Checkerboard structures

Compatibility to the functionalized substrate of the morphology on the layers through the depth is plotted at different time spots. The depth of the film in the time spot concerned is divided by 16 nodes. In the case considering evaporation, there was no significant change in the value of Cj in the depth direction, but in cases with a constant solvent composition the compatibility alternated from the surface to the bulk domain, which indicates that the dominant polymer type had changed from the surface to the depth. This result was in accordance with the checkerboard structure in the depth direction. As stated above, the surface attraction can affect only the neighboring surface of the ternary blends, and the domain that is not connected to the substrate is influenced only indirectly. The influence of the functionalization decays very quickly into the depth from the substrate surface. 

The numerical simulation was consistent with experimental data with regards to influences of substrate pattern width, polymer weight ratio and polymer molecular weight of PAA. Both, experimental and simulated results showed that the intrinsic characteristic length should be compatible with the substrate pattern size for a reflned phase separation pattern, according to the substrate pattern. Simulations also showed that the increase in polymer molecular weight can increase the speed of morphologic evolution. As the film thickness is very small the checkerboard structure of spinodal decomposition cannot be seen in these results, but they are present. 

The second area of modeling research relates to the constitutive modeling of the rheological behavors (e.g. viscosity and elasticity) and thermal properties (e.g. density, specific heat, and thermal conductivity) of polymeric materials to better simulate the experimental observations. For example, a checkerboard structure of the... 

ISimilaar zigzag structures have been observed in two-dimensional systems, where they appear as a checkerboard pattern (kapralSS). 

The author believes that dipoles cause deformation hardening because this is consistent with direct observations of the behavior of dislocations in LiF crystals (Gilman and Johnston, 1960). However, most authors associate deformation hardening with checkerboard arrays of dislocations originally proposed by G. I. Taylor (1934), and which leads the flow stress being proportional to the square root of the dislocation density instead of the linear proportionality expected for the dipole theory and observed for LiF crystals. The experimental discrepancy may well derive from the relative instability of a deformed metal crystal compared with LiF. For example, the structure in Cu is not stable at room temperature. Since the measurements of dislocation densities for copper are not in situ measurements, they may not be representative of the state of a metal during deformation (Livingston, 1962). 

Fig.1 Schematic structures of a DNA, b butynedioic acid and c KDP. Large striped circles represent potassium ions and medium filled circles oxygen ions. Small filled circles are protons and checkerboard filled circles represent phosphorous ions, d Schematic structure of squaric acid...

A pot of water, heated gradually on a stove, is seen to develop highly structured convection patterns ( Benard cells ), resembling a checkerboard of ascending and descending columns. Clearly, such order out of chaos represents a process with A S < 0, proving that the second law is invalid. 

Attapulgite and palygorskite have a fibrous texture and a chain structure. The structure proposed by Bradley (1940) is that of a 2 1 layer structure with five octahedral positions (four filled) four Si tetrahedra occur on either side the octahedral sheet with their apices directed towards the octahedral sheet. These structural units alternate in a checkerboard pattern leaving a series of channels between the structural units. These channels contain water molecules. 

Figure 18-C-1 One plane of the idealized MogOa structure. The shear planes that disturb the otherwise perfect checkerboard arrangement of Mo06 octahedra sharing only comers are shown by heavy lines.

Table 4 Properties of Extruded Cordierite Diesel Filters with 100/17 Cell Structure and Checkerboard Plugging Pattern...

Figure 20.10. Amphiphilic ionic self-complementary peptides. This class of peptides has 16 amino acids, c. 5 nm in size, with an alternating polar and non-polar pattern. They form stable (3-strand and 3-sheet structures thus, the side chains partition into two sides, one polar and the other non-polar. They undergo self-assembly to form nanofibers with the non-polar residues inside positively and negatively charged residues form complementary ionic interactions, like a checkerboard. These nanofibers form interwoven matrices that further form a scaffold hydrogel with a very high water content ( 99.5%). The simplest peptide scaffold may form compartments to separate molecules into localized places where they can not only have high concentration, but also form a molecular gradient, one of the key prerequisites for prebiotic molecular evolution.

Fig. 10. Adsorbate superstructures on 100) surfaces of cubic crystals. Atoms in the top-layer of substrate are shown as white circles, while adsorbate atoms are shown as full black circles. Upper part shows the two possible domains of the c(2x2) structure, ohtained by dividing the square lattice of preferred adsorption sites into two sublattices following a checkerboard pattern either the white sublattice or the black sublattice is occupied with adatoms. The (2x1) structure also is a 2-sublattice structure, where full and empty rows alternate. These rows can be interchanged and they also can run either in -t-direction (middle part) or y-direction (lower part), so four passible domains result and one has a two-component order parameter.

Figure 12.23 The crystal lattice and the unit cell. A, The lattice is an array of points that defines the positions of the particles in a crystal structure. It is shown here as points connected by lines. A unit cell (colored) is the simplest array of pointsthat, when repeated in all directions, produces the lattice. A simple cubic unit cell, one of 14 types in nature, is shown. B, A checkerboard is a two-dimensional analogy for a lattice.

The theory seems to agree splendidly with experiments, he concluded. So, by October, 1914, Langmuir had assembled the kinetic theory tools to attack the problem of heterogenous catalysis. But he lacked the checkerboard and the idea of chemical forces. He hadn t specified the structure of the metal surface, or indicated the sites it... 

Most finely divided catalysts must have structures of great complexity. In order to simplify our theoretical consideration of reactions at surfaces, let us confine our attention to plane surfaces. If the principles in this case are well understood, it should then be possible to extend the theory to the case of porous bodies. In general, we should look upon the surface as consisting of a checkerboard. .. 

The most studied and applied particulate trap is the wall flow monolith [82-84]. It consists of a ceramic structure with parallel channels, of which half are closed at the upstream end in an alternate, checkerboard manner, and the other half are closed at the downstream end. Thus, exhaust gases are forced to flow through the porous walls, which then act as filters. 

Although a number of designs have been proposed over the years the dominating filter design used by the majority of applications is the wall-flow filter shown schematically in Fig. 20.3. The filter is made of an extruded honeycomb structure with walls made of a porous refractory ceramic. The channels are plugged in a checkerboard pattern at alternate ends. This results in a pattern that force the exhaust flow from the inlet channels, through the porous walls into the outlet channels. On the path through the porous wall particulates are removed by filtration. 

---