The main reason of the low exploitation of FFF multi-material approach to the monolithic fabrication of bendable coplanar capacitive sensor lies in the difficulty to print, with this technology, conductive tracks with a high level of details, that is very thin tracks and really close each other. Low detail levels are related to low capacitance, which is difficult to be measured by common measurement instrumentations. To obtain thin and close tracks, i.e. high capacitance, the Design for Additive Manufacturing (DfAM) approach was used, and several considerations have been pointed out, in order to overcome some typical issues related to the extrusion of conductive filaments.
Two versions of the sensor were manufactured: the main difference between them concerns the top coverage (in the first version it is missing, whereas in the second one it is embedded).
2.1 Design
Two versions of the capacitive, coplanar sensor were designed and manufactured: the first version named “Uncovered” consists of a flexible substrate and two coplanar electrodes, the second version named “Covered” consists of the same two elements of the first one more a top coverage which seals off the electrodes. Basically, after the manufacturing, the “Covered” sensor, is ready to be used, the “Uncovered” sensor, instead, needs a further manual task: a sealing adhesive tape was glued on the top of the sensor to isolate the top electrodes from the surrounding environment.
All the elements shared by the two versions are characterized by the same dimensions. The substrate dimensions are 55 mm and 171 mm along x- and y-axis (see Fig. 1), while the width of the substrate is 0.4 mm.
The design of the electrodes is a crucial point to obtain a measurable capacitance value. In fact, the thinner and closer the electrodes, the higher the capacitance is, but, at the same time, technological (FFF) constraints must be taken into account when conductive filaments are extruded. In accordance to [16] the capacitance of the coplanar capacitive sensors is defined by the following equation:
![](data:image/png;base64,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)
where\(C\) (\(pF\)) is the capacitance of the whole sensor, \(N\) (dimensionless) is the number of electrodes pairs, \(l\) \(\left(mm\right)\) is the length of each electrode along x-axis,\({\epsilon }_{0}\) is the vacuum dielectric constant \(\left(\frac{pF}{mm}\right)\), \({\epsilon }_{ea}\) (dimensionless) is the effective dielectric constant of capacitive sensor in the air (further details about this parameter are well explained in [16]), and \(K\left({k}_{0}\right)\) (dimensionless) is the elliptical integral of the first kind in terms of \({k}_{0}\), where \({k}_{0}\) is defined as follows
![](data:image/png;base64,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)
where \(s\) (\(mm)\)and \(w\) (\(mm)\)are the electrodes spacing and width, respectively.
Thus, the only design parameters that can be set in order to maximize the final capacitance are \(N\), \(l\), \(s\) and \(w\) (see Fig. 1).
As a matter of fact, the free design variables are the \(l\) parameter (length of the single electrode along x-axis) and the active electrodes length (along y-axis), which have been suitability set as 25 mm and 150 mm, respectively. Consequently, considering all the manufacturing constraints (detailed in Sect. 2.1), it was found that the best \(N\), \(s\) and \(w\) values to maximize the final capacitance were 57, 0.8 mm and 0.4 mm, respectively.
In particular, the DfAM approach was used to successfully set \(w\): considering the printing orientation (sensor flat over the build plate with flexible substrate in contact with it), \(w\) parameter depends on the line width process parameters, which in turn depends on the dimension of the nozzle. From Eq. (1), the need to minimize \(w\) stands out, but this is in contrast with the processability of the conductive materials ( the bigger the nozzle, i.e. from 0.6 mm up to 1 mm, the less are the printing issues such as filament breakdown and coggled nozzle): by setting further process parameters (detailed in Sect. 2.2) it has been possible to use a 0.4 mm nozzle and set \(w=0.4\) mm, i.e. a single extruded line. Similar considerations can be drawn for the \(s\) parameter: using a trial-and-error approach it was found that the minimum spacing between two adjacent electrodes lines allowed by FFF machine for the conductive material and the 0.4 mm nozzle was 0.8 mm, lower values involved contamination (contact) among adjacent electrodes. The height of the electrodes was arbitrarily set as 0.8 mm, however lower values are allowed.
All the above mentioned features are common to both the “Uncovered” and “Covered” versions; the latter, in addition, presents a 0.3 mm thick top cover over the electrodes made of the same material, i.e. thermoplastic polyurethane, used for the flexible substrate (see Fig. 2). Moreover, both sensors were equipped with two square pads (side equal to 10 mm) to weld electrical wires, to connect the sensors to a benchtop digital multimeter or a read-out circuit.
