A novel method for the determination of bonded area of individual fiber-fiber bonds

Tags: fiber width, cross sectional area, bonds, area, morphological parameters, bonded area, fiber morphology, Fundamental Research Symposium, image plane, vertical angle, fiber axis, wall thickness, fiber mats, bond, light microscopy, Paper strength, Wolfgang Bauer, Fiber Technology, fiber surface, Graz University of Technology, fiber diameter, predictor variables, microscope images, microscope image, cross section, Multiple linear regression, geometric parameters, Literature Asunmaa, Institute of Paper Science and Technology, Christian Doppler Society, Tappi
Content: Paper physics A novel method for the determination of bonded area of individual fiber-fiber bonds
Lisbeth Kappel, Ulrich Hirn, Wolfgang Bauer and Robert Schennach, Graz University of Technology, Austria
KEYWORDS: Fiber-fiber bond, Bonded area, Paper strength SUMMARY: A method is presented for determining the bonded area of single fiber-fiber bonds, the method is based on microtome serial sectioning and Image Analysis. The size and three-dimensional structure of the bonded area are assessed together with cross sectional fiber morphology. Additionally, holes and overlapping but unbonded fiber regions can be measured. 87 fiber-fiber bonds from an unbleached and unbeaten softwood kraft pulp were analyzed. The statistical evaluation of the results showed that basic geometry (fiber width and crossing angle) explain only 55% of bonded area. Incomplete bonding (holes and overlapping but unbonded edges) additionally account for 27% of the bonded area, while fiber morphology only plays a minor role. This is a contradiction to the conventional theory that fiber conformability controls the bonded area in paper. An explanation for this might be that one cannot rationalize the three-dimensional network of paper directly from twodimensional fiber-fiber bonds. ADDRESSES OF THE AUTHORS: Lisbeth Kappel ([email protected]), Ulrich Hirn ([email protected]) and Wolfgang Bauer ([email protected]): Graz University of Technology, Institute for Paper, Pulp and Fiber Technology, CD-Laboratory for surface chemical and physical fundamentals of paper strength, Kopernikusgasse 24, 8010 Graz, Austria. Robert Schennach ([email protected]): Graz University of Technology, Institute for Solid State Physics, CDLaboratory for surface chemical and physical fundamentals of paper strength, Petersgasse 16, 8010 Graz, Austria. Corresponding author: Lisbeth Kappel Paper strength is developed from the strength of single fibers and the strength of the fiber-fiber bonds. Furthermore, the strength of the fiber-fiber bonds depends on the size of the bonded area as well as on the specific bonding strength. Measuring the actual size of the bonded area helps to understand the governing factors for fiber-fiber bond strength. In this study the bonded area of individual fiber-fiber bonds and its distribution are investigated. We propose a novel method for determining the bonded area based on microtome serial sectioning of fiber-fiber bonds. Geometrical and morphological parameters of 87 single fiber-fiber bonds have been analyzed with statistical models in order to explain the factors that govern the size of bonded area. Related research ­ preparation of fiber-fiber bonds Various descriptions of how individual fiber-fiber bonds can be prepared are given in the literature. They are either based on manipulation of individual fibers or using a highly diluted fiber suspension.
