3.1. Calculating Stearic Acid and Its Effects
The coverage index is dependent on the molecular weight and projected area, and is equal to 2.3 mg·m−2 for stearic acid. At this point, measuring or defining the powder surface area as accurately as possible becomes critical for feedstock development.
One feedstock preparation without fibers contains 88.88 g TM-DAR powder, and the BET surface area is 11.8735 m2
. According to the BET measurements, the surface area of the powder for a given recipe,
, equals to 1055.317 m2
, and the corresponding amount of stearic acid is 2.43 g by using
. On the other hand, the BET surface area of the fibers is 0.1201 m2
, so that the total surface area of the fibers,
for the feedstock with 50 vol % fibers is 5269 m2
, which is much smaller than for the powder. In Table 3
, the total stearic acid quantities and the weight fractions of SA for powder and fibers, based on BET measurements, are given for each feedstock with different fiber contents and stearic acid concentrations. It is clear that the required amount of stearic acid for fibers is much lower than for the powder, and varies from 0.25 to 1.03 weight percentage of the total required stearic acid for the relevant feedstock.
Further experiments include investigations on the effects of different dispersant concentrations from 1.1 to 5.5 mg·m−2
. The corresponding quantities are given in Table 3
Increasing the amount of stearic acid has a significant influence up to a certain point, where it reaches a quasi-balance range of the final kneading torques between 2.2 and 3.3 mg·m−2
within standard deviation, because the amount of stearic acid most probably does not increase the wettability and compatibility between powder and binder anymore, as seen in Figure 5
for the paraffin wax-based feedstocks.
Despite the fact that such an amount of stearic acid theoretically cannot coat the whole solid surface, feedstock with 0 vol % fiber and 1.1 mg·m−2
stearic acid has the lowest final torque in its group. The reason could be the inadequate quantity of stearic acid and applied stress to break down the agglomerates during kneading. Since the agglomerates decrease the total surface area, 1.16 g stearic acid could be sufficient to cover the surface of the agglomerates. However, it is not sufficient if the dispersant molecules can diffuse in the agglomerates. On the other hand, without breaking the agglomerates, the powder has a bimodal size distribution behavior, which could also lead to a better packing [28
] and flow behavior [29
], thus, a decrease in the final kneading torque. The particle size distributions are given in Figure A1
and Figure A2
, and correspond to two variations: the powder agglomerates are mixed with alcohol and then attempted to be broken down by ultrasonic bath (UsB) before measurement, or are measured directly. The d50 of the TM-DAR powder without UsB is 17.40 µm whereas, with UsB, it is 0.11 µm.
By adding fibers to feedstocks, there is a general increase in final torques that will be evaluated later. With the presence of fibers, the surface area definitions have become relatively more reliable, because not only do the fibers have significantly lower surface areas than powders but, also, they hold their shape even when they break down into smaller fibers. For example, if all fibers are chopped from 3200 µm into 50 µm, the increase in stearic acid should be less than 1 weight %, because the initial lateral area remains the same, and only the fractured surface areas should be considered. For these reasons, increasing stearic acid improves the flow behavior of the feedstocks with fibers as expected, and 3.3 mg·m−2 is the lowest point for fiber-filled variations.
The viscosities of all variations are represented in Figure 6
. The viscosities have not been changed by increasing either the amount of dispersant, the amount of fibers, or both. The reason for this could be that the exchange of paraffin by stearic acid does not result in any change in the linear viscoelastic behavior. This can be explained by the fact that the paraffin wax is an oligomer of polyethylene in its chemical structure, and also acts as a plasticizer. This means that an exchange by stearic acid does not alter the basic rheological behavior of the binder.
By evaluating the viscosity results separately as in Figure A3
, the viscosities are higher, at 1.1 mg·m−2
, for the fiber-filled feedstocks. At higher SA concentrations, there are only very slight changes. The reason for this is that the paraffin wax-based binder system has almost no polar component (see Table 4
) that decreases the adhesion force between binder and the solid content. This could also cause formation of a layer on the surface of the measurement channel, which could cloud at least the effect of an increasing fiber content on the rheological behavior.
