Sequencing spherical

Fig. 5.8. Correspondence between phase behaviour (micellar, lamellar and sponge) and morphological sequence (spherical, cylindrical and bilayer)...

FIG. 19 Scheme of a simple fluid confined by a chemically heterogeneous model pore. Fluid modecules (grey spheres) are spherically symmetric. Each substrate consists of a sequence of crystallographic planes separated by a distance 8 along the z axis. The surface planes of the two opposite substrates are separated by a distance s,. Periodic boundary conditions are imposed in the x and y directions (see text) (from Ref. 77). 

It is well known that block copolymers and graft copolymers composed of incompatible sequences form the self-assemblies (the microphase separations). These morphologies of the microphase separation are governed by Molau s law [1] in the solid state. Nowadays, not only the three basic morphologies but also novel morphologies, such as ordered bicontinuous double diamond structure, are reported [2-6]. The applications of the microphase separation are also investigated [7-12]. As one of the applications of the microphase separation of AB diblock copolymers, it is possible to synthesize coreshell type polymer microspheres upon crosslinking the spherical microdomains [13-16]. 

Generally, the number of the shell chains in a microsphere ranges from a few hundred to a few thousand. The range of the diameter of the core is from 10-100 nm. Such a core-shell structure is very similar to the (AB)n type star block copolymers, which have many arms and spherical polymer micelles of the block or graft copolymers formed in selective solvents that are good for the corona sequence and bad for the core sequence. In fact, many theoretical investigations of the chain con-... 

On the contaminated and slightly hydrophobic surface, the spherical droplets grow continuously with time, as shown in the sequence of images in Figure 11. This behavior is... 

In our earlier efforts to synthesize dendritic amphiphiles, we described a triden-dron (43) which was prepared by a two-step (alkylation-amidation or triester-tris) reaction sequence applied to l,3,5-tris(bromomethyl)benzene [117]. TEM and light scattering experiments suggested that 43 aggregated by stacking of its hydrophilic exterior into a spherical array of ca. 20 nm (diameter) reminiscent of globular micelles. 

The micelles are spherical, but when the concentration of surfactant increases, the shape of the ionic micelles changes following the spherical sequence cylindrical-hexagonal-laminar [22], In the case of nonionic micelles the shape... 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

Figure 2.21 shows the dependence of dimensionless net peak currents of ferrocene and ferricyanide on the sphericity parameter (note that A0p = AT], andy = p)-The SWV experiments were performed at three different gold inlaid disk electrodes (ro = 30, 12.5 and 5 pm) and the freqnencies were changed over the range from 20 to 2000 Hz [26]. For ferrocene the relationship between AT], and p is linear A Fp = 0.88 + 0.74p. This indicates that the electrode reaction of ferrocene is elec-trochemically reversible regardless of the frequency and the electrode radius over the range examined. For ferricyanide the dependence of AT], on p appears in sequences. Each seqnence corresponds to a particular value of the parameter The results obtained with the same freqnency, but at different microelectrodes, are cormected with thin, broken lines. The difference in the responses of these... 

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