McIntosh (1963), Thorpe at al. (1976) and Kang et al. (2004), prepared fiber-fiber bonds by placing two fibers (or one fiber and one shive) orthogonally on a glass slide in water and covering it with another glass slide. This sandwich was pressed and dried. Stratton (1992) placed two fibers at a right angle between two Teflon-coated discs under water. The fibers were clamped with tabs that were cut into the Teflon. The bonds were then dried under heat and pressure. Mayhood et al. (1962) prepared fiber-fiber bonds by dewatering a very dilute suspension on a wire. After drying, single fiber-fiber bonds could be taken off the wire. Forsstrцm, Torgnysdotter (2005) dried small drops of a very dilute fiber suspension between two Teflon-coated silicon discs under heat and pressure. Orthogonally crossed fibers were then selected from the small fiber mats. Related research ­ determination of bonded area of fiber-fiber bonds Several methods to analyze the bonded area of fiber-fiber bonds have been described in the literature. These methods can be grouped in dyeing methods, microtome methods and polarization microscopy methods. Torgnysdotter et al. (2007) dyed fiber-fiber bonds and then ruptured them. The un-dyed fiber surfaces were evaluated under the light microscope and considered as formerly bonded. Fluorescence microscopy was used by Thomson (2007). One fiber was dyed with a donorfluorescence dye and one with an acceptor-fluorescence dye, so that under a fluorescence microscope bonded area becomes visible. Asunmaa, Steenberg (1958) and Yang et al. (1978) both used microtome cuts to determine the bonded fraction of the fiber surface by analyzing images of paper Cross Sections. The most commonly used method was developed by Page (1960), who applied PolarizEd Light microscopy to determine the optically bonded area. He stated that bonded areas appear dark under vertical polarized illumination, while unbonded areas are bright. This method was also used by Jayme, Hunger (1961), who additionally analyzed broken bonds with Electron Microscopy and evaluated the roughness of the fiber surface. Quantitative measurement of the bonded area has only been performed applying the method of Page (1960). These results will be addressed below in more detail. All Other references did not give quantitative results for the bonded area, rather they provided qualitative information about the bond. The method introduced in this paper provides additional information to the measurement of bonded area. It gives a more comprehensive view of fiber-fiber bonding,
Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009 199
because the bonded area is measured together with the morphological parameters of the fibers and the bonding region. Holes in the bond and overlapping but unbonded fiber edges can be identified correctly. Materials and Methods An unbleached softwood kraft pulp was used in all experiments. The pulp was a mixture from spruce and pine wood, it had a number of 42. The pulp was once-dried and unbeaten. Preparation of fiber-fiber bonds Fiber-fiber bonds were prepared from a dilute suspension, similar to the method described by Forsstrцm, Torgnysdotter (2005). Dry pulp was dispersed and allowed to swell in water for at least 12 hours. The fibers were disintegrated according to DIN EN ISO 5263-1. A highly dilute suspension with a consistency of 0.01% was prepared. Small drops of the suspension were put on a piece of Teflon foil (4 cm x 4 cm), which was subsequently covered with another piece of Teflon foil. This sandwich was dried in a conventional sheet dryer for 45 minutes. After drying, the thin fiber mats could be taken off the Teflon foil. From such fiber mats, seen in Fig 1, individual crossings were selected for further preparation (black circle mark). Specimens were prepared as depicted in Fig 2 (top). A single fiber-fiber bond was fixed with glue on a strip of paper across a hole. Fig 2 (bottom left) shows a microscope image of such a fiber-fiber bond that is glued to a strip of paper. A magnification of this bond is shown in Fig 2 (bottom right), with the crossing angle, , and the vertical angle, , shown. Measurement of the bonded area The method for the determination of the bonded area is based on microtome serial sectioning and image analysis. The size of the bonded area together with the threedimensional structure of the bonded area and morphological fiber parameters can be obtained from this measurement. The samples were embedded in a gelatin capsule using a cold-polymerizing resin based on hydroxyl-methylmethacrylate (Technovit 71001). After curing, the threedimensional structure of the bonded region was analyzed using an automated microtomy system (Wiltsche et al. 2005). Slices having a thickness of 3 µm were sequentially cut off the embedded sample with the microtome. The cutting area was imaged automatically after every cut, pixel size was 0.161 µm. This process yields a stack of images of the fiber cross section, representing the three-dimensional shape of the fiber-fiber bond. In the images presented in following figures, the x- and y-coordinates correspond to the image plane, while the third coordinate is the slicing direction. 1 Heraeus Kulzer GmbH & Co KG, Germany: www.Kulzer-Technik.de 200 Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009
