that
is interesting, because this depends on temperature. The important point
is that Pebax, thanks to its better wetting power, has a higher critical
concentration. This is ultimately the only finding that can be gained from
these measurements. By means of regression and interpolation the wealth of measured values was reduced to a more manageable level. But even this drastically reduced quantity of measured values is still too unwieldy for a graphic presentation. For this reason the three measurement series, each covering the entire range of concentrations, were combined to form a single series. Thus the measurements used in the graphs are to be seen as the result of 8-10 individual measurements.
The regression lines are primarily intended to permit an estimation of the fluctuations in measured values and to document the possible deviation from a linear course. This is discussed in the next subsection, but the correlations should already be noted at this stage.
Another interesting point that should be noted when examining the graphs is the fact that the variance from the straight lines is spread fairly evenly over the entire concentration. This would appear to document the extent to which the viscosity depends on the state of dispersion of the specimen, and not on the concentration alone. To this end the non-logarithmic dynamic viscosities are shown below the graph. These deviations and even overlaps can be seen clearly from the figures.
When considering the graphs one should also form an impression of the accuracy of the measurements, in order to be able to assess during the discussion whether the statements made are "shaky" or whether they can be supported with the degree of accuracy achieved here. The reader should, as it were, take his personal error estimate as the yardstick for assessing the aspects discussed. This does not mean that consideration of errors is simply pushed off onto the reader, but rather that the entire discussion is entering a new area that is to some extent subject to highly subjective judgements and that every reader must be able to decide for himself what is a well-founded result and what is bordering on interpretation.
Fig. 3.7: Pebax 2533 with Printex XE-2 and wax
Fig. 3.8: Pebax 2533 with Printex XE-2
Fig. 3.9: PS N 2000 with Printex XE-2 and a wax
Fig. 3.10: PS N 2000 with Printex XE-2
Fig. 3.11: Pebax 2533 with Black Pearls 880 Monarch and 2% wax
Fig. 3.12: PS N 2000 with Black Pearls 880 Monarch and a wax [7]
Fig. 3.13: PS N 2000 with Black Pearls 880 Monarch
Fig. 3.14: PS N 2000 with titanium dioxide RL 90
3.3.2 Comparison of regression lines at constant shear rate
While the graphs in sub-section 3.3.1 are more suitable for documenting the quality and the basic course of the measurement series, this sub-section sets out to compare the various specimen compositions with one another. To this end all the graphs are reproduced first, after which the striking points are all discussed together.
| Key to curves: | 1: Pebax 2533 | with Printex XE-2 and a wax |
| 2: Pebax 2533 | with Printex XE-2 | |
| 3: PS N 2000 | with Printex XE-2 and a wax | |
| 4: PS N 2000 | with Printex XE-2 | |
| 5: Pebax 2533 | with Black Pearls 880 Monarch and 2% wax | |
| 6: PS N 2000 | with Black Pearls 880 Monarch and a wax | |
| 7: PS N 2000 | with Black Pearls 880 Monarch | |
| 8: PS N 2000 | with titanium dioxide RL 90 |
Fig. 3.15
Fig. 3.16
Fig. 3.17
Fig. 3.18
Fig. 3.19
An analysis of the graphs reveals a number of expected points, but also several surprising curves. The remarkable features are merely pointed out here. An evaluation of the results and an attempt to explain them will be found in the discussion sub-section.
| Fillers: | The course of the straight lines depending on the filler is in line with expectations. For example, Printex XE-2 with its very large specific surface area has the steepest gradients, whereas BP 880 and TiO2 (in that order) possess shallower gradients. The only exception is line 5, but this seems to be due to the relatively high wax content, especially at low concentrations. |
| Matrix polymers: | Here too the basically expected situation was confirmed. The viscosity of the more viscous matrix (PS N 2000) shows a more marked increase than that of the less viscous matrix. The only exception is once again line 5, the course of which appears to result from overlapping of several effects. |
Conclusions
For initial investigations the composition of the specimens must be kept as simple as possible, and only one variable must be altered from one specimen to the next. For this reason the specimens with additive are only to be regarded as a first approximation for an investigation of the influence of adjuvants. Owing to the changed dosages the specimens are not suitable for comparison purposes.
