1 Introduction

The (BaSr)TiO3 ceramics, a intensively investigated ferroelectric, have received lots of attentions due to their unique properties including high permittivity and tunability [1, 2]. They are considered as promising candidates in a wide range of electronic applications, such as microwave phase shifters, tunable phased-array antenna and varactors [3–5]. In fact, the dielectric ceramics possess excellent dielectric properties. However, they also have some drawbacks like poor flexibility which is not satisfied with the fabrication of electric devices. On the other hand, from the application point of view, in order to meet the impedance matching [6, 7] the dielectric properties for tunable devices should have relatively low permittivity and high tunability. Nevertheless, the reality is not so optimistic that the dielectrics with high tunability usually possess high permittivity [8]. Thus, several methods have been applied for the sake of reducing the permittivity of dielectrics including ion doping, solid solution, and air bubbles, etc [9, 10]. Among others, a strategy to obtain composites by combining polymers with ceramic fillers has been developed to solve this problem [11–18], which may follow up with the application of microwave tunable devices and possess the benefits of appropriate dielectric constant, easy fabrication as well as relatively low dielectric loss [19, 20].

In recent years, 3D printing has received broad interest because of its high efficient, low cost and potential of fabricating complex devices in a single direct process from computer design and control. However, dielectric functional devices that might be obtained by 3D printing are restricted due to the limitation of current dielectric materials made by the 3D printing process [21, 22]. Acrylonitrile–butadiene–styrene (ABS) resin (copolymer of styrene, acrylonitrile and butadiene), one of the widely 3D printing used materials with low dielectric constant (~4.5), dielectric loss (~0.045) and excellent dielectric strength (~206 kV/mm), is an important interchangeable thermo-plasticity engineering plastic in which nitrile and phenyl group will provide compatibility while unsaturated double bond will give the copolymer good mechanical flexibility. In addition, their properties can be tuned to meet the requirement by changing the proportions of constituents. Hence, ABS copolymer can be used as the polymer matrix of ceramic/polymer functional dielectric composites which could be applied to 3D printing. Considering above all, composites combined the advantages of (BaSr)TiO3 ceramics and ABS copolymer while eliminating the drawbacks are expected to be a desirable material for 3D printed microwave tunable device which also has scarcely been studied.

In this paper, Ba0.6Sr0.4TiO3 (BST) ceramic powders were obtained by conventional solid state reaction and the surface of these powders was modified by H2O2 to introduce plenty of hydroxyl groups that can ameliorate the interface contact between polymer and ceramics [23, 24]. BST/ABS composites were fabricated by tape casting and hot pressing method. The microstructure, thermal and dielectric properties of these composites as a function of ceramic concentration were investigated and the interfacial connection mechanism was discussed. Various dielectric theoretical models, such as Lichtenecker, Maxwell–Garnett, Landzu–Lifshitz and Yamada model were employed to analyze and simulate the dielectric constant.

2 Experimental procedure

2.1 Preparation of BST/ABS resin composites

In this work, BST/ABS resin composites were obtained from Ba0.6Sr0.4TiO3(BST) ceramic powders and ABS copolymer based on the general formula ABS + xBST, where x is 10, 20, 30, and 40 vol%, respectively. The micron-size Ba0.6Sr0.4TiO3 with amorphous morphology powders were prepared by traditional solid state reaction with a stoichiometric mixing of BaCO3, SrCO3, and TiO2 which were heating at 1400 °C for 2 h accompanying repeated grinding [8]. The BST powders were dispersed in an aqueous solution of H2O2 (30%, 500 mL) by a magnetic stirring at 80 °C for 2 h, and then modified BST powders were obtained after vacuum drying at 60 °C for 10 h. The resulting BST particles had an amorphous microstructure [23].