Fig 1. Thin fiber mat with orthogonally bonded fibers, which was used for measurement of the bonded area. Fig 2. Top: A single fiber-fiber-bond fixed with glue on a strip of paper across a hole. Bottom left: Microscope image of a fiber-fiber bond glued across a hole. Bottom right: Image of the same bond as bottom left at higher magnification. The crossing angle, , and the vertical angle, , are drawn in. Three light microscope images of the bond shown in Fig 2 (bottom left) are presented in Fig 3 at different cutting positions. The first image (a.) shows the edge of the bond, where the fiber contact region is small. The left fiber is fully collapsed and folded, whereas the right fiber is fully collapsed and unfolded. The following two images (b. and c.) proceed deeper into the bond. Because of the irregularity of the fold, the contact between the fibers is interrupted. Fig 3 (b.) shows, that the fibers are separated in the upper part of the bond. In the next image (c.), the fibers are in contact over a greater length, although the contact is interrupted. Cut slices and the viewing direction of these images are also indicated in Fig 2 (top). Segmentation of the fiber regions was performed by
Fig 3. a., b., c.: Microscope images of fiber-fiber bond cross sections at different positions of the bond in Fig 2 after microtome serial sectioning. d.: Manually segmented fibers from image c., the bonding line (white) was determined image analytically. the operator, and the fiber outline was drawn into the microscope image by hand (Fig 3d). The morphology of the bonded region and the fibers is determined from the fiber outline images using image analysis (Fig 3d). For bonded area measurement, the fiber regions are considered to be bonded where the fibers in the microscope images are in direct contact. This region is determined using image analysis, resulting in a bonding line for every cut, as indicated by the white line in Fig 3 (d). We are aware that the resolution of the optical microscope is too low to quantify whether the fibers are really in contact on a nanometer scale, we measure optically bonded area. The bonded area is calculated from bond line length multiplied with the cut thickness (3 µm). It is inherently assumed that there is no change in bonding state in the cut slice, where no information is available. A three-dimensional representation of the bonding region is obtained by plotting the bonding lines from each image taken within a bond (Fig 4). The rightmost line corresponds to the length where the fibers were in contact in the first cut (Fig 3a). The line which is marked gray belongs to the image in Fig 3 (d). The interruption caused by the fold of the left fiber can be seen as break in the bonding line. The distance between the lines is equivalent to the cut thickness (3 µm). Measurement of morphological parameters In addition to bonded area, several morphological parameters of fibers and bonding region are measured from the images. Fiber cross sectional area, fiber perimeter, fiber wall thickness, fiber collapse, fiber width and incomplete bonding (holes and overlapping but unbonded edges) give comprehensive information regarding the fiber-fiber bond. The position of the fiber cross section's center of mass through all cuts can be plotted for both fibers, which is shown in Fig 5. The main fiber axis is computed from
Fig 4. Three-dimensional representation of the bonded area. The bonding line for each cut is plotted, the distance between the lines equals the cut thickness (3 µm). The gray highlighted line corresponds to the bonding line in Fig 3 (d.). Fig 5. The run of the fiber cross section's center of mass through the cut slices defines the fiber main axis. This yields the crossing angle, , and the vertical angle, . The plot that is presented corresponds to the bond in Fig 2 (bottom). Fig 6. The angular face of a fiber cross section as it is seen in the images. The cutting area does not show the real fiber dimensions if the main fiber axis is not perpendicular to the x, y image plane, i.e. the vertical angle does not equal /2. linear regression of the center of mass points. This yields the vertical angle, , of each fiber, being the angle between the fiber axis and the image plane. Also, the crossing angle, , between the fibers can be determined. Fig 5 corresponds to the bond shown in Fig 2 (bottom). When the image plane is not perpendicular to the main fiber axis, the apparent fiber cross sectional area in the images is larger than the real area. The angular face that is seen in the image of the cutting area would therefore overestimate the real fiber dimension, as depicted in Fig 6. The vertical angle, , gives a reasonable approximation of the angle between image plane and main fiber axis. The real shape of the fiber cross section was computed from the apparent shape using a procedure similar to the Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009 201
one described by Kritzinger et al. (2008). The apparent y-coordinate is transformed to the corrected y-coordinate, while the x-coordinate remains unchanged. All morphological parameters were measured from this corrected fiber cross section. Fiber width is measured directly as marked in Fig 6. For determining fiber wall thickness fiber collapse has to be considered. If the fiber is completely collapsed, the fiber wall thickness can be determined by dividing the fiber thickness by 2. Otherwise the uncollapsed lumen has to first be subtracted. Also, the fiber perimeter and cross sectional area are measured from the corrected fiber cross section. For quantification of the fiber collapse the fill factor was used (Kritzinger et al. 2008). The fiber cross sectional area is first determined with consideration of the lumen (AL), as it is shown in Fig 7 (left). Then the lumen area is filled, and the filled fiber cross sectional area (AF) is determined (Fig 7, right). The fill factor is calculated using Eq 1.
