Fluctuation intensity plots

Figure 33.2 shows results obtained by studies of electrochemical noise for the corrosion behavior of carbon steel A516-70 in carbonate solutions with and without NaCl as an activator (Cheng et al., 2000). It can be seen that in ordinary carbonate solution the fluctuations of potential of a test electrode and the fluctuations of current flowing between a pair of identical electrodes are small. Added NaCl causes a drastic increase in intensity of the electrochemical noise. The PDS plots (Fig. 33.3) differ accordingly. 

Figure 4 Expected SRI plots for 13C CPMAS (top) and DDMAS (bottom) NMR peak intensities (solid lines) against fluctuation frequency (Hz). The fluctuation frequencies were divided into the following three regions, static (/a or /b), slow (//a or //b), and high frequency (///a or ///b) regions. The maximum intensities are given by S. In the presence of slow fluctuation motions, the peak intensities can be modified as the dotted lines (//a or //b ). In the nearly static region, the peak intensities could be changed into the dotted lines /a or /b, depending upon efficiency of cross-polarization or Tn values. From Ref. 29.

Dynamically raised processes in the dispersion, such as Brownian molecular motion, cause variations in the intensities of the scattered light with time, which is measured by PCS. Smaller the particle, higher the fluctuations by Brownian motion. Thus, a correlation between the different intensities measured is only possible for short time intervals. In a monodisperse system following first-order kinetics, the autocorrelation function decreases rather fast. In a half logarithmic plot of the auto correlation function, the slope of the graph enables the calculation of the hydrodynamic radius by the Stokes-Einstein equation. With the commercial PCS devices the z-average is determined, which corresponds to the hydrodynamic radius. 

Figure 5. Scattering intensity Ax for q = 0 as obtained from the OZ-plots as function of the reduced temperature. The original data ( ) are corrected for local laser heating and background scattering to give the scattering of the critical fluctuations (O)-...

A quantitative comparison between the mean field prediction and the Monte Carlo results is presented in Fig. 15. The main panel plots the inverse scattering intensity vs. xN. At small incompatibility, the simulation data are compatible with a linear prediction (cf. (48)). From the slope, it is possible to estimate the relation between the Flory-Huggins parameter, x, and the depth of the square well potential, e, in the simulations of the bond fluctuation model. As one approaches the critical point of the mixture, deviations between the predictions of the mean field theory and the simulations become apparent the theory cannot capture the strong universal (3D Ising-like) composition fluctuations at the critical point [64,79,80] and it underestimates the incompatibility necessary to bring about phase separation. If we fitted the behavior of composition fluctuations at criticality to the mean field prediction, we would obtain a quite different estimate for the Flory-Huggins parameter. 

Fig, 15 (contd.). (b) Peak intensity of second-order spots at 65 cV as a log-log plot vs. reduced temperature 1 — T/Tc below TCl after division by the Debye-Waller factor. Straight line corresponds to an exponent fi — 0.085. (c) Ixtg-log plot of peak intensity of fluctuations vs. reduced temperature 1 - 7C/T above Tc. Squares are first-order oxygen spots at 52 eV circles and triangles arc second-order spots at 36.5 and 65 eV, respectively. Straight line is a fit to eq. (6) with y — 1.08. (d) Same as (c) but for correlation length . Straight line is a fit to eq. (38) with u = 0.68. From Piercy and Pfniir (1987). 

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