Development and application of a 3D image analysis strategy for focused ion beam – Scanning electron microscopy tomography of porous soft materials

In recent years, the potential of porous soft materials in various device technologies has increased in importance due to applications in fields, such as wearable electronics, medicine, and transient devices. However, understanding the 3‐dimensional architecture of porous soft materials at the microscale remains a challenge. Herein, we present a method to structurally analyze soft materials using Focused Ion Beam – Scanning Electron Microscopy (FIB‐SEM) tomography. Two materials, polymethyl methacrylate (PMMA) membrane and pine wood veneer were chosen as test‐cases. FIB‐SEM was successfully used to reconstruct the true topography of these materials in 3D. Structural and physical properties were subsequently deduced from the rendered 3D models. The methodology used segmentation, coupled with optimized thresholding, image processing, and reconstruction protocols. The 3D models generated pore size distribution, pore inter‐connectivity, tortuosity, thickness, and curvature data. It was shown that FIB‐SEM tomography provides both an informative and visual depiction of structure. To evaluate and validate the FIB‐SEM reconstructions, porous properties were generated from the physical property analysis techniques, gas adsorption analysis using Brunauer‐Emmett‐Teller (BET) surface area analysis and mercury intrusion porosimetry (MIP) analysis. In general, the data obtained from the FIB‐SEM reconstructions was well‐matched with the physical data.

• Reconstruction data is compared to physical data: MIP, gas adsorption isotherms which are analyzed via BET and Barrett-Joyner-Halenda (BJH) analysis to yield a full picture of the materials.

K E Y W O R D S
3D reconstruction, focused ion beam, membrane, mercury porosimetry, porous materials, scanning electron microscopy, soft materials, tomography, wood
The successful integration of soft materials into these devices can be attributed to their unique chemical, physical, and electronic properties, which include improved flexibility (Li et al., 2020), degradability (Fu et al., 2016), and functionality, such as self-healing and wearable devices with improved mechanical strength (Karolina Pierchala et al., 2021).New soft material devices require particular properties for specific functionalities; hence, it is essential to deepen our understanding of the inner 3D morphology of soft materials at the microand nano-scales.This is particularly true for porous materials since they often have complex morphologies, and most traditional characterization methods, such as measurement of gas adsorption isotherms with Brunauer-Emmett-Teller (BET) analysis and mercury intrusion porosimetry (MIP) give either "average" data (Neusser et al., 2017;Zeng et al., 2020) or show 2D structural representations (Buckman et al., 2017).3D tomographic techniques, such as x-ray tomography (Rashidi et al., 2020), optical and laser tomography (Goorsenberg et al., 2020;Podoleanu, 2012;Tan et al., 2013) and electron tomography (Jinnai & Jiang, 2013) can be utilized for 3D reconstructive analyses.However, many of these techniques were originally developed for the structural characterization of hard materials, metals and conductive materials, and do not necessarily perform as effectively on softer materials (Ercius et al., 2015;Fager et al., 2020;Jinnai & Jiang, 2013;Rashidi et al., 2020).Thus, the need to explore novel, innovative strategies for the tomography of porous, poorly conductive and organic materials.
Focused ion beamscanning electron microscopy (FIB-SEM) methodology is one useful method for volume reconstructions for various types of materials (Bassim et al., 2014;Fager et al., 2020;Gu et al., 2020;Williams et al., 2004).Although FIB-SEM is a destructive technique, it can be used to reconstruct the true topography of materials that interact with the SEM electron beam.The principle is as follows: FIB is used to mill the sample, with SEM images being acquired at specific intervals during the milling process.The milling and imaging parameters must be carefully optimized depending on the material of interest.The resultant images are reconstructed via computational means and structural properties are thus deduced from the rendered 3D model (Cocks et al., 2018;Müller et al., 2021;Reimers et al., 2019).Different SEM detectors are sometimes preferentially used for reconstructions, such as backscatter (Cantoni & Holzer, 2014), mid-angle backscatter (Fager et al., 2020), secondary electron detectors (Lasagni et al., 2007) and various combinations such as backscatter and secondary electron detectors in tandem or through-lens detector (Matthijs De Winter et al., 2009;Meffert et al., 2020;Nan & Wang, 2019;Neusser et al., 2017;Xu et al., 2017) aimed at gathering structural, elemental information (Lasagni et al., 2008) as well as reduction of charging effects (Liu et al., 2016).
