Dielectric spectroscopy of PETG/TiO2 composite intended for 3D printing

ABSTRACT
 3D-printed electronics belong to new approaches to how to build a complex object with multiple desired functions. For that purpose, materials with specific electric properties are needed: conductors, insulators, magnetics, or dielectrics with high permittivity. However, such materials are not commonly available in the form of filament for fused deposition modelling since the development is still ongoing. This paper describes the electrical properties of PETG-ceramic composite filaments. PETG (polyethylene terephthalate glycol-modified) was filled with titanium dioxide (10 and 20 wt.%) to increase the dielectric constant and, simultaneously, to preserve printing simplicity as the material key advantage. Dielectric spectroscopy and measurement of volume resistivity were performed on printed samples. Relative permittivity increased by 50% for a composite filled with 20 wt.% of ceramic particles (ϵr  = 2.5÷4.4) against pure PETG. Permittivity and dielectric loss exhibited frequency and temperature independence. The prepared composite can be used for dielectric applications in electronics.


Introduction
3D printing has become a very popular process in the field of producing physical parts.Additive manufacturing (AM) allows building models beforehand designed in computer software in a relatively short time.The model is transformed into a tangible product by layering the chosen material using one of the available AM techniques.Fused deposition modelling (FDM) based on extruding the thermoplastics or stereolithography utilising photoreactive resin are methods falling under the umbrella of 3D printing technology.FDM printers are classified as low-budget and technologically most accessible from the user's point of view (Rahim, Abdullah, and Md Ail 2019).They consist of an extrusion heated head that is equipped with a filament feeder.The filament is melted and passes through the nozzle.The desired object is created on the heated platform layer by layer.Many printing parameters, such as infill ratio, working temperatures, number of perimeters, nozzle speed, etc., can be adjusted, thereby influencing the thermal and mechanical properties of the resulting object (Canessa, Fonda, and Zennaro 2013;Trhlíková et al. 2016;Ning et al. 2017;Ngo et al. 2018;Wongwisitchai, Hongsriphan, and Patanathabutr 2018).In addition, (Goulas et al. 2019) reported the impact of printing adjustment on the dielectric parameters of printed samples using composite filament.FDM printing technique also offers to locally control the capacitance of the printed structure by infill ratio (Tomassoni et al. 2016;Massoni et al. 2017).
FDM provides fabrication of objects using polymers that can be melted, deposited with appropriate viscosity to adhere, and then solidified again while keeping the original properties.Favoured thermoplastics applicable for FDM are polylactic acid (PLA), polyethylene terephthalate glycol-modified (PETG), acrylonitrile butadiene styrene (ABS), polycarbonate (PC), and polypropylene (PP) (Ngo et al. 2018;Shahrubudin, Lee, and Ramlan 2019).Acrylonitrile styrene acrylate (ASA) is another promising material capable of replacing ABS since it has better thermal properties and is more resistant to UV irradiation (Afshar and Wood 2020;Kalaš et al. 2021).Printed products are usually compared to those obtained by injection moulding.Certain drawbacks of FDM have been pointed out.The missing pressure during printing brings about weakened mechanical properties (Dawoud, Taha, and Ebeid 2016).Moreover, the mechanical endurance varies according to the printing direction.The anisotropy behaviour must be evaluated in terms of product deployment.FDM printed parts are also prone to moisture absorption because of the high porosity rate.These two concerns may be successfully eliminated by utilising some of the post-processing techniques (Tamburrino et al. 2021).
Printed parts of neat polymers have advantageous electric properties inherently.For instance, they may directly serve as electric insulators since the volume and surface resistivity of the parts printed from the most used polymers ranges in the interval of 1 × 10 15 -1 × 10 18 Ω•cm as reported by (Kalaš et al. 2021).The incorporation of some filler can successfully achieve a shift to a broader spectrum of utilisation in electronics.New areas of application of printed parts arise from employing conductive filaments.Enriching the polymer matrix with metal particles leads to a transformation from an insulating character to a conductive mode.The exact implications are delivered by the addition of carbon modification, such as carbon black, carbon or graphene fibres (Lamberti et al. 2018;Horst et al. 2020;Tirado-Garcia et al. 2021).The development of conductive filaments allows substituting inks and pastes to establish conductive traces.Conductive composites with higher resistivity are applicable in resistive traces and components.
