EFFECTIVE RELATIVE PERMITTIVITY OF 3D-PRINTED HIGH-IMPACT POLYSTYRENE STRUCTURES IN THE MICROWAVE FREQUENCY RANGE
DOI:
https://doi.org/10.30857/2786-5371.2026.4.2Keywords:
gyroid infill, 3D printing, high-impact polystyrene, effective relative permittivity, free-space method, S-parameters, effective-medium modelsAbstract
Purpose. To establish the relationship between the effective relative permittivity of 3D-printed high-impact polystyrene (HIPS) structures with gyroid infill and the actual volume fraction of the polymer phase over the 4–20 GHz frequency range, and to assess the suitability of classical effective-medium models for the analytical description of this relationship.
Methodology. Measurements were performed using the free-space method on a Compass Technology Group benchtop system over the 4–20 GHz frequency range. The study examined 10 mm thick 3D-printed HIPS specimens with nominal gyroid infill levels ranging from 10 to 100%, together with a 10 mm thick PE-300 high-density polyethylene control specimen. The effective relative permittivity was retrieved from the measured S-parameters using Compass Technology Group software. To verify the numerical consistency of the retrieval procedures, the same S-parameters were additionally processed using the Nicolson–Ross–Weir method. The resulting relationships were fitted using the linear mixing, Maxwell–Garnett, Looyenga, and symmetric Bruggeman models as functions of the actual polymer volume fraction, determined from the specimen mass and external volume. The dependence on the nominal infill level was treated as an engineering correlation with the slicer setting. The internal architecture of the specimens was interpreted using an idealised normalised sheet-gyroid model based on a triply periodic minimal surface.
Findings. For the 10 mm thick PE-300 polyethylene control specimen, a mean value of ε′ = 2.3996 was obtained over the 4–20 GHz frequency range. The difference between the result obtained using Compass Technology Group software and the NRW retrieval from the same S-parameters was approximately 0.02%, indicating numerical consistency between the applied processing procedures. For the gyroid specimens, ε′ increased monotonically from 1.1224 to 2.4855 as the nominal infill level increased from 10 to 100%. Fitting against the actual polymer volume fraction was substantially more accurate than fitting against the nominal infill level. When ε′p was optimised separately for each model, the Maxwell–Garnett model gave the lowest RMSE (0.0077); when ε′p was fixed at 2.4855, the ranking shifted in favour of the Looyenga and Bruggeman models.
Originality. An experimental relationship between the effective real part of the relative permittivity and the actual polymer volume fraction was established for 3D-printed high-impact polystyrene structures with gyroid infill over the broad frequency range of 4–20 GHz. The ranking of the effective-medium models was shown to depend both on how the polymer-phase fraction is defined and on how ε′p is specified: free optimisation favours Maxwell–Garnett, whereas independent fixing of ε′p favours the Looyenga and Bruggeman models.
Practical value. The obtained relationship may be used for the preliminary selection of internal-architecture parameters in the design of lightweight polymer microwave components with tunable effective permittivity. In particular, the established relationships may support the development of metamaterials for radio-frequency absorption, gradient-index lenses, impedance-matching layers, and electromagnetically transparent structures.
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