A new method for determining the relative bonded area, TAPPI JOURNAL, June 2005

Correlations of scattering coefficient with sheet tensile strength and with sheet density were examined to see if they could be used to determine the scattering coefficient of an unbonded sheet, from which the relative bonded area (RBA) could then be calculated. The data showed that neither correlation was useful because the fiber cross-sectional shape in the sheet changes with the extent of wet pressing. A new method has been developed in which the scattering coefficient and sheet density are corrected for changes in the fiber cross-sectional shape. With the corrected data, the scattering coefficient was linearly related to sheet density, from which a simple new formula was derived for calculating the RBA. The total area available for bonding was not constant, so the RBA alone is not sufficient to describe fully the bonding in the sheet. Application: A new method has been developed for calculating the relative bonded area from sheet density and fiber cross-sectional shape. VOL. 4: NO. 6 TAPPI JOURNAL 23 24 TAPPI JOURNAL JUNE 2005 FIBER BONDING density is a direct measure of the compaction of the sheet and the interaction between tensile strength and bonded area is much more complex [12]. In this work, we tested correlations of scattering coefficient with tensile strength and with density for a set of data obtained from sheets made from a neverdried, unbleached kraft pulp from radiata pine.We found neither correlation to be correct. Therefore, we developed and tested a new method for calculating the RBA by correcting the measured scattering coefficient and sheet density for fiber cross-sectional shape. EXPERIMENTAL METHODS Data were collected for a series of pulps generated from a single starting stock of an unbleached kraft pulp, kappa no. 30, made in the laboratory from radiata pine [13]. Handsheets were also made from the accepts and rejects produced by double hydrocyclone fractionation of this starting material furnish. We also varied the fiber length of the starting stock by cutting wet handsheets. Three sets of handsheets were produced from wet cutting.The procedure was to form the starting stock into handsheets and then to cut the wet handsheets with a die. We varied the number of cuts to give each set a different length-weighted fiber length.The length-weighted fiber lengths of the three sets were 2.53 mm, 2.10 mm, and 1.80 mm, whereas the fiber length for the starting stock was 3.14 mm. The starting stock was labelled L 0 , and the other three sets were labelled L 1 , L 2 , and L 3 , respectively. The cutting process reduced the fiber length without affecting the other sample dimensions. For each of the pulps, five sets of handsheets were made at different pressing levels. Changing the pressing level varied the degree of bonding, the tensile strength, and the scattering coefficient. Further details of the experiments are given elsewhere [13, 14]. Fiber shape and fiber dimensions were measured on the fibers in the sheet cross sections with a combination of resin embedding and confocal microscopy [13–15]. We calculated the dimensions of the fibers in the sheet by fitting a rectangular bounding box around each measured fiber, by calculating the width and height of the bounding box, D w and D h , and by calculating the fraction of the bounding box filled with fiber, f. Tensile strength and sheet density were tested by the relevant ISO standards. The scattering coefficients were measured at 700 nm. EXTRAPOLATION METHODS Scattering coefficient vs. tensile strength Figure 1 plots the scattering coefficient against tensile strength. Six data sets are shown, one for sheets made from the starting pulp, three made after cutting the starting pulp to reduce fiber length, and two made by fractionating the starting pulp into accepts and rejects. The scattering coefficient measurements have also been presented elsewhere [13]. In that research, the same six sets of sheets were examined in light of nitrogen-adsorption measurements to determine the total surface area in the sheets.We also measured the surface area of unbonded sheets, which we prepared by spray drying very dilute suspensions of fibers onto Teflon and allowing them to dry. The measured surface areas of unbonded sheets for samples L 0 , L 1 , L 2 , and L 3 were found to be 905, 920, 921, and 927 m2/kg, respectively. For the accepts and the rejects, the surface areas measured were 993 m2/kg and 1063 m2/kg, respectively [13]. Thus there is only a 15% difference between largest and smallest total surface area, as determined by nitrogen adsorption, which indicates that the values determined for the different pulps should be quite close