Polymer crystal surface

Whenever a phase is characterized by at least one linear dimension which is small, the properties of the surface begin to make significant contributions to the observed behavior. We shall examine the structure of polymer crystals in more detail in Sec. 4.7, but for now the following summary of generalizations about these crystals will be helpful ... 

Polymer crystals most commonly take the form of folded-chain lamellae. Figure 3 sketches single polymer crystals grown from dilute solution and illustrates two possible modes of chain re-entry. Similar stmctures exist in bulk-crystallized polymers, although the lamellae are usually thicker. Individual lamellae are held together by tie molecules that pass irregularly between lamellae. This explains why it is difficult to obtain a completely crystalline polymer. Tie molecules and material in the folds at the lamellae surfaces cannot readily fit into a lattice. 

At this point a third intermediate approach deserves mentioning. It is due to Allegra [43] who proposed that polymer crystallization is controlled by a metastable equilibrium distribution of intramolecular clusters, the so-called bundles , forming in the liquid phase. These subsequently aggregate to the side surfaces of the crystals, driven by van der Waals interactions. The lamellar thickness is determined by the average contour length of the loops within the bundles. Although the model can... 

The retardation factor ft governs the rate of transport of polymer to the crystal surface and as we are considering the actual crystallization process it is... 

Despite the above comments on the application of roughening to thin polymer crystals it is certainly possible that thermal effects could cause a significant number of surface steps, and that this is all that is required to lead to a breakdown of the nucleation argument. 

A drastic departure from nucleation theory was made by Sadler [44] who proposed that the crystal surface was thermodynamically rough and a barrier term arises from the possible paths a polymer may take before crystallizing in a favourable configuration. His simulation and models have shown that this would give results consistent with experiments. The two-dimensional row model is not far removed from Point s initial nucleation barrier, and is practically identical to a model investigated by Dupire [35]. Further comparison between the two theories would be beneficial. 

A very similar technique is atomic force microscope (AFM) [38] where the force between the tip and the surface is measured. The interaction is usually much less localized and the lateral resolution with polymers is mostly of the order of 0.5 nm or worse. In some cases of polymer crystals atomic resolution is reported [39], The big advantage for polymers is, however, that non-conducting surfaces can be investigated. Chemical recognition by the use of specific tips is possible and by dynamic techniques a distinction between forces of different types (van der Waals, electrostatic, magnetic etc.) can be made. The resolution of AFM does not, at this moment, reach the atomic resolution of STM and, in particular, defects and localized structures on the atomic scale are difficult to see by AFM. The technique, however, will be developed further and one can expect a large potential for polymer applications. 

Figure 19 illustrates key steps of the FI2O2 formation at the nanostructured catalyst surface. An important feature is the imprintment and maintenance of the (11 0) crystal surface through the polymer template because the specific row of metal atoms favours the formation of hydrogen peroxide while minimizing byproducts such as water. 

The parameters K1/ K2/ and K3 are defined by the refractive indices of the crystal and sample and by the incidence angle [32]. If the sample has uniaxial symmetry, only two polarized spectra are necessary to characterize the orientation. If the optical axis is along the plane of the sample, such as for stretched polymer films, only the two s-polarized spectra are needed to determine kz and kx. These are then used to calculate a dichroic ratio or a P2) value with Equation (25) (replacing absorbance with absorption index). In contrast, a uniaxial sample with its optical axis perpendicular to the crystal surface requires the acquisition of spectra with both p- and s-polarizations, but the Z- and X-axes are now equivalent. This approach was used, through dichroic ratio measurements, to monitor the orientation of polymer chains at various depths during the drying of latex [33]. This type of symmetry is often encountered in non-polymeric samples, for instance, in ultrathin films of lipids or self-assembled monolayers. 

The growth of thin lamellae takes place at their side surfaces, where polymer chains partially adsorbed to the surface are continually being taken in the basic elementary process in the conventional polymer crystallization theory is the completion of a single patch of two-dimensional lamella on the growth surface. We first consider the polymer crystallization in 2D space assuming that the whole molecule is strongly adsorbed on the growth surface (substrate), the potential on which is represented by in Eq. 4. The... 

Fig. 18 Schematic picture of the system for simulating polymer crystallization from the dense melt. Polymer chains that should be crystallized are sandwiched between parallel side surfaces of the lamellae made of the same polymer chains. The z-axis is taken normal to the substrate, while the y-axis is along the chain direction of the substrate crystals...

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