Tuning the Solar Performance of Building Facades through Polymer 3D Printing: Toward Bespoke Thermo‐Optical Properties

Façades are the primary interface controlling the flow of solar energy in buildings and affecting their energy balance and environmental impact. Recently, large‐scale 3D printing (3DP) of translucent polymers has been explored as a technique for fabricating façade components with bespoke properties and functionalities. Transmissivity is essential for building facades, as the response to solar radiation is crucial to obtaining comfort and greatly affects electricity and cooling demands. However, it is still unclear how 3DP parameters affect the optical properties of translucent polymers. This study establishes an experimental procedure to relate the optical properties of PETG components to design and 3DP parameters. It is observed that printing parameters control layer deposition, which governs internal light scattering in the layers and overall light transmission. Moreover, the layer resolution determines angle‐dependent properties. It is shown that printing parameters can be tuned to obtain tailored optical properties, from high normal transparency (≈90%) to translucency (≈60%), and with a range of haze levels (≈55–97%). These findings present an opportunity for large‐scale 3DP of bespoke façades, which can selectively admit or block solar radiation and provide uniform daylighting of a space. In the context of the building sector decarbonization, such components hold great potential for reducing emissions while ensuring occupant comfort.


Introduction
After a global drop due to the COVID-19 pandemic, energy consumption and emissions from buildings rebounded above 2019 record levels, reaching their highest ever. [1] To date, the building emissions, facades also account for a significant part of buildings' embodied emissions, only second to structural components, and hold great potential for CO 2 reduction. [12] For facades' structural and insulation layers, bio-based materials, such as wood, clay, and hemp, represent a valid, low-emission material alternative. However, for transparent components, low-impact replacements for glass are still missing.
The last years saw a growing interest in large-scale 3D printing (3DP) of facades, taking advantage of the novel capabilities of additive manufacturing. [13] The geometrical freedom, the potential for mass customization, and the possibility to integrate multiple performances into a single component are unprecedented opportunities to design and fabricate integrated, site-specific facades. Research on 3D printed glass highlights that this novel fabrication technique offers a high degree of control over light reflection, transmission, and redirection through the control of geometry and surface texture. [14,15] Nevertheless, this technique has not reached a relevant scale for building facades due to the challenging temperature conditions required for the melting and cooling of glass. A few studies demonstrate the capabilities of large-scale polymer printing and explore multi-performance integration for indoor climate control. [16][17][18][19] Polymers represent a valid material alternative to glass in buildings thanks to their optical properties, easy processability, and low cost. Moreover, their mechanical properties can be enhanced by controlling the macro geometry of the components to achieve stiff and lightweight parts suitable for application in building facades. [16] Finally, the low density, the limited energy intensity of the production process, and the recent advancements in the recycling process are promising aspects from an environmental standpoint. [20] To date, there is a lack of understanding of the influence of printing parameters on the optical properties of 3D printed polymers, which hinders the possibility of controlling and tuning optical transparency. [21,22] Identifying the interplay of material properties and manufacturing parameters holds great potential for combining 3DP geometrical capabilities with bottom-up control of the material structure, as demonstrated for stiff lightweight structures, [23] electronics and energy storage, [24] and heat and mass transfer applications. [25] This work investigates the optical properties of 3D printed polyethylene terephthalate glycol-modified (PETG) and their dependency on fabrication parameters such as extrusion temperature, speed, cooling rate, and layer resolution. We establish an experimental procedure to design, fabricate and test printed samples with varying optical appearances. Using a goniophotometer setup, we measure the light scattering through 3DP structures and derive their angle-dependent optical transmissivity and reflectivity. By relating these properties to the morphology of the 3D printed samples, we observe that the layered material deposition and the resulting geometrical features are crucial in determining the light scattering behavior. In the samples, the orthogonal orientation of the layer deposition with respect to the incident light direction causes light redirection effects. Moreover, the uncontrolled definition of the layer interfaces and the presence of air bubbles between the layers result in a reduction in the overall light transmission, with an increase in diffused transmission compared to direct. We analyze the effect of fabrication parameters on the layer morphology and identify contour number and thermal parameters as the most decisive in the samples' optical response. Moreover, we highlight the relations between layer resolution and angle-dependent optical behavior. Finally, by defining application-oriented performance metrics, we identify the opportunities for application in optically-tuned 3D-printed facade components.

