Development of a Novel Diffuse Reflector Filament for Additive Manufacturing of 3D-Printed Plastic Scintillators

2.1. Filament Composition and Fabrication

The core innovation lies in the filament's material composition. The base polymers are PC and PMMA, chosen for their thermal and mechanical properties suitable for FDM. To achieve high, diffuse reflectivity, these polymers are loaded with scattering agents:

• Titanium Dioxide (TiO₂): A highly reflective white pigment providing primary scattering centers.
• Polytetrafluoroethylene (PTFE): Added to further enhance reflectivity and potentially improve layer adhesion and surface properties.

2.2. Optical Characterization Setup

The optical performance of printed reflector samples was quantitatively evaluated. A dedicated setup was used to measure:

• Total Reflectance: The fraction of incident light reflected by the sample across a relevant wavelength range (likely matching the scintillator emission spectrum).
• Transmittance: The fraction of light passing through the sample, which should be minimal for an effective reflector.

2.3. Prototype Fabrication and Cosmic Ray Testing

A functional 3D-segmented plastic scintillator prototype was fabricated to validate the concept. The manufacturing likely involved a dual-extrusion or multi-step process:

1. Printing the structural reflective matrix/grid using the novel white filament.
2. Filling the cavities within this matrix with liquid scintillator material, possibly using a technique akin to Fused Injection Modeling (FIM) as mentioned in the abstract.

• Light Yield: The amount of scintillation light collected per cube, indicative of detector efficiency.
• Optical Crosstalk: The percentage of light signal detected in a neighboring, non-hit cube, which degrades spatial resolution.

3.1. Reflectivity and Transmittance Measurements

The optical characterization confirmed the effectiveness of the PC/PMMA+TiO₂+PTFE composite. The printed reflective layers exhibited high total reflectance and very low transmittance, confirming their suitability as optical isolators. The optimal composition and a layer thickness of 1 mm were identified, providing a balance between optical performance and mechanical integrity/printability.

3.2. Light Yield and Optical Crosstalk Performance

The cosmic ray tests on the 3D-printed prototype yielded promising results:

• Uniform Light Yield: The light output was consistent across different cubes in the segmented matrix, demonstrating the uniformity of the printing and filling process.
• Low Optical Crosstalk: The optical crosstalk was measured to be less than 2% for the matrix with a 1 mm thick printed reflector wall. This is a critical improvement over previous attempts and is deemed acceptable for applications requiring combined particle tracking and calorimetry.
• Performance Parity: The overall performance of the 3D-printed detector was found to be analogous to that of standard, monolithic plastic scintillator detectors, while offering the inherent advantages of segmentation and design freedom from additive manufacturing.

4.1. Technical Details and Mathematical Formulation

The effectiveness of a diffuse reflector can be modeled by considering light transport. A key parameter is the diffuse reflectance $R_d$, which for a thick, scattering medium can be approximated by Kubelka-Munk theory. For a layer of thickness $d$, the reflectance is given by: $$R \approx \frac{1 - R_g (a - b \coth(b S d))}{a - R_g + b \coth(b S d)}$$ where $a = 1 + K/S$, $b = \sqrt{a^2 - 1}$, $K$ is the absorption coefficient, $S$ is the scattering coefficient, and $R_g$ is the reflectance of the backing material. For an ideal, thick reflector backing a scintillator cube, we want $R \to 1$ and $K \to 0$. The high loading of TiO₂ ($S \gg K$) in the PC/PMMA matrix directly maximizes $S$, driving $R$ close to 1 and minimizing transmitted light that causes crosstalk.

The light yield $LY$ for a single scintillator segment can be expressed as: $$LY \propto \eta_{scint} \cdot \eta_{coll} \cdot \eta_{det}$$ where $\eta_{scint}$ is the scintillation efficiency, $\eta_{coll}$ is the light collection efficiency, and $\eta_{det}$ is the photodetector quantum efficiency. The printed reflector directly optimizes $\eta_{coll}$ by trapping scintillation photons within their cell of origin through total internal reflection and diffuse reflection at the printed walls.

4.2. Analysis Framework: Material Selection Matrix

Selecting materials for 3D-printed detector components requires balancing multiple, often conflicting, properties. The following decision matrix framework can be used to evaluate candidate materials for the reflector filament:

Analysis: The chosen PC/PMMA composite scores highly across the board. It avoids the fatal flaw of polystyrene (material mixing with PS scintillators, as noted in prior work [19,20]) while offering superior reflectivity to pure PMMA and good mechanical properties from PC. This framework justifies the material choice as a robust engineering compromise.