Surface fold free energy

Lamellar thickness Minimum stable thickness Thickness deviation l — lmin Surface area of the fold surface Width of a stem Thickness of a stem Fold surface free energy Lateral surface free energy... 

Furthermore, different fold surface free energies for the different sectors and a maximum crystallization temperature are predicted. For details the reader is referred to the original paper. 

Fig. 11 Role of loop entropy on the fold surface free energy...

This result is to be contrasted with the standard model [53] of Fig. 13, where the fold surfaces are simply treated as planar interfaces with fold surface free energy oy per unit area. In the latter case, the free energy of the nucleus is given by... 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

At high crystallisation temperatures, the high molar mass polymer crystallised alone. Data for the fold surface free energy obtained from linear growth rate data supported the view that the nature of the fold surface of the dominant lamellae was related only to the molar mass of the crystallising component and was not affected by the composition of the melt. 

The lamellar habit adopted by crystalline polymers adds surface terms to the specific Gibbs function (chemical potential), most importantly the fold surface free energy, ae, which contributes 2ae/Xg for a lamella of thickness k and crystalline density q. In consequence melting points are lowered from T, for infinite thickness, to Tm according to the Hoffman-Weeks equation... 

Fig. 5 Chain deposition on the side surface of a polymer crystal, a and ae are side-surface and end- (fold-) surface free energies, and b is the width of the chain (after [16])...

Here, cre(oo) is the fold-surface free energy for I = 00 and S is a small constant, reflecting the fact that some finite supercooling is required for crystal growth. In the case of m > 1, S also accounts for the additional supercooling necessary for G(Fm) to overtake G(Fm i) (see Fig. 6). 

Martuscelli [1984] studied the influence of the molecular weight of the crystallizable component (PEG) on the sphemlite growth rate of PEG/PMMA blend. In contrary to Calahorra et al. [1982] they found that the fold surface free energy, decreases with increasing PMMA content in the blend. It should be mentioned, however, that the... 

Table 6.2 Folding Surface Free Energy, for PB-l/HOCP, iPP/PB-1, and iPP/HOCP Blends.

Eq. 1 fits quite well with the experimental data for the iPP/PiB and iPP/EPDM blends. From the intercept and the slope it was possible to calculate, for every composition, the values of the folding surface free energy and of LogGo. Note that in the calculation of AF, the Tg of the blend was assumed to be equal to that of pure iPP (Tg =... 

Crystallization in miscible blends can occur with rejection of the noncrystallizing component, so that its concentration in the amorphous phase increases. Alternatively, if it can be accommodated in the unit cell, it may be entrapped, with consequent alteration in the mean unit cell volume (Tomlin and Roland, 1993). In NR, there is also a shift to formation from a-lamellae to the )3-lamellar form (Zemel and Roland, 1992b) (Figure 3.25). These crystal structures have the same unit cell, but the latter has a greater fold-surface free energy. Thus, the noncrystallizing blend component is more readily accommodated into the fold plane at the crystal surface. 

Fold surface free energy mj m Calculated data from plot of as function 38 6 (26)... 

The slopes of the secondary nucleation plots can be used to estimate the fold surface free energies of the two polymers. In order for these calculations to be carried out it is necessary to have estimates of the parameters which appear within Eq. 39.5. The equilibrium melting point has to be determined in separate experimentation (see Chapter 11). 

Determination of the Lateral and Fold Surface Free Energies from the Growth Rate... 

Table 3.6 Pre-exponential factor (G°), lateral (cr), and fold surface free energy and/or their product (crcr ) as calculated from Eqs. 3.8, 3.11, or 3.13...

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