3D Printing of PETG Polymer
In this study, we address extrusion-based 3DP of PETG. PETG is a well-established material for additive manufacturing for medical products and food applications due to the combination of material properties such as optical transparency, chemical, and structural resistance. [26] It is a co-polyester derived from PET by replacing the ethylene glycol in the molecular chain with a larger monomer (Figure 1d). This extra monomer suppresses the crystallization process in the polymer [27] and lowers its forming temperature, making it especially suitable for extrusion-based printing such as Fused Filament Fabrication (FFF). In FFF, the feedstock of thermoplastic polymer is fed into a print head, where the material is heated above melting temperature and pushed out of the print nozzle. As the print head moves along a described pattern, the filament is deposited in successive layers on a heated print bed (Figure 1a,b).
When extruded, the molten filament cools down and solidifies by convective heat exchange with the ambient and conductive heat exchange with the adjacent layers. In the case of amorphous polymers, like PETG, solidification gradually occurs through a glass transition. Instead, for semi-crystalline polymers, the phase change occurs suddenly through crystallization. Before reaching a stable solidified state, the layers experience successive re-heating and cooling cycles due to the deposition of the successive layer. [29] At this stage, the filament's temperature remains above the glass transition, and diffusion of molecules at the interfaces occurs, ensuring bonding between layers ( Figure 1e). Therefore, thermal history plays a crucial role in determining the mechanical properties of the final part. High temperatures and low speed can enable better layer adhesion; however, excessively high temperatures can cause degradation of the polymers and loss of mechanical properties. [30] A fast cooling rate results in shrinkage and warping due to the rise of internal stresses, compromising the accuracy of the part and the printing process. [31] We investigate these effects on optical performance by fabricating a set of 20 PETG samples of dimensions 20 cm × 20 cm with a maximum thickness of 1 cm ( Figure S1, Supporting Information). These were fabricated through a desktop printer using a combination of fabrication parameters (Experimental Section). Based on the 3D printer capabilities and the allowed level of control over the parameters, we consider thermal parameters (Figure 1c), namely extrusion temperature and cooling fan use, process parameters, such as extrusion speed, and slicing parameters, such as layer height and the number of contours (Figure 1f ). The combination of parameters in the different samples was defined according to a design of experiments approach, as further explained in the Experimental Section. The samples exhibit variations in optical appearance from a high degree of transparency to diffuse translucency, and the measured data reflects this behavior (Table S1, Supporting Information).

Morphology of Translucent Printed Polymers
Figure 2f,g demonstrate how the tuning of printing parameters affects transparency, as the two samples were fabricated with the same PETG filament and 3D-printer (Experimental Section). Transmissivity is a key property that differentiates thermoplastics from most building materials. In fact, thermoplastics It is deposited onto the printing bed, which is heated at 70 °C, below the polymer's glass transition temperature (80 °C). A temperature profile builds up in the part during the deposition process. c) Thermal and process parameters controlling the fabrication: extrusion temperature, printing speed, and cooling fan power. d) In PETG, the ethylene glycol molecule is substituted with cyclohexane dimethanol, which inhibits crystallization associated with PET and lowers its melting point. Optical transparency and clarity are a result of suppressed crystallization. e) During printing, the material undergoes thermal cycles and phase transitions that affect layer bonding and the properties of the final part. f) Slicing parameters for 3D-printing: layer height and number of contours. Layer width is a function of layer height (Experimental Section) can achieve a high level of transparency comparable to that of glass. [31,32] Optical properties depend on polymer morphology: amorphous polymers (Figure 2a) can let light pass through much easier than their crystalline counterpart. In crystalline polymers, refractive-index fluctuations at the interfaces between more and less dense regions cause light diffraction and scattering. [33] Transparent and translucent polymers used in FFF belong either to the low-crystallinity polymers or the amorphous polymers class. Polylactic acid (PLA) and polyethylene terephthalate (PET) fall into the former category, while acrylonitrile butadiene styrene (ABS), thermoplastic polyurethane (TPU), polycarbonate (PC), and PETG, which we investigate in this study, belong to the latter. [34] Beyond the polymer material structures, the phase change and deposition Adv. Mater. Technol. 2023, 8, 2201200 Figure 2. The influence of polymer and layer morphology on optical behavior. a) Amorphous polymers, such as PETG, are characterized by a glass transition temperature that marks the shift from a hard solid-like state to a viscous rubber-like one. The lack of crystalline structures increases the ability to let light pass through the material. b) The perpendicular orientation of layer deposition and incident light direction cause scattering. According to the incoming light, 3D-printed parts can show specular or scattered transmission behavior. c) The layer dimensions affect internal reflections and refractions within the part, and high width-to-height ratios result in a maximization of these effects. d) Light scattering happens at the layer interfaces, and the presence of multiple contours causes a higher number of interfaces and air gaps. e) Irregular layer interfaces are responsible for light transmission attenuation, as air can get trapped in between layers causing light refraction and scattering. f,g) Two out of the 20 samples from the experimental batch. Samples were printed with the same printer and material, but printing parameters determined low transparency in one case and high clarity in the other. h,i) Scanning electron microscope (SEM) images reveal the presence of irregular layer interfaces in the less transparent sample and straight and regular ones in the clear one. j,k) SEM images of the layers cross section reveals a perfectly monolithic part in the transparent sample and the presence of air gaps in the other.
