Porod invariant values

Figure 4.- Relative Porod Invariant values (calculated relative to the maximum Porod Invariant value for each sample) corresponding to the measurement carried out across the fiber diameter for the samples CFC50 and CFS48.

Since all the parameters on the righthand side of this expression should be constant with activation, except for (j)s. the value of the Porod invariant should follow the behavior of < >s(l- s)- Thus, division of the scattering intensities by this factor can be used to correct for the variation of ( )s. It is emphasized, however, that this is only an approximation for a number of reasons, including the fact that when l(q) varies with q to an exponent less than -2 (as at high q for the current data), the integral diverges [3], and accurate values of the Porod invariant cannot be obtained. 

Scattering data for a cellulose char sample activated isothermally at 425°C are presented in Figure 6. These data show that this carbon, like the saran char, initially exhibits a significant amount of microporosity, as indicated by the plateau centered at about q = O.lA". The Porod invariants for these data initially increase and then decrease with activation, also like the saran char. The scattering data, corrected by the PI values, are presented in Figure 7, which shows somewhat different behavior than for the saran char. 

By immersing the sample in water at room temperature for several hours, we found that the PIP-Mg and PB-Ti samples did not swell significantly. However, a very thin layer on the surface became opaque. The SAXS maximum was displaced to lower q values by 7% and 3%, respectively. The most dramatic effects, however, were found for the samples of PB-Mg (Figure 4) neutralized to 80% and 100%. In these specimens, the swelling appeared uniform and the peak sharpened dramatically and was shifted to lower q s by as much as 25%. As expected, the water uptake was accompanied by an increase in domain size from 6.2A to 11.5A for PB-Mg (100%) and from 5.8A to 13.6A for PB-Mg (80%) with a very slight increase in Ed. The Porod invariant Q and zero-order scattering also decreased. 

The quantity/], arises from density fluctuations and Kp is the Porod constant Note the strong positive deviation in the Porod plot (f(q)q versus q ) illustrated as an inset to Figure 2. Positive deviations from Porod s law are caused by thermal density fluctuations [6]. A regression analysis of tiie linear part of the curve gives values of = 0.0S and = 356. A most be subtracted from the raw intensity data before both dj and the invariant are calculated. 

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