Crystalline layer thickness

The nature of the NIF form, at least in alkanes, has only been understood after electron density profiles normal to the lamellae had been reconstructed using SAXS intensities of a number of diffraction orders.59 It turns out that NIF is up to one-third amorphous, with some chains integrally folded in two and others not folded at all but traversing the crystalline layer only once (see Figure 6b). These latter chains are only half-crystalline, with their protruding ends, or cilia, forming the amorphous layer. From the crystalline layer thickness /<, determined from the electron density profile, and from 7lam = U2, determined from time-resolved Raman spectroscopy,61 it was established that the chains are tilted at 35° to the normal in the crystalline layers. 

This method was used to determine the structure of a number of PE-contain-ing diblocks. An example of a correlation function calculated for a PE-poly(ethyl ethylene) diblock, together with its interpretation in terms of amorphous and crystalline layer thicknesses is shown in Fig. 2. The PE crystal thickness in these... 

Hocquet, S. et al.. Lamellar and crystalline layer thickness of single crystals of narrow molecular weight fractions of linear polyethylene, Macromolecules 35 (13), 5025-5033, 2002. 

The details of the lamellar morphology, such as crystalline layer thickness l and amorphous layer thickness /, are quantitatively evaluated using SAXS [18]. For example, they are conveniently derived from the one-dimensional correlation function, that is, Fourier transform of SAXS curves, assuming an ideal lamellar morphology without any distribution for and l [19]. More detailed information on the lamellar morphology can be obtained by fitting theoretical scattering curves (or theoretical one-dimensional correlation functions) calculated from some appropriate model to SAXS curves (or Fourier transform of SAXS curves) experimentally obtained. The Hosemann model in reciprocal space [20] and the Vonk model in real space [7,21] are often employed for such purposes. 

In miscible binary blends, amorphous homopolymers are completely accommodated within amorphous layers of the lamellar morphology formed after the crystallization of crystalline homopolymers. Stein et al. [51], for example, observed the lamellar morphology formed in a miscible blend of PCL and poly(vinyl chloride) (PVC) using SAXS as a function of composition. They found that PVC existed in amorphous layers of the lamellar morphology to yield a linear increase in the amorphous layer thickness with increasing PVC composition, whereas the crystalline layer thickness remained constant irrespective of composition. Wenig et al. [52] obtained similar results for a miscible blend of poly(2,6-dimethylphenylene oxide) (PPO) and isotactic polystyrene (iPS). However, a different result was reported for a miscible blend of iPS and atactic polystyrene [53], where the amorphous layer thickness was almost constant irrespective of composition. Stein et al. [51] explained this difference in... 

The lamellar morphology formed in miscible blends is usually observed using SAXS as described in Section 10.2.2, because its typical repeating distance is in the order of 10nm. In addition, a combination of SAXS and differential scanning calorimetry (DSC) results straightforwardly provides the crystalline layer thickness and amorphous layer thickness if we assume a perfect lamellar morphology with no transition zone between both layers. 

DlMarzio et al. [78] and Whitmore and Noolandi [79] theoretically predicted an equihbrium lamellar morphology formed in crystalline-amorphous diblock copolymers. The long period of the lamellar morphology L, that is, a sum of crystalline layer thickness and amorphous layer thickness, is expressed by a scaling form ... 

Colloidal crystals can be grown by a templated approach too. Thus van Blaadcren and Wiltzius (1997) have shown that allowing colloidal spheres to deposit under gravity on to an array of suitably spaced artificial holes in a plate quickly generates a single crystalline layer of colloidal spheres, and a thick crystal will then grow on this basis. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

Application in the Field of Scattering. Let us consider two important distribution functions, hc (x) and lu. (x). These functions shall describe the thicknesses of crystalline layers and the distances (long periods) between them, respectively. In this case we take into account polydispersity of the crystalline layers, if (at least) the two parameters dc and ac/dc are determined which are defined as the average thickness of the crystalline layers,... 

Model Construction. In the stacking model alternating amorphous and crystalline layers are stacked. Likewise the combined thicknesses in the convolution polynomial are generated by alternating convolution from the independent distributions hi =h h2, h4 = hi hi, andh = hi h2- In general it follows... 

The films are epitaxial in the sense that the lattice constant is intermediate between those of copper and nickel. As indicated above, that modulated strain is probably responsible for the increased hardness. Other authors (5) have tried to explain similar effects by stating that the layers were specifically oriented. Our example (6) demonstrates that these considerations must be reexamined since it was possible to achieve the effect in a crystalline multilayer deposited on an amorphous nickel-phosphorus underlayer. It appears that layer thickness is the important parameter here. 

---