The ABS matrix was commercial product supplied by Zhuhai Three Green Industrial Co., Ltd., and N,N-dimethyformamide (DMF, anhydrous 99.8%) was picked up from Sinopharm Chemical Reagent Co., Ltd. The modified BST powders and ABS particles were dispersed in DMF under magnetic stirring for 2 h at 50 °C and ultra-sonicated for 1 h to obtain an uniform suspension. Then the slurry was achieved by mechanical milling the mixed solution at 600 rpm for 12 h. The BST/ABS composite thick film was subsequently made by casting the mixture on a glass substrate. After that, the film was kept in a vacuum oven overnight at 60 °C to evaporate the organic solvent of DMF. Then the BST/ABS films with 0.02 ~ 0.2 mm in thickness were produced by hot pressed at 150 °C for 2 h. The surface of the specimen was coated by silver paste as the electrode to fulfil dielectric measurements.

2.2 Characterization

The microstructure and morphology of composites were observed by scanning electron microscopy (SEM, TESCAN VEGA3). To measure the thermal properties of BST/ABS films at the temperature range from 20 to 800 °C and at a heating rate of 10 °C/min in flowing N2 atmosphere (flow rate: 50 mL/min), the TA Instruments (USA model: TA-SDT2960) with alumina as the reference material were employed. In addition, the dielectric properties were analyzed using a high-precision impendence analyzer (WK P6505). The relative tunability of the composites was measured at 1 kHz with a bias voltage source.

3 Results and discussion

3.1 Microstructure of BST/ABS composites

Figure 1 shows the cross section morphology images of the BST/ABS resin composites with 10, 20, 30 and 40 vol% volume concentration of ceramic phase, respectively. It can be observed that BST particles are included and well-dispersed in ABS matrix without evident agglomeration and quantity of porosity due to the molecule interaction between BST and ABS. Thus, it demonstrates that uniform BST/ABS composites can be formed by solution casting method. In addition, the increasing content of BST ceramic fillers can break down the ABS macro-continuity that can be replaced by hydrogen bonds between the –CN group of ABS molecular chains and the –OH group on the surface of ceramic particles [25, 26].

Fig. 1
figure 1

SEM images of the BST/ABS composites with different BST contents: a 10 vol%; b 20 vol%; c 30 vol%; d 40 vol%

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The schematic mechanism of the hydroxylation of BST particles and hydrogen bonding reaction between BST and ABS is shown in Fig. 2. Large quantity of hydroxyl groups is adhered to the BST surface by reacting with H2O2 due to the hydrophilicity of BST particles. Hydrogen bonds generate from the –CN and –OH groups through ball-mill mixing so as to produce a strong interface interaction between BST fillers and ABS matrix and the former becomes uniformly dispersed in the latter as a consequence.

Fig. 2
figure 2

Forming mechanism of the BST/ABS composites

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3.2 Thermal properties of BST/ABS composites

Figure 3 shows thermal analysis curves of pure BST or ABS and BST/ABS composites that were measured by using TGA and DSC, respectively. It can be seen from Fig. 3a that pure ABS and BST/ABS composites exhibit a little total mass loss at around 150 ~ 200 °C. The mass loss is mainly due to the evaporation of DMF solvents hidden within materials and water molecules absorbed on the surface of materials. Secondly, it can be observed that pure ABS and BST/ABS composites experience a drastic weight loss at the range of 350 ~ 500 °C that are attributed to the decomposition of organic matter while the pure BST ceramic powders do not, which indicates remarkable temperature stability. Moreover, the endothermic peak in the range of 100 ~ 150 °C originates from the transformation of their glassy state into switched from their glassy into elastomeric state of the ABS organic matrix that is an endothermic physical reaction, as shown in Fig. 3b. In addition, it is well known that ABS is composed by the acrylonitrile-styrene copolymer as continuous matrix phase and the polybutadiene particles as dispersed phase. Hence, the presence of two exothermic peaks around 350 ~ 500 °C are produced by thermal degradation of the two parts of ABS matrix, which is in correspondence to the result of TGA measurement. It can also be concluded that the decrease of weight loss and exothermic peaks of composites are attributed to the addition of BST fillers which can improve the thermal stability of the composites.