In this study, we demonstrate a robust and accessible FIB-SEM methodology for analyzing two soft materials with anisotropic morphologiespoly(methyl methacrylate) (PMMA) membrane and pine wood veneer.PMMA membranes with inter-connected porous network structures were prepared via air-cast, thermally-induced phase separation (TIPS) (Gu et al., 2001;Zeman & Fraser, 1993).Sample embedding was avoided as it can affect the observed morphology of soft materials (Roberge et al., 2022) as well as incurring extra processing steps.Optimized thresholding, image processing, and reconstruction methods are describedthe methods used depend on the morphological features of a given sample as well as the image quality.
The rendered models were also informed by physical property measurements obtained from BET and MIP analyses.

| RESULTS AND DISCUSSION
PMMA membrane 3D structural analysis.The first reconstructed sample is a network PMMA membrane, produced via an air-cast, TIPS method.The detailed rationale for the membrane production method is outlined in the Supporting Information; the casting conditions are shown in SI Figure S1A.The 5 wt.%PMMA membrane morphology is displayed in Figure 1.
The average pore sizes for the PMMA membranes are 3.07 ± 1.38 μm for the skin side of the membrane and 3.80 ± 1.41 μm for conveyor side, as determined from the SEM images.Membrane thickness was estimated from SEM as 77.64 ± 2.31 μm.It can be seen that a wide range of pore sizes exist.The conveyor side is consistently porous relative to the skin side; hence, such membranes should be used with skin side as the selective surface to control rejection of solutes.Porosity was also estimated from FIB cross-sections.Resin embedding was avoided since the sample displays low tensile properties such as tensile strength below 2 MPa as shown in SI Figure S1B.Furthermore, resin embedding was primarily not employed to simplify the protocol and to demonstrate that reconstruction without highlighting the membrane matrix with heavy metals or dyes is possible.Figure 2 shows a schematic representation of FIB milling/SEM imaging as well as SEM and FIB views prior to milling.The secondary electron (SE2) Everhart-Thornley detector (ETD) was used in order to obtain each slice.
The stages of initial image preparation are outlined in Figure 3.
The threshold and bandpass filters were applied according to Neusser et al (Neusser et al., 2017).Initially, the stack was processed with a Fast Fourier Transform (FFT) bandpass filter (Figure 3b) and subsequently the stack is binarized (Figure 3c).Filtering adjusts the intensity levels and filters out structures by size in order to obtain uniform brightness in all images in the stack.Binarization allows for differentiation between pores or empty space versus the membrane branches.
The threshold application (Otsu) (Otsu, 1979) was used to distinguish effectively between background and foreground features, in this particular case.The sample volume under investigation is from a section of the membrane midway between the skin and conveyor sections and is a small yet representative portion of the real membrane.
The porosity for the sample volume as shown in Figure 3d (16682.4μm 3 ) was measured as 70.50% ± 4.50%.
FIB reconstruction provides a way to visualize and understand how a given morphology (Figure 3d) might be suited to a specific application, such as a flow-through membrane filter, or a porous chromatographic media, for example.Ideally, multiple reconstructions should be analyzed but the process is slow and costly.
The pore size distribution of overall pore space was analyzed using xlib continuous pore size distribution (PSD) (Münch, 2022;Münch & Holzer, 2008) which is displayed as a cumulative pore distribution (on a volume basis) in Figures 3e.The continuous PSD calculates the pore radii in 3D for our purposes where the pore space is regarded as regions (i.e., continuous not discrete) that are filled with balls of different radii (Münch & Holzer, 2008).The radii per location are represented as a continuum versus the volume of the pore region (Münch & Holzer, 2008).The average pore diameter calculated was 1.68 μm with a sample deviation of 1.10 μm.The continuous PSD provides a useful representation of pore size, and pore sizes in the sample as a whole, over a wide range, 1-5000 nm approx.For comparison purposes, an MIP simulation on the images was also run with the intrusion start area set as the XY plane (Münch, 2022;Münch & Holzer, 2008).The MIP simulation is similar to continuous PSD, however the volume is intruded (i.e., balls of different radii are intruded) from a specific face of the cube comprising binary image stack (Münch & Holzer, 2008).This yielded a mean diameter of 1.10 μm.