Consequently, these results do not mean that 3.3 mg·m−2 is the ultimate concentration for these certain types of powder, fiber, and dispersant combinations. However, it is important to restrict the framework of further experiments, and a concentration of stearic acid of 3.3 mg·m−2 is sufficient to fulfill the requirements.
3.2. Effect of Solid Content
Once the stearic acid quantity has been defined as being constant, the effects of solid content on the final torque (FT) and kneading energy (KE) of different feedstocks were investigated and demonstrated in Figure 7
a,b. The experiments included the paraffin wax-based feedstocks without fiber and with 50 vol % fiber content. It is clear that relatively higher torques are needed for the fiber-filled feedstocks to achieve the same rotational speed during kneading, as for the feedstocks without fibers (e.g., ca. 8.1 Nm with fibers vs. 4.8 Nm without fibers at 50 vol % solid content). This behavior changes at a point between 60 and 65 vol %, where the standard feedstock without fibers shows a gradually higher final torque and kneading energy. With increasing solid content in the feedstocks, the corresponding final torques and kneading energies increase with similar exponential growths, because the particle–particle interactions or, in highly fiber filled feedstocks, rather particle–fiber and fiber–fiber interactions, started to dominate the mixtures from a critical solid content instead of polymeric slip layers between particles and fibers, which means an increase in inner friction.
In Figure 8
, the solid content dependency of relative viscosity at different shear rates is demonstrated. The figure on the right side represents the focus on a range between approx. 47.5 and 52.5 vol % of solid content, in which feedstocks with and without fibers reach the same viscosity. From that equilibrium point, the feedstocks with 50 vol % fibers in solid content show lower viscosities, and the difference between two variations increases with increasing solid content. Although the torque measurements are available for both feedstocks at 65 vol % solid content, the viscosity of 65 vol % for feedstock without fiber variation could not be measured, which means that the feedstock has reached the infinite viscosity and shows no flow anymore. Additionally, 65 vol % is relatively near to the theoretical maximum filling degree of about 70 vol % (see “Phi max.” for 0 vol % in Figure 9
). On the other hand, the viscosity of highly fiber-filled feedstock at 65 vol % solid content could be measured, where the fibers that enable flowability even at higher solid contents [28
] most probably are oriented and flow together.
shows that, using OriginPro 2017, the Krieger and Dougherty
model was applied to relative viscosity vs. solid content at a shear rate of 30 1/s, that is in between the minimum and maximum shear rates during kneading for specific device conditions [31
]. The maximum calculated solid contents are 70.6 vol % ± 0.6 for 0 vol % fibers, and 86.7 vol % ± 2.5 for highly fiber-filled feedstocks. The value for non-fiber feedstock, 70.6%, is under 74%, which is the theoretically highest packing for spherical mono size particles [1
], that is expected with an irregular shape and size distribution of TM-DAR powder.
As seen in Figure 8
, the curves start to show exponential growth between 45 to 52.5 vol % solid contents for the feedstock without fibers. Additionally, in Figure 9
, feedstocks show similar flow behaviors very near to 50 vol %. For these reasons, the further experiments will be done at a 50 vol % filling degree.