Fig. 3
figure 3

The thermal analysis of ABS, BST and BST/ABS composites: a TGA; b DSC

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3.3 Dielectric properties of BST/ABS composites

The frequency dependence of the dielectric constant of the composites with BST volume fraction at 0, 10, 20, 30 and 40 vol% are shown in Fig. 4a. It can be found that there is an increase of dielectric constant from 4.5 to 18 (at 1 kHz) with increasing the volume fraction (i.e., 10–40 vol%) of BST, since the BST particles possess relatively high dielectric constant. The mechanism of this phenomenon can be explained by the interfacial polarization occurring in the inner microstructure of the BST/ABS composites which is shown in Fig. 5. There are lots of defects at the interface location between BST and ABS. There is no doubt that carriers like electron, hole and ion vacancy, etc. are assembled easily toward the defects. These restrained carriers migrate difficultly and distribute randomly without applied electric field, as shown in Fig. 5a. Then, the interfacial polarization is caused by the produced and ordered electric dipole moments with applied electric field, as shown in Fig. 5b. As a result, the interfacial polarization reaction increases and contributes to higher dielectric constant of composites with the ceramic loading volume increase. On the other hand, the dielectric constant of all the composites decreases with increasing frequency, which could be due to the polarization relaxation happened in the microstructure of composites, including interface polarization and dipole orientation polarization. Under the condition of low frequency, all polarization mechanisms mentioned above can respond timely on the change of frequency, while the interfacial polarization of composites does not under relatively high frequency. Consequently, the decrease of dielectric constant is thought to be responsible for weakening of the dipole orientation resulted from the increase of frequency.

Fig. 4
figure 4

Frequency dependence of dielectric properties of BST/ABS composites: a Dielectric constant; b Dielectric loss

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Fig. 5
figure 5

Model of interfacial polarization in the BST/ABS composites

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Dependence of dielectric loss of composites on frequency in the range of 102 ~ 106 Hz at room temperature is shown in Fig. 4b. The result of dielectric loss is analyzed for the change trend which can be expounded that the loss decreases at low frequency range (102 ~ 105 Hz) while gradually move higher, besides, the pure ABS shows higher dielectric loss than others at comparatively high frequency. The conductive loss originated from the interfacial polarization strongly affects the dielectric loss at low frequency. The results demonstrate that dielectric loss increases from 0.021 to 0.082 at 1 kHz due to the increased interaction strength of interfacial polarization as the ceramic fillers volume increases. As frequency increases, there is a down trending in dielectric loss data. The reason is that the interfacial polarization fails to follow the electric field change and hasn’t contributed to dielectric loss of composites. On the other hand, the slightly increasing dielectric loss depends heavily on a Debye relaxation behavior at high frequency that stems from the –CH and –CN dipoles orientation polarization of the ABS matrix [27]. That is because the response time of dipoles orientation polarization is slightly slower than electric filed change and the former lags behind the latter.

The temperature dependence of dielectric constant on temperature for composites at 1 kHz is given in Fig. 6a. It is found that the dielectric constant increases with temperature increasing from 25 ~ 120 °C due to the lifting dipole orientation polarization level. In the low temperature range, relatively low dielectric constant is related to freezing dipoles in the amorphous region that cannot move with the change of applied electric filed, causing the obstruction of the relaxation polarization. An increasing dielectric constant in the range of 70 ~ 120 °C is ascribed to the decreasing relaxation time that can keep up with the change of applied electric filed. One reason is that the dipoles attached to the polymer chain that accompanied with enough thermal energy can rotate quickly. Another important cause is that the thermal expansion of ceramic crystal produced gradually with the rising of temperature resulting in the movement of domains located in the single large grains, which can also lead to the increasing dielectric constant [28].

