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Cellulose fibers come in a wide range of shapes and sizes. The heterogeneity of the fiber length, width, wall thickness, curl and external fibrillation is detrimental to the mechanical performance of products such as paper and paperboard. Although micro-mechanical models of these materials sometimes incorporate features of this heterogeneity, so far there is no standardized method of fully incorporating this. We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have. We find that the method must allow for both non-Gaussian distributions and dependence between the variables. We present a method of characterizing mechanical pulp under these conditions that views the individual fiber as outcome of a sampling process from a multivariate distribution function. The method is generally applicable to any dataset, even a non-Gaussian one with dependencies. Using a micro-mechanical model of a paper sheet the proposed method is compared with previously presented methods to study whether incorporating both a varying fiber size and dependencies is necessary to match the response of a sheet modeled with measured characterization data. The results demonstrate that micro-mechanical models of paper and paperboard should not neglect the influence of the dependence between the characteristic shape features of the fibers if the model is meant to match physical experiments. © 2022 The Authors

Particles in mechanical pulp show a wide variety but are commonly described using averages and/or collective properties. The authors suggest using distributions of a common bonding factor, BIND (Bonding INDicator), for each particle. The BIND-distribution is based on factor analysis of particle diameter, wall thickness, and external fibrillation of several mechanical pulps measured in an optical analyser. A characteristic BIND-distribution is set in the primary refiner, depending on both wood and process conditions, and remains almost intact along the process. Double-disc refiners gave flatter distributions and lower amounts of fibres with extreme values than single-disc refiners. More refining increased the differences between fibres with low and high BIND. Hence, it is more difficult to develop fibres with lower BIND. Examples are given of how BIND-distributions may be used to assess energy efficiency, fractionation efficiency, and influence of raw material. Mill scale operations were studied for printing-grade thermomechanical pulp (TMP), and board-grade chemi-thermomechanical pulp (CTMP), both from spruce.

    Cellulose fibers exhibit a wide range of shapes and sizes. This variation influences the mechanical performance of paper and paperboard by affecting the stress distribution inside the network and the degree of fiber-to-fiber bonding which is possible at a given density. However, the methods used to characterize the distribution of fiber sizes in the pulp neglect that the characteristic features of a fiber are generally not independent.

    Here, we resolve this shortcoming by fitting the fiber population to a multivariate distribution without enforcing normality or independence between the properties. The high-dimensional multivariate function is recast as a set of univariate distribution functions and a series of bivariate distributions connected by a canonical vine. 

    Using a micro-mechanical model of a paper sheet the influence of this improved characterization is investigated. Reasonable margins and a description of the dependency is shown to be superior to assuming independence even for perfectly preserved marginal distributions. This result demonstrates that micro-mechanical models of paper and paperboard cannot by assumption neglect the influence of the interdependence between the characteristic features of fibers. 

Characterisation of fibres in mechanical pulps is important for process evaluation and control, and necessary to be able to optimise the refining process with respect to the total electric energy consumption. There are large variations of cross-sectional fibre characteristics in the wood raw material which influence the properties of the product. Despite this, it is common to evaluate the fibre characteristics as averages instead of distributions. This study shows that the raw data from a FiberLab analyser can be used to make distributions of measured and predicted fibre characteristics. The factor BIN (Bonding ability /Nfluence), which correlates to long fibre tensile index, includes both the external fibrillation and wall thickness of each fibre. Distributions of BIN, fibrillation and wall thickness which take the Characteristics of each fibre into Consideration have higher resolution than histograms. These distributions weighted by length and wall volume with maintained resolution revealed more information about the pulps than average values.