The MIP PSD displays distinctive steps which are indicative of several peak pore diameters, for example at 1.00, 1.40, and 3.00 μm.This is quite typical of an actual mercury porosimetry experiment, whereby mercury surrounding the sample is subjected to ever increasing pressure, and mercury, being non-wetting, will only enter available pores when specific pressures are reached.Rapid intrusion of mercury can occur and, as such, the raw, volume-intruded graph can appear erratic and "discontinuous."The occurrence of several distinct intrusions suggests the presence of different subsets of pores within a sample, that is, the porosity within the sample is variable and anisotropic.
Skeletonise and Analyze Skeleton plugins were used to estimate the branch length of the membrane fibers (Arganda-Carreras et al., 2010;Doube et al., 2010;Lee et al., 1994).The average branch length for the sample is 1.03 ± 0.79 μm while the maximum and minimum lengths are 8.04 and 0.04 μm, respectively.The number of branches and junctions are estimated as 1.95 branches μm À3 and 1.05 junctions μm À3 , respectively.The number of connected branches per μm 3 is calculated as 0.5.A low branch-junction density per volume is expected for these highly porous network membranes.The pore connectivity is similarly $0.5 μm À3 .The Analyze Skeleton plugin was used to estimate tortuosity of pores from Euclidian distance and actual branch or pore length in 3D.A tortuosity value, τ = 1.43 ± 0.81 was calculated for the PMMA membrane.The branch length distributions, tortuosity distributions and Euclidean distance distribution of pore to matrix for both PMMA and pine samples is also shown in SI Figure S2 for the ease of visualization.
Pine veneer 3D structural analysis.Pine veneera naturally porous materialwas also investigated to compare and contrast against the synthetic PMMA membranes.The pore variation is again large, in this case, as there are natural cavities in the wood, as well as vessel lumen.Pine micrographs showing large-area SEM and localsurface AFM are displayed in Figure 4a-c.The lumen pore sizes were estimated from the SEM images collected prior to the FIB-SEM processing as 11.93 ± 4.26 μm.The trenches were prepared by FIB in the same manner as for PMMA; the material was removed around the area of interest prior to the reconstruction (SI Figure S3).The sample required substantial processing prior to reconstruction.
Image processing details for the pine sample are summarized in Figure 5.In general, image processing of the pine was more challenging than PMMA, due to large discrepancies of gray levels in foreground "dense" wood and background porous regions.Also, a shadowing effect (Lasagni et al., 2008;Matthijs De Winter et al., 2009) could be observed inside the pore regions when the lumen was slightly tilted with respect to the SEM field of view.
The shadowing effect is due to the sample orientation specifically the lumen cell wall being oriented at an angle to the SEM detector.SI Figure S4A further annotates regions of the shadowing effect where areas facing the detector appear bright and areas away from the detector appear dark as the lumen is tilted.It is noted that the curtaining is not removed as image processing becomes inherently complicated after applying an FFT bandpass filter to the original stack resulting in the loss of contrast differences between lumen (void) and wood matrix.SI Figure S4B further demonstrates how the contrast is evened out after an FFT bandpass filter is applied.An automated segmentation method was attempted using Ilastik software (Berg et al., 2019), however our segmentation approach, that is, the method provided in Figure 5, was found to yield better results when compared to the raw image.The porosity is estimated as 65.75% ± 2.05% from a reconstructed volume of 7143.41 μm 3 , as shown in Figure 4d.It is important to note that care and expertise is required, as thresholding can have a tendency to pass over pores inside the dense fiber layers between lumen, leading to the porosity of a sample being underestimated.The voxel resolution in XY was 82.20 nm pixel À1 with a depth of 30.04 nm which is sufficient for given feature sizes ($micron range).Here, the connectivity is low as expected (0.06 branches μm À3 ) since the pores in the lumen structures run in parallel.The tiltcorrected Feret diameter of an individual lumen in the reconstruction is 16.29 ± 0.64 μm due to 30 tilt in the YZ plane as shown in SI This is expected as the sample contains variable lumen sizes and triangular cavities between lumen cylinders.