3.3. Investigating the Effects of Increasing Fiber Content, Fiber Coating, and Alternative Binding Systems on Rheological Properties
At constant amounts of stearic acid, 3.3 mg·m−2
, and a solid content of 50 vol %, further feedstocks were compounded for 30 min at 125 °C (see Table 1
) by increasing the fiber content from 0 to 50 vol % in solid fraction with/out PVA sizing variations, and were evaluated in comparison to an alternative binding system based on PEG-4000, as shown in Figure 10
. The first thing to note is the generally increasing trend with increasing fiber content. Moreover, all these feedstock variations were produced with relative lower standard deviations that show their reproducibility. This can also be seen in Figure A4
In general, paraffin wax (PW)-based feedstocks have a lower final torque (4.9 vs. 6.0 N·m) and kneading energy (28.5 vs. 34.9 kN·m) than the PEG-based feedstocks, until they are highly filled with fibers. The final torque and kneading energy values of PW-based feedstocks converge towards 50 vol % of fibers in solid content at 8 N·m and 47 kN·m, respectively, and the effect of PVA sizing is noteworthy only at 30 vol % fibers. Furthermore, the final torques of PEG-based feedstocks do not converge at a certain point, and the amount of PVA sizing increases together with an increasing fiber content, which causes a growing distance between values, in which the feedstocks with PVA have lower final torque values, e.g., 8.49 vs. 7.52 N·m at 50 vol % fibers in solid content. On the other hand, the effect of PVA sizing is not significant for kneading energies, yet the feedstock with PVA has, still, a lower kneading energy. The effect of PVA sizing can also be seen in the viscosity results (see Figure 11
The differences in viscosity results are prominent between two binding systems. PW-based feedstocks show very similar viscosities, where PVA sizing leads to a slight decrease compared to 0 vol % fiber variations. On the other hand, the PEG-based systems have lower viscosities, as a whole, and the viscosities decrease with increasing fiber content from 182.7 (0 vol %) to 69.5 (50+ vol % (“+” means fibers are used with PVA sizing)) Pa·s at 100 s−1
apparent shear rate within the group. Additionally, the effect of PVA sizing is also apparent in both systems, in which the sizing leads to a decrease in viscosity at different ratios, as shown in Table 5
. The PW-based systems show linearity in the viscosity measurements that caused the same percentage of decrease. On the other hand, PEG-based systems tend to change the slope with increasing shear rates, also with PVA sizing. Additionally, it must be considered that the amount of PVA increases with increasing fiber content.
Consequently, the binding system defines the flow characteristics of the feedstock with the intrinsic viscosities and adhesion capabilities of the solid content. In this work, the PEG-based binding system shows lower viscosities than the PW-based system because of higher adhesion forces between the polar matrix of PEG/PVB and the solid particles (both fibers and powder), which probably made the decrease in viscosity recognizable by an increasing fiber content, which is not the case with PW-based systems. Additionally, the sizing on the fibers improves the flowability of feedstocks during mixing and rheological investigations.
3.4. Effects of Kneading Time, Temperature, and Binding System on the Fiber Length
The feedstock preparation steps definitely have an effect on the fiber length. This becomes apparent due to the applied stresses on the fibers and particle–fiber and fiber–fiber collisions, especially during kneading. Through several kneading sessions, the PW-based feedstocks with 30 and 50 vol % fibers in solid content under kneading conditions as in Table 2
, and PEG-based feedstocks with 30 and 50 vol % fibers in solid content for 30 min at 125 °C, were compounded. The fiber lengths were measured on the images of lightly pressed specimen from each variation, as shown in Figure 12
Along with fiber length measurements, the effect of PVA sizing was investigated qualitatively on the same images. The fibers were produced and delivered in bundles with PVA, as shown in Figure 13
; the PVA grade is kept secret by the company. As a result of this, the material properties of PVA, e.g., the melting temperature which is normally in the range of 150 to 230 °C, are unknown. The compounding temperature of 125 °C is normally not enough to melt the sizing, and could lead to fiber bundles being preserved and orientated as clusters (see Figure 14
). Analyses of the images showed that the fiber clusters or bundles were dispersed and relatively homogeneously mixed with the binder. The reason could be that the mixing temperature was high enough to soften the PVA and, together with the physical load in the mixing chamber, the PVA could not hold fibers together anymore and was mixed with the binder.
demonstrates the mean values of fiber lengths with standard deviation versus feedstock and process parameters, including fiber content, presence of fiber sizing, kneading temperature and time, and alternative binding system. The maximum and minimum fiber lengths were also added to the diagram for comparison. In general, the concept of kneading ruptured the fibers from 3200 µm to ~300 µm, which were also in the region of 50 to 500 µm, as given in the literature for injection molding of short fiber-reinforced polymers [8
]. This led us to expect further breakage during injection molding down to 100 µm or lower. It is also noticeable, for both binding systems, that the increase in fiber amount lead to a decrease in fiber length, from ca. 300 to 200 µm. However, the fiber lengths are slightly higher in PEG-based systems. On the other hand, increased kneading temperature and time show almost no effect on the fiber length. For these reasons, the processing parameters were fixed at 125 °C and 30 min kneading temperature and time during feedstock production for injection molding experiments.