The high potential of FDM lies in the preparation of ceramic filament composites filled by particles based on perovskite structure characterised by ferroelectricity property.These composites may be suitable for printing functional components in electronic devices like transducers, sensors, and capacitors.In the case of capacitors, the aim is to produce a filament with high dielectric constant (relative permittivity) that would be predominantly independent of temperature and frequency.Examples of possible materials employable for FDM dielectric composites are lead zirconate titanate (Pb[Zr x Ti 1-x ]O 3 , 0 ≤ x ≤ 1), lead magnesium niobate (MgNb 2 O 9 Pb 3 ), strontium titanate (SrTiO 3 ), or barium titanate (BaTiO 3 ) (Şakar-Deliormanlı, Çelik, and Polat 2008;Cholleti 2018;Fu et al. 2022).The last-mentioned inorganic compound is preferred on account of environmentally friendly attribution with excellent dielectric properties, while the two former listed compounds are adequate for piezoelectric purposes.(Khatri et al. 2018) examined ABS/BaTiO 3 composite up to 35 vol.% (74.2 wt.%) of filling ratio.At maximum filling, the permittivity increased four times.The same composite with a maximum loading of 70 wt.%was tested by (Castles et al. 2016).The permittivity reached the value of 8.7 at the highest incorporation ratio of BaTiO 3 .(Wu, Isakov, and Grant 2017) utilised surfactant and plasticiser to facilitate the distribution of BaTiO 3 micro-particles in ABS and reduce the void occurrence.After optimising the additives, they testified permittivity of 11 for composite containing 32.5 wt.% of BaTiO 3 .
A disadvantage of ceramic composite deployed for dielectric applications is the declined efficiency because the permittivity of the filler embedded in a polymer matrix is strongly attenuated.Furthermore, the dispersion of the added particles is required to be homogenous without significant agglomerations (Carthy et al. 2009).An efficient way to achieve that is through the functionalisation of the particles (Roberson et al. 2015).Despite uniformly distributed particles, mechanical and functional properties are usually worsened.Deterioration of mechanical properties has been confirmed by our investigation in the already published study focused on the same composites as evaluated here (Froš and Veselý 2022).Likewise, (Torrado et al. 2015) ascertained the mechanical weakening upon titanium dioxide (TiO 2 ) incorporation into ABS.
In this work, TiO 2 in the form of rutile was incorporated into PETG to enhance dielectric properties.Rutile comprises two TiO 2 units in the tetragonal crystal lattice.Overall, the dipole moment is zero due to the symmetrical lattice structure.Therefore, rutile is ranked as a non-polar dielectric, which induces stability of permittivity magnitude through a wide range of frequencies (Marinel et al. 2013).This property, in conjunction with the low loss factor, makes the TiO 2 promising material that is intensively studied as potential excellent material for preparing dielectric ceramics, coating, etc. (Noh et al. 2006;Noh et al. 2007;Liu et al. 2020).Comparing frequently mentioned BaTiO 3 and employed TiO 2 , dielectric linearity favours TiO 2 over BaTiO 3 .Furthermore, BaTiO 3 exhibits Curie temperature at 115°C and undergoes a phase change.It may cause trouble when using the compound in production processes in which the stated temperature is reached.
The relative permittivity of pure TiO 2 takes on the value of 15-170, and the loss factor is 0.0016 under standard temperature conditions and a frequency of 1 MHz, as reported by (Richerson and Lee 2018).Considering the study conducted by (Li et al. 2014), attributes governing the relative permittivity include porosity, purity, suitable dopants, temperature, and time of the sintering process.
PETG is derived from PET by glycol modification to reach better processability via FDM.Recycling PETG is feasible (Latko-Durałek, Dydek, and Boczkowska 2019).Hence this copolymer belonging to the polyesters group is favourable from a sustainable point of view and, thereby, future utilisation.According to (Vidakis et al. 2021), PETG does not show significant deterioration of mechanical and thermal properties after several recycling processes.A combination of described materials has not been yielded in any published research except for (Jiao et al. 2014), who utilised TiO 2 for FDM, but the polymer matrix comprised in the composite is not specified in the study.Furthermore, our study is extended by comparing the experimental results with those received from various mathematical models.
A lot of applications like capacitors for A/D converters, filtration capacitors, or dielectric resonation antennas can be listed for potential utilisation of dielectric composite.Moreover, the composite can possible be deployed in energy storage facilities in various applications or sensors (Barber et al. 2009;Zha et al. 2021;Yang et al. 2022).For instance, based on comparatively high dielectric constant and breakdown voltage (Marinel et al. 2013) (more than 100 kV/cm), TiO 2 is potentially suitable for high energy and voltage applications in combination with PETG printed by FDM.(Veselý et al. 2018) reported break down voltage approx.300 kV/cm of product made by the combination of PETG material and FDM method.For all mentioned applications, many composites have been developed and tested but they are not qualified for FDM.Hence, research on dielectric composites printable via FDM as one of the most common AM techniques is relevant.

