Fractogram

The parallelization of crystallites, occurring as a result of fiber drawing, which consists in assuming by crystallite axes-positions more or less mutually parallel, leads to the development of texture within the fiber. In the case of PET fibers, this is a specific texture, different from that of other kinds of chemical fibers. It is called axial-tilted texture. The occurrence of such a texture is proved by the displacement of x-ray reflexes of paratropic lattice planes in relation to the equator of the texture dif-fractogram and by the deviation from the rectilinear arrangement of oblique diffraction planes. With the preservation of the principle of rotational symmetry, the inclination of all the crystallites axes in relation to the fiber axis is a characteristic of such a type of texture. The angle formed by the axes of particular crystallites (the translation direction of space lattice [c]) and the... 

Like chromatography, the FFF instrument consists of a pump to deliver the carrier fluid, a separation medium (FFF channel), a detector responding to the eluting species, and a computer to control the operative parameters (e.g., field, flow) and to acquire the digitized fractogram (see Figure 12.1). 

FIGURE 12.11 Differential SdFFF principles. The mass increase due to the adsorption of a molecular layer reflects a shift in retention time in the fractogram the mass of the coating can be computed from the difference in X values. 

FIGURE 12.12 FIFFF fractogram achieved by injecting Degussa P-25 Ti02 sample. On the right axis the concentration (ppb = ag L ) of Ti determined by ICP-AES. 

Polymer analysis searches for M distribution. In both ThFFF and SEC, this is achieved by the calibration procedure that allows one to transform the retention time axis and the signal axis, respectively, of the fractogram or chromatogram into molar mass distribution [3]. In SEC, calibration has to be executed on each new column and repeatedly checked during its current employment... 

The potential storage of the mass spectrometer output in digital form has made possible the matching of mass fractograms against computer file stored reference data and hence the rapid identification of the material so that multi-component systems, after prior separation by GC or LC techniques, can be analyzed within the time frame required for the thruput of the sample... 

Single crystals for electron micrography and diffraction were obtained by dissolution of the polymer in nitrobenzene at 170°C followed by filtration. The solution was slowly cooled to 134°C and kept at this temperature for 12 h. The polymer that had crystallized was filtered and redissolved in nitrobenzene at 170°C, cooled to 139°C then very slowly to 136°C, kept at this temperature for 24 h and cooled to room temperature leaving the polymer single crystals in suspension in nitrobenzene. A total of 25 reflections could be observed on the electron dif-fractogram (hkO section) of this material. This was an improvement over the X-ray fiber diagram since only five reflections had been recorded on the equator (see Table I). 

Figure 1. Fractograms for preparative DGC separation runs on PSOC-2 and PSOC-858. The heavy lines indicate density ranges of the samples used for NMR analysis. Letter designations ...

Table II shows the results of combining SFFF and PCS measurements on a broad unimodal distribution of PVC in water. The manufacturer of the PVC (The BFGoodrich Company) reports the density as 1.4 g/cm. The results reported here were obtained in Prof. K. D. Caldwell s laboratory at the University of Utah. Six fractions were collected near the peak of a broad fractogram obtained in the SFFF experiment. Each fraction was measured using the BI-90. Given the reported density, the average diameter of each fraction was calculated using SFFF theory. These values are given in column 2. Column 3 shows the average diameter of each fraction as measured by PCS, and column 4 shows the calculated density using the measured PCS diameter and the raw SFFF result for each fraction.

Narrow particle fractions approaching a monodisperse distribution are particularly easy to treat and characterize when the above equations are applied to experimental data. Figure 2 shows an example of the elution profile (fractogram) obtained by running a mixture of four samples of "monodisperse" polystyrene latex beads. It is clear from the figure that a rather precise value of retention volume Vr can be identified with each bead size. With Vr known, it is easy to obtain R and X from Equation 5 and thence particle diameter d from Equation 4. This operation, as noted, yields diameters accurate to approximately 1-3%. 

While the simple process of comparing fractograms with appended particle diameter scales will provide all the information needed in many particle characterization studies, the fractogram does not constitute a finished particle size distribution (PSD) curve. To obtain a quantitative PSD curve, corrections must be applied. The first correction, which we call a scale correction, is necessary because elution volume and particle diameter are not proportional to one another. Thus the particle content of a fixed volume of eluted sample will correspond to a different increment in d depending upon the point of collection. A simple correction factor, detailed elsewhere (3), can be applied to this scale problem. 