Mechanical pulps are used in paper products such as magazine or news grade printing papers or paperboard. Mechanical pulping gives a high yield; nearly everything in the tree except the bark is used in the paper. This means that mechanical pulping consumes much less wood than chemical pulping, especially to produce a unit area of printing surface. A drawback of mechanical pulp production is the high amounts of electrical energy needed to separate and refine the fibers to a given fiber quality. Mechanical pulps are often produced from slow growing spruce trees of forests in the northern hemisphere resulting in long, slender fibers that are well suited for mechanical pulp products. These fibers have large varieties in geometry, mainly wall thickness and width, depending on seasonal variations and growth conditions. Earlywood fibers typically have thin walls and latewood fibers thick. The background to this study was that a more detailed fiber characterization involving evaluations of distributions of fiber characteristics, may give improved possibilities to optimize the mechanical pulping process and thereby reduce the total electric energy needed to reach a given quality of the pulp and final product. This would result in improved competitiveness as well as less environmental impact. This study evaluated the relation between fiber characteristics in three types of mechanical pulps made from Norway spruce (Picea abies), thermomechanical pulp(TMP), stone groundwood pulp (SGW) and chemithermomechanical pulp (CTMP). In addition, the influence of fibers from these pulp types on sheet characteristics, mainly tensile index, was studied. A comparatively rapid method was presented on how to evaluate the propensity of each fiber to form sheets of high tensile index, by the use of raw data from a commercially available fiber analyzer (FiberLabTM). The developed method gives novel opportunities of evaluating the effect on the fibers of each stage in the mechanical pulping process and has a potential to be applied also on‐line to steer the refining and pulping process by the characteristics of the final pulp and the quality of the final paper.

The long fiber fraction is important for the properties of the whole pulp. It was found that fiber wall thickness and external fibrillation were the fibercharacteristics that contributed the most to tensile index of the long fiber fractions in five mechanical pulps (three TMPs, one SGW, one CTMP). The tensile index of handsheets of the long fiber fractions could be predicted by linear regressions using a combination of fiber wall thickness and degree of external fibrillation. The predicted tensile index was denoted BIN, short for Bonding ability INfluence. This resulted in the same linear correlation between BIN and tensile index for 52 samples of the five mechanical pulps studied, each fractionated into five streams(plus feed) in full size hydrocyclones. The Bauer McNett P16/R30 (passed 16 meshwire, retained on a 30 mesh wire) and P30/R50 fractions of each stream were used for the evaluation. The fibers of the SGW had thicker walls and a higher degree of external fibrillation than the TMPs and CTMP, which resulted in a correlation between BIN and tensile index on a different level for the P30/R50 fraction of SGW than the other pulp samples. A BIN model based on averages weighted by each fiber´s wall volume instead of arithmetic averages, took the fiber wall thickness of the SGW into account, and gave one uniform correlation between BIN and tensile index for all pulp samples (12 samples for constructing the model, 46 for validatingit). If the BIN model is used for predicting averages of the tensile index of a sheet, a model based on wall volume weighted data is recommended. To be able to produce BIN distributions where the influence of the length or wall volume of each fiber is taken into account, the BIN model is currently based on arithmetic averages of fiber wall thickness and fibrillation. Fiber width used as a single factor reduced the accuracy of the BIN model. Wall volume weighted averages of fiber width also resulted in a completely changed ranking of the five hydrocyclone streams compared to arithmetic, for two of thefive pulps. This was not seen when fiber width was combined with fiber wallthickness into the factor “collapse resistance index”. In order to avoid too high influence of fiber wall thickness and until the influence of fiber width on BIN and the measurement of fiber width is further evaluated, it is recommended to use length weighted or arithmetic distributions of BIN and other fiber characteristics. A comparably fast method to evaluate the distribution of fiber wall thickness and degree of external fibrillation with high resolution showed that the fiber wallthickness of the latewood fibers was reduced by increasing the refining energy in adouble disc refiner operated at four levels of specific energy input in a commercial TMP production line. This was expected but could not be seen by the use of average values, it was concluded that fiber characteristics in many cases should be evaluated as distributions and not only as averages.

