Lateral surfaces, lamellae

An alkali halide (NaCl, KCl, KBr, etc.) which has a freshly cleaved (001) face is introduced into a polymer solution and then the pol5nner is to be crystallized epitaxially onto the face of the alkali halide. In general, flexible-chain polymers are apt to be crystallized as rod-like crystals on such an alkali halide these rod-like crystals are edge-on lamellae with their lateral surface being mostly in contact with the (001) face of the alkali halide. A given polymer deposited on an alkali halide can be melted and subsequently crystallized there in an epitaxial fashion. 

The small ratio of lamellar thickness to the contour length of a polymer molecule clearly implies that chains must fold back and forth into stems with chain direction essentially perpendicular to the lamellar surface, as originally declared by Storks. The large surfaces of the lamellae containing the chain folds are called fold surfaces, and the thin surfaces are called lateral surfaces. 

The estimated value of the free energy of the fold surface (q3 = oy) is 90 mJ/m for polyethylene, whereas that of the lateral surface (ai = a/) is 15 mJ/m. Therefore we expect the lamellar thickness to be 6 times larger than the lateral dimension, specifically, a cylinder shape, instead of a disklike shape. This is in stark contrast to the facts described in Section II. The thermodynamic estimate of lamellar thickness is about two orders of magnitude larger than the observed values for polyethylene and other polymers. In view of this discrepancy, we are led to the conclusion that lamellae are not in equilibrium. 

The free energy of a lamella, where the fold surface area A(= L1L2) is taken to be much larger than lateral surface area (L3L1 + L2L3), follows from Eq. (1.20) as... 

Inspection of the lamellae would indicate that the surfaees eontaining the chain stems are usually the short sides and have a small area compared with the sides that contain the folded chains. As indicated previously, it is the surfaces that contain the folded chains that make the major contribution to the surface free energy. It is therefore appropriate to assume that the total area of the four lateral surfaces is small compared to the area of the fold surfaces and the contribution to the total surface free energy of the crystal can be neglected ... 

Figure 4 Schematics depicting the basics of the Lauritzen-Hoffman secondary nucleation theory. G indicates the lateral rate of grovrth accessible in the experiments, while stands for the propagation rate of the nucleus in the row direction until it reaches a dislocation defect or impinges on a neighboring nucleus /.stands for the so-called persistence length of the lamellar crystal while /c is the fold length of the lamella a and b are the lateral dimensions of a crystalline stem and a are the surface energies for the fold and lateral surface, respectively.

In eqn [18], the first three terms represent baseline heat capacity and the fourth term represents the excess heat capacity due to fusion. If heat capacity and enthalpy functions are available, for example, from the ATHAS-DB, then eqns [16] and [17] can be solved. Because the partition between Wma and Wra is not known, eqns [18] and [19] cannot be solved without further assumptions. If at the lateral surfaces of each lamellae an RAF layer with the same thickness (often 2 nm) exists, the problem can be solved iteratively." " Righetti et developed a method based on an assumption regarding the availability of baseline heat capacity in certain temperature regions from TMDSC measurements. 

For a theoretical analysis of SFA experiments it is prudent to start from a somewhat oversimplified model in which a fluid is confined by two parallel substrates in the z direction (see Fig. 1). To eliminate edge effects, the substrates are assumed to extend to infinity in the x and y directions. The system in the thermodynamic sense is taken to be a lamella of the fluid bounded by the substrate surfaces and by segments of the (imaginary) planes x = 0, jc = y = 0, and y = Sy. Since the lamella is only a virtual construct it is convenient to associate with it the computational cell in later practical... 

Preferential attraction of one of the blocks to the surface brakes the symmetry of the structure and results in layering of microdomains parallel to the surface plane through the entire film thickness. The energetically favored film thicknesses are then quantinized with the characteristic structure period in the bulk through the formation of surface relief structures, also called terrace formation. These structures were established initially for lamella systems [37-39] and later for cylinder- [40-43] and sphere-forming block copolymers. 

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