Irregular series

Increasing the ion radius within the above named mono and trivalent ions (thus Li — Na —> K or Ce —La) increases the reversal of charge concentration. This does not apply to the divalent ions (Mg, Ca, Sr, Ba) in which irregular series appear. The relatively small Ca ion has here often the lowest reversal of charge concentration. These irregular series will be discussed further in 2 g (p. 288). 

Very interesting results were obtained with the sodium salts of the dicarboxylic acids. They form an irregular series, which can however be written in the way as given in Fig. 31 as two regular sequences connected by the succinate ion ... 

The only experimental finding, that at first sight suggests the presence of polarisation effects, namely the irregular series of the dicarboxylic acid anions — constituting a typical transition sequence —, could be explained on a quite different basis ( 4c). 

Fig 13. Irregular series of FcfOH) sol with NaOH d Mutual influence of sols... 

In the frame work of Gouy s theory, addition of electrolyte can never lead to a reversal of the sign of the charge or potential. In reality, however, there are several electrolytes that lead to a reversal of the charge, as is proved both by electrophoresis and by the appearance of a second region of stability (Irregular series). Schematically the phenomenon is illustrated in Fig. 7 where stability and electrophoresis are plotted against the amount of electrolyte. 

When an irregular series is produced by addition of potential-determining ions (negative silver halide sol -f Ag NO3, positive Fe(OH) sol -j- NaOH) the explanation is simply that the surface passes its zero point of charge. 

There are, however, many cases of irregular series produced not by potential determining ions, but by highly charged or strongly... 

The abnormally low flocculation values of complicated organic ions have already been cited in sect. 3. Closer inspection shows that many of these ions give rise to reversal of charge and an irregular series, e.g, in the case of the silver iodide sol, laurylpyridi-nium bromide or strychnine nijrate... 

Irregular Areas Let yQ, yi,. . . , y be the lengths of a series of equally spaced parallel chords and h be their distance apart. The area or the figure is given approximately by any of the following ... 

As of this time, no one has solved the problem of the effect of asperities on a curved surface nor has anyone addressed the issue of crystalline facets. Needless to say, the problem of asperities on an irregular surface has not been addressed. However, Fuller and Tabor [118] have proposed a model that addresses the effects of variations of asperity size on adhesion for the case of planar surfaces. Assuming elastic response to the adhesion-induced stresses, they treated surface roughness as a random series of asperities having a Gaussian height distribution (f> z) and standard deviation o. Accordingly,... 

Fig. 33(a,b) shows a series of snapshot pietures as a result of a eomputer experiment probing the kineties of dewetting. The loeal darkness of eaeh snapshot indieates the loeal eoverage of the substrate surfaee. Coverage fluetuations (white spots) appear rather early and get rapidly amplified. The substrate regions, eovered with polymer, have very irregular surfaee initially and are eonneeted with many weak links later, these hnks disappear, and the droplets of adsorbed polymer eompaetify, a pattern similar to spinodal deeomposition. 

Redox processes, which of necessity entail a change in the occupancy of the 4f shell, vary in a very irregular manner across the series. Quantitative data from direct measurements are... 

The point that contacts the shaft is attached to a spindle and rack. When it encounters an irregularity, it moves. This movement is transmitted to a pinion, through a series of gears, and on to a hand or pointer that sweeps the dial of the indicator. It yields measurements in (-I-) or (—) mils. 

General laws for the flow of fluids were determined by Reynolds, who recognized two flow patterns, laminar and turbulent. In laminar flow the fluid can be considered as a series of parallel strata, each moving at its own speed, and not mixing. Strata adjacent to walls of the duct will be slowed by friction and will move slowest, while those remote from the walls will move fastest. In turbulent flow there is a general forward movement together with irregular transfer between strata. 

This equation is the first term of an infinite series which appears in the rigorous solution of the quasi-diffusion. This equation describes the regular process of quasi-diffusion. For the low values of the Fourier number (irregular quasi-diffusion) it is necessary to use Eq. (5.1) or Boyd-Barrer approximation [105, 106] for the first term in Eq. (5.1)... 

There is a concomitant decrease in the length of the carbon-sulfur bonds in the thiirene series, but irregularity is apparent in the decrease of the carbon-sulfur bond in the thiirane series. Thus, r(CS) 19b carbon-sulfur bond lengths of 20a and its oxide (16a) are essentially identical. 

Within the general trend in the behavior across the actinide series, their alloys, and their metallic compounds from superconductors to local moment magnets, the only serious irregularity occurs in some plutonium compounds. These compounds should be magnetic but turn out to be temperature independent paramagnets. 

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