BIN distributions of various types of mechanical pulps from Norway spruce showed results that were expected based on knowledge of the particular pulps and processes. Measurements of mixtures of a news‐ and a SC (super calendered) gradeTMP, showed a gradual increase in high‐BIN fibers with higher amounts of SCgrade TMP. The BIN distributions also revealed differences between the pulps that were not seen from average fiber values, for example that the shape of the BINdistributions was similar for two pulps that originated from conical disc refiners, a news grade TMP and the board grade CTMP, although the distributions were on different BIN levels. The SC grade TMP and the SC grade SGW had similar levels of tensile index, but the SGW contained some fibers of very low BIN values which may influence the characteristics of the final paper, for example strength, surface and structure. This shows that the BIN model has the potential of being applied on either the whole or parts of a papermaking process based on mechanical or chemimechanical pulping; the evaluation of distributions of fiber characteristics can contribute to increased knowledge about the process and opportunities to optimize it.

To improve the operation and energy efficiency of mechanical pulping processes, the effect of each stage of the process on the fibres should be carefully evaluated. Fibre-data from an optical analyser were used to predict tensile index by calculating BIN (Bonding ability /Nfluence). Wall volume weighted averages of wall thickness index and fibrillation index gave the most accurate predictions of the tensile index of laboratory sheets made from long fibre fractions of various mechanical pulps. Fibre width index, when used as a single factor, reduced the accuracy of the model. The ranking of some samples changed when fibre width was wall volume weighted compared to arithmetic. When fibre width was combined with wall thickness to give a collapse resistance index, no rankings changed. Weighted averages based on squared fibre length (length(2)) showed poor correlation to wall volume weighted averages for cross-sectional fibre dimensions, and resulted in different levels of correlation to long fibre tensile index for the five evaluated pulps.

Low consistency (LC) refining and high consistency refining (HC) has been studied in a TMP mill. When strength properties were increased, the development of fiber properties was different in LC- and HC-refining. Fiber curl decreased in LC-refining but increased in HC-refining. LC-refining decreased fiber curl and increased tensile index simultaneously in this study. It is therefore likely that the decreased fiber curl contributes to the increase of tensile index in LC-refining. Furthermore, fiber wall thickness decreased and external fibrillation increased in HC-refining, while these properties were only slightly influenced in the LC-refining. Fibrillation was found to decrease in most cases for LC-refining while fiber wall thickness index increased slightly but consistently, which might indicate a less dense structure of the fiber wall or its surface layers. Double-disc HC-refining with the same energy input as in a conical single-disc refiner resulted in fibers of higher external fibrillation, lower fiber wall thickness and higher fiber curl at a given fiber length. The results indicate that analyzing individual fiber dimensions could be a better tool for understanding how fibers develop in different kinds of refining than analyzing conventional handsheet properties.

This study discusses how fiber dimensions affect the tensile index and density of long fiber laboratory sheets. Five commercial mechanical pulps (three TMP grades, one SGW and one CTMP) were fractionated into five streams in a hydrocyclone pilot plant. Fiber dimensions and fibrillation were analyzed of the P16/R30 and P30/R50 fractions and compared to the sheet properties. For comparison, samples were also analyzed by SEM cross-sectional image analysis and in a MorFi Lab optical analyzer. Fibrillation index showed a high positive influence on long fiber tensile index and density, whereas fiber wall thickness, fiber width, and collapse resistance index a negative. Fiber width showed the vaguest correlation to long fiber tensile index and density of the analyzed fiber properties, but this increased when combined with fiber wall thickness into collapse resistance index, CRI. The correlations between fiber properties and sheet properties were on different levels for the different mechanical pulping processes, but a combination of collapse resistance index and fibrillation index into the novel factor BIN, Bonding ability INfluence, gave one linear relation of high correlation to long fiber tensile index for all pulps, except the SGW P30/R50 fraction, which showed the same linear correlation on a slightly lower level. BIN should be a useful tool in characterizing mechanical pulp fibers.