Crystallites fold surface

Assuming that the surface free energy of the fold surfaces is 93 mJ that the density of the crystallites p,. = 1-00 x 10 kg m and that the increase in enthalpy per unit mass, Ah, on melting is 2.55 x 10 J kg for an infinitely thick crystal, determine the equilibrium melting temperature. 

Fig. 5.19 Addition of chain segments to a growing crystallite according to (a) the Lauritzen-Hoffman theory and (b) the Sadler-Gilmer theory. Note that, in the Sadler-Gilmer theory, there are no perfectly regular fold surfaces, ((a) Adapted by permission of Kluwer Academic Publishers.)...

A good example of the above statement are experiments with temperature-modulated dsc (TMDSC) on samples of hnear PE (112). Here a programmable temperature controller is set up in such a way that the temperature/time profile follows exactly the profile that in an off-line modulated dsc instrument is applied to the sample. By carefully assessing the correlation between the temperature profile and the influence this exerts on the invariant Q, as well as on the ciystalhnity derived from the waxs, it is possible to show that reversible melting and crystallization take place at the lamellar fold surface and not on the lateral surfaces of the crystallites (see Figs. 26a and 26b). 

Even if one solves the indexing problem and then proceeds with the analysis by an evaluation of measured reflection intensities, one cannot expect to achieve an accuracy in the crystal structure data that would be comparable to those of low molar mass compounds. This is not only a result of the lack of single crystals, but also represents a principal property In small crystallites, as they are found in partially crystalline polymers, lattice constants can be affected by their size. Furthermore, disorder is more frequently found as in low molar mass systems, in particular, in the region near the fold surface. 

The model used in these investigations is represented by Figure 5.2. It consists of a tie molecule (t) which forms part of a crystal lamella (c), leaves it perpendicularly to the crystal fold surface, (I), extends straightly through an amorphous region (a) and enters the adjacent crystallite of which it forms a part. The crystal boundaries are assumed to be ideally sharp. No interaction between the tie chain and the amorphous material outside of the crystallite is taken into account. 

The mesomorphous phase, also called an intermediate phase or a mesophase, is formed by molecules occurring in surface layers of the crystallites. It can be assumed that the mesophase is made up largely by regularly adjacent reentry folds. However, it cannot be excluded that the mesophase is also composed of some irregular chain folds, which are characterized by a long length and run near the crystal face in the direction perpendicular to the microfibril axis. 

It is unfortunately the case that when we incubate apoferritin with a certain number of iron atoms (for example as ferrous ammonium sulfate), the product, after elimination of non-protein-bound iron, does not have a homogeneous distribution of iron molecules which were able to (i) take up iron rapidly through the three fold channels, (ii) quickly transfer it and form a diiron centre on a ferroxidase site, and (iii) to transfer the iron inward to a nucleation site, where (iv) it will begin to catalyse iron oxidation on the surface of the growing crystallite, will accumulate iron much more rapidly, and in much greater amounts than molecules in which steps (i), (ii) and (iii) are slower, for whatever reasons (perhaps most importantly subunit composition, and the disposition of subunits of the two types H and L, one with regard to the other). This polydispersity makes the analysis of the process of iron uptake extremely difficult. 

Figure 7 Chain folding in a polymer crystallite. The number of re-enttrant folds. per unit surface area would be much higher than sketched here,.

An interesting observation reported in Table XLIX is the increase in the hydroquinone/catechol ratio from 1.44 to 1.99 when the dielectric constant of the medium is decreased from 58.9 to 39.2 by addition of methanol to water. A similar increase in the hydroquinone/catechol ratios was also observed in phenol hydroxylation catalyzed by TS-1 (266) in dioxane-water and tert-butyl alcohol-water mixtures. The para/ortho ratio increased nearly 10-fold when 10% dioxane was added to water. Similarly, the para/ortho ratio more than doubled (1.3-3.0) when 10% tert-butyl alcohol was added to water. An opposite trend, namely, a decrease in the para/ortho ratio from 1.4 to 0.6, was observed when 10% formamide (s = 108) was added to water. Because of geometric constraints in the MFI pores, catechol is expected to be formed more easily on the external surface of TS-1 crystallites than in the pores (91). Hydroquinone, less spatially demanding, can form in the TS-1 channels. A greater coverage of the hydrophobic... 

Figure 5. Replica of platinum shadowed, fractured, (010) hydrogen-bonded surface showing chain folded crystallites aligned with their molecular axis along the draw direction arrowed...

For polymers manifesting the most common type of crystalline morphology (folded chain lamellae), the "equilibrium" values (asymptotic limits at infinite lamellar thickness) of Tm, of the heat of fusion per unit volume, and of the surface free energy of the lamellar folds, are all lowered relative to the homopolymer with increasing defect incorporation in the crystallites. By contrast, if chain defects are excluded completely from the lamellae, the equilibrium limits remain unchanged since the lamellae remain those of the homopolymer, but the values of these properties still decrease for actual specimens since the average lamella becomes thinner because of the interruption of crystallization by non-crystallizable defects along the chains. 

---