Fill factor = AL
A fill factor of unity occurs if the fiber is completely collapsed. The fill factor becomes smaller with less fiber collapse.
Fig 7. For the determination of fiber collapse, the fiber cross sectional area is first measured (AL, left). Then the filled fiber cross sectional area is measured (AF, right). Fiber collapse is the ratio of these two values (see Eq 1).
Three specific aspects of incomplete bonding have been evaluated: holes, unbonded edge regions of the bond and fiber overlap area. Fig 8 shows the segmented fibers that are presented in Fig 3. In Fig 8, the bonded length (LB) and unbonded edge length (LUE) occur at both sides of the hole. The total overlap length (LO) is the maximum possible length that is available for bonding. The hole fraction (FH) and edge fraction (FE) can be calculated to express incomplete bonding using Eqs 2 and 3.
The corresponding areas (e.g. hole area) can be
calculated by multiplying the various length scales with
the cut thickness. For example, the bond in Fig 4
contains one hole and unbonded parts at the edges of the
bond (also see Fig 3). For this example, the hole fraction
is 4.1% and edge fraction is 20.1%.
202 Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009
Fig 8. Diagram denoting the bonded length (LB), hole length (LH), unbonded edge length (LUE) and the overlap length (LO) that is available for bonding. The incomplete bonding can be calculated from these terms with Eqs 2, 3 and 4.
The hole fraction (FH) and edge fraction (FE) can further be combined to calculate the incomplete bonding (B ), incomplete as seen in Eq 4.
Bincomplete = FH + FE
Results The bonded area and morphological parameters of 87 fiber-fiber bonds of unbleached and unbeaten softwood kraft pulp were analyzed. Multiple linear regression modeling was performed to find factors influencing the size of bonded area. The mean value for the bonded area was 1130 µm2 and the standard deviation was 602 µm2. Fig 9 shows a histogram of all measured values of the bonded area. The distribution is positively skewed. The origin of the strong variation and influencing factors on the size of bonded area are now discussed in greater detail. Factors influencing the bonded area Based on the measured bonded areas and morphological parameters, several factors that may affect the bonded area were investigated. Multiple linear regression was
Fig 9. Histogram of values of the bonded area. mean = 1130 µm2, variance = 602 µm2, skewness = 0.9495.
performed to quantify the significance (F*-statistics) and impact (ANOVA) of the explanatory variables (Neter et al. 1996). For this Statistical Analysis, the mean value of the morphological parameters of the two bonded fibers was taken. Fig 10 shows that the bonded area depends to a large extent on the basic geometry, being the fiber width and the crossing angle.
Fig 10. The basic geometric parameters crossing angle () and fiber width (w1 and w2 ) yield calculated bonded area, Acalc.
According to Fig 10 the calculated bonded area, Acalc, is given by:
where w1 and w2 are the widths of the fibers and is the crossing angle. Apart from fundamental geometry, the parameters that govern the bonded area were found by multiple linear regression. Acalc and all of the measured morphological parameters were taken as predictor variables. The results of this model are listed in Table 1. The R2 value is given for all parameters. Because of interactions and redundancies between the variables, interpreting this value is not straightforward. A parameter might have a significant R2 value but still be redundant, because its information is also contained in other variables. In order to eliminate these redundancies a multiple variable linear regression model was built (Neter et al. 1996). The R2 values are only given for the sake of completeness. Interpretations have been made on basis of the stepwise R2 values, i.e. the ANOVA, of the linear multiple regression model. The p-Value shows the significance of the parameters on a 95% confidence level. The significant parameters in Table 1 have a white background, while some non-significant parameters that might be of interest are shaded gray.
Table 1. Results of multiple linear regression and ANOVA with the measured bonded area as the response variable and the calculated bonded area and morphological parameters as the predictor variables. Significant parameters have a white background, while non-significant parameters are shaded gray.
R2 stepwise
Acalc Edge fraction Hole fraction Fiber perimeter Crossing angle Fiber wall thickness Fiber collapse Fiber cross sectional area
0.547 0.853 0.873 0.879 0.886 0.073 0.018 0.017
R2 alone 0.547 0.280 0.017 0.219 0.020 0.905 0.149 0.934
p-Value Sign of Coeff.
