/Penton [Guo, 1990]. Table 3.10 represents equilibrium melting points derived from... 

Figure 3.19. Hoffman-Weeks plot for PVDF/PMMA blends with 50.1 vol. % of PVDF [Stein et al., 1981].

Table 3.10. Equilibrium melting points derived from Hoffman-Weeks plots for several crystallizable miscible blends...

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. 

HIPS/PPS HIPS/SBS Historical notes Hodge model Hoffman-Weeks plot Homogenization... 

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. 

FIGURE 8 Hoffman-Weeks plots for PCL of= 80 000 g/mol(H), data after Chong et al. (2004), and PEO = 13 000 g/mol (o), data after Alfonso and Russell (1986), the arrow marks the distance to equilibrium after Equation (20). 

The Equilibrium Melting Temperature in Miscible Blends Hoffman-Weeks Plot... 

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). 

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... 

Jonza and Porter could not determine values of equilibrium melting points for PC in the blends from Hoffman-Weeks plots [126] because the plots were... 

Estimates of equilibrium melting temperatures of PCL crystallites were made, for various binary and ternary systems, with the aid of Hoffman-Weeks plots. The observed melting points of PCL were between 55 ° C and 65 ° C and varied by about 3 °C with changes in from 38 °C to 48 °C. From the melting-point depressions, as a function of composition and pressure-volume temperature data, Kim and Paul estimated equation-of-state parameters. During the course of this study Kim and Paul determined specific volume data for PCL at a series of hydrostatic pressures (Fig.51) [87]. 

Melting point depressions in isothermally crystallised blends were analysed in terms of the Nishi-Wang equation (Eq. 10) [40] using equilibrium values of the melting point determined from Hoffman-Weeks plots melting points were determined by DSC and optical microscopy [137]. Values of the melting-point... 

Figure 4.42 Hoffman-Weeks plot to obtain the equilibrium melting point for PEO in blends with PU. All samples were quenched from 100 "C to T,. and crystallized at for 24 h...

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