process they undergo during 3DP further affect the light transmission phenomenon.
We observed that optical properties are inherently related to layer-to-layer interactions. Light scattering and redirection effects depend on the direction of the layer deposition relative to the incoming light direction. Incident light with an azimuthal axis perpendicular to the layer deposition direction gets scattered along non-specular directions, while parallel orientation ensures specular transmission (Figure 2b). In fact, due to the layered deposition, the optical transparency of 3DP objects is direction-dependent. First, layer resolution along the z-axis affects light transmission through the x-y plan: a small layer height and width result in an increased number of layer interfaces which cause light scattering. However, small layer height also results in smaller-scale defects and allows for better control of layer interfaces. [35] Second, the layer width-toheight ratio affects internal light reflections, so more spherical layers result in less internal scattering than oblong layers ( Figure 2b). The deposition of material can introduce voids among vertically deposited 3D printed layers and horizontal contours, which cause light scattering due to refractive index change and attenuation of transparency (Figure 2c,d). These effects can be observed by comparing two samples, characterized by a transparent and translucent appearance, respectively (Figure 2f,g). The transparent sample features a fine layer deposition with straight layer interfaces ( Figure 2h). Its layers are perfectly bonded to form a monolithic part, as shown in Figure 2j. Instead, the translucent sample exhibits a poor definition of the layer interfaces, and the presence of irregularities and air inclusions can be observed both in the front view and cross-section (Figure 2i,k).

Relating Optical Properties to Fabrication Parameters
The optical characterization of 3DP parts can be studied using the complex fenestration systems (CFS) framework. CFS are facade components that feature non-specular transmission and angle-dependent optical behavior, as opposed to clear glazing. Therefore, their characterization is based on the angularly resolved transmissionand reflection of light through these components. [36] Similar to CFS, 3D printed components cause angle-dependent, non-specular light transmission and should be characterized in the same way. This can be done through the bi-directional scattering distribution function (BSDF), a mathematical equation describing the scattering of light from a surface as a function of the angular positions of the incident and scattered beams (Experimental Section). A common method to derive the BSDF is based on the use of ray-tracing or photon mapping [37] algorithms which account for the macro-geometry of the component and the surface properties of the base materials. Such computational methods, however, fall short in the study of 3D printed components, as they cannot account for scattering at the 3D printed layer interfaces and for the fabrication-induced features. [15] Therefore, we propose a data-driven optical characterization of the 3DP samples based on goniophotometric light scattering measurements (Experimental Section). These measurements are taken on both sides of the samples to account for reflec-tion and transmission and consider a sub-set of incident light direction. We assumed symmetry over the orthogonal axis of the sample's layered structure. From the measurements, we derive the discrete BSDF for each sample using the full Klems basis. [38] This representation is based in the subdivision of the hemisphere by 145 patches of approximately equal solid angle (Figure 3b). [39] Each patch corresponds to a light direction, which can also be described as an angle in a polar coordinate system θ, φ as shown in Figure 3a. Details about the Klems resolution can be found in Table S3, Supporting Information. The visualization of the results using the Klems basis allows the generation of 2D projected maps representing the intensity and spatial distribution of transmitted and reflected light for a chosen incident light direction (Figure 3c,e).