Materials
The composite filament was prepared in cooperation with the company Prusa Polymers (Czech Republic).As a polymer matrix, polyethylene terephthalate glycolmodified (PETG) was used.TiO 2 particles (ca.50-300 µm) in the form of 'sand' powder of natural rutile mineral (supplied by A.C.I.Trading, Nicosia, Cyprus) were compounded with PETG pellets and melted.The melted batch was homogenised by mixing auger prior to extrusion into uniform granules.Subsequently, the final filament of a precisely defined diameter of 1.75 mm was extruded from the granules employing a heated screw extruder.During cooling in water tubs and winding, the filament's diameter was checked by a laser sensor in two perpendicular axes a few times per second.According to the signal from the sensors, the speed of winding is modified to ensure that the diameter falls within a range of ±0.02 mm.Larger particles were chosen to avoid problems with their agglomerations that may occur in the case of single-microns or nanometric dimensions.Two composite filaments were fabricated, varying in the weight content of TiO 2 particles -10 and 20 wt.%.We chose the weight ratios after literature research, testing experiments, and production possibilities.The filling ratio of 20 wt.% was found as the maximum that did not cause any production and printing difficulties.As a reference, a neat filament was also included in the study.The properties of the neat PETG filament are listed in Table 1 in reference to the technical datasheet by the filament producer (Prusa Polymers 2022).The images of extruded FDM filaments can be seen in Figure 1.
For the measurement of dielectric properties, the samples printed from the filaments were cylindrical shaped with a diameter of 19.1 mm and thickness of 2.8 mm (design A), respectively, 9.5 and 3 mm (design B), depending on the measurement method described in the following chapter 2.2.Twelve samples were prepared for each variant (neat polymer/ composite with 10 wt.% of TiO 2 / composite with 20 wt.% of TiO 2 ).

Samples preparation
The samples were printed by i3 MK3S Printer (Prusa Research, Czech Republic).Detailed information about the printer settings is listed in Table 2.The infill ratio of the printed samples was set to 100%.Reducing the infill ratio would imply lower capacitance and dielectric losses of the samples due to air gaps within the  volume of the samples (Tomassoni et al. 2016).Six samples per variant were printed with the device placed outside the enclosure and used for the main results from the dielectric spectroscopy.Another six samples were printed inside the enclosure to evaluate the enclosure utility in terms of monitored parameters.
The printed samples are portrayed in Figure 2.
Besides the printed samples, we prepared one sintered sample from the ceramic powder used for PETG filling.The sample had a cylindrical shape with a diameter of 18.6 mm and a thickness of 4.9 mm.The sintering process is described in Table 3.This sample was used to measure the relative permittivity (ε r ) of TiO 2 powder in order to attain reference parameters for mathematical modelling.

Visual evaluation
After printing, the visual analysis was performed employing a scanning laser confocal microscope (SLCM) VK-X1000 (Keyence, Japan).From this analysis, the particle distribution and size were obtained in the polymer matrix employing image processing by ImageJ software.Furthermore, surface roughness (expressed by R athe average height of the surface profile) was determined for each type of filament according to the ISO 4287 standard.

