Hexagonal contours

Figure 12. Diffraction pattern from a single hexagon. Each contour is a factor of 10 lower than the last.

Figure 9.12 Three-dimensional map of the calculated electrostatic potential at 0.25 nm above the symmetry plane in a hexagonally ordered network of dipoles with a dipole-dipole distance of 1.61 nm and a dipole moment of 10 D. The dipoles are positioned at the minima. Note that the potential is lowered at every position on the surface. Equipotential lines for -1.05, -0.84, -0.63 and -0.42 V are indicated in the bottom plane. The contours are circular at short distances from a potassium atom, indicating that at these sites the nearest potassium atom largely dominates the potential. The equipotential tine for -0.42 V, however, has hexagonal symmetry due to the influence of the dipoles further away (from Janssens et al. [40]).

Tilted hexagons assembled to match the contours of their menisci. For example, although the [1,2] hexagons (1.2 mm thick) could assemble in two different ways to juxtapose their hydrophobic faces - trimers and parallel lines (Fig. 4.10a, b, c) - only trimers formed. This selection in structure occurred because hexagons that assembled into trimers matched the contours of their menisci hexagons that assembled into the parallel lines did not match the contours of the menisci (Fig. 4.1 la). Parallel lines assembled by hand were stable to agitation. We conclude that the preference for trimers lies in the kinetics of formation and stabilities of the dimers of the [1,2] hexagons. 

Figure 4.11. The tilt of the hexagons determined the contour of the menisci. The shape of the meniscus is indicated by the + symbol the larger this symbol, the higher the meniscus at that point on the face. There are at least two ways to form dimers of the [1,2], [11.2.i>21.2.1], [1,2,3], and [1,2,3,4] hexagons. In (a), (c), and (d), the favored cm configuration matches the contours of the menisci well the disfavored trans configuration matches the contours of the menisci less well. In (b), the [11.2.1,21.2.1] hexagons float almost parallel to the interface, and there is little or no preference between the cis and...

The [1,2,3,4] hexagons assembled into lines through interactions between the [1] and [4] faces (Fig. 4.13). These lines showed four interesting characteristics, (i) The lines assembled so that the [1] faces were in contact with the [4] faces. The contours of the menisci on the faces were matched when two hexagons assembled with the [1] and [4] faces in contact contacts between two [1] faces, or between two [4] faces mismatched the contours of the menisci on the faces (Fig. 4.lid), (ii) The [2] and [3] faces were buried into the interface and had small, positive menisci. Thus, the lines did not assemble into contact at high rates of agitation, but did assemble under weak agitation and low shear, (iii) The lines assembled into a loose, parallel array, with individual lines a small distance apart. Since the menisci on the juxtaposed [2] and [3] faces were mismatched, the lines assembled with a small distance between them, (iv) The vertex between the 5 and 6 faces had a small positive meniscus because it was pulled out of the interface (Fig. 4.13). This meniscus caused the hydrophilic faces to attract the exposed hydrophobic faces weakly. 

Figure 3. Map of a theoretical biological activity. The biological activity has been contoured against the structures arising from a particular combination of amine and ketone fragments. If at first the amine fragment is held constant (amine A) the ketone associated with maximal activity is 1. If the ketone is held constant as 1, the most potent amine is B, resulting in the false optimum B-l (in square). The true optimum C-3 (in hexagon) is never found.

Ftg. 5 d)—The hexagonal pattern of channels normal to the c-direction in levynite. O denotes a cavity centre in a reference plane, and -f a cavity centre above this plane. Thus, the network is puckered. The free dimensions are given by the line contour. 

Figure 4 Maps of the average density of nitrogen adsorbed in three nanotube bundles. The contours are for constant density in the x, y planes i.e., for an observer looking in the z direction parallel to the pore axes. The pore diameters are (a) 1.37mn, (b) 1.43 nm, and (c) 0.69 nm. The in-plane coordinates x, y are defined so that unit x, y= 0.07, 0.14 run, respectively. The larger blobs show density contours inside the tubes and the smaller ones are for molecules adsorbed in the interstices between the hexagonally packed tubes. The interaction potential for the Nj is diatomic thus, the approximate molecular length is 0.1 run greater than the width which is 0.35 nm. The consequence is that the tube of (c) is too small to admit the N2 molecules so that the adsorption shown there is essential all interstitial. Also, in (a) and (b), the N2 appears to lie parallel to the tube axis and is adsorbed on the tube walls. The differences between the (a) and (b) contours are at least partly due to the differences in the numbers of molecules in these systems. These amount to 334 and 199 in (a) and (b).

Fig. 8a. Time-resolved small-angle diffraction from a dispersion of a hexagonal-phase forming lipid (l-hexadecyl-2-oleoyl-phosphatidylethanolamine, HOPE) in the presence of excess water (c, p 0.2), during a heating- and cooling experiment. The temperature course are shown in the inserts, b contour-line plots of the intensities. (From Ref. 74, with permission)...

Fig. 7. Contour lines of the type obtained by Benard for the free surface of a hexagonal convection cell using the Fabry-P6rot interferometer.

With the aim of designing a biologically inspired carrier in which the encapsulation and the delivery of DNA can be efficiently controlled, Amar-Yuli et al. have designed two lipid-based columnar hexagonal LLCs [58], which can accomplish two opposite roles while maintaining the same liquid crystalline symmetry. The first system was based on a nonionic lipid, such as monoolein, while the second system was modified by a low additional amount of the oleyl amine cationic surfactant. DNA was enzymatically treated to generate a broad distribution of contour lengths and diffusion characteristic times [58]. 

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