As the data-driven BSDF consists of two 145 × 145 matrices for transmission and reflection of light, we derive relevant optical properties and propose a tailored representation system to visualize them. Specifically, we observe total transmission, direct transmission, and haze for chosen incident angles. Total transmission designates the amount of light transmitted through a material considering the direct and diffuse components. Direct light transmission represents the ratio of the total incoming light that is transmitted in the same direction through the sample (Figure 3d). Due to the layered surface definition, specular transmission in the 3D printed samples is significantly reduced compared to perfectly smooth material.
This results in a reduction in the clarity of the material and determines haze. Haze is defined as the percentage of light passing through a material that deviates from the incident beam by more than 2.5°. [40] In polymers, high haze levels describe a milky or cloudy appearance and make the material translucent rather than transparent. Owing to the resolution of the Klems representation system (Table S3, Supporting Information), in this study, we define haze as the ratio of transmitted light that deviates more than ≈5° from the incident beam.
The total transmission of incident light perpendicular to the part is used as a base comparison between the different samples. Overall, for the tested samples, transmission range from 61% to 90%, demonstrating the possibility to 3D print parts with high transparency (Table S1, Supporting Information). Samples with similar values of total transmission exhibit different directional behavior with specular and diffuse light transmission properties (Figure 4c). We observe that total transmission is a function on the incoming light elevation angle θ (Figure 4a The presence of two contours also affects the direct transmission, and these samples are characterized by low transmission values, independent of the incident angle (Figure 4b).
Single-contour samples exhibit the highest direct transmission for incoming light at θ = 0°, then a significant drop at θ = 10-20°. Depending on the layer height, successive peaks in direct transmission happen at θ = 30°, 40°, 50°. It follows that we observe lower haze in single-contour samples. In most of these samples, low values of haze are found for upward and downward incoming light at φ = 0° and at φ = 40°. For the rest of the incoming light azimuth angles, the clarity of the samples is compromised due to high haze (Figure 4e). Double contour samples show a distinct diffusive behavior with high haze values due to the light scattering effect caused by multiple layer interfaces (Figure 2d).
After verifying the replicability of the experimental characterization ( Figure S4, Supporting Information), we use statistical analysis to observe the optical response in relation to fabrication parameters, considering total transmission and haze for perpendicular incident light. The analysis results can be used to predict the optical response of samples featuring a specific combination of fabrication parameters within the ranges explored in this experimental study (see Figure S5, Supporting Information). The fitted regression models show that for both properties, the number of contours represents the most statistically significant parameter (Figure 5d,e). An increasing number of contours also increases the presence of microscopic air bubbles, which, together with defects in layer bonding, cause attenuation of transparency (Figure 2d). The highest transmission values are found in samples with a single contour, while the lowest is found in a double-contour one (Sample 8). The mean reduction in transparency in double-layer samples was found to be 15%. Similarly, high haze values are associated with double-contour layers, demonstrating that the presence of an additional contour attenuates the overall transmitted light and increases light diffusion (Figure 5c).
While layer height determines the angle-dependency of light properties, it does not play a significant role when only perpendicular incoming light is considered. Extrusion temperature is also a relevant parameter, but contrary to expectations, lower temperature levels are associated with improved transparency and clarity. This could be explained by the higher-order interactions with cooling and printing speed, which influence the fluidity of the material. In fact, high fluidity determines the material's ability to fill inter-layer gaps and adhere to the previous layer. [31,41] However, high fluidity must be paired with appropriate cooling to allow the layer to retain its shape and create a regular adhesion plane. High temperatures can also    The regression model relating total transmission at θ = 0°, φ = 0° shows that the number of contours is the most statistically significant parameter. The total transmission also correlates to printing temperature and its interactions with the cooling fan operation and printing speed. b,d,f) The regression model relating haze at θ = 0°, φ = 0° also reveals the big influence of contour numbers and its interaction with layer height and cooling fan operation. Haze also correlates to the thermal process parameters: high temperature and cooling fan operation are associated with high haze values. cause degradation in PETG and although we determined that the extrusion temperature is far from the polymer's degradation temperature ( Figure S3, Supporting Information), prolonged time in the heated extruder can accelerate the process. Finally, high extrusion temperature causes the residual moisture content that may be present in the polymer to expand with an associated risk of air entrapment. [42] A further experimental study focusing on printing temperature, speed, and cooling rate could isolate and closer display the interplay of these parameters in relation to optical transmission.