The R2 value of the stepwise regression states that 54.7% of the size of bonded area can be explained in terms of the basic geometry of the bond, as the fiber width and crossing angle are accounted for in Acalc. An additional 30.6% of variance is explained by the unbonded edge regions, which is indicated by an increase from 0.547 to 0.853 of R2 stepwise. Finally, the hole fraction explains another 2% of the variance. The signs of the model coefficients confirm the expected relationship: a high calculated bonded area (Acalc) corresponds to a larger bond area. A high edge fraction (FE) and a high hole fraction (FH) respectively correspond to smaller bond area. The fiber perimeter and crossing angle together only explain 1.3% of variance. Although they are statistically significant, they only have a marginal impact. Other morphological parameters that should be related to conformability (fiber wall thickness, fiber collapse and fiber cross sectional area) are not significant on a 95% confidence level (p>0.05), suggesting they did not significantly influence the bonded area. In the linear model for the single fiber-fiber bonds, 87.3% of the variance in the bonded area is explained by basic geometry (Acalc accounts for 54.7% of the variance) and incomplete bonding (FE and FH, together account for 32.6% of the variance). It should be noted that the unbonded regions represented by FH and FE are not causing a reduction in the bonded area, rather they are the result of incomplete bonding in the overlapping regions of the fiber-fiber bond. The dominating effect was the unbonded regions at the edge of the bond, as their impact on the actual bond size is fifteen times larger than the effect of holes in the bond. Fig 11 illustrates the fact that the potential bonded area was not fully exploited in the bonds that were examined. The plot compares the calculated bonded area (Acalc) with the measured bonded area. The diagonal indicates equal values. In most cases the bonded area was overestimated by the geometric calculations. The main reason for the deviations is incomplete bonding (B ), incomplete as previously discussed above and also seen in Table 1. Fig 11. The calculated bonded area Acalc plotted versus the measured bonded area for each fiber-fiber bond. The geometric calculation overestimates the bonded area, which is mainly attributed to incomplete bonding (B ), incomplete compare Table 1. Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009 203
Analyzing the influence of fiber morphology on incomplete bonding The examined data set showed that the bonded area is to a large extent explained by basic geometry and regions that are unbonded, even though the fibers are overlapping (incomplete bonding, B ). incomplete The final step of the analysis is to determine which fiber morphological parameters might be responsible for these overlapping but unbonded regions. Multiple linear regression was again performed, using incomplete bonding (B ) incomplete as the response variable and the morphological parameters as the predictor variables. Table 2 shows which variables can be used to explain incomplete bonding (B ) incomplete (white) and which cannot (shaded gray). Only 5.3% of the incomplete bonding (B ) incomplete can be explained by fiber collapse, which is related to fiber conformability. Fibers that easily collapse also usually have higher conformability. Still, a larger interrelation between conformability related fiber morphology and incomplete bonding of overlapping fiber parts was expected.
Table 2. Results of multiple linear regression and ANOVA with incomplete bonding (B ) incomplete as the response variable. The fiber morphological parameters were used as predictor variables. Significant parameters have a white background, while non-significant parameters are shaded gray.
R2 stepwise R2 alone
Fiber collapse Fiber cross sectional area Fiber wall thickness Fiber width Crossing angle Fiber perimeter
0.053 0.010 0.003 0.004 0.005 0.004
p-Value Sign of Coeff.
Preparation of fiber-fiber bonds When working with single fibers or single fiber-fiber bonds, the pre-selection of only a certain kind of fibers can be problematic. This is especially true when single fibers are manipulated, as straight and long fibers are more easily separated from the pulp. This effect is strongly reduced when the bonds are made from suspension. Still there occurs some pre-selection, only longer fibers were used in the present work, as the bonds must be glued across a hole with a diameter of 1 mm. This is only possible with fibers longer than approximately 3 mm.
