Estimation of apparent permittivity value of polylactyde polymers using reflectrometric technique

This work deals with the estimation of the apparent permittivity value of PLA polymers using the reflectometric technique. Physical and chemical properties of polylactide are discussed. Test samples were prepared using 3D and FDM printing technology. The samples were examined using a time domain reflectometry multimeter, and then the obtained results were analyzed. The work was summarized with final conclusions.


Introduction
The availability of production materials on the market is increasing.Along with the development of modern manufacturing technologies, one can notice a great interest in emerging research on the strength of these materials or their chemical properties.Currently, all kinds of polymers are used to produce many things.They are widely used in 3D printing in the FDM (Fused Deposiotion Modeling) method [1,2].Polymers are the substances with a very high molecular weight, consisting of multiple repeating units.There are the polymers that are fully biodegradable.These include the group of polylactides, which are classified as aliphatic polyesters.It is worth noting that PLA (polylactide) is obtained from natural raw materials [3,4].PLA is obtained by lactide ring-opening polymerization or by polycondensation of lactic acid.In the process of fermentation of plant materials, lactic acid is formed, which is first oligomerized in the polycondensation reaction, and then in the dehydration reaction, a cyclic dimer is formed, which is polymerized in the ROP (ring opening polymerization) reaction [5].The ring-opening polymerization can be carried out in solution, bulk, melt and suspension.It is assumed that the mechanism of this polymerization reaction may be cationic, anionic, coordination or also radical [6].The polylactide chain in shown in figure 1. Due to the catalysts used in its polymerization, polylactide can be isotactic or atactic.In terms of properties, PLA is similar to polystyrene, however, when modified, it has properties similar to polypropylene and polyethylene.PLA as a polymer has the ability to crystallize by stretching, to crystallize with temperature, which allows you to modify its impact strength, copolymerize and process on most processing equipment [7].It has excellent organoleptic properties.PLA can also be used in contact with food.In 3D printing, PLA is used to create 3D models [2].Thanks to the many possibilities of modification, it is also given different colours, which diversifies selected 3D prints.Since it is an improved material, its properties are being studied.There is little information in the literature about the apparent permittivity of PLA.In order to check this property of the material, this work focused on making measurements using the reflectometric technique.

Autodesk Inventor 2023
The Autodesk Inventor 2023 program was used to model the sample.This software is an example of a solid modeler.On the basis of 2D sketches made in this program, you can make assemblies, illustrative drawings, and above all, a 3D model.It is also possible to prepare 3D models for an.stl file dedicated to a 3D printer [1].The program can import CAD files with the.dwg extension.Working files are saved in.ipt format.MES (Manufacturing Execution System) strength analysis can also be performed in Inventor.This analysis is based on the ANSYS solver.
The basic modules of the program are: The downside of the software is that it is only functional on Windows.There is currently no program for macOS.The .ipt module was used to prepare the sample.
In the Autodesk Inventor program, a model of the sample for reflectometric tests was prepared.
A cylinder with a diameter of 5 cm and a length of 11 cm was modelled using a circle with a diameter of 50 mm.2D sketch for model is presented in figure 2..The 3D model extruded to a height of 11 cm is shown in figure 3.

Creality Slicer
Then, in the Creality Slicer software, a gcode file dedicated to 3D printing was prepared.Layers have been cut.The fill of the model was set to 100% and the layer thickness to 0.2 mm.Creality Slicer is software dedicated to 3D printers by Creality.The 3D printer on which the sample was printed is Ender 3 V2.The view of the model in the slicer is shown in figure 4.

PLA materials
The filament, Stone PLA, which is an imitation of stone, was used for the research.It is characterized by very good masking of layers, and the printed elements have a roughness similar to real stone.The key features of studied material are a beautiful, aesthetic stone imitation or the ability to mask layers.The material is not abrasive and has high stiffness of the elements.After cooling down the sample follows no shrinkage.The properties of the material are given in table 1.

