Shell width

Taking into account some ambiguity in the choice of the hydration shell width D, it is reasonable to estimate its effect on the temperature of the percolation transition. Such analysis was performed in Ref. [566] for various choices of D from 3.8 to 5.4 A. Such variations of D were also useful for an accurate location of the percolation threshold at every temperature studied. Depending on the chosen value of D, the number of water molecules in the hydration shell varied up to about a factor of two. Due to the increasing number of water molecules in the hydration shell, a percolation transition occurs at some value of D, particular for each temperature studied. Example of a percolation transition at constant temperature is shown in Fig. 131. With increase in the thickness of hydration shell, larger deviations from a strict 2D to 3D percolation transition may be expected. The respective power laws for ns at the 2D and 3D percolation thresholds are shown in Fig. 131. Obviously, the behavior of ns allows the location of the percolation threshold between = 147 and JVw = 153 without any assumption about the dimensionality of the transition. This means, in particular, that atT = 300 K, water network around a peptide is spanning, if all water molecules within hydration shell of 4.75 A width are considered as hydration water. 

Figure 132 Temperature of the percolation threshold of water in the hydration shell of ELP as a function of the hydration shell width D. Percolation thresholds, estimated from the distributions P(5 max) of the largest cluster size (open circles), from the distributions ns of the cluster size (closed circles) and linear fit of the joint data set (solid Une). The shell widths, where the mean cluster size 5 mean passes at a given temperature through a maximum, are shown by closed squares. The temperatures at which the spanning probability D, determined from the distribution P(5 max) at a given shell width, is about 50% are shown by open squares. Dot-dashed line is a guide for eyes only. Reprinted, with permission, from [566].

Add all profile coordinate files to the input file list. A number of options are available. Spatial resolution is the resolution for the immunogold labeling (see above). Shell width specifies a zone outside the profile border, outside of which gold particles are discarded from the analysis—a shell width of zero thus discards all gold particles that are exterior to the profile. Moreover, a variety of... 

Whitney and Pagano [6-32] extended Yang, Norris, and Stavsky s work [6-33] to the treatment of coupling between bending and extension. Whitney uses a higher order stress theory to obtain improved predictions of a, and and displacements at low width-to-thickness ratios [6-34], Meissner used his variational theorem to derive a consistent set of equations for inclusion of transverse shearing deformation effects in symmetrically laminated plates [6-35]. Finally, Ambartsumyan extended his treatment of transverse shearing deformation effects from plates to shells [6-36]. 

The heavy bar in Figure 2 indicating completion of the K shell of neutrons in the core extends from N = 14.4 to N = 26.8. These limits correspond to 1.5 1.0 neutrons in the core, 1.5 being the value for transition from Is to Is2, and 1 representing the uncertainty in the equation. The bars for other completed shells have been similarly drawn, and those for completed subsubshells have been drawn with only half this width (the uncertainty, however, is as great). 

The emission spectmm of Co, as recorded with an ideal detector with energy-independent efficiency and constant resolution (line width), is shown in Fig. 3.6b. In addition to the expected three y-lines of Fe at 14.4, 122, and 136 keV, there is also a strong X-ray line at 6.4 keV. This is due to an after-effect of K-capture, arising from electron-hole recombination in the K-shell of the atom. The spontaneous transition of an L-electron filling up the hole in the K-shell yields Fe-X X-radiation. However, in a practical Mossbauer experiment, this and other soft X-rays rarely reach the y-detector because of the strong mass absorption in the Mossbauer sample. On the other hand, the sample itself may also emit substantial X-ray fluorescence (XRF) radiation, resulting from photo absorption of y-rays (not shown here). Another X-ray line is expected to appear in the y-spectrum due to XRF of the carrier material of the source. For rhodium metal, which is commonly used as the source matrix for Co, the corresponding line is found at 22 keV. 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

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