The drops of suspension were dried in a conventional sheet dryer, and the pressing and drying conditions were similar to laboratory sheet forming. Measurement of bonded area To verify if the results for bonded area are in a realistic range, the bonded areas were compared to values given in the literature. The values given by Page et al. (1962) and Stratton (1992) cannot be directly compared, as a pulp with differing fiber diameter was used. Still, the distributions were similarly found to be positively skewed. Mayhood et al. (1962) also used pulp from a mixture of spruce and pine. The pulp was produced from both, sulfite and kraft cooking, and the bonded area was determined for both pulps separately. The fiber-fiber bonds were also made from an unbleached and unbeaten pulp and dried in a sheet dryer without additional pressing. Polarized light microscopy had been used for the determination of bonded area, using the method developed by Page (1960). Mayhood et al. (1962) point out that polarized light microscopy gives more reliable results when flat and ribbon shaped springwood fibers are used. This is why only bonds of ribbon-shaped springwood fibers were analyzed. A comparison of the bonded areas from both methods is presented in Table 3. For both pulps (sulfite and kraft) the values for bonded area given by Mayhood et al. (1962) are clearly larger than ours (Fig 9). The standard deviation is also smaller. The pre-selection of only ribbon-shaped and collapsed springwood fibers might explain the differences between the measured values. There also might be a systematic increase in the size of the bonded area. If the fibers are fully collapsed, the fiber width will be larger. Calculation of the bonded area (Acalc) showed the significant influence of the fiber width. The restriction to only one type of fibers could also be the reason for the smaller standard deviation. However, this is only based on speculation as no objective evidence for this exists. A benefit of the method used in the present study is that holes and unbonded regions can be correctly identified. Information is not available if holes in the bond cannot be detected with dyeing methods, for example, used by Torgnysdotter et al. (2007). According to Mayhood et al. (1962), it is also unclear whether holes in the bond can be identified with polarized light microscopy. The current results showed that holes in the bond only have a moderate size. Although percentage of the total bonded area due to holes was between 0 and 46.9%, the average value was only 5.1%. Thus it was found that
Table 3. Comparison of values for bonded area given in the literature with results from our measurements.
Bonded area
Standard deviation
(Mayhood et al. 1962) (Mayhood et al. 1962) (Kappel et al. 2009)
Mixed spruce and pine sulfite pulp Mixed spruce and pine Kraft pulp Mixed spruce and pine Kraft pulp
25-45 µm 25-45 µm 25-45 µm
Polarized light microscopy Polarized light microscopy Microtome serial sectioning
1591 µm2 2097 µm2 1130 µm2
478 µm2 321 µm2 602 µm2
NA NA 0.9495
204 Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009
it is more important to measure incomplete bonding at the border of the bond than holes in the bond. It has to be pointed out that only the optically bonded area was measured, since light microscopy was used. A 50x objective was used and the pixel size was 0.161 µm. Although the resolution was high enough to see details like fiber collapse, it is difficult to make any statement about actual bonding between the fibers on a nanometer scale, i.e. molecular contact. It is believed that the bonded area in paper is mainly influenced by fiber morphology, namely the fiber conformability. However, a connection between fiber morphology and bonded area was not observed in this study. An explanation might be that the single fiber-fiber bonds that were examined are almost two-dimensional structures. In contrast, paper is a truly three-dimensional network. Conformability might not be so important to develop the bonded area in the two-dimensional case. The effect of beating or higher wet pressing during the sample preparation procedure still needs to be examined. In this case a stronger interrelation between fiber-fiber bonded area and morphology might be found. The results might also be different for hardwood pulp. The main disadvantage of microtome methods is that the bonds are destroyed during the analysis, and further measurements cannot be performed. It would be possible with a non-destructive method to additionally measure, for example, the bonding force. This would allow the specific bond strength to be measured. Investigating the formerly bonded areas after rupturing the bond, as performed by Jayme, Hunger (1961), is not possible after microtome serial sectioning. Conclusions The proposed method seems to be a useful tool to investigate the bonded area