Crossover diameter

The crossover between weak and strong confinement occurs when < =b 4/5 i.e. when the correlation length is equal to the size of a linear chain, made of b monomer, in good solvent conditions = b=ab3/5. This corresponds to a crossover diameter for the tube... 

A field emission source uses a needle-like tungsten or carbon tip as the cathode, shown in Fig. 14.28. The tip is only nanometers wide, resulting in a very high electric field at the tip. Electrons can tunnel out of the tip with no input of thermal energy, resulting in an extremely narrow beam of electrons. Electron beams from heated filaments have a focal (cross-over) diameter of about 50 p,m while a field emission source has a crossover diameter of only about 10 nm. Field emission sources can serve as probes of surfaces at the nanometer scale (an Auger nanoprobe). 

The shape of the crossover diameter dco> which is the virtual electron source, is controlled by the geometry of the electrodes that compose the electron gun and the associated voltages (Fig. 

The fast relaxation pseudorate 6f also shows 1,2) a crossover between small- and large-particle behaviors. The crossover diameter for 9f is the same as the crossover diameter for 0. For small (d < R,) probes, 0f is nearly independent of d for large d >Rj) probes, 0f falls as d is increased. For all probes, large and small, 0f is nearly independent of c. 

Implications of the probe-size crossover diameter Figure 1 reveals a crossover between small-probe and large-probe behavior. As seen in Figure 1, the crossover... 

It gives the crossover between diffraction-limited and turbulence-limited resolution. For aperture diameters smaller than ro, close to diffraction limited imaging is possible without phase correction, for aperture diameters larger than ro, the resolution is limited by the turbulence. For a circular aperture of diameter D, the phase variance over the aperture is... 

Multistranded cables and ribbons were also observed for calcitonin (Bauer et al, 1995). These appeared to contain laterally associated 8-nm-wide fibrils, whereas the diameter of the individual strands within the multistranded cables could not be measured directly from the images. To estimate this diameter, the authors plotted the helical crossover spacing of the cables as a function of their diameter. Using a linear regression fit, the data were extrapolated to zero, yielding a width of 4.1 nm, similar to the width of the single protofibrils (Fig. 2A Bauer et al., 1995). 

Actin filaments are thought to exist in a double-stranded, right-hand helix with 14 subunits (per strand) per complete turn (Fig. 4.4), and a crossover distance of 38 nm. This strings of beads appearance is 70 A in diameter and thought to represent the structure of thin filaments. As the new fila-... 

For moderately doped substrates the crossover from tunneling to avalanche breakdown occurs at pore diameters of about 500 nm, corresponding to a bias in excess of 10 V. Above doping densities of 1017 cm-3 breakdown is always dominated by tunneling. Tunneling is therefore expected to dominate all pore formation in the mesoporous regime and extends well into the lower macropore regime, while avalanche breakdown is expected to produce structures of macropor-ous size. 

Figure 4c is the dififractogram obtained from a circular area about 175 A in diameter, with the dislocation at the center. All reflections with the spatial frequencies for resolving the two adjacent atoms appear with rather dominant intensity. This implies that no significant reflection is lost by CTF crossovers. Based on the Thon difffactogram [36] method, the defocus value is roughly determined to be -390 A. 

We will take a somewhat different but equivalent criterion in order to describe the crossover. As the crossover time r, we take the Rouse relaxation time of a polymer section, spanning the tube diameter ... 

Ferri, F., Greco, M., Arcovito, G., De Spirito, M., and Rocco, M. (2002). Structure of fibrin gels studied by elastic light scattering techniques Dependence of fractal dimension, gel crossover length, fiber diameter, and fiber density on monomer concentration. Phys. Rev. E. 66(1 Pt 1), 011913. 

The crossover from stars to bottlebrushes is expected to take place at Mw= lxl 05 which corresponds to nK=0.29 and L=9.7 nm in the polymacromonomers. The diameter of the bottlebrush may be calculated to be 7.8 nm from the Z1/2 of a PEO chain. Thus, the crossover may take place when the chain length of the backbone becomes more or less comparable to the diameter of the bottlebrush. 

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