Two Parallel Rods

The interaction energy V R) per unit length between two dissimilar thin rods 1 and 2, having molecular densities N and N2, respectively, separated by a distance R between their axes (Fig. 19.9) can be given by 

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It is interesting to note that Eq. (19.56) agrees with the energy between two parallel rods of length 2nr carrying molecules of line densityTV [9]. 

Two initial forms of each of these polymers were created. The first were 60- to 100- mi-diameter cured polymer fibrils of 10cm length wound around two parallel rods spaced 1 cm in a fignre of eight conformation and tied in the center to form bundles. 

The term capillarity is used to designate the physical process by which a liquid penetrates into a single capillary tube or in multiple pores in a porous material. A pore does not necessarily has to be a closed tube the space between three or even two parallel rods or fibers is also considered as a pore indeed, this is the kind of pore normally found in fibrous materials. So, it is not the cross-sectional shape but the size which determines the definition of a capillary tube its radius must be smaller than the capillary length which is the length scale above which gravitational... 

Our experimental techniques have been described extensively in earlier papers (2, 13). The gamma ray irradiations were carried out in a 50,000-curie source located at the bottom of a pool. The photoionization experiments were carried out by krypton and argon resonance lamps of high purity. The krypton resonance lamp was provided with a CaF2 window which transmits only the 1236 A. (10 e.v.) line while the radiation from the argon resonance lamp passed through a thin ( 0.3 mm.) LiF window. In the latter case, the resonance lines at 1067 and 1048 A. are transmitted. The intensity of 1048-A. line was about 75% of that of the 1067-A. line. The number of ions produced in both the radiolysis and photoionization experiments was determined by measuring the saturation current across two electrodes. In the radiolysis, the outer wall of a cylindrical stainless steel reaction vessel served as a cathode while a centrally located rod was used as anode. The photoionization apparatus was provided with two parallel plate nickel electrodes which were located at equal distances from the window of the resonance lamp. 

We perform flexural testing on polymer rods or beams in the same basic apparatus that we use for tensile or compressive testing. Figure 8.6 illustrates two of the most common flexural testing configurations. In two-point bending, shown in Fig. 8,6 a), we clamp the sample by one end and apply a flexural load to the other. In three-point bending, shown in Fig. 8.6 b), we place the sample across two parallel supports and apply a flexural load to its center. 

The acetylcholine receptor has four subunits (a, /3, y, and 5, with Mr 52, 56, 63, and 66 x 103, respectively). The complete receptor includes two copies of the a subunit, and one of each of the others. The overall structure, as visualized by electron microscopy, resembles a cylindrical bundle of five, approximately parallel rods, with a water-filled channel along the axis of the cylinder (fig. SI. 12). This assembly projects about 70 A into the synaptic cleft on one side of the membrane and about 40 A into the intracellular... 

Cholesteric liquid crystals Historically, the name is derived from cholesterol chiral molecules like the steroids show a certain form of the nematic phase, the cholesteric one. The rigid rods are oriented parallel within virtual layers in one preferred direction (director) the director changes from one single virtual layer to the next continuously, with a certain value creating a helix. The distance between two parallel oriented directors is called the pitch (ca 0.2 pm). 

The quadrupole mass analyzer [1] consists of four parallel metal rods arranged as in Fig. 1. Two opposite rods are electrically connected and have an applied potential of U+V cos (ot, and the other two rods, also electrically connected, have a potential of -(U+V cos cot), where U is a DC voltage and V cos cot is an RF voltage, co being the angular frequency (co = 2irf). 

Here g(l, 9 = 0) is an energy per unit length each rod in A, say, interacts with all rods in B. Think of the second derivative as the interaction between two infinitesimally thin slabs at separation Z. If we say that these slabs are parallel to the x, y plane and that the parallel rods all point in the direction x, then we must integrate over direction y parallel in order to collect all interactions between a rod in slab A with rods in the apposing slab B. 

The interaction g(l,9 = 0) = g (I) per unit length, between two parallel thin rods, is succinctly written as... 

Following the Pitaevskii strategy for extracting small-particle van der Waals interactions for the interaction between suspensions, we specialize the general expression for ionic-fluctuation forces to derive forces between cylinders (Level 3). As with the extraction of dipolar forces between rods, consider two regions A and B, dilute suspensions of parallel rods immersed in salt solution interacting across a region of salt solution m (see Fig. L2.19). 

In the limit at which /cm goes to zero, these functions reduce to the correct form for dipolar fluctuations only. It is the product of these times e 2VpZ+i i that must be integrated over dir and pdp to obtain the interaction of the two arrays A and B. We know in advance that it is the second and third derivatives with respect to l that give us at-an-angle and parallel rod-rod interactions. The second derivative creates a factor 4 (p2 + k ). 

There are two anode assemblies in each cell. They consist of 12 carbon anode blades arranged in two parallel rows. At a current load of 4,000 A the current density at the anodes equals 13.5 A/sq. dm. The current is led to the anodes by means of copper rods which pass through stuffing boxes in the cover. 

It is common in corrosion laboratories and in field corrosion monitoring probes to immerse two vertical rods parallel to one another in an electrolyte. In the lab, one of the rods consists of a high-density graphite counterelectrode while the other is a working electrode. A reference electrode may be placed in between the two rods. In the field, polarization resistance or electrochemical noise measurements are often made between two nominally identical rods that both consist of the material of interest. The primary current distribution is nonuniform with respect to circumferential position about each electrode when the distance between the two rods is small in comparison to the radius of the rod, Fig. 10a (16). Again, the value of Ra varies from where the rods face each other to where they... 

FIGURE 19.9 Two parallel thin rods separated by a distance R. 

Quadrupole mass analysers use two pairs of parallel rods on either side of the ion beam. By modulating the voltage across these rods, species of particular m/z ratios are selected to pass to the detector and other species are lost. 

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