### Abstract

We show that attenuation X-ray microcomputed tomography (μ-CT) offers a route to extract the three-dimensional pore space of paper reliably enough to distinguish samples of the same kind of paper. Here, we consider two sack kraft papers for cement bags with different basis weights and thicknesses. Sample areas of approximately 5 mm^{2} with a resolution of 1.5 μm are considered, i.e. sizes that exceed sample areas of 2 mm^{2} for which the pore structure was previously studied in the literature. The image segmentation is based on indicator kriging as a local method that removes ambiguities in assigning voxels as pore or as fibre. The microstructures of the two samples are statistically compared in terms of descriptors such as sheet thickness, porosity, fractions of externally accessible pores and mean geodesic tortuosity. We demonstrate that a quantitative comparison of samples in terms of porosity and thickness requires a common definition of the sheet surfaces. Finally, the statistical pore space analysis based on the μ-CT scans reliably reveals structural differences between the two paper samples, but only when several descriptors are used. Lay description: This paper is a seemingly abundant material. Its intrinsic porosity enables a vast number of commercial applications. Particularly packing products, e.g. cement bags, often incorporate sack kraft paper due to its high porosity and its additional mechanical strength. A direct quantification of the porosity of sack kraft papers is, hence, particularly desirable. However, experimental quantification of paper porosity or its pore network properties is difficult and often highly indirect. A nondestructive statistical analysis of the 3D microstructure holds the promise to directly assess the pores. In particular, X-ray microcomputed tomography (μ-CT), frequently with sub-μm resolution, has been established as a method to study the fibre and pore structure of paper. The question arises, whether statistical analysis of the microstructure based on μ-CT imaging is sufficient to reliably distinguish between different sack kraft papers. Here, we explore whether the pore structure of paper can be extracted and statistically analysed for larger sample areas despite the fact that a larger sample size directly translates into a lower resolution of the μ-CT scan. We expect that a large sample size increases the region of interest on the basis of which samples can be better distinguished. A lowered resolution poses a severe challenge for the reliable identification of voxel data as pores or as fibres, because the contrast between paper fibres (made of cellulose) and air, which is established due to X-ray absorption, is weak. We show that we can reliably assign each voxel by using an indicator kriging as a two-step method. This method performs an initial voxel identification based on the overall distribution of measured grey values and refines the identification by inspecting the local environment of each voxel. For the pore space extracted in such a way, we can then compute quantities that are related to the geometry and connectivity properties of the pores. Furthermore, we address a paper-born challenge for such an analysis, i.e. we cannot always unambiguously tell whether a pore is located inside the paper sheet or at the surface of the paper. The way the paper surfaces are extracted from the microstructure decisively determines the final specifications of the predicted properties. A significant distinction of the samples is only possible when comparing the properties of the pore network.

Original language | English |
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Pages (from-to) | 35-46 |

Number of pages | 12 |

Journal | Journal of microscopy |

Volume | 272 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Oct 2018 |

### Keywords

- Paper structure
- pore space
- porosity
- sack kraft paper
- segmentation
- statistical data analysis
- μ-CT

### ASJC Scopus subject areas

- Pathology and Forensic Medicine
- Histology

### Fields of Expertise

- Advanced Materials Science

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## Cite this

*Journal of microscopy*,

*272*(1), 35-46. https://doi.org/10.1111/jmi.12730