Measurements of electrical properties
Prior to electrical measurements, a thin film electrode system was created by physical vapour deposition of aluminium that complies with the ASTM D150 standard.
LCR meter E4980AL (Keysight, USA) combined with a unique electrode system compatible with A-design specimens was adopted for low-frequency (LF) spectroscopy in the range of 20 Hz-1 MHz.High-frequency (HF) measurement in the range of 1 MHz-3 GHz was performed by impedance analyzer E4991 (Keysight, USA) in another electrode system for B-design specimens.The applied measuring AC voltage was 1 V in both cases.The electric field was applied along the Z axis related to the printing process (i.e.perpendicular to the substrate surface).A relative permittivity (ε r ) was calculated    from the sample's measured capacity and geometrical dimensions.Further, the loss factor (tanδ) was measured utilising the same equipment.The measurement workplace is depicted in Figure 3. Furthermore, the temperature dependence of relative permittivity and loss factor was analysed in the range of 25°C-60°C at measuring frequencies 1 kHz, 1 MHz and 1 GHz, using the equipment listed above.Controlled heating was provided by a Novotherm Heating Unit 2108 (Novocontrol Technologies, Germany).
DC resistance of the samples was measured in a special resistivity adapter 6105 by electrometer 617 C (both Keithley, USA) with an applied voltage of 100 ± 2 V.The resistance measurement was conducted inside the Novotherm oven, serving as a Faraday cage with the purpose of eliminating the parasitic phenomena.The measurement of each sample lasted for 30 min to ensure that polarising processes were stabilised and did not affect the measured values.Subsequently, the volume resistivity was calculated from the obtained resistance value and dimensions of the specimen.

Porosity determination
The approach utilised for porosity w A determination is based on Archimedes' principle (Song et al. 2018).The method is based on saturating the pores with liquid.Deduction of porosity is feasible if the volume needed for saturation of the porous material is known.The following equations were involved in the porosity calculation.At first, the density of samples (ρ S ) was determined according to (1).Then using (2), the porosity (w A ) was calculated.
where w D is the sample weight in a dry state, w W is the sample weight in the water, ρ F is the density of filament, and ρ W is the density of pure water.

Effect of TiO 2 particles incorporation on polymer matrix structure
The distribution of particles through the material is a crucial factor influencing the overall dielectric properties.Therefore, a visual evaluation of the printed samples was performed.In Figure 4, samples of neat PETG and PETG filled with TiO 2 particles are depicted.
The images obtained by SLCM demonstrate homogeneous dispersion of the incorporated TiO 2 .Further, we verified the particle size as described in the previous chapter (2.2). Results in the form of probability density function showing average values of six samples for both filling ratios are presented in Figure 5. Included vertical dashed lines determine the IQR (Interquartile range).Uniform distribution of particle size for all samples was attained.The grain size distribution in all samples is mostly symmetrical around the mean value according to obtained curves for individual samples.
The effects of added particles on density, porosity, and roughness were also analysed.All these parameters are summarised in Table 4.Even the 100% fill factor does not ensure the non-porous product, as the 2.3% porosity for pure PETG printed samples was calculated by adopting the Archimedes method.Further, the increase of porosity for filled variants was proved.The main attributes contributing to the porosity magnitude in pure PETG samples were the areas at the interface of the shells determining the circular shape of the sample and adjoining the infill pattern that created the volume.In the enriched samples, the particles constrained the proper adhesion of the adjacent layers, and consequently, the air pockets were entrapped in the samples during printing.The density of the assessed samples was increased when the content of the TiO 2 was higher.The roughness of the specimens is, on average, nearly 30% higher for composite than for pure polymer.In contrast, the difference between the composite variants is insignificant.
Surface roughness may cause uncertainty in the measured ε r magnitudes according to the following equation: where C m is the measured capacitance of the sample, C s is the actual capacitance of the sample, and C a is the capacitance of air space between the sample and the measuring electrode.Thus, the higher roughness implies lower ε r because of the air space and subsequently induces a distinct difference between the real and measured value of capacitance.