The pore tortuosity in this case is approx.1.26 ± 0.90 μm, which is consistent with wood lumen structure.The pore connectivity is low, that is, approx.0.03 interconnected pores per μm 3 .This value is two times smaller than that of branches and signifies standalone pores, in an otherwise dense structure.The low connectivity is consistent with large cavities, in accordance with the visual representation (Figure 4).3D rendered models.The binarized stacks were rendered in Blender (Community, 2018) to yield 3D models of our structures.
Thickness 3D maps normal to the surface (Páli, 2016) were also generated.PMMA membrane and pine reconstructions are shown in Figure 6.The thickness maps show the packing density, as well as the pore space, in 3D.Understanding thickness variability can help to define the structural properties and how they effect tensile properties, flow rates of filtrates, and so forth for a given sample.Furthermore, connected pore regions were obtained via Labeling 2D 3D in xlib (Münch, 2022) and visualized via Volume Viewer (Barthel, 2005) in Fiji/ImageJ (SI Figure S6).The connected components are displayed in the same color.The analysis was conducted using 3D Manager as part of 3D Suite (Ollion et al., 2013).It is useful to quantify and understand the pore discontinuity as it can affect properties, such as thermal conductivity (Arriagada et al., 2019), tensile parameters (Gao et al., 2021;Jones et al., 2009) and acoustic transmission of the material (Shang et al., 2022).It also provides insight around the mechanism of material formation in bulk; for instance, during PMMA membrane casting air bubbles can get trapped which results in cavities.For PMMA, a total of 501 different porous phases were identified, that is, 500 disconnected particles, which account for approx.0.03% of the total volume.The pine sample was processed via MorpholibJ (Legland et al., 2016) for better visual representation and 3D labeller, which identifies the lumen and triangular cavities as the same phase.The pore volume that was not part of lumen or triangular cavities at lumen borders was approx.0.10% as assessed via xlib segmentation.In this case, the number of particles is not relevant as lumen voids can be considered as the same region or different phases depending on the segmentation method.Mercury intrusion porosimetry (MIP) and Brunauer-Emmett-Teller (BET) analysis.To evaluate and validate the FIB-SEM reconstructions, pore size distributions were generated from physical MIP and gas adsorption isotherm measurements with BET and BJH analyses.Figure 7 shows the mercury intrusion profiles and pore size distributions obtained for PMMA and pine, respectively.
In the case of PMMA, there is evidence of pores as large as 10,000 nm, down to about 2000 nm, at which point a sharp intrusion end, the slope of the curve points to the existence of pores >10,000 nm, with the likelihood of a second peak existing in this region, beyond the upper measurement range of the instrument.A second peak is expected on account of the pores of approximately 15-20 μm in diameter (cylindrical vessel lumen) observed from the SEM and FIB images (Figure 4a,b and SI Figure S3).In Figure 7b a second intrusion of mercury occurs, corresponding to pores in the range 10-40 nm.However, this only manifests as a very minor peak on the volume-based pore size distribution plotthe peak is dwarfed by the magnitude of the much larger pores.Of note is the total intruded volume of 0.46 cm 3 /g, approximately one fifth that of PMMA, however it must be noted that pores larger than 10 μm (as observed in Figure 4) are not included in this pore volume value.As such, the true, total pore volume of the pine sample is likely to be considerably higher than 0.46 cm 3 /g.BET surface area analysis was conducted on both samples, with a value of 13.0 m 2 /g measured for PMMA, and 2.8 m 2 /g for pine.Both values are in keeping with samples that are dominated by micrometer-sized pores.The largest contribution to surface area will come from the smallest pores, and while both samples have prominent peaks at 1000 nm, the pore volume of these pores is approx.five times larger for PMMA than for pine.Also, the open, interconnected nature of the pore morphology will strongly influence the surface area.Likewise, although the pine has obvious cylindrical lumen pores, they are of the order of 15-20 μm and run parallel to each other with very limited connectivity.As such, their contribution to surface area will be low.
