Lamellarity

One production line of a paper mill consists according the size and the quality of the produced paper sometimes from more than 50 steam drums to dry and flatten the produced paper. These drums (cylinders with flat bottoms, see figure 1) will be used with a steam pressure up to 500 kPa (5 bar) and additionally with a rotation speed up 1200 m.min the material is mainly grey cast iron (with lamellar graphite). The diameters can reach up to 2.2 m and the cylindrical lengths up to 10 m. For the specific flattening drums the cyhndrical diameters can be up to 5 m and more. 

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

Figure Al.7.14. 3.4 mn x 3.4 mn STM images of 1-docosanol physisorbed onto a graphite surface in solution. This image reveals the hydrogen-bonding alcohol molecules assembled in lamellar fashion at the liquid-solid interface. Each bright circular region is attributed to the location of an individual hydrogen...

Lamellar morphology variables in semicrystalline polymers can be estimated from the correlation and interface distribution fiinctions using a two-phase model. The analysis of a correlation function by the two-phase model has been demonstrated in detail before [30,11] The thicknesses of the two constituent phases (crystal and amorphous) can be extracted by several approaches described by Strobl and Schneider [32]. For example, one approach is based on the following relationship ... 

Figure Bl.9.11. The analysis of correlation fimction using a lamellar model.

This intensity can be used to calculate the correlation fiinction (Bl.9.101) and the interface distribution fiinction (B 1.9.102) and to yield the lamellar crystal and amorphous layer thicknesses along the fibre. 

Figure Bl.9.13. Time-resolved SAXS profiles diirmg isothennal crystallization (230 °C) of PET (the first 48 scans were collected with 5 seconds scan time, the last 52 scans were collected with 30 seconds scan time) calculated correlation fiinctions j(r) (nonnalized by the invariant 0 and lamellar morphological variables...

Figure Bl.19.29. AFM image of poly sty rene/poly butadiene copolymer, showing lamellar stnicture. (Taken ftom [140], figure 1.)...

Figure B3.6.4. Illustration of tliree structured phases in a mixture of amphiphile and water, (a) Lamellar phase the hydrophilic heads shield the hydrophobic tails from the water by fonning a bilayer. The amphiphilic heads of different bilayers face each other and are separated by a thin water layer, (b) Hexagonal phase tlie amphiphiles assemble into a rod-like structure where the tails are shielded in the interior from the water and the heads are on the outside. The rods arrange on a hexagonal lattice, (c) Cubic phase amphiphilic micelles with a hydrophobic centre order on a BCC lattice.

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

Gompper G and Zsohooke S 1991 Elastio properties of interfaoes in a Ginzburg-Landau theory of swollen mioelles, droplet orystals and lamellar phases Euro. Phys. Lett. 16 731... 

Gonnella G, Orlandini E and Yeomans J M 1997 Spinodal decomposition to a lamellar phase effect of hydrodynamic flow Phys. Rev. Lett. 78 1695... 

Chandrasekhar S 1998 Columnar, disootio, nematio and lamellar liquid orystals Their struotures and physioal properties Handbook of Liquid Crystais Voi 2B. Low Moiecuiar Weight Liquid Crystais / ed D Demus, J Goodby, G W Gray, H-W Spiess and V Vill (New York Wiley-VCH)... 

This parameter corresponds to cylindrical packing shapes. Surfactants and amphiphiles falling in this range often produce planar bilayers and lamellar mesophases. Such cylindrical building blocks also contribute to many... 

A lamellar solid of especial interest is montmorillonite, a clay mineral. 

Twisting of the lamellar ribbons along the radial direction is responsible for the banding superimposed on the Maltese cross in Fig. 4.12. From the spacing of the bands, the period of the twist can be calculated and is found to depend on crystallization conditions. 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Table 13 is a representative Hst of nickel and cobalt-base eutectics for which mechanical properties data are available. In most eutectics the matrix phase is ductile and the reinforcement is britde or semibritde, but this is not invariably so. The strongest of the aHoys Hsted in Table 13 exhibit ultimate tensile strengths of 1300—1550 MPa. Appreciable ductiHty can be attained in many fibrous eutectics even when the fibers themselves are quite britde. However, some lamellar eutectics, notably y/y —5, reveal Htde plastic deformation prior to fracture. 

Mg yA1 2> or P-(MgAl). Thus aluminum occurs in magnesium alloys both in soHd solution and as the intermediary intermetaUic phase. The latter is clear white and in slight rehef in poHshed and etched samples. In as-cast alloys, the hard phase occurs in massive form, but when precipitated from sohd solution a lamellar stmcture is formed similar to peadite in steel. When produced by aging at low temperatures, it appears as fine particles. 

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