Solar Control through 3D Printed Building Envelopes
The experimental results show that the optical properties of 3D printed parts can be altered through printing parameters to obtain angle-selective features, clear and diffuse characters, and different levels of light transmission. Therefore, we identify the potential of this novel concept to tune the optical properties of 3D-printed building facades for solar control. The methodology proposed in this study can also be applied to other printing materials, and the findings on the influence of contours and layer height are potentially shared across materials. In this study, PETG is considered an exemplary 3D printable transparent polymer; however, recycled thermoplastics, such as rPET and rPETG, would significantly decrease the environmental impact of polymer 3D printed facades. The results of differential scanning calorimetry ( Figure S2, Supporting Information) and thermogravimetric analysis ( Figure S3, Supporting Information) on un-extruded and extruded filament samples reveal that the polymer morphology and the thermal stability are not affected by the printing process, thus indicating promising opportunities for recycling of 3D printed parts through remelting and re-processing.
From the modeling perspective, the BSDF derived from the optical measurement, describing the angularly resolved transmission and reflection from a sample, can be used to model material in daylight simulations. [43] Especially in the case of 3D printed components, tabular BSDF data describe the effect of the layered surface resolution without the need to model the geometry explicitly. Furthermore, the layer-to-layer interactions and fabrication-dependent morphological features can be accounted for. [44] Therefore, 3DP microscopical features are described as material properties and applied to the macroscopic component geometry. This greatly reduces the computational cost of ray-tracing simulations and allows for a higher level of realism of the model. [45] With this representation, daylighting algorithms can solve for light transmission through a 3D printed component and predict illuminance, color, and glare values in a building space. [46] From the application perspective, the control of solar penetration through the facade is a critical factor in buildings. It dramatically affects heat gains, daylighting, energy consumption, and thermal and visual comfort. [47] Solar control strategies need to account for the seasonal variation of solar irradiation, the dependence on latitude and orientation, and the local user requirements. Therefore, the optical properties would ideally need to be tuned locally in the facade. While this is difficult to achieve with traditional manufacturing techniques, 3DP offers great opportunities for such a level of customization. This can be achieved by working with micro-geometry features resulting from the 3D printed layers and the macro-geometry of the component, whose design can be informed by solar conditions. We identify base scenarios where optically tuned 3D printed components can be implemented. For mid-latitude regions, it is essential to tune the admission of sunlight to favor passive solar heating in winter and limit solar transmission in summer. Even for heating-dominated climates, and especially for office buildings, reducing summer solar gains is a crucial step to reducing peak cooling loads. [48] In fact, facade systems coupling windows and angle-selective static shading have been reported to achieve a 30-50% reduction in energy use for midlatitude and subtropical climates. [49] By tuning the geometry and the 3DP parameters, facade components can be designed and fabricated, which admit low-angle sunlight and block the high-elevation one.
Light distribution inside a room is also an essential factor affecting visual comfort and the need for artificial lighting. Deep penetration and even light distribution on working planes (e.g., office desks) can be achieved by integrating light-redirecting features in the facade, which can generate up to 40% lighting energy savings. [52] The upper part of a facade can be designed to stop direct sunlight from falling on the occupants and redirect it to the ceiling, thus allowing the penetration of diffuse light in the space. At the same time, eye-level parts of the facade can be designed to provide visual connection of the building occupants to the surrounding environment. [53] Finally, glare caused by the direct view of the bright sky from the interior of a building can be controlled by minimizing the contrast between the interior and exterior environments. [54] For this, it is crucial to ensure high illuminance levels in a room and block direct sun penetration at low angles.
Components integrating different optical properties for angle-selectivity and light redirection can be designed and embedded into a single 3D printed component with tailored properties (Figure 6d). The optical properties described in this study can be used to derive relevant performance metrics for the design of building facades and determine fabrication settings that will tune the optical properties as required (Figure 6a-c). According to the facade orientation, a cut-off elevation angle can be defined to distinguish between summer and winter incident sunlight (e.g., θ = 40°) and identify appropriate angle-dependent transmission properties. Similarly, low elevation angles associated with the risk of glare (e.g., θ = 25°) can be identified for which direct transmission should be minimized. Finally, by tuning haze values for application-specific angular directions, glare-free daylighting in a space can be achieved along with visual connection to or protection from the outdoor environment.

Discussion
In this work, we presented the potential of optical properties tuning with polymer 3DP for application in bespoke building envelopes. We established an experimental procedure to measure the optical properties of different 3D printed components and demonstrated how printing parameters affect optical properties. The proposed methodology can potentially be applied to any thermoplastic polymer to identify and quantify the relation between optical properties and 3DP settings.
