Symposium SF03—Paper-Based Packaging—21^st Century Perspectives on an Ancient Material

Flexible packaging is expected to witness continuous growth in coming years. The current flexible packaging market is dominated by plastic materials. However, consumer demand for sustainable packaging is fueling interest and growth in alternative packaging materials. Paper is increasing in popularity as a repulpable and recyclable packaging material. However, its porous nature and the lack of heat-sealability bring challenges in delivering performance equivalent to incumbent technologies. In this talk, we will discuss efforts to drive this industry with sustainable waterborne paper coating technologies. Dow’s BLUEWAVE™ Technology enables solvent-free waterborne dispersions with low viscosity at high solids content which can be applied to surfaces and thermally cured to form films. Flexible paper packaging treated with such dispersions could lead to single or combined property improvements to meet the demands of various paper packaging customers, including but not limited to: barrier properties (liquid water, moisture vapor or oil), adhesion properties (heat seal and hot tack), as well as surface properties (coefficient of friction reduction).

The replacement of plastic packaging by paperboard can significantly contribute to meet sustainability goals in important application fields, such as in food packaging. Paperboard is a bio-based, versatile and inexpensive material, however, paperboard has poor barrier properties due to its porous structure. Therefore, a barrier coating is required to improve the quality and shelf-life of packaged goods by protecting it against specific substances such as water (vapor) and oil. In order to meet these requirements, we prepared a waterborne barrier coating by emulsion polymerization. An alkali-soluble resin is used as polymeric surfactant, which is acid-rich and dissolves in water in alkaline conditions. When the dispersion is applied to paperboard, water and base evaporate whereby the carboxylate groups protonate and a water-insoluble coating is formed. In this talk, we will demonstrate the relation between the coating preparation methods and both water and oil barrier performance of ASR-based waterborne coatings.

The applicability of various polymer substrates to conjugate metal-organic frameworks (MOF) is mostly limited owing to inferior mechanical properties and the high costs of synthetic polymers. Additionally, the use of synthetic polymer substrates and solution phase synthesis of MOF to fabricate MOF/fiber composites present several drawbacks, including agglomeration of MOF particles, time-intensive fiber making process, reduced MOF functionality after its incorporation and large consumption of organic solvents. Herein, we report a sustainable approach to integrate MOF via vapor phase synthesis, on a cost-effective and mechanically strong lignocellulosic fibrous banana paper (BP) substrate developed from the biomass of banana harvest. Uniform and conformal metal oxide is deposited on the substrate through atomic layer deposition (ALD), followed by exposure to the organic linker. We systematically investigate the effect of the amount and conversion time of the metal oxide on the MOF growth. The resultant MOF-BP composites demonstrate a high surface area of 552 m²/g. Uniform surface growth of MOF via the vapor phase approach and a hierarchical porous structure of the BP facilitate gas diffusion properties of MOF, while the mechanical strength of the substrate is well retained after the MOF growth. We have investigated the full accessibility of MOFs on the fibrous substrate via CO₂ adsorption. Additionally, enhanced antibacterial properties of the BP-MOF composites are verified via antibacterial contact assays, while preliminary studies indicate a promising sorption profile of volatile organic compounds. We believe that the sustainable nature of the lignocellulosic BP substrate and uniform growth of MOF on the hierarchical porous structure impart impressive attributes to these composites which can be explored in diverse applications ranging from antibacterial packagings to sensors.

This work reports the ceramic hybrid packaging films with a compound of polyethylene polymer and mesoporous silica, which enhances the oxygen permeability and moisture permeability of the films for the keep-freshness properties of the product. In this process, a compound in micron size containing 14% of mesoporous silica was produced using a twin-screw extruder. Furthermore, using this compound, films containing mesoporous silica were made with a blown film making machine. The dispersity and contents of mesoporous silica material in masterbatch and packaging film were analyzed using a field-emission scanning electron microscope (FE-SEM) and thermogravimetric analyzer (TGA). In addition, the oxygen transmission rate (OTR) and water-vapor transmission rate (WVTR) of the mesoporous silica-PE packaging films were calculated. Furthermore, the evaluation of the shelf lives of bananas showed that the film containing vermiculite showed less browning of bananas. This means that the use of vermiculite increases oxygen and water-vapor permeability, and thus can control the oxygen concentration related to the respiration of agricultural products within the films.