3.3.3 Other measured results
Fig. 3.20: PS N 2000 with carbon black
The continuous line represents the expected shape (determined from earlier
measurements). The deviations, especially at low concentrations, are due
to inaccuracies in the measurement procedure.
The only information that should be gleaned from this graph is the substantial
differences in pyrolysis residue that exist between the different sorts
of carbon black.
Fig. 3.21: PS N 2000 with titanium dioxide RL 90
A glance at the intercepts makes it clear how small the pyrolysis residue
is by comparison with carbon black.
Fig. 3.22: Pebax 2533 with carbon black
In this graph the similarity of the measured results to the expected results is more readily apparent. But what is much more important here too is the marked difference between concentrates with XE-2 and the concentrate with BP 880. The specific surface area appears to be a crucial factor in pyrolysis as well.
3.3.3.2 Conductivity
The conductivities – or resistances – measured are not particularly
interesting as individual values. They are values that are specific to
the measurement setup, and cannot therefore be generalised (see sub-section
3.2.3.3). But they do serve the purpose for which they were taken.
From the very rough approximated curves one can see that the two different
matrix materials display marked differences in the critical concentration
c. Here again it is not so much the absolute position of that
is interesting, because this depends on temperature. The important point
is that Pebax, thanks to its better wetting power, has a higher critical
concentration. This is ultimately the only finding that can be gained from
these measurements.
No conductivity measurements were made on the specimens with BP 880,
as there is merely a shift in the position of to
higher concentrations, and the findings would otherwise have remained the
same.
Fig. 3.23: Carbon black concentrates with Printex XE-2
3.3.4 "Thermodynamic interaction factor"
In accordance with the approximation equation
(3.13)
figures for a were calculated on the basis of the regression lines.
The following values are arranged by specimen composition and shear rate. The values for a given shear rate fluctuate across the various concentrations, but the figures given here are the calculated mean values (fluctuations are in the region of 0.1-0.25 around the mean). In view of the fact that this is a first approximation, this procedure seems justified.
| Composition of specimens | Shear rates / s-1 | ||||
| 20 | 50 | 100 | 500 | 1000 | |
| Pebax + XE-2 + wax | 23.6 | 20.4 | 18.4 | 15.1 | 14.0 |
| Pebax + XE-2 | 21.3 | 18.5 | 16.9 | 13.9 | 13.2 |
| PS + XE-2 + wax | 21.5 | 20.6 | 20.3 | 20.9 | 20.9 |
| PS + XE-2 | 24.8 | 22.4 | 21.4 | 22.0 | 23.2 |
| Pebax + BP 880 + wax | 19.5 | 16.8 | 15.0 | 11.4 | 10.2 |
| PS + BP 880 + wax | 10.1 | 9.9 | 10.2 | 11.8 | 12.3 |
| PS + BP 880 | 13.4 | 12.5 | 12.0 | 12.7 | 12.6 |
| PS + TiO2 | 9.1 | 8.5 | 8.1 | 7.5 | 7.4 |
The thermodynamic interaction factor is, as it were, a product of
a) "intensity" of the interaction and
b) size of the surface at which the interaction takes place. If, with this concept in mind, one looks at the various factors in connection with the composition of the specimens, one arrives at the following results: – Pebax displays a stronger interaction intensity than PS.
– As the specific surface area decreases, so does the factor, but as expected this effect is stronger for PS than for Pebax.
– the effect of wax in different, depending on whether it improves dispersion of the filler (i.e. factor increases), or it improves the flow of the matrix (i.e. factor decreases).