Fig. 6
figure 6

Temperature dependence of dielectric properties of BST/ABS composites: a Dielectric constant; b Dielectric loss

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Figure 6b shows the temperature dependence of loss tangent of BST/ABS composites at 1 kHz. The loss increases dramaticly with increasing temperature from room temperature to T g and then decreasing after reaching a maximum at temperatures of 70 ~ 120 °C. The change trend of dielectric loss is consistent with the dielectric constant. Again, the dielectric loss peak is broadened and flattened with increasing amount of BST fillers in ABS matrix. These phase transitions occur over a wide range of temperature when the BST content increases. This dispersion of phase transitions is a typical dielectric relaxation that stems from two factors. One factor is the Debye relaxation behavior which is associated with the rotation and orientation of the –CN groups of the polymer matrix under applied electric field. The other is attributed to the interface polarization occurring in the heterogeneous interface between BST fillers and ABS polymers.

In order to measure a non-linear change that occurs in the dielectric permittivity and the applied electric field, the dielectric tunability (T) of the material is determined from Eq. (1):

$$T=\frac{{{\varepsilon }_{\left( 0 \right)}}-{{\varepsilon }_{\left( E \right)}}}{{{\varepsilon }_{\left( 0 \right)}}}\times 100\%$$
(1)

where ε(0)and ε(E) are the dielectric permittivity under zero direct current (dc) electric field and under some given electric filed, respectively. In this work, E = 1.0 and 2.0 kV/mm are applied as the criterion for comparing the tunability of composites and the results are shown in the Fig. 7. It is clear that the dielectric tunability of BST/ABS composites increases as the BST loading volume increases at 1 kHz. In particularly, the dielectric tunability of BST/ABS composites reached 1.41, 2.21, 2.65 and 3.36% with different BST filler contents (under the bias voltage 2.0 kV/mm). It is known that ABS polymer possesses the characteristic of low dielectric constant and no dielectric tunability measured experimentally. As a result, BST can improve the dielectric tunability properties of ABS polymer matrix.

Fig. 7
figure 7

The dielectric tunability of BST/ABS composites

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3.4 Theoretical simulation for the dielectric constant of BST/ABS composites

Several kinds of models were used to predict the dielectric constant of the composites which could reduce the uncertainty of preparation process and improve the efficiency of research and development. Lichtenecker model [29] is a fundamental analytical model characterized by the logarithmic mixture rule. The rule can be expressed as follows:

$$\log {{\text{ }\!\!\varepsilon\!\!\text{ }}_{r}}={{\delta }_{c}}\log {{\text{ }\!\!\varepsilon\!\!\text{ }}_{c}}+{{\delta }_{p}}\log {{\text{ }\!\!\varepsilon\!\!\text{ }}_{p}}$$
(2)

where ɛ c , ɛ p , δ c and δ p are the dielectric constants of BST and ABS, the volume fraction of BST and ABS, respectively. However, this relation is only appropriate to forecast the dielectric constant of composites with similar value of dielectric constant of two constituent phases. Thus, the modified formula called Landzu-Lisfshitz’s model is shown as follows [30].

$${{\varepsilon }_{r}}={{\varepsilon }_{p}}\left[ 1+3{{\delta }_{c}}\left( \frac{{{\varepsilon }_{c}}-{{\varepsilon }_{p}}}{{{\varepsilon }_{c}}+2{{\varepsilon }_{p}}} \right) \right]$$
(3)

This formula is more applicable to the composites with great difference dielectric constant between fillers and matrix. Maxwell–Garnett model is also used to predict the dielectric constant of composites [31], which is formed by dispersing fillers homogeneously into matrix.

$${{\varepsilon }_{r}}=1+\frac{3{{\delta }_{c}}\left( {{\varepsilon }_{c}}-{{\varepsilon }_{p}} \right)}{{{\delta }_{p}}\left( {{\varepsilon }_{c}}-{{\varepsilon }_{p}} \right)+3{{\varepsilon }_{p}}}$$
(4)

While this model does not take into account the conductivity and spherical shape of the filler particles, which lead to produce error between experimental values and calculated results.