Frequency variation of dielectric constant and loss factor
An investigation of the dielectric constant against frequency is presented in Figure 6.The blue curve   represents the results for pure PETG polymer.The dashed lines stand for ε r standard deviation, calculated from six measurements.ε r slightly declines with rising frequency, and the decrease can be characterised as linear.Namely, ε r reaches 2.3 at a frequency of 100 Hz and terminates by 1.6 at 1 GHz.A discontinuity apparent at 1 MHz in the interval containing all measured values can be attributed to the replacement of the measuring apparatus.The same phenomenon appears at an average value too.However, both parts of the average curves link each other with high accuracy.
The orange curve represents ε r of composite filled with 10 wt.% TiO 2 .The relative permittivity increased by 0.4 compared to neat polymer.Also, ε r magnitudes are not affected by unequal particle size distribution.The statement arises from a very narrow interval of measured values, especially in the low-frequency range.Moderate disconnection of the permittivity curve at 1 MHz can be seen when changing the equipment.
Admixing of 20 wt.% TiO 2 led to further improvement of the permittivity.The course of frequency dependence is expressed by the dark red curve.ε r with this TiO 2 content is about one time higher than that for pure PETG.Thus, the relative permittivity was enhanced by 50%.
Another fact arising from the uniformity and low variance of ε r values is the possible change of material behaviour that suggests the inclination to crystal rather than amorphous polymer material.At higher frequencies, the relative permittivity varies more noticeably because the measurement is influenced by external effects relating to the inductance of the connection terminals.
The dependency of the loss factor on frequency is shown in Figure 7.The loss factor curve for a neat polymer (the blue one) can be broken down into three sections.The first section ranging from 100 to 1000 Hz, is typical for the variability of the loss factor resulting from external disturbances.The second part terminating at 10 MHz includes a gradual increase of loss factor with the greatest value at 1 MHz.Then, tanδ slightly falls to the border of this section.At the end of the monitored frequency interval (approx.at 0.1 GHz), tanδ begins to rise.Overall, the dielectric losses maintain in the range beginning at 0.003 and reaching 0.04 on average.
Results represented by the orange curve belong to measurement of the samples filled with 10 wt.% of TiO 2 .Tanδ versus frequency has a similar course as that for pure PETG.At high frequencies, adverse effects impacting the impedance values are also responsible for higher magnitudes of loss factor because it is inversely proportional to capacitance and resistance.The course of tanδ for the most embedded composite behaves similarly to the mentioned types formerly, but the variance of this dielectric parameter is attenuated.Presumably, it is due to the prevailing crystal character of the composite.
We cannot offer a direct comparison of our results with the other research articles due to the uniqueness of the prepared composite in conjunction with FDM.Hence, the discussion parts are committed in a more general manner.Our results regarding negligible frequency dependence are consistent with (Carthy et al. 2009), who performed dielectric spectroscopy on a composite comprised of TiO 2 micro-particles and poly (styrene-ethylene-butadiene-styrene).However, mentioned composite was created by the deposition of a thin layer.(Wu, Isakov, and Grant 2017;Khatri et al. 2018) also reported composite (ABS/BaTiO 3 ), whose relative permittivity is not appreciably affected by frequency.

Dielectric constant and loss factor temperature characteristics
Every sample type was subjected to evaluation of ε r and tanδ in dependence on temperature.Temperature characteristics of the relative permittivity that were collected for 1 kHz, 1 MHz, and 1 GHz are visible in Figure 8.It can be stated that the permittivity is independent of temperature throughout the whole measured range.Temperature independence is also valid in the case of filled PETG, which makes the composite favourable from the potential for applications in changing thermal conditions.
Figure 9 demonstrates the loss factor against the temperature.The behaviour was identical for all comprised samples.A slight distinction in the characteristics of the loss factor can be observed for the monitored frequency magnitudes.When tested at 1 kHz, the loss factor slightly decreases along the temperature range.The loss factor maintains at the same level regardless of the temperature during the measuring at 1 MHz.During testing at 1 GHz, a moderate increase in loss factor is recognisable.It is relevant to mention that dielectric losses are highest for the most filled sample at 1 kHz, but with the growing frequency, this specimen turns into the least loss dissipating version (0.02 at room temperature and 1 GHz).
The constancy of the relative permittivity regarding temperature was registered up to 60°C.It is an excellent property finding, but it can be presumed that with further temperature increment, ε r would change substantially.This assumption is supported by work conducted by (Sugumaran and Bellan 2014).Although they tested composite based on different polymer matrices and produced by dip coating, the results showed a tremendous rise of ε r with increasing temperature.