as well as the morphology of the fiber cross sections and the bonding region. The method is able to measure the area of holes in the bond and overlapping but unbonded fiber regions. This combined measurement of fiber morphology and bonded area morphology might contribute to a comprehensive understanding of fiber-fiber bonding. A comparison of the measured and geometrically calculated bonded area (only dependent on fiber width and crossing angle) showed great difference for an unbeaten, unbleached softwood kraft pulp. The actual bonded area was on average 60% lower than geometrically calculated bonded area. Incomplete bonding of overlapping fiber regions was mainly responsible for this difference. It occurred preliminarily at the edges of the bond. Holes in the bond had less impact. Morphological fiber parameters that can be related to conformability (fiber wall thickness, fiber cross sectional area, fiber collapse) could not explain the bonded area and incomplete bonding. This stands in opposition to the papermaker's experience that fiber conformability controls bonded area. This leads to the conclusion that the currently used technique to prepare single fiber-fiber bonds does not reflect the development of bonded area in
paper sheets. Modified specimen preparation, potentially including beating and strong wet pressing, might deliver a closer similarity between development of the bonded area in paper, which is a three-dimensional structure, and development of the bonded area of single fiber-fiber bonds, which are almost two-dimensional structures. Acknowledgements The authors want to acknowledge Mondi and the Christian Doppler Society for funding this work. We especially want to thank Elisabet and Andrew Horvath for linguistic revision of the article and for the valuable discussions in the course of this work. Literature Asunmaa, S. and Steenberg, B. (1958): Beaten Pulps and the Fibre-to-Fibre Bond in Paper, Svensk Papperstidning, 61, 686. Forsstrцm, J. and Torgnysdotter, A. (2005): Influence of fibre/fibre joint strength and fibre flexibility on the strength of papers from unbleached kraft fibers, Nord Pulp Paper Res. J. 20(2), 186. Jayme, G. and Hunger, G. (1961): Electron microscope 2- and 3-dimensional classification of fibre bonding, in Formation and Structure of Paper, IInd Fundamental Research Symposium, Oxford, 135. Kang, T., Paulapuro, H. and Hiltunen, E. (2004): Fracture mechanism in interfibre bond failure ­ microscopic observations, Appita J. 57(3), 199. Kritzinger, J., Donoser, M., Wiltsche, M. and Bauer, W. (2008): Examination of Fiber Transverse Properties Based on a Serial Sectioning Technique, Progress in Paper Physics Seminar Proceedings, Helsinki, 157. Mayhood, C.H., Kallmes, O.J. and Cauley, M.M. (1962): The mechanical properties of Paper Part II: Measured Shear strength of Individual Fiber to Fiber Contacts, Tappi, 45(1), 69. McIntosh, D.C. (1963): Tensile and Bonding Strengths of loblolly pine Kraft Fibers Cooked to Different Yields, Tappi, 46(5), 273. Neter, J., Kutner, M.H., Nachtsheim, C.J. and Wassermann W. (1996): Applied linear statistical models, Fourth Edition, Richard D. Irwin, Illinois (USA). Page, D.H. (1960): Fibre-to-fibre bonds Part 1 ­ A method for their direct observation, Paper Technology, 1(4), 407. Page, D.H., Tydeman, P.A. and Hunt, M. (1962): A Study of Fibre-to-Fibre Bonding by Direct Observation, in Formation and Structure of Paper, IInd Fundamental Research Symposium, Oxford, 171. Stratton, R.A. (1992): Fundamentals of internal strength Enhancement Part 2 ­ Studies on the Bonding of Single Fibers, Progress Report, Institute of Paper Science and Technology, Atlanta, Georgia. Thomson, C.I. (2007): Probing the Nature of Cellulosic Fibre Interfaces with Fluorescence Resonance energy transfer, PhD Thesis, Georgia Institute of Technology. Thorpe, J.L., Mark, R.E., Eusufzai, A.R.K. and Perkins, R.W. (1976): Mechanical properties of fiber bonds, Tappi, 59(5), 96. Torgnysdotter, A., Kulachenko, A., Gradin, P. and Wеgberg, L. (2007): The Link Between the Fiber Contact Zone and the physical properties of Paper: A Way to Control Paper Properties, Journal of composite materials, 41(13), 1619. Wiltsche, M., Donoser, M., Bauer, W., Bischof, H. (2005): A New Slice-Based Concept for 3D Paper Structure Analysis Applied to Spatial Coating Layer Formation, in Advances in Paper Science and Technology, Fundamental Research Symposium, Cambridge, 853. Yang, C.F., Eusufzai, A.R.K., Sankar, R., Mark, R.E. and Perkins Jr, R.W. (1978): Measurement of geometrical parameters of fiber networks Part 1 ­ Bonded surfaces, aspect ratios, fiber moments of inertia, bonding state probabilities, Svensk Papperstidning, 13, 426. Manuscript received October 7, 2008 Accepted February 12, 2009 Nordic Pulp and Paper Research Journal Vol 24 no. 2/2009 205

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