2.2 Additive Manufacturing
The two versions of the sensor have been fabricated in a monolithic way, exploiting the advantages of the FFF technology. A multi-material FFF 3D printer (Ultimaker 3, Ultimaker, Netherland) and two commercial materials were used. For the flexible substrate (and top coverage of “Covered” version) a commercial flexible thermoplastic polyurethane was employed, namely the red color Ultimaker TPU,with shore A hardness equal to 95 (henceforth called TPU), characterized by a tensile modulus of 26 MPa and an elongation at break of 580%; whereas for the electrodes a commercial conductive polylactic acid (PLA)- based filament was employed, doped with carbon black and carbon nanotubes (CNTs), and characterized by a resistivity of 15 Ω · cm along the layers and 20 Ω · cm perpendicular to the layers, namely the AlfaOhm by FiloAlfa (Italy) henceforth called AlfaOhm. All technical data are reported on the data sheets of that materials. For TPU and AlfaOhm, 0.8 mm and 0.4 mm nozzles were used, respectively.
As a matter of fact, the smaller the nozzle size is, the more the level of detail is: when conductive materials (generally PLA-based doped with CNTs) are used, the general advice provided by filaments suppliers is to use nozzles with dimensions larger than 0.6–0.8 mm. The main problem which could occur when nozzles smaller than 0.6 mm are employed is the filament breakdown between the gears which push it into the extruder; in fact, the doping elements (i.e. CNTs) make the filament very brittle.
As demonstrated in Percoco et al [21] in 2021, the reduction of the total force (inside the nozzle + counterpressure) is the key to overcome filament breakdown between the gears: by reducing the total printing force, the pushing force of the gears on the conductive filament will be reduced too. The main process parameters affecting the total force are layer height and printing temperature: when they increase, the total printing force decreases. Both these process parameters are the key enablers to obtain high level of details with a brittle filament such as TPU doped with carbon nanoparticles and nanotubes, allowing the exploitation of 0.4 mm nozzle. Hence, in this case the exploitation of 0.4 mm nozzle is allowed by setting the layer height parameter as 0.2 mm, unlike the classic printing scenario, in which high details are reached setting a low value of layer height (i.e. 0.05 mm) [22]. Moreover, the printing temperature of the conductive filament was set to 225°C, higher than the suggested printing temperature range of 190–210°C provided by the supplier. By setting the above mentioned process parameters (layer height as 0.2 mm, and printing temperature as 225°C), it has been possible to use 0.4 mm nozzle and create electrodes with a width ( \(w\) parameter in Sect. 2.1) equal to the nozzle diameter, i.e. 0.4 mm, without any filament breakdown despite a huge number (more than 20) of consecutive printed sensors.
In Table 1 the main process parameters for both the materials are summarized.
The total cost of the “Uncovered” and “Covered” sensor, estimated by the slicer (Ultimaker Cura 4.6) was 0.27 € and 0.38 €, while the printing time was 42 minutes and 56 minutes.
Figure 3-a) shows the proposed sensor during the 3D printing.
Table 1
|
TPU
|
AlfaOhm
|
Nozzle size (mm)
|
0.8
|
0.4
|
Layer height (mm)
|
0.2
|
0.2
|
Printing temperature (°C)
|
223
|
225
|
Line width (mm)
|
0.8
|
0.4
|
Printing speed (mm/s)
|
30
|
25
|
Flow (%)
|
106
|
110
|
The core difference between “Covered” and “Uncovered” sensor is that the first one can be employed without recurring to any further post-processing, while the second one needs to be sealed in order to isolate the electrodes from the surrounding environment. For the “Uncovered” version, a common adhesive tape was manually glued on the top. A not negligible advantage of the “Covered” version concerns the total absence of the necessity to seal the electrodes, which may require further post-processing such as coating, often a manual task strongly related to operator’s skills [23], [24]. In Fig. 4 the two manufactured versions are shown.
Another main benefit of these kinds of 3D printed capacitive sensors is their flexibility (see Fig. 3-b)): they can be easily attached to irregular and non-conventional shapes paving the way for their exploitation in the field of the wearable sensors.
Finally, to prove the manufacture method robustness, 10 samples of each version have been printed, carrying out the following conclusions: i) no filament breakdown occurred, and ii) for “Covered” and “Uncovered” versions, the mean capacitance value (calculated after the manufacturing and the manual tape attachment, respectively) was 0.1517 nF and 0.1542 nF with a very low standard deviation of 0.0007 nF and 0.001 nF respectively, due to not uniform electrical resistance of the raw conductive filaments (before of being melted into the nozzle) and noise effects occurring during the printing such as vibrations, room conditions etc.