1961 Volume 1

Despite considerable advance during the last twenty years in the technology of paper and papermaking, there has been scarcely any explicit consideration of the subject that underlies all of our knowledge and all of our problems in these fields the structure of paper. A brief survey of papermaking literature brings home forcibly our state of ignorance . None of the classic reference or textbooks includes even a reference to structure in its contents list or index. Even the few papers explicitly referring in their titles to structural considerations are indexed under alternative headings . An enquirer from another industry or technology might be forgiven for inferring that paper is a structureless body defying the normal laws of physical analysis and description!

This is an exaggeration, of course, for ideas about structure are implicit in a wide range of theories, discussions and practical operations on paper and papermaking, but the absence of explicit reference to structure does clearly indicate the superficial and empirical nature of our current knowledge and of the technology of paper and papermaking. At the same time, there are now many indications of a revolutionary change in this situation.

The statistical geometry of fibrous networks is described in terms of the fibre and sheet dimensions and geometric probability. The method has been developed for random- two-dimensional structures and extended to cover deviations from randomness (orientation and flocculation). It is also applied to a multiplanar structure as a first approximation to three-dimensional structures . Further approximations to three-dimensional networks are discussed. Experimental results for two-dimensional structures are presented.

This contribution illustrates the structure of paper by presenting a selection of light micrographs of the surfaces of papers. In addition to illustrating a wide range of papers, the effects are portrayed of progressive beating; coating; creping; machine glazing and the glazing of handsheets; parchmentising; supercalendering ; and watermarking. The two-sidedness of the surfaces of several papers is clearly brought out and the contribution of the surface of mechanical printing papers to their printability is illustrated.

Of particular interest are the effects of progressive beating on the density of the sheet, the closeness of its surface structure and its response to glazing. It was observed that cellulosic material has the ability to replicate fine scratches on a surface with which it is dried in contact.

An examination has been made of eight paper samples by means of the scanning electron microscope at the Pulp and Paper Research Institute of Canada. This is the first step in a programme of examination of paper surfaces and fractures that is planned for this instrument. The scanning microscope(^1,2) bridges a gap between the capabilities of the light microscope and the conventional transmission electron microscope and the results obtained in this study may therefore be of interest to those attending a symposium on paper structure . The capabilities and limitations of the two more conventional techniques are described in detail in other papers of the symposium and will not be discussed here.

A study of the morphology and energetics of fracture can shed some light on adhesion . Two approaches are made and both lead to the same general conclusions . In the first, the fracture of liquids of increasing viscosities or their cavitation leads to the ideas that fracture of polymers is governed by flaws or imperfections, not by molecular parameters. The second approach is that of Griffith, who postulated his now famous ‘crack theory’. The fracture of materials is again seen as a statistically controlled process dependent on the presence of flaws. Qualitatively, it is known that fracture of paper is explicable by stochastic considerations, too; however, quantitatively, the crack or flow theory fails.

In order to explain the mechanical failure of paper, it becomes necessary to apply the statistical approach to the bonds between the molecules . These are the hydrogen bonds joining cellulose molecules together. It is found that, if a variance is assumed to exist around the mean value of the bond energy, the rupture energy of paper can be related to its content of hydrogen bonds. Thus, the adhesion of the elements of paper is quantitatively explicable in terms of characteristics of this bond.

Using a technique developed by the authors, an examination by electron microscopy of coniferous wood tracheids has shown that the secondary alterations in the texture of the cell wall layers during drying play an important role in fibre-to-fibre bonding. Differences between late wood and early wood are indicated, together with the typical behaviour of each of the cell wall layers in such bonding. The effects of beating, of drying a sheet of paper and reforming it from the disintegrated pulp are dealt with, particularly regarding their influence on sheet strength.

An examination has been made of the size and shape of fibre-to fibre bonds and their frequency of occurrence in paper sheets. Definitions have been proposed for parameters associated with these bond properties. The effects of beating and drying tension on these parameters have been investigated and the likely effect of other papermaking variables has been considered. The significance of the parameters in controlling the physical properties of paper is discussed.

In earlier papers,^{(1, 2)} the possibility of the use of light microscopic methods for the observation of optical contact regions between fibres in paper sheets was described and arguments were put forward that these areas of contact define the regions within which strong adhesive forces operate. While sufficient confidence in this view was held to use the technique for studies relating to geometry of fibre-to-fibre bonding in paper, it was considered that the question of the fine structure within these contact regions was sufficiently important to warrant a separate investigation, the initial results of which are given here.

Mathematical theories for some of the mechanical properties of a well-consolidated anisotropic fibrous web are developed in two major divisions : the elastic and the plastic regimes of stress/strain relationships . For each of the principal directions in the plane of the sheet, theories of the elastic regime are developed for external load, Poisson’s ratio, Young’s modulus and the modulus of rigidity. Applications of the theory to improve pulp evaluation and to studies of important sheet properties (in the elastic regime) such as stiffness and sheet rigidity are discussed. A complex of phenomena of the plastic regime is inferred from theory . Stresses tending to cause rupture of fibre-to-fibre bonds are found in two important groups: those associated with torque on bonds resulting from shearing force in fibre segments (and combined with stress caused by anisotropic shrinkage of the fibres) and those associated with tension in fibres (and combined with the anisotropic shrinkage stress) . The incidence of fibre-to-fibre bond rupture as the sheet strain is increased from the elastic range into the plastic regime is governed by equations developed for torque and tension bond failures. A brief discussion of the theory of the zero-span tensile test is included.

The purpose of this contribution is to describe how statistical-geometrical analysis [such as that developed in the paper by Corte and Kallmes, this vol., pp. 13-46] can be extended and applied to the determination of the joint probability density function p(s, e), which arises so naturally and importantly in Van den Akker’s very interesting theoretical analysis of some of the fundamental mechanical properties of paper exhibited in the elastic regime (this vol., pp. 205-241).