Implications of printer embedded enclosurepermittivity and loss factor
This part is designated for evaluating the dielectric properties of samples printed with an open printer and printer enclosed in the box.Enclosure adoption aims to reduce temperature gradients and possess homogeneous products with enhanced properties.The temperature stable environment with a higher average temperature level during printing may lead to better  adhesion of adjacent layers, thereby creating smaller air gaps among them.Furthermore, the enclosure is capable of creating a printing environment easier to reproduce.According to Figure 10(a-c), the enhancement in permittivity is observable, and the shift is about 1.However, an increase of 1.5 is achievable if we compare the maximal differences in permittivitythen, the maximum obtained value of relative permittivity was 4.4 for PETG doped by 20 wt.% of TiO 2 .As for the loss factor (see Figure 10(d-f)), the impact in the form of its higher magnitudes was detected.Especially starting at 1 kHz, the higher frequency, the more pronounced the difference is.

Porosity of printed samples
We examined the porosity of the samples prepared by the uncovered printer and equipped with the cover.Subsequently, the porosity figures were put into relation to permittivity.Regarding the porosity rate graphically  illustrated in Figure 11, we may say that the apparent influence of the enclosure was observed only for the neat polymer.Filled samples did not show a clear tendency of porosity appearance.However, the higher content of the ceramic admixture led to a higher porosity level.This is expectable because of many internal boundaries in case of a high quantity of the dopant.Although, the correlation of printer layout, porosity, and consequent implication toward dielectric constant value could not have been established.On the contrary, (Castles et al. 2016) reported the correlation of the porosity degree with the dielectric constant.Nevertheless, our results suggest a rather insignificant effect of porosity on the dielectric constant.

Volume resistivity of printed samples
Another evaluated parameter in connection with printer layout was volume resistivity.Experimentally acquired figures of resistivity are presented in Figure 12.
Apart from pure PETG, no crucial impact of the enclosure was identified.Pure PETG printed with a covered printer indicated a volume resistivity near the value of 20 GΩ⋅m.Referring to Figure 11, the positive change of resistivity is a definite consequence of porosity reduction.Perhaps, small voids in more porous samples are ionised during testing and make the polymer part more electrically conductive.

Theoretical models for dielectric properties estimation
Various mathematical models were selected, and their outputs were compared to measured values.At first, we introduce the used models.Then, the comparison in order to determine the model with the best agreement follows.Finally, that model is used for forecasting the permittivity with a higher filling ratio than those reported in this study.

Utilised models
The listed models consider material formed of two components.Table 5 offers a description of the parameters involved in the models.
Maxwell-Garnett equation reckons spherical-shaped dispersed particles in the polymer volume.This model neglects the resistivity of the composite components.Maxwell-Garnet equation is given below (Dang et al. 2012).
Jaysundere and Smith established a model that respects the interaction between the particles of the filler.Neglection of the interaction for the highly filled medium is not accurate since the distance between the particles is significantly diminishing.The Jaysundere-Smith equation marked as (5) arose from the calculation of electric field  Volume fraction of ceramic filling considering the dielectric sphere implanted in continual dielectric mass and the polarisation effect of surrounding particles (Dang et al. 2012).
Raleigh model, accessible in the literature by Raju, is a common tool for predicting the permittivity of the two-component compound.The model is based on the presumption of incorporation of cylindrical-shaped particles into the medium having the resulting permittivity according to the following relation (Raju 2017): Formula ( 7) is called Hanai-Bruggeman.The model's benefit is considering the proximity of the particles and their agglomeration.Model accuracy is assumed to be retained for the filling fraction volume of approximately up to 50% and under the condition of a non-crossed percolation threshold (Zhou, Hinojosa, and Nino 2012).
The last-mentioned Raju model deals with the prediction of the loss factor.The equation for estimating the loss factor is defined as follows (Raju 2017). tan