Barrett-Joyner-Halenda (BJH) analysis was conducted to thoroughly investigate the porosity below 70 nm approximately.Type IV isotherms were observed for both samples, and the resultant BJH pore distributions are shown in Figure 7c,d.For pores <70 nm, the measured pore volume of PMMA (0.09 cm 3 /g) was the same as that of pine (0.09 cm 3 /g).As expected, the volume intruded profiles for both samples assumed an upward trajectory at 70 nm, indicating the presence of pores >70 nm, beyond the measurement range of the instrument.Unlike pine, the PMMA sample showed evidence of porosity sub-10 nm (0.008 cm 3 /g), but in the overall context this is of little significance, that is, 0.008 cm 3 /g of 2.3 cm 3 /g total, equalling 0.35%.

| COMPARISON OF MIP AND BET WITH THE FIB-SEM ANALYSIS
PMMA sample.xlib continuous PSD and MIP simulation from images pore size distributions were generated as per Figure 3e.As can be seen, the accessible pore diameter range was 0-5000 nm using xlib PSDs (continuous and MIP simulation), which is somewhat lower than that available from the physical MIP analysis.The xlib simulation shows a continuous pore size distribution, with significant porosity from approx.4000 to 200 nm approx., with the steepest section of the curve occurring at approx.1000-2000 nm.The MIP simulation on the images is more specific and less continuous in terms of the intrusions detected.For example, notable intrusions occur at 3000, 1400, and 1000 nm, respectively.These intrusions are in good agreement with the peaks and sub-peaks observed for PMMA in Figure 7a.
However, the simulation appears somewhat lacking in terms of pore detection >3000 nm.This is likely due to the fact that the simulations are carried out on localized regions, 50 μm 2 approx., whereas a mercury porosimetry experiment uses several cm 2 of sample.
A parallel scenario to the one discussed here is the use of SEM to measure particle size; the measurement can be successfully made but is limited to a relatively low number of particles.Depending on the image resolution and slice, thickness certain small features might be excluded, that is, below the pixel resolution.Furthermore, FIB milling can generate cavities which can also overestimate small features conversely.Thus, FIB milling area as well as SEM image resolution should be chosen keeping those factors in mind, such as anticipating expected feature sizes the user would like to reconstruct.On the other hand, the physical measurement equivalentlaser diffraction particle size analysiscan measure several thousand or tens of thousands of particles in a single measurement, resulting in very comprehensive and robust measures of mean particle size, and so forth.
Pine sample.xlib and MIP pore size distributions were generated as per Figure 4e.The accessible pore diameter range in this case was 0-25 μm, which is much larger than that available from the physical porosimetry analysis.The xlib and continuous simulations are quite well-matched.The most significant finding is the presence of sharp intrusions at approx.22 μm, 14 μm, and again at 11 μm, accounting for approx.50% of the total intruded volume.These peaks are beyond the range of the mercury porosimetry analysis, but they are in good agreement with the SEM imagery, which clearly show the presence of cylindrical lumen pores in the 15-20 μm range.Further intrusions of note are observed at 6000 and 1500 nm approximately.Some discrepancy from the physical measurement data is expected since mercury porosimetry measures pore entrances (the "throat diameter") as mercury is forced into pore openings, whereas simulations are derived from a series of sample cross-sections.

| CONCLUSION
FIB-SEM is adept at interrogating local structures, but it can also be instrumental in predicting bulk properties.This work demonstrates the development of an accessible and novel strategy based on the FIB-SEM technique for analyzing porous soft materials; PMMA and pine.The detailed methodology does not require embedding during sample preparation, allows variable FIB-SEM tomography settings and does not necessitate high computational processing power.Furthermore, the reconstructions utilize free, open-source software.
In general, in the ranges where meaningful cross-comparisons could be made, FIB-SEM reconstructions were well-matched with physical mercury porosimetry data.The two methods complimented each other as image reconstruction interrogates specific areas of the sample while physical porosimetry gives and overall bulk porosity insight.However, it is noted that results can be contradictory (Münch & Holzer, 2008) either due to the choice of sample area with FIB-SEM or how the pore measurement models are applied to images, or due to how mercury or nitrogen interact with the sample of interest.FIB-SEM reconstruction is a particularly helpful accessory in cases of small sample sizes; too small for porosimetry analysis, or in cases where a non-destructive technique is required.A drawback is the localized nature of the reconstruction approach, that is, it is based on a limited number of μm-scale microscopy slices.