Using the same material (PETG) and 3D printer, we obtained a range of optical behaviors in the samples. We observed total transmission values from approximately 60% to 90% and direct transmission values from 3% to 45% relative to perpendicular incoming light. These properties depend on the number of layer interfaces and their quality. The presence of multiple printing contours attenuates light transmission due to the scattering effects at the interfaces between polymer material and air gaps, resulting in a diffusive behavior. Such scattering effects are enhanced by the presence of air inclusions in between the layers, which can be controlled by the tuning of printing temperature, speed, and cooling rate. Finally, layer height determines angle-selective total and direct transmission properties.
These findings demonstrate the possibility of tuning 3DP parameters to obtain targeted optical properties. In combination with the geometrical freedom offered by 3DP, the transfer of this knowledge to full-scale fabrication holds great potential for designing and manufacturing bespoke building envelopes. Such components can regulate the amount and quality of daylight entering a building according to its location, orientation, and functional requirements, thus reducing the energy demand for cooling and electricity and improving indoor comfort. The monomateriality and the emerging possibilities for closed-loops recycling through 3DP make it possible to envision building envelope components fabricated with recycled polymer feedstock. [53] Therefore, besides operational energy reduction, 3D printed facades can provide reduced embodied emissions as an alternative to traditional glazed facades.
The upscale of this technology and its application will mean a shift to large-scale 3DP set-ups and controlled industrial settings. Experimental data acquisition and correlation analysis with printing parameters will be necessary to calibrate limited combinations of printing set-ups and materials. As in metal [54] and composite manufacturing, [55] we envision that these calibration processes will contribute to the creation of material databases relating to fabrication setups and resulting material properties. As the next step of this research, we will demonstrate how to transfer the findings of this study to large-scale 3DP using recycled polymers (e.g., rPETG), and how to create gradients of optical properties within the same components. Moreover, we will research their thermal performance and its interaction with optical behavior. A complete characterization of 3D printed building envelopes will allow us to assess the performance of these components at the building scale and create computational frameworks to inform the design process.

Experimental Section
Design of Experiments: To evaluate the effect of printing parameters and any interaction effects between those on the optical behavior of 3D printed components, an experimental study was conducted. The study was based on a design of experiments (DoE) approach, using Minitab data analysis software. [58] Given the number of factors and the required resources for the experimental procedure, a 2k −1 fractional factorial design with 5 factors of interest was selected, namely layer height, number of parallel printed contours, printing temperature, printing speed, and cooling fan use. A resolution V design, with design generator I = ABCDE, was selected. In this model, no main effect or two-factor interaction was confounded with any other main effect or two-factor interaction. Still, at least one two-factor interaction was aliased with a three-factor interaction. [59] It was assumed that the higher-order effects were negligible to achieve information about the main effects and low-order interactions with fewer runs.
Test samples were printed and tested in a random sequence to limit the effect of extraneous factors. Moreover, a duplicate of sample 20 was printed and remeasured for replicability ( Figure S4, Supporting Information). An overview of the DoE is presented in Table 1. By creating a fit regression model, statistical analysis was used to describe the relationship between printing parameters (predictors) and optical properties (responses). This allowed to identify relationships among variables as well as how variables influence one or more responses.
Sample Design and Fabrication: The samples described in this paper were fabricated on a custom 3D printer with a build volume of 1.2 m × 0.8 m × 1.0 m. The extruder was an "All Metal BMG" and used 1.75 mm diameter filament as a feedstock. The hot-end was a "Mosquito Magnum" and was equipped with a 60 W 24 V heater cartridge and a PT1000 temperature sensor (Figure 7). The printing material was a PETG filament produced by "Extrudr FD3D GmbH." All samples were printed in a ratio of 2:1 (layer width to height). This is a common setting in most slicing software and reflects the findings that the layer thickness plays a significant role in the structural performance of the finished part, [60] as well as the angles possible to print. The samples had a size of 20 cm×20 cm and were designed to either consist of a single outline or a double outline. In total, three different nozzle sizes were used for fabrication (0.8, 0.4, and 0.2 mm) to obtain desired layer heights of 1, 0.55, and 0.1 mm, respectively.
