The hyperbolic theory of light scattering, tensile strength, and density in paper

The hyperbolic theory of light scattering, tensile strength, and density in paper describes a sheet of paper as a matrix of cellulose with a characteristic material strength and open and closed pores dispersed through the cellulose, forming solid foam. This paper presents two principle hyperbolic equations. The first describes the conservation of tensile strength and the second describes the conservation of mass as functions of light scattering. Three additional equations are derived. The first relates tensile strength to sheet density, the second relates light scattering to total pore volume, and the third relates tensile strength to total pore volume. The conservation of tensile strength equation varies with processing for a given cellulose pulp. Variable refining levels at constant levels of wet-pressing produce separate curves for each wet-pressing level. Correspondingly, variable wet-pressing levels produce separate curves for each level of constant refining. Hydrolyzing pulps or cutting fibers to shorten the average degree of cellulose polymerization shifts the curves to lower tensile strengths. The conservation of mass equation results in a single curve, regardless of processing or reduction in the degree of cellulose polymerization. The concept of relative bonded area measurement using light scattering as developed by Ingmanson and Thode is shown to be invalid for paper by this hyperbolic theory. The validity of relative bonded area by any technique is also questioned.