In the case of the pine sample (with variable cylindrical and tilted pores), FIB-SEM reconstruction proved especially useful to assess specific regions such as the wood cell wall.Quantitative data such as tortuosity, pore size distributions, structural thickness, interconnectivity and curvature distribution in 3D were obtained to derive secondary information for local structure (such as flow rates, ionic transport, tensile properties etc.) which were not accessible by bulk testing techniques.The calculable pore sizes accessible in the simulation developed here (0-25,000 nm) were well in excess of the measurable range using mercury porosimetry.The simulation successfully captured porosity in this extended range; ones which accounted for as much as 50 vol% of the total sample porosity.
Different thresholding methods for images depending on the SEM artifacts are also presented which can inform the design of data processing procedures for FIB-SEM of new materials.A shadowing effect was observed for the pine sample, as well as tilted structures.
To overcome this, two approaches based on manual and machine learning software (ilastik) were developed.We anticipate that our findings will be applicable for non-conventional soft samples and can further the development of FIB-SEM tomography to facilitate the design of new and emerging materials.

Mercury intrusion porosimetry (MIP) was conducted via
Autoscan-33 porosimeter (Quantachrome).The pore diameter D was calculated according to: (Zhang et al., 2014) where θ is the contact angle between the solid and mercury, γ is the surface tension of mercury (485 dyne cm À1 ) (White, 1968), and P is the hydraulic pressure applied to force penetration of the mercury into the pores.θ = 150 is used for PMMA and θ = 140 for pine samples.
Brunauer-Emmet-Teller (BET) surface area analysis was carried out using a Nova 2400e Surface Area Analyzer (Quantachrome, UK) with nitrogen gas as the adsorbate.Surface areas were calculated from the adsorption branch of the isotherm in the linear region (P/P 0 : 0.1-0.3).The BJH method was used to calculate pore size and pore volume from the adsorption branch of the isotherm.ImageJ (Schindelin et al., 2012) setting translation in XY as the only transformation (Lowe, 2004;Neusser et al., 2017).Subsequently the stack was cropped.The filtering and thresholding was conducted differently on each stack due to differences in artifacts present and feature sizes and shapes under consideration as follows: PMMA samples: a bandpass FFT filter and Otsu threshold was applied (on a stack histogram) to yield binary images for all samples.
The porosity of sample volume was measured from binary image stacks, that is, pores or cavities were set to 0 intensity (black) and membrane structure was set as 255 (white).
Pine veneer samples: The pine sample area exhibited pores/ lumen seen as both bright and dark areas while the dense background appeared gray.In order to effectively create a mask of only the "hole" regions, a series of filters were applied in the following order: gaussian (3D) filter with 1σ, bright outliers were removed with radius of 2 pixels and a threshold of 10, minimum (3D) filter with radius of 2 pixels, variance (2D) filter with radius of 2 pixels.Morphological segmentation analysis was conducted with MorpholibJ plugins (Legland et al., 2016).
The resultant segemented regions were set as white with a black background.The original stack was thresholded manually to identify all dark features and outliers were removed with dilation and subsequent erosion command (open command).The segmented binarized output and manually thresholded dark regions were added together to produce the required stack.Overall process is defined in SI Figure S3.Ilastik software was also used to threshold the stack (Berg et al., 2019), but a manual method was employed for analysis.
The samples were analyzed with various Fiji/ImageJ (Schindelin et al., 2012) plugins and other software.3D object counter was used to analyze disconnected pore volume in PMMA (Bolte & Cordelières, 2006).
