F. F. Wangaard Basis for the Model

Based on a model developed for hardwood fiber strength-pulp property relationships, multiple-regression equations involving fiber strength, fiber length, and sheet density were determined to predict the properties of kraft pulps of slash pine (Pinus elliottii) . Regressions for breaking length and burst factor accounted for 88 and 90 percent, respectively, of total variation in these properties resulting from a large number of beater runs. At a given level of sheet density, fiber strength and fiber length had a positive influence on both breaking length and burst, and this effect was more pronounced the higher the level of sheet densitY. An equation that accounted for 80 percent of total variation in tear factor was also developed. At higher levels of sheet densitY, shorter fibers gave superior tear resistance. The benefits in tear factor generally ascribed to longer (stronger) fibers may be reconciled with these f"mdings when pulp properties are compared at the densities associated with a common level of freeness rather than at specified levels of sheet densitY as was done here. fiber length and fiber strength in populatio of kraft pulps produced from a diverse grol of hardwood species. Handsheets for physi( testing were made from pulps before beating well as after Valley-beater processing. In thc studies sheet density (a corrdate of fiber d( sity) was employed in the analysis as a measu of the degree of interfiber bonding. Fi~ length was the original whole fiber len~ based on mildly macerated wood samples, a. fiber strength (at least insofar as the prest discussion is concerned) was based on zero-sp T HE IlOLE OF FIBEIl LENGTH and fiber strength in influencing the properties of pulp handsheets has been discussed by many authors. Numerous inconsistencies in experimental findings have been reported. One of the purposes of this study is to explain some of them. In a comprehensive review published in 1965, Dinwoodie (3) summarized the principal fiber factors controlling the strength properties of paper as: fiber density, fiber length, and fiber strength. Fiber density relates to the degree of interfiber bonding in a sheet; fiber length, among other things, is associated with the number of bonding sites available on an individual fiber; and fiber strength assumes its controlling role when interfiber bonding becomes so intense as to transfer stress sufficient to cause fibers to rupture. The authors are, respectively, Head, Departml of Forest and Wood Sciences, Colorado State U versity, Fort Collins, Colo., and former Gradu; Student, Department of Forest and Wood Scient Colorado State University, currently Associ Wood Scientist, USDA Forest Service, South. Forest Experiment Station, Pineville, La. T paper was presented at Session 22 Pulp ( Pa~r of the 26th Annual Meeting of the For Products Research Societr, June 21, 1972, Dallas, Texas. It was received for publication May 1972. Basis for the Model The senior author in collaboration with others (4, 5,7) has demonstrated the role of WOODSCIENCE Vol. 5, No.3 counted for 72 ~rcent of the total variation in tear factor, fiber lmgth alone accounted for 22 percent of the variance. It should be mentioned here that fiber length and fiber strength in these pulps produced from 17 different species were unrelated to each other. breaking length of handsheets. Equations summarizing relationships influencing breaking length, burst factor, and tear factor of hardwood handsheets are given in Table 1. These equations depict for breaking length and burst factor a negligible influence of fiber strength at low sheet densities on the order of 0.30 gl cml and an increasing positive effect of fiber strength at increasing sheet densities at least up to 0.80 gl cml. These relationships accounted for 80 and 71 percent of the total variation in breaking length and burst factor, respectively. An attempt to introduce fiber length as a variable in multiple regression contributed less than 1 percent additional accountability to the relationships and was consequently abandoned. The equation for tear factor shows a similar negligible effect of fiber length and fiber strength at the lowest sheet densities. As sheet density increases, however, increasing fiber length exerts a strong positive effect until maximum tear factor values are attained at sheet densities at or beyond 0.50 gl cml. Beyond this point of culmination, the influence of fiber length diminishes and, at the highest levels of sheet density examined, an increase in fiber length actually exerts an adverse effect upon tear resistance. Fiber strength has a positive influence on tear factor at all but the very lowest levels of sheet density, and the effect of this variable continues to increase throughout the entire range of sheet densities studied. In this equation, which acThe Present Study Table 1. MULTIPLE-REGRESSION EQUATIONS FOR HARDWOOD KRAFT PULPS SHOWING THE INFLUENCE OF FIBER LENGTH AND FIBER STRENGTH ON SHEET PROPERTIES. This study of slash pine kraft pulps is an analysis of data available from previous research on relationships between fiber morphology and pulp properties (6). Briefly summarized, these data were based on 66 pulps prepared from top and butt sections of 11 slash pine trees selected to provide a wide range of wood and fiber characteristics within normal limits of variation for slash pine. (The original study involved pulps from 12 trees but one of these was not available for this analysis.) All pulps were cooked at a kraft sdledule selected to produce pulps having a uniform permanganate No. 25. A published report on the original study includes a detailed description of the selection of trees, collection and treatment of bolts, wood and fiber characteristics, pulping, beater processing, and handsheet testing (6). For the purpose of this discussion it may be sufficient to say that our present analysis is based on tests of handsheets made after 0, 30, 50, 70, and 90 minutes of processing in a Valley beater. Of the 330 pulp samples potentially available from this procedure, 312 were actually tested and used in this analysis. A basic premise of the present study was to employ the parameters shown for mixed hardwoods in Table 1 zero-span breaking length, fiber length, sheet density, and combinations of these in multiple regression for the purpose of predicting sheet properties of pulps of slash pine (PinllI elliottii). One difference in the significance of fiber length as a predictor of sheet properties was recognized from the start. The equations of Table 1 were based on variation between species. The equations to be developed for slash pine involve variation within a single species. The variables of fiber length and fiber strength in Table 1 were unrelated to one another. The earlier study of slash pine, however, had established a positive correlation between latewood fiber length and zero-span breaking Breaking length Y. 100 m Y = 10.00 + 32.34 SD + 7.50 IIBL X SD) Bunt 'ador Y, 19/-1) /Ig/ml) Y = 29.16 so + 5.19 IIIL X SOl Tear factor Y, glIB/mil Y = 4.29 L 446.17 5D + 20.55 (IlL X 5D) + 501.80 (L X 5D) + 912.78 5Ds 1330.50 IL X Sol) in which: L = fiber length, mm (based on wood samples) SO = sheet density 0.30, g/cm3 IlL = sheet zero-span breaking length, km