Fractal Dimension Analysis of Surface Roughness for Paper and Paperboard

Yong Ju Lee; Na Young Kang; Ji Eun Cha; Ji Min Lee; Do Young Lee; Hyoung Jin Kim

doi:10.7584/JKTAPPI.2023.8.55.4.3

All Issue

2023 Vol.55, Issue 4 Next Page

Research Article

Fractal Dimension Analysis of Surface Roughness for Paper and Paperboard 종이 및 판지 표면 거칠음도의 프랙탈 차원 분석

30 August 2023. pp. 3-11

PDF XML

Abstract

Fractal geometry is characterized by its similarity and hierarchical organization. It exhibits a hierarchical structure composed of elements that share the same shape but vary in size, ranging from the largest to the smallest. In this study, the fractal-dimension values of a paper and paperboard were calculated, which reveal distinct properties of fractal dimensions in contrast to Euclidean geometry. The variogram method was employed to characterize the surface roughness profiles using fractal-dimension analysis to obtain the fractal dimensions of paper products. A decrease in the fractal-dimension value was observed following the coating process. These findings imply the promising applicability of fractal-dimension analysis for evaluating the effects of postprocessing techniques, including printing, coating, creping, and embossing.

Keywords

Surface roughness

fractal geometry

fractal dimension

variogram

autocorrelation

mean absolute deviation

profilometry

profile

stylus

contact method

References

Ko, Y. C., Melani L, Park, N. Y., and Kim, H. J., Surface characterization of paper and paperboard using a stylus contact method, Nordic Pulp & Paper Research Journal 35(1):78-88 (2020). 10.1515/npprj-2019-0005

Neimark, A. V., Ruetsch, S., Kornev, K. G., Ravikovitch, P. I., Poulin, P., Badaire, S., and Maugey, M., Hierarchical pore structure and wetting properties of single-wall carbon nanotube fibers, Nano Letters 3(3):419-423 (2003). 10.1021/nl034013x

Vernhes, P., Bloch, J. F., Mercier, C., Blayo, A., and Pineaux, B., Statistical analysis of paper surface microstructure: A multi-scale approach, Applied Surface Science 254(22):7431-7437 (2008). 10.1016/j.apsusc.2008.06.023

Vernhes, P., Bloch, J. F., Blayo, A., and Pineaux, B., Effect of calendering on paper surface micro-structure: A multi-scale analysis, Materials Processing Technology 209(11):5204-5210 (2009). 10.1016/j.jmatprotec.2009.03.005

Hiemenz, P. C. and Rajagopalan, R., Principles of colloid and surface chemistry, Mareei Dekker, 105-114 (1997).

Kornev, K. G., Neimark, A. V., and Rozhkov, A. N., Foam in porous media: thermodynamic and hydrodynamic peculiarities, Advances in colloid and interface science 82(1-3):127-187 (1999). 10.1016/S0001-8686(99)00013-5

Richardson, L. F., The problem of contiguity: an appendix to statistics of deadly quarrels, General Systems Yearbook 61:139-187 (1961).

Ko, Y. C., Park, J. M., and Shin, S. J., The Principles of fractal geometry and its applications for Pulp & Paper Industry, Korea TAPPI 47(4):177-186 (2015). 10.7584/ktappi.2015.47.4.177

Mandelbrot, B. B., The fractal geometry of nature, W.H. freeman, New York (1982).