3D printers
Ender 3V2 -Creality printer was used for 3D printing.The Creality Ender-3 v2 printer has a table with a working area of 220 x 220 x 250 mm 3 .The total size of the 3D printer is 475 x 470,620 mm 2 .The table platform heats up to a maximum temperature of 110°C in 5 minutes.The basic variant, the Ender 3 printer, is designed to work with PLA, as well as TPU, gradient and carbon-enriched filaments.The maximum print speed ranges from 100 mm/s (Creality Ender-3 V2) to 180 mm/s (Ender-3 and Ender-3 Pro).The printer is controlled via LCD displays, with the Creality Ender-3 V2 3D printer featuring a 4.3-inch color graphic display.The thickness of the layer can be from 0.1mm to 0.4mm, and the printing precision is 0.1 mm.The printer supports filaments with a diameter of 1.75 mm.Stable operation of the device is ensured by a 24 V power supply, which is rare in this price range.In the figure 5 shows process of printing sample.

TDR multimeter
The study used the TDR multimeter with an invasive probe FP/mts.TDR multimeter was produced by ETest manufacturer, Lublin, Poland [8].It was emitting needle peak signal with rise-time equal 300 ps.
During reflectometric measurements, a signal is emitted propagates along the coaxial cable to the sensor where reflections occur on the characteristic points of the propagation line.Those reflections come from both the beginning of the sensor and its termination and they the serve as the measurement markers.Important is time difference between those reflections returns to the TDR meter and can be automatically or manually recalculated into the apparent permittivity value.

FP/mts probe
FP/mts probe is invasive sensor.Probe is shown in figure 6.Its main functional elements are the two 10 cm long sharpened acid-resistant steel rods (2 mm in diameter, separated by 14 mm), sensor support is made from a section of a PVC tube of 2 cm outer diameter and length from, and coaxial cable length equal 1.5 to 6 m from the sensor to the terminating SMA connector [8].The FP/mts sensor is primarily intended for measuring building materials.In order to study the PLA sample in this work, special holes had to be drilled so that the probe could be fully inserted into the sample.

Methods
The tests consisted in measuring the apparent permittivity of a dry material made of PLA.Measurements were made on one dry sample (5 readings for statistical purposes).The tests were carried out in constant conditions of temperature (20 °C) and relative humidity (50%).
The FP/mts invasive probe was introduced into the structure of the tested material [9].The sample adhered perfectly to the probe.FP/mts probe in PLA sample is shown in figure 7.

Results
In connection with the conducted measurement tests, the following results were obtained.Table 1 presents the results of measurements of the PLA sample using the TDR invasive probe.
The dielectric permittivity of a porous material is determined by the formula [10,11]  In measurement practice, we use the following relationship: where: tptime of signal propagation along the measuring probe rod determined with the TDR meter [s], Lprobe length [m].Specifying the number 2 in the denominator is necessary because the electromagnetic pulse propagates along the rod in both directions and this time of flight is measured by a reflectometric meter.
The permittivity of studied material was 2.12.Detailed measurement results are presented in table 2. Measurements were made five times.The standard deviation was approximately 0.03.Tables 3 and 4 present measurements of water and air.Apparent permittivity for air is 1.16 and for water is 79.5.The tested polylactide showed a permittivity of 2.12, while other plastic materials that are present on the market, e.g.polymethylene oxide, have a permeability of 3.8 [11].For comparison, photopolymer has a dielectric constant of 2.00 to 3.10 [12].

Conclusion
Polylactide is a very good material.It is fully biodegradable, which helps protect the environment, and if studied material gets into the soil, it does not threaten the long decomposition process.It is possible to test the permeability of materials used in 3D printing.As a result of the measurements, the permittivity of PLA with properties similar to the stone structure was measured.The measurement was performed five times.The air and water permeability test showed values close to the relative tabulated values.The electrical permittivity of the considered measured polylactide is very low.It was 2.12.The sample was set to 100% filling without passing other factors.Perhaps this has an impact on the final permittivity result.The obtained permittivity for a given polylactide is similar to Teflon.In the future, it is planned to consider samples with less filling.The value is favorable from the point of view of the construction of potential TDR sensors and studied material can be used for their construction.

Figure 4 .
Figure 4. Model 3D in the slicer
dielectric permittivity of the tested material [-], cthe speed of light in a vacuum [3•10 8 m/s], Vpropagation speed of the electromagnetic pulse along the measuring rods [m/s].

Table 1 .
Properties of stone PLA

Table 2 .
Measurement of PLA sample

Table 3 .
Measurement of water

Table 4 .
Measurement of air