Yamada [32] proposed a new model where the shape factor of ceramic fillers was adequately considered. The dielectric constant of composites can be obtained from the following equation:

$${{\varepsilon }_{r}}={{\varepsilon }_{p}}\left[ 1+\frac{n{{\delta }_{c}}({{\varepsilon }_{c}}-{{\varepsilon }_{p}})}{n{{\varepsilon }_{p}}+{{\delta }_{p}}({{\varepsilon }_{c}}-{{\varepsilon }_{p}})} \right]$$
(5)

where “n” is the geometry-dependent parameter of the ceramic particles. The decrease inaccuracy of simulated and experimental values by adjusting the value of “n” is benefit to predict precisely the dielectric constant.

According to Eq. (5), the values of dielectric constant could be calculated by substituting the ɛ c and ɛ p with 3800 and 4.5 (at 1 kHz). Figure 8 shows the results with different shape factors (n) and volume fractions of ceramic fillers (δ c ); the values of δ c are 0.1, 0.2, 0.3, 0.4 and n values are 0.5, 1, 3, 3.2, 3.5, respectively. As the figure illustrates, the simulation value increases with increasing δ c and n. The results show that the simulation values using n = 3.2 and δ c  < 0.4 are consistent with the experiment data and the maximum error is less than 2%. Based on the above, one can draw a point that n = 3.2 corresponds to micron-size BST particles with amorphous morphology. Therefore, the dielectric constant and its changing rule with different ceramics shape can be accurately simulated by adjusting n parameter.

Fig. 8
figure 8

The variation of dielectric constant of BST/ABS composites with shape factor and volume fraction of BST ceramics

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The theoretical predictions values (TV) and experimental values (EV) of BST/ABS composites in terms of frequency with different volume fractions of BST are shown in Fig. 9. It is observed that the Yamada model has a good reliability to predict the dielectric constant of composites as the experimental values have a little error to the theory values when the content of ceramics is less than 40 vol%. On the contrary, the deviation of TV and EV enlarges when ceramic content approach to 40 vol%. This is assumed that more considering defects are generating and they can capture the carrier charge with increasing the ceramic content. As a result, the strengthening interfacial polarization produced by charge array orderly in the defects under the applied electric field causes the EV higher than theoretical values.

Fig. 9
figure 9

Theoretical predictions values (TV) and experimental values (EV) of BST/ABS composites in terms of frequency at different volume fractions of BST

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Furthermore, all those models mentioned above are employed to calculate the dielectric constant of composites. The simulation and experiment values are shown in Fig. 10. According to the results, the predicted ɛ r values deviate tremendously from the experimental values using Lichtenecker model which is suitable for the composites with similar dielectric constant in two parts. Again, there exists a big deviation of EV and TV using Laudzu-Lifshitz model when the content of ceramic is more than 20 vol%. Therefore, it is further proved that this model applies to the composite material containing low content ceramic fillers. Besides, the simulation value and test results of dielectric constant of composites are compared and analyzed, which proved the high accuracy of Yamada and Maxwell models. Particularly, simulation curve obtained by Yamada model with n = 3.2 is most close to the experimental results.

Fig. 10
figure 10

Experimental and theoretical dielectric constant of BST/ABS composites

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4 Conclusions

In summary, the effect of different content BST fillers on microstructure and dielectric properties of BST/ABS composites has been performed with a systematic experimental and theoretical investigation. SEM images of composites demonstrated the excellent distribution of BST fillers in ABS matrix. The permittivity and the dielectric tunability of BST/ABS composites increased with increasing the volume fraction of BST fillers. And the dielectric constant of BST/ABS composites decreased with increasing frequency (102 ~ 106Hz). The dielectric constant and loss tangent increased gradually from room temperature to T m and exhibited typical dielectric relaxation characteristics. Moreover, the dielectric constants of composites were simulated by using Lichtenecker, Maxwell, Landzu–Lifishitz and Yamada models. Among them, the predicted permittivity of composites by Yamada model exhibited close correspondence to the experimentally determined results, when the shape factor n = 3.2 was employed. The work of BST/ABS dielectric functional composites developed a suitable functional material for 3D printed electronic devices.