The samples were designed to have a clean central part for the measurements and a reinforcing structure on the backside. This reinforcing structure is a rectangular grid rotated by 45 degrees in relation to the printing platform, which can be printed without additional support. The depth of the ribs increases toward the edges of the samples to not interfere with the goniophotometer measurements. These reinforcement ribs were introduced to overcome the deformation of the samples. These deformations are typical in either large-flat or thin parts fabricated using FFF 3D printing. [59] As shown in Figure 8, a sample without reinforcement ribs deformed during the process of printing; the thinner the sample, the stronger the deformation observed. The samples with a 1 mm layer height with a double outline did not show any deformation-whereas the 0.1 mm layer height with a single outline was deforming too much to allow for accurate measurement.  Therefore the sample size was reduced to 10 cm × 10 cm for samples 1,3,5,7,9,11,13,15.
To obtain high-quality printing results, no off-the-shelf slicing software was used. Regular slicing software relies on the 3D printer's capability to print, stop the extrusion, move to a new printing position, and continue printing. However, the accumulation of debris was observed when printing in this manner. While these imperfections would be negligible for regular objects and did not influence the part's functionality, the optical properties may be influenced by these imperfections. Therefore, a custom computational tool was developed which is able to contour a given geometry and provided a continuous print path for the 3D printer. In this way, no travel movements were created, and the cleanest printing results was achieved.
Gonio-Photometer Measurements: All evaluated optical properties of each sample were calculated from gonio-photometric light scattering measurements in terms of the bidirectional scattering distribution function (BSDF). The BSDF describes light propagation by transmission or reflection for any pair of incident (θ1, φ1 ) and scattered (θ2, φ2) direction. [62] Therefore, the overall radiance exiting in direction (θ2, φ2) can be defined as as reported in. [69] The employed scanning goniophotometer implemented the sampling of this function by rotation of the sample with respect to the fixed light source and movement of a set of detectors on a spherical path surrounding the sample [63,64] (Figure 9). The parameterization of the measurement was asymmetric in that it combined a small number of regularly spaced incident directions with a larger number of scattered directions. [65] These can resolve narrow peaks and allow to account for even subtle differences between the samples.≈250000 samples were taken per incident direction. These covered the half-spaces on both sides of the sample to account for transmission and reflection. Since the instrument aims at high acquisition speed, the detector head performed a continuous rotation while the samples were taken at randomly distributed but accurately measured directions. Assuming that these distributions change only gradually between adjacent incident directions, only a small number of the latter was represented by sub-sets of a regular angular basis. This subset covered one quadrant of each half-space, assuming symmetry over two orthogonal axes according to the layer structure of the evaluated samples.
Generation of Data-Driven BSDF: The goniophotometer measurements of exiting transmittance and reflectance for selected incident directions need to be processed to build a model which can predict transmission from any incident direction. A continuous description of the BSDF over the 4D domain was derived by interpolating between sparse incident directions. [65] To do this, an interpolant model for the measured incident directions based on a fit to the measured exiting distribution was first generated using Gaussian radial basis functions (RBF). [66] This fitting was implemented in radiance through the function pabopto2bsdf. [67] Then, the interpolated BSDF was reduced to the target Klems resolution to obtain a tabulated dataset. [44] The Radiance function bsdf2klems implements this step. Through the processes of interpolation and reduction of interpolated data to a discrete angular basis, the measured BSDF for each sample was transformed into the final tabulated BSDF for further analysis.
Electron Microscope Imaging: The printed samples were fractured mechanically. The fragments were mounted pre-tilted with conductive carbon cement onto stubs. For conductivity, the samples were sputter coated with platinum/palladium while being planetary rotated. Samples were introduced into a JEOL JSM-7100F scanning electron and tilted to expose the fracture plane. Images were acquired at 3 kV in secondary electron mode.
Differential Scanning Calorimetry: DSC measurements on 3DP filaments were conducted with TA Instruments TA2500 differential scanning calorimeter with a 10 K min −1 heating rate under nitrogen purge of 50 mL min −1 .
Thermogravimetric Analysis: The thermal behavior of filaments and printed PETG was studied using a thermogravimetric analyzer (TGA Q50, TA instruments waters L.L.C, New Castle, DE, USA) under a nitrogen purge flow of 40 mL min −1 . The sample was loaded on an aluminum pan (TA instruments-waters L.L.C, New Castle, DE, USA) and heated at a rate of 10 °C min −1 from room temperature to 600 °C. Data were analyzed using TA Instruments Universal Analysis 2000 software