Inputs and acquired models
Input fractions of the admixed particles are necessary to be inserted in percentage by volume.For this reason, the fractions were recalculated from weight percent in conjunction with a known density.The filler loadings in PETG 10 and 20 wt.% corresponds with 4 and 9.9 vol.%, respectively.Table 6 summarises the permittivity and loss factor inputs respecting printer layout and working frequency.ε 2 and tanδ 2 refer to ceramic sample created by the sintering process.Thereby the arrangement of the printer is inconsequential for those values.
Comprehensive graphs in Figures 13-16 comprise measured values, estimated curves according to used models, and bounded area.Boundaries delineating the area result from parallel and serial models indicating the maximal and minimal obtainable magnitudes.Formulas describing these models are stated above ( 4)-( 7).The insets were provided to better compare specified models in the previous chapter.
Comparisons in Figures 13 and 15 that are valid for printer without enclosure suggest inclination of measured values to models by Maxwell-Garnett and Jaysundere-Smith.Note that the experimentally observed magnitudes follow the models with the sharpest curve rise.Another finding is related to unchanging behaviour for both tracked frequencies.Thus, these two models can be expected to be correlated with the measured dependencies for various frequencies.Figures 14 and 16 present the same evaluation with the distinction of printer arrangement (printing in the enclosure).Obviously, in view of the similarity of the measured values, the trend of following the Maxwell-Garnett and Jaysundere-Smith was maintained.Francis and Jain (2017) addressed inclusion of nano clay to ABS polymer with the intention of permittivity increment, and they also utilised empirical models for the comparative analysis.Maxwell-Garnett, Looyenga and Monecke formulas were all in good agreement with their experimental data.
Regards the loading of ceramic in polymer, the ultimate value is found to be around 35-40 vol.%.Already  cited (Khatri et al. 2018) reported printing concerns when loading was higher than mentioned 35 vol.%.Kurimoto et al. (2016) created functional composite acrylic/ Al 2 O 3 in which alumina formed 40 vol%.However, the composite was UV-curable resin based, thus intended for the SLA technique.
Figure 17 is the plot illustrating calculated tanδ values using ( 6) and values experimentally measured for 1 kHz and 1 MHz.Models obtained for 1 kHz indicate a moderate increment of tanδ with a higher TiO 2 filling fraction.In contrast to that, curves of 1 MHz predict a slight gradual descent of tanδ.Considering the results of Castro et al. (2017) and ours for 1 MHz, we suppose incorrectness of the model's outcome for the lower assessed frequency.The improper prediction of the model may originate from imperfect input values attained during the spectroscopy of sintered sample with a considerably porous structure (approx.20%) and grain size of about 20 μm.Such a structure is capable of affecting the tanδ adversely, as (Penn et al. 1997) corroborated.

Sensitivity analysis
Measured data correlates the most with the Maxwell-Garnet model.Therefore, we adopted this formula for the sensitivity analysis of the permittivity.An illustration of the analysis is visible in Figure 18, representing the dependence of obtainable ε eff on the inputting ceramic filler ε k lying within the interval <15;170> (interval boundaries stated according to [Richerson and Lee 2018]).Created curves for various filling fractions increment substantially up to ε k = 40.Then, the increase becomes almost imperceptible, especially in the case of a lower incorporation ratio.
Another fact that can be derived from the analysis is the higher sensitivity of resulting permittivity (ε eff ) on  the entering filler permittivity (ε k ) when the filler is represented with a higher fraction.Specifically, when the ratio is 5 vol%, the permittivity acquires a greater value by 0.2 over the whole analysed interval of ceramic material permittivity.Supplement of 20 vol% TiO 2 induces enhancement by 1. Besides, an impact of the frequency on the composite behaviour is evident for lower ceramic addition.With the highest studied ratio, the permittivity settled at a vicinity of 5.25 for both frequencies.
Figure 19 shows the prospective losses considering the change in ceramic permittivity.The differential behaviour of tanδ in terms of frequency is clearly demonstrated.In the case of 1 kHz, the losses rapidly descend with increasing permittivity of the filler.On the other hand, the dissipation of the composite at 1 MHz would not be touched by the filler permittivity as well as the filling ratio.It can be generally concluded that ceramic powder of superior quality, i.e. characterised by high permittivity, induces low losses (in order of thousandths) no matter the frequency and fraction volume.