Skeletonise and Analyze Skeleton plugins were used as part of BoneJ plugin to measure membrane branch length and pore tortuosity (Arganda-Carreras et al., 2010;Doube et al., 2010;Lee et al., 1994).Purify plugin was used to remove unconnected particles for Connectivity analysis (Odgaard & Gundersen, 1993).Pore size distributions were obtained

F
I G U R E 1 (a-c) SEM images of skin (top), conveyor (conveyorside) layers and cross-section of 5 wt.%PMMA membrane dried at 30 C. (d) AFM image of the skin layer with an associated z-profile scale.F I G U R E 2 (a) schematic of the FIB-SEM slicing and imaging and subsequent reconstruction.Trench area to be milled prior to FIB-SEM processing of PMMA membrane.(b) SEM micrograph (5 kV, 380 pA, 60 μm aperture) of the trench to be milled.(c) FIB top-down micrograph (30 kV, 4 nA) with the area used for serial sectioning process enclosed in rectangle selection.

F
I G U R E 3 Image processing representation applied to image stack after FIB milling and SEM recording.(a) Raw 5 wt.%PMMA SEM image.(b) FFT bandpass-filtered image.(c) Binarised image using Otsu method (Otsu, 1979).(d) 3D volume representation of a bandpass FFT-filtered 5 wt.%PMMA sample.(e) Continuous pore size distribution and MIP simulation on the images via xlib plugin.

Figure S5 .
Figure S5.Minimal tilt (<5 ) is observed in the XZ, thus the minimum Feret diameter should not vary from the estimate of 15.02 ± 0.14 μm.The circularity of the tilt-corrected lumen was calculated as 0.77 ± 0.07.Average pore size of 14.87 μm (xlib, continuous PSD) and 14.05 μm (xlib, MIP simulationon the images with intrusion at XY) were calculated, as shown in Figure 4e.It is worth noting that both distributions yield similar shapes, and both feature several distinctive peaks.

F
I G U R E 4 SEM images of the pine veneer where (a and b) represent the top-down and cross-section views, respectively.(c) AFM image of the pine veneer with an associated z-profile scale.(d) 3D volume representation and (e) Continuous pore size and MIP simulation on the images via xlib plugin.
Gaussian curvature 3D maps were obtained via MorphoGraphX 2.0(Strauss et al., 2022) as shown in SI Figure S7 with a neighborhood of 1 μm.Gaussian curvature is useful as it is intrinsic to the surface and independent of deformation (Rueda-Contreras et al., 2021).The curvature helps to visually interpret whether the surface is flat (a 0-value curvature) or not (positive values indicating peaks or local valleys and negative values indicating saddle points)(Gupta & Saxena, 2012).Overall, it is possible to display 3D information as color-coded maps to represent various attributes of the material under review.

F
I G U R E 5 Image processing stages for the pine veneer sample.The scale bar is 5 μm. of mercury occurs, peaking at approximately 1000 nm.Intrusion of mercury continues to approx.200 nm, beyond which only minimal intrusion occurs.The resultant pore size distribution, plotted as an overlay in Figure 7a is in good agreement with the morphology observed from the SEM micrographs (Figure 1), where cavernous openings are seen at the exterior of the morphology, which then give way to a denser fibrous network of smaller pores.Of significance for the PMMA sample is the large pore volume value of 2.3 cm 3 /g, typical of an open, interconnected porous morphology with a high percentage porosity.For pine, the intrusion profile is similar to PMMA insofar as a prominent peak occurs at approximately 1000 nm.At the large pore F I G U R E 6 Rendered 3D models for membrane samples.(a-d) Show the PMMA membrane, branch thickness map, membrane pore space and pore space density map, respectively.(e-h) Represent the pine, pine thickness map, lumen space and lumen space density respectively.F I G U R E 7 Mercury porosimetry intruded volume and pore size distributions (dV/dP) as a function of pore diameter for (a) PMMA and (b) pine.BJH analysis showing cumulative pore volume of pores below 70 nm and pore size distribution (dV(d)) for (c) PMMA and (d) pine.