Russ, J. C., Modeling fractal profiles and surfaces, Fractal Surfaces 149-190 (1994). 10.1007/978-1-4899-2578-7_6

Moon, B. G., Park, N. Y., Ko, Y. C., and Kim, H.J., Characterization of paper surfaces by friction profilometry, BioResources 17(4):6067-6078 (2022). 10.15376/biores.17.4.6067-6078

Park, N. Y., Ko, Y. C., Kim, H. J., and Moon, B. G., Surface Characterization of paper products via a stylus-type contact method, BioResources 16(3):5667-5678 (2021). 10.15376/biores.16.3.5667-5678

Jeong, H. S., Ko, Y. C., and Kim, H. J., Effects of a stylus on the surface roughness determination in a contact method for paper and paperboard, Nordic Pulp & Paper Research Journal 34(4):442-452 (2019). 10.1515/npprj-2019-0011

Leger, D., Mathieu, E., and Perrin, J. C., Surface roughness measurement by use of laser speckle technique, Japanese Journal of Applied Physics 14(S1):299 (1975). 10.7567/JJAPS.14S1.299

Hladnik, A. and Lazar, M., Paper physics: paper and board surface roughness characterization using laser profilometry and grey level cooccurrence matrix, Nordic Pulp & Paper Research Journal 26(1):99-105 (2011). 10.3183/npprj-2011-26-01-p099-105

Xie, X. N., Chung, H. J., Sow, C. H., and Wee, A. T. S., Nanoscale materials patterning and engineering by atomic force microscopy nanolithography, Materials Science and Engineering 54(1-2):1-48 (2006). 10.1016/j.mser.2006.10.001

Kawabata, S., The standardization and analysis of hand evaluation (1980).

Militký, J. and Bajzík, V., Surface roughness and fractal dimension, Journal of the Textile Institute 92(3):91-113 (2001). 10.1080/00405000108659617

Constantine, A. and Hall, P., Characterizing surface smoothness via estimation of effective fractal dimension, Royal Statistical Society: Series B (Methodological) 56(1):97-113 (1994). 10.1111/j.2517-6161.1994.tb01963.x

Lee, Y. J., Ko, Y. C., Moon, B. G., and Kim, H. J., Surface characterization of paper products by profilometry with a fractal dimension analysis, BioResources 18(2):3978-3994 (2023). 10.15376/biores.18.2.3978-3994

ISO 187, Paper, board and pulps - standard atmosphere for conditioning and testing and procedure for monitoring the atmosphere and conditioning of samples (2022).

Ko, Y. C., Park, J. Y., and Kim, H. J., Characterization of surface properties of paper towels, Journal of Korea TAPPI 49(6):81-89 (2017). 10.7584/JKTAPPI.2017.12.49.6.81

Lee, S. H., Kim, H. J., Ko, Y. C., Lee, J. H., Park, J. Y., Moon, B. G., and Park, J. M., Characterization of surface properties of hygiene paper by fractal dimension analysis technique, Journal of Korea TAPPI 49(6):90-101 (2017). 10.7584/JKTAPPI.2017.12.49.6.90

ISO 4287: Geometrical Product Specifications (GPS)-Surface texture: Profile method-Terms, definitions, and surface texture parameters (1997).

Lee, Y. J., Kim, J. H., Cha, J. E., Kang, N. Y., and Kim, H. J., Analysis of surface characteristics of printing paper using contact profilometry, Journal of Korea TAPPI 55(2):48-58 (2023). 10.7584/JKTAPPI.2023.4.55.2.48

Lee, Y. J., A Study on the quality characterization of printing and writing paper using surface parameters and data mining techniques, Master thesis, Kookmin University, Korea (2022).

Lee, W. N. and Kim, H. J., The control of anti-slip characteristics of packaging paper using nano-colloidal silica, Journal of Korea TAPPI 37(3):33-40 (2005).

Information

Publisher :Korea Technical Association of The Pulp and Paper Industry
Publisher(Ko) :한국펄프종이공학회
Journal Title :Journal of Korea TAPPI
Journal Title(Ko) :펄프종이기술
Volume : 55
No :4
Pages :3-11
Received Date : 2023-06-14
Revised Date : 2023-07-26
Accepted Date : 2023-07-28
DOI :https://doi.org/10.7584/JKTAPPI.2023.8.55.4.3

Journal of Korea TAPPI ISSN:0253-3200(Print) 펄프종이기술

All Issue