Particles cylinder-like

In this chapter, we give exact expressions and various approximate expressions for the force and potential energy of the electrical double-layer interaction between two parallel similar plates. Expressions for the double-layer interaction between two parallel plates are important not only for the interaction between plate-like particles but also for the interaction between two spheres or two cylinders, because the double-interaction between two spheres or two cylinders can be approximately calculated from the corresponding interaction between two parallel plates via Deijaguin s approximation, as shown in Chapter 12. We will discuss the case of two parallel dissimilar plates in Chapter 10. 

The maximum q-values (first maximum) are plotted in Fig. 53 for both, H+ and Cs+ counter-ions. No clear picture evolves as the slope of the sample with Cs+ counter-ions is 0.44 whereas that for H+ counter-ions is 0.34. The dotted line in Fig. 53 would result according to qmax = - j with < d > the mean distance of the particles if the particles were evenly distributed throughout the solution, i.e. formed a fee lattice of spheres. For rod like particles this is only to be expected if the interparticle distance is much larger than the rod length I, i.e. NPlt-,j, where Ny is the number concentration. This is shown by the arrow in Fig. 53 assuming a cylinder length per mono-... 

Remarkable is the presence of drop-shaped structures at the tips of cylinder-like fragments (Fig. 1, b-c). Similar structures are inherent in well-known vapor-liquid-solid (VLS) mechanism of crystal growth. If this is the case, the copper particles entering the compression flow due to a weak erosion of the MFC copper electrodes... 

Pileni and colleagues [100] have also used cylindrical droplet formation for synthesis of rod-like particles by increasing the surfactant content. In a later work [250], Pileni showed that the presence of salt anions, instead of the available template, may control the particle shape. Thus, chloride ions help formation of nanorods, while nitrate ions can hinder formation of cylinders and rods. 

This can be observed in Figure 12.2, which shows the surface area-to-volume ratio (A/V) as a function of the aspect ratio (a = l/d) of a cylindrical particle (disk/platelet-like or cylinder/fiber-like), for a given particle volume. Values of l/d < 1 correspond to platelet-like particles, while l/d > 1 correspond to rod-like particles. It can be seen that A/V increases faster for platelet-like particles than for rod-like particles with respect to their aspect ratio [6]. Hence, for an equivalent volume of particles and for the same aspect ratio, platelet-like particles have higher contact surfaces, which makes them more difficult to be dispersed. 

If we characterise composites by particle geometry, we can distinguish fibres and particles (in the narrow sense). In fibres, one dimension is larger than the others by at least one order of magnitude, thus they are shaped like long and slender cylinders. In particles, the extension is approximately the same in aU directions. Other structures are also possible the phases may, for example, also be arranged in a sandwich structure or laminate with alternating layers of different materials. 

Another proj rty of powders that could affect the results obtained with diffraction based instruments is the shape of the particles. As many particles are approximately spherical or at least circular in projection this might not be a big problem. Ne le shaped particles or cylinders pose a completely different problem. Swithenbank et al have considered the effect of cylinders. Obviously, a cylinder, like a slit has a linear not a circular diffraction pattern. However, for randomly orientated cylinders an equivalent circular diffraction pattern was produced which gave a dimension 12% smaller than the cylinder diameter. The scattered light is insensitive to the cylinder length (assuming L/D>3). 

So far it has been tacitly assumed that the rod-like particles are completely rigid. Particularly for rod-like polymers this is frequently not the case. For these systems the wormlike chain model, which can be seen as a thin cylinder with an elastic bending modulus provides a better description than the completely rigid rod. This flexibility of the particles has a pronounced effect on the isotropic-nematic phase transition, which has been extensively reviewed by Odijk l. In the following I will limit myself to systems that consist of (almost) perfectly rigid rods. 

Flard spherocylinders (cylinders witli hemispherical end caps) were studied using computer simulations [118]. In addition to a nematic phase, such particles also display a smectic-A phase, in which tire particles are arranged in liquid-like layers. To observe tliis transition, ratlier monodisperse particles are needed. The smectic-A phase was indeed observed in suspensions of TMV particles [17]. 

Both (i) and (ii) necessitate recourse to a model of pore shape. By far the commonest, chosen on grounds of simplicity, is the cylinder but the slit model is being increasingly used where the primary particles are plate-like, and the model where the pore is the cavity between touching spheres is beginning to receive attention. 

The geometrical factor, like the filling factor, shifts the position of the resonance peak. When = 0 we have the case of an infinite cylinder (see Table 1). An infinite cylinder connects one side of the crystal to the other. Therefore, the electrons travel freely through the crystal. Actually, this is not the situation of metallic particles dispersed in an insulator any more. The situation corresponds... 

A more detailed view of the dynamies of a ehromatin chain was achieved in a recent Brownian dynamics simulation by Beard and Schlick [65]. Like in previous work, the DNA is treated as a segmented elastic chain however, the nueleosomes are modeled as flat cylinders with the DNA attached to the cylinder surface at the positions known from the crystallographic structure of the nucleosome. Moreover, the electrostatic interactions are treated in a very detailed manner the charge distribution on the nucleosome core particle is obtained from a solution to the non-linear Poisson-Boltzmann equation in the surrounding solvent, and the total electrostatic energy is computed through the Debye-Hiickel approximation over all charges on the nucleosome and the linker DNA. 

---