The chemicals of analytical grade used in this report were purchased from Sigma-Aldrich.PMMA was purchased from Altuglas (BS572), number average molecular weight, M n = 440.5 kg mol À1 and polydispersity index (PDI) = 1.04, as measured by Gel-Permeation Chromatography (GPC).Acetone (ACS reagent, ≥99.5%), ethanol (dehydrated, 200 proof), acetic acid (glacial, ≥99%) and glycerol (≥99.0%) were purchased from Sigma-Aldrich and used without further purification unless otherwise stated.Pine veneers were supplied by MEDITE SMARTPLY and used without pre-treatment.PMMA membrane preparation.PMMA membranes were cast from solutions containing 5 wt% PMMA, 40 wt% acetone and 55 wt% ethanol.The PMMA solutions were left to stir at 30 C overnight prior to casting.Membranes were prepared in a custom apparatus consisting of a conveyor belt and casting and drying chambers.The casting conditions were kept constant and monitored via temperature and humidity sensors.Incoming desiccant air flow was maintained at flow rate of 1.5 Ls À1 and air was removed at a rate of 38 Ls À1 as measured with an anemometer.Melinex backing film was attached to the conveyor and the motor speed was set to 3 Â 10 À2 ms À1 .The cutting knife at the solution inlet was set to a height of 1 mm over the Melinex backing film.The membrane solution was pumped with a peristaltic pump at 50 rpm.The air temperatures in curing and drying chambers were adjusted to 25 C initially for 30 min and gradually raised to 30 C to ensure complete solvent removal.The conveyor temperature was adjusted to 20 C and kept constant.The membranes were recovered after approx.90 mins from the beginning of casting.Characterization.PMMA and pine samples were cut with a dumbbell mold with dimensions of 50 mm in length and 4 mm width.The strain increase rate was set to 2 mm/min.The experiments were set to stop after membrane fracture.The test was repeated 6 to 10 times for each sample.Tensile strength and Young's modulus measurements on PMMA were performed via a Mechanical Analysis machine (Zwick Roell -Instron) using a 100 N load cell, and setting grip to grip separation to 41 mm.Pine veneer tensile properties were measured with an Instron 3366 Tensile Tester using a 2.5 kN load cell and the same grip separation.Scanning electron microscopy (SEM, Zeiss Ultra Plus) images were recorded with an accelerating voltage of 2 kV, 30 μm aperture under pressures below 9 Â 10 À5 mbar and a working distance of 4 to 5 mm.SEM cross-sections of macro membranes were obtained at a 90 angle.PMMA membranes were cleaved after freezing in liquid nitrogen in order to preserve morphology.Other samples were cleaved with a knife.Samples were sputter coated with gold/palladium prior to analysis on SEM to prevent charging effects.SEM images were utilized to measure pore sizes manually as largest open pore diameter and cross-sectional thickness taking an average and standard deviation from 20 measurements.Atomic force microscopy (AFM) (Park systems, XE7) was operated in NCM (non-contact mode) under ambient conditions using silicon microcantilever probe tip (force constant of 42 Nm À1 ).
FIB-SEM tomography.FIB-SEM tomography (Zeiss AURIGA) was performed at a tilt angle of 54 (tilt correction 36 for SEM), 5 mm working distance (eucentric point).Samples were sputter-coated with gold/palladium prior to milling and copper tape was used in proximity of the area of interest.SEM imaging was conducted with an accelerating voltage of 5 kV for PMMA samples and 2 kV for pine samples.SEM images were acquired using 60 μm aperture and high current (380 pA) option for all samples.Trenches were milled around the area of interest to reduce interference and allow for image collection.FIB trenches were prepared at 30 kV and 10 nA beam voltage and current at the edge of sample.FIB current was reduced to 1 nA during milling and secondary electron (SE2) image collection.PMMA and pine samples SEM images were collected as slices determined by the ZEISS Auriga FIB at intervals of 1 as pre-set in the FIB Control menu, Options tab in the SMART SEM software.(The intervals are the voxel depth or z-resolution for those samples as the software does not allow to preset slice thickness it is calculated afterwards from the milled depth).The entire process of milling and image collection took less than 6 h.FIB reconstruction and data processing.The image stack was aligned via Linear Stack Alignment with SIFT, Registration plugin on Fiji/ from xlib (Münch, 2022; Münch & Holzer, 2008) plugins; MIP simulations on the images were additionally conducted via xlib.Surfaces of binarized samples were exported from 3D Viewer on Fiji/ImageJ (Schmid et al., 2010).3D rendering is performed via Blender (Community, 2018) (loose objects were removed for all samples).Thickness 3D maps were constructed in Blender normal to the surfaces (using normal dependent F I G U R E 8 Workflow of image alignment and binarization stages.