Conclusions
In this work, a novel ceramic composite filament designated for FDM printing was prepared, and subsequently, the printed specimens were characterised via dielectric spectroscopy and measurement of electrical resistivity.By doping PETG with 10 and 20 wt.% of TiO 2 powder, the relative permittivity ranged between 2.5 and 3, which is a 50% increase compared to the neat polymer.Better results were achieved by printing in the enclosure, making the permittivity increase up to 4.4, which is the maximum value measured for PETG doped by 20 wt.%.The composite also exhibited frequency and temperature independence of the relative permittivity (in the range 10 2 -10 9 Hz).The loss factor was almost unaffected by TiO 2 incorporation.It exhibited a slight increment in the area of 1 MHz.However, the magnitudes ranged from 0.001 to 0.01 in the entire frequency spectrum.The volume resistivity of PETG did not significantly change with TiO 2 doping and was around 10 10 -10 11 Ω•m.The obtained  experimental results inclined the most to Maxwell-Garnett and Jaysundere-Smith's mathematical models.The presented composite could be further improved by a higher dotation ratio or the use of TiO 2 with higher permittivity.
Considering the advantages of FDM and current 3D printing materials enhancement, using the printed parts in electronic applications is feasible.Ceramic composite comprehensively tested in this paper could be utilised for dielectric applications such as capacitors for A/D converters, filtration capacitors, or dielectric resonation antennas.Using such material in conjunction with FDM opens up opportunities for the production of prototypes or small-batch products in a simple way.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This work was supported by the Internal Grant Agency of the Czech Technical University in Prague, grant number SGS22/ 054/OHK3/1T/13.

Notes on contributors
Petr Veselý is a researcher at Czech Technical University in Prague.His research activities include interconnections in electronics, in particular, soldering and related process issues, material diagnostics (microscopy, thermal analyses, mechanical testing), and additive manufacturing/3D printing (materials and technologies).
Denis Froš is a doctoral student at Czech Technical University in Prague.He studies the properties of materials used for fabricating printed circuit board substrates.His further research work focuses on the evaluation of technology and materials involved in 3D printing.
Tomáš Hudec studies at the Czech Technical University in Prague.His research is mainly focused on the dielectric spectroscopy of novel ceramic materials, as well as polymerceramic composites printed by the FDM method.
Josef Sedláček is an assistant professor at Czech Technical University in Prague.In research, he focuses on impedance (dielectric) spectroscopy of plasma sprayed ceramic materials and SPS materials and materials produced by additive manufacturing/ 3D printing.He also deals with the general diagnostics of materials for electronics applications.
Pavel Ctibor is a researcher at the Czech Academy of Sciences, Institute of Plasma Physics.Here, his work included plasma spraying and spark plasma sintering.He is also a lecturer at the Czech Technical University in Prague.His research on the dielectric properties of plasma-treated materials is an activity joining the field of interest of both institutions.
Karel Dušek is an associate professor at Czech Technical University in Prague.His current research interests include the reliability of electronic devices, diagnostic of material properties, manufacturing reliability, and manufacturing processes within electronics assembling.He has published 40 papers in impact journals in these fields of interest.

Figure 11 .
Figure 11.Porosity of printed samples in dependence on incorporation ratio of TiO 2 and printing environment.

Figure 12 .
Figure 12. Volume resistivity of printed samples in dependence on incorporation ratio of TiO 2 and printing environment.

Figure 18 .
Figure 18.Sensitivity analysis evaluating the response of composite permittivity when filler permittivity is modified for various volume incorporation ratios of TiO 2 .Plot (a) links to 1 kHz and (b) to 1 MHz.

Figure 19 .
Figure 19.Sensitivity analysis evaluating the response of composite loss factor when filler permittivity is modified for various volume incorporation ratios of TiO 2 .Plot (a) links to 1 kHz and (b) to 1 MHz.

Table 3 .
Settings of the sintering process.

Table 4 .
Summary of porosity, density, and surface roughness of printed samples.

Table 5 .
Meaning of quantities occurring in the equations of the models.

Table 6 .
Overview of specific values inputting the equations.