Figure 3. Fractogram of PVC latex with superimposed particle diameter scale. Field = 82.6 g, flow = 226 ml/hr, V° = 2.0 ml, sample = 40 pi of 6% PVC. Reproduced with permission from Ref. 20. Copyright 1980 John Wiley.

While either the fully corrected PSD or the noncorrected PSD represented by the fractogram will provide all of the information needed by most users, sedimentation FFF is sufficiently versatile to provide more information if required. A useful approach is the physical collection of small fractions of size-sorted material. 

Similarly, collected fractions can be reinjected into the sedimentation FFF system operated with a different carrier density. The degree to which the retention volume for any particle type is shifted by this operation will depend upon the density of the particle. In theory, the shape of the fractogram following fraction reinjection will yield a density distribution curve for the fraction. 

Figure 4. Cross-hatched area in fractogram A denotes a 5 ml fraction collected from a synthetic mix of polystyrene (PS) and polyvinyl chloride (PVC) run at 43.4 g with carrier density p = 1.00 g/ml. Same fraction is rerun (B) at 111 g in carrier of density p = 1.03 g/ml.

Information about sample composition, homogeneity and purity from qualitative evaluation of the fractogram ... 

The simplest analytical information that can be obtained with the aid of FFF is the homogeneity of the sample or evidence for the presence of a compound of interest in the fractionated sample by the appearance of a peak in the expected interval of retention volume. In some cases, comparison of the retention volume and the peak shape of the investigated component with the peak shape of a reference sample can provide sufficient qualitative analytical information on sample purity and homogeneity. The peak areas in the fractogram can be used to evaluate quantitatively concentrations of the detected components provided that the relationship between detector response and concentration or quantity of the detected component is known. This relationship is usually determined by a calibration procedure. However some sample is lost in the void peak so that it is not possible to relate the detected concentration to that of the original sample consequently, concentration determinations can more advantageously serve to compare the relative concentrations of the fractionated components. 

An FFF experiment involves several phases. In most FFF experiments, the carrier liquid flow is started and the cross-field is adjusted. The sample is then injected and a careful procedure of sample introduction and relaxation must be followed [28,97]. This procedure is illustrated in a schematical FFF fractogram (Fig. 11). One can see five basic phases of an FFF experiment. Special care must be taken to determine the time the sample spends in the tubing and connections outside the channel, textra, as this shifts the void peak as well as the sample peak towards longer retention times. 

Fig. 11. Schematic FFF fractogram with the different phases of an FFF experiment. Reproduced from [157] with kind permission of Societa Chimica Italiana...

Fig. 14. S-FFF apparatus designed by Giddings group (A) the separation principle with smaller particles (X), bigger particles (7) and floating particles (Z) with a density smaller than that of the solute [These particles are equally well separated as retention depends on Ap I (B)]. C Fractogram of a separation of polystyrene latexes of different sizes at two different rotational speeds. The ability to shift retention by changing the rotational speed is demonstrated. D The same mixture analyzed by a programmed field run demonstrating that a wider particle size range can be condensed into a reasonable elution span. Reproduced from [14] with kind permission of the American Association for the Advancement of Science...

In FFF, however, the fractogram is recorded in dependence of time so that a correction via extrapolation to infinite time in order to eliminate diffusion effects is not possible. A different strategy may be used for the correction of zone spreading which suffers from a number of assumptions and restrictions. A number of authors, reviewed by Janca [459], have dealt with the methods of correction for zone spreading which was found to be particularly extensive at high flow rates or low retentions. The results are summarized below. 

V and Vf are the initial and final retention volumes between which the integration of experimental fractograms is performed. 

Fig. 34.A Correction for zone broadening of a model fractogram. a represents the original curve and the corrected one whereas b is the uncorrected fractogram. Reproduced from [460] with kind permission of the American Chemical Society. B Comparison of differential particle size distributions of narrowly distributed polystyrene latex standards derived by MALLS and Fl-FFF without correction for zone broadening. Reproduced from [461] with kind permission of Academic Press...

The efficiency of the presented correction method was verified on model frac-tograms for different conditions. A very good correlation between the original distribution and the corrected fractogram was found for simulated data. The ne-... 

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