Hoffman-Weeks equilibrium

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... 

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... 

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

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... 

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). 

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... 

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). 

Figure 4.42 shows the application of the Hoffman-Weeks procedure [17] to separate the morphological effect on melting point depression and to determine the equilibrium melting point of PEO in the blend and in the pure state. The observed melting temperature (T. ) of PEO and the PEO-PU blends increases linearly with increase in crystallization temperature for a wide range of undercooling. A depression of T, for the same T, is observed for blends. The analysis is based on the relationship... 

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...

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.]...

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