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Cellulose (2021) 28:5775–5791
Introduction
apparent that in order to increase the strength of a sheet, the inter-fiber bonds must be strengthened. Strengthening of the tensile properties in the dry state is traditionally done with so called dry strength agents. Additionally, pulp refining (Lindstro¨m et al. 2016) and wet pressing (He et al. 2003) of sheets can be used to adjust and control sheet tensile properties. A variety of macromolecules have been used in order to increase the dry tensile strength of paper. Examples are bio- based polymeric additives, such as starch, chitosan, or carboxy methyl cellulose (CMC), as well as synthetic polymeric systems, such as polyacrylamide (PAM), polyvinylamine, polyethyleneimine or polyelectrolyte multilayers (Lindstro¨m et al. 2005). There are at least three proposed mechanisms that explain the dry strengthening effect of additives, including increased inter-fiber bond strength by the reinforcement of existing and/or the contribution via additional bonds, decreased stress concentrations in the sheet while drying and by enhancing the consolidation of the sheet (Lindstro¨m et al. 2016). Upon rewetting, cellulose fiber networks loose nearly their entire strength. This can be explained by the hydrophilic nature of cellulose fibers and their swelling behavior in contact with water (Lindner 2018). Water molecules penetrate the cellulose fibers and fiber walls and consecutively weaken the attrac- tive hydrogen bonds between cellulose chains and fibrils. In addition to that, the swollen fibers are highly malleable, and the aforementioned frictional forces holding fibers together are weakened as well. It is widely discussed, that in order to increase the wet strength, the introduction of covalent bonds between adjacent fibers is necessary, however, other treatments such as wet pressing or the use of microfibrillated cellulose (MFC) have also been shown to increase the wet strength of paper. In the industrial application so called wet strength agents are used to increase the tensile strength of paper in wet conditions. The two main working models of those additives are the protection and the reinforcement mechanism, respec- tively (Lindstro¨m et al. 2005). With the protection mechanism, a firm non-polar polymeric sleeve wraps around fiber crossing points thereby limiting the access of water molecules to the area of fiber contact. Typically, such polymers are cross-linked hydropho- bic resins such as for example phenol–formaldehyde resins, where the used polymeric precursors typically react with one another but do not significantly bind to
The tensile strength of paper sheets in their dry or wet state is one of the most important relevant properties for a large number of paper grades progressing from packaging, to hygienic paper, and specialty paper, such as filter or bank notes, respectively. In addition to such classical applications of paper, in recent years, fueled by the ongoing effort for environmentally friendly products, the use of paper has expanded into a variety of new sectors, such as paper for construction materials (Auslender et al. 2017) and the use in diagnostics, microfluidic and lab-on-paper devices (Credou and Berthelot 2014). Due to its wet-layed production, the strength of the paper sheets is a complex interplay of the properties of individual lignocellulosic paper fibers (length, kink, width, degree of polymerization, fibrillation, defects) and the bonds formed between them, constituting a non-woven fiber network. Tejado and van de Ven (2010) conducted a detailed analysis of the processes in paper formation and the associated forces. They argue, that the fibers are held together via entangle- ment between smaller cellulose fibrils on the macro- scopic fiber surfaces and the main reason for the wet- web strength of undried paper are friction forces. Belle et al. (2015) analyzed freeze-dried wet webs of different solids content with field emission-scanning electron microscopy (FE-SEM) and were able to show such entanglement between fibrils of adjacent fibers and the inter-fiber bonds produced thereby. Another mechanism leading to inter-fiber bond strength can be described by the diffusion of macromolecular cellu- lose chains into adjacent fibers in close contact (Lindstro¨m et al. 2005; Hubbe 2006). While inter- fiber bonding is the subject of many research projects, the exact mechanism of it is still not fully understood. However, it is widely accepted that hydrogen bonding, van der Waals and Coulomb forces, mechanical interlocking of fibrils and diffusion of cellulose chains on the surface of fibers, all play a crucial role in this complex interaction, leading to the intrinsic macro- scopic tensile strength of a paper sheet (Hirn and Schennach 2015). A first attempt describing the tensile strength of paper in a quantitative manner was done by Page (1969). Considering that the strength of a single cellulose fiber is significantly higher compared to the strength of a respective paper sheet, it becomes
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