This work reports the preparation of hydrophobic mesoporous silica particles (MSPs) modified with non-fluorinated alkyl silanes. Alkyl silanes were grafted onto the surface of the MSPs as a function of the length of non-fluorinated alkyl chains such as propyl-triethoxysilane (C₃), octyl-triethoxysilane (C₈), dodecyl-triethoxysilane (C₁₂), and octadecyl-triethoxysilane (C₁₈). Moreover, the grafting of the different alkyl silanes onto the surface of MSPs to make them hydrophobic was demonstrated using different conditions such as pH changing the pH (0, 4, 6, 8, and 13), solvent types (protic and aprotic), concentration of silanes (0, 0.12, 0.24, 0.36, 0.48, and 0.60 M), reaction time (1, 2, 3, and 4 d), and reaction temperature (25 and 40 °C). The contact angles of the alkyl silane-modified MSPs were increased as a function of the alkyl chain lengths in the order of C₁₈ > C₁₂ > C₈ > C₃ and the contact angle of C₁₈-modified MSPs was 4 times wider than that of unmodified MSPs. The unmodified MSPs had a contact angle of 25.3 °, but C₁₈-modified MSPs had a contact angle of 102.1 °. Furthermore, the hydrophobicity of the non-fluorinated alkyl silane-modified MSPs was also demonstrated by the adsorption of hydrophobic lecithin compound, and showed the increase of lecithin adsorption as a function of the alkyl chain lengths. The cross-linking ratios of the modified silanes on the MSPs was confirmed by solid-state ²⁹Si-MAS NMR measurement. Consequently, the hydrophobic modification on MSPs using non-fluorinatedalkyl silanes was best preferred in a protic solvent, with a reaction time of ~ 24 h at 25 °C, and at a high concentration of silanes.

World is now currently being hugely affected with the toxic legacy of disposable electronic gadgets from a tech-hungry society with the short lifespans of these technologies that results an unwanted by-product of electronic waste (e-waste) which is becoming an enormous threat to our planet. According to the U.N. the world produces 50 million tonnes of e-waste in each year, among which only 20% of this is formally recycled. However, in this rapid progressing digital age, we cannot absolutely turn away its exceptional growth in smart technology. On the other hand, with the burgeoning development in wireless technology and smart devices, we need to ensure the access of affordable, sustainable and modern systems for all which will be smart, portable, flexible, eco-sustainable and full recyclable products and systems, full green, for low cost and disposable applications. In this context we will deploy the list of things to be done for a better global equity as far as science and technology is concerned towards a better exploitation of materials and systems to serve the welfare and comfort of human kind, focus in 4 main areas; affordable and clean energy; electronics interfaces to serve the Internet of Things and the Cloud; Water and Food sustainability’s.

Cellulose-based electrodes for the use in energy storage devices have been demonstrated in numerous publications over the past decades. Although cellulose is an electrical insulator, properties such as electrochemical stability and an amphiphilic nature make it an excellent material for acting as a hosting material for conducting and/or electroactive materials. Perhaps the most compelling opportunity with cellulose-based electrodes is the vision of a fast, cheap, and green production of energy storage materials on paper machines. While paper-based energy storage is not expected to compete with high-end solutions in terms of performance, the presumed low cost and recyclability of such devices should be preferable in applications such as grid energy storage or to power smart paper packaging. However, as most such investigations have been done on nanocellulose composites, the majority of the reported material concepts are not applicable to the existing production assets.

To meet this challenge, it is important to investigate material systems based on cellulose-rich pulp fibers in paper-making settings. The present investigation was carried out on a pilot paper machine with the aim to fabricate supercapacitor electrodes. Activated carbon (AC) was selected as the main charge-storing material. Process parameters and fiber properties, in combination with the electrical characteristics of the formed electrode papers, have been analyzed to establish the relationship between the manufacturing process, raw material characteristics and the product performance.

The results showed a positive relationship between the electrode conductivity and the measured specific capacitance. This stresses the importance of introducing good conductors in the electrode along with the charge-storing AC, and indeed motivated the investigation of using such additives. Post-impregnation of the electrode papers with small amounts of the conductive polymer poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) indicated a synergetic effect with the AC in terms of conductivity. The impregnation lead to conductivity increases which exceeded the separate conductivities of AC-loaded and PEDOT:PSS-impregnated papers alone, with an observed corresponding increase in charge storage capacity.

The pilot paper machine trials resulted in several 10-meter-long rolls of paper electrodes. With a measured electrode specific capacitance of about 50 F/g and a specific capacitance per mass unit of loaded AC of more than 80 F/g, this demonstrates the feasibility of using paper making techniques for supercapacitor electrode fabrication. Along with the knowledge provided about important aspects in their material and process design, this work advances the technological readiness of paper-based energy storage.

The global food packaging market is a 311.4-billion-dollar industry in 2020 and is estimated to reach 456.6 billion dollars by 2027. The rising demand for food packaging systems is accompanied by an increasing need for improving food quality and guaranteeing food safety. Monitoring the quality of packaged food is an important step in reducing food spoilage and improving food quality and food safety. Since humidity levels inside a package, pH, and chemical changes of meat products are good indicators of food quality, several sensors such as colorimetric sensors and active sensors have been developed to monitor them. While colorimetric sensors are cheap and can be easily embedded into transparent packages, they cannot be used for non-see-through packages and require laborious and time-consuming manual inspection. Although active sensors support automation in reading the sensors, they are expensive and not always biocompatible due to the presence of batteries and electronic chips in the sensors. Battery-less chipless wireless sensors have been widely used in food packaging because of their low cost, and wireless sensing capability. However, the main drawbacks in commercializing chipless sensors are the issues associated with their manufacturing process. Scalable manufacturing techniques such as printing techniques have been widely used for chipless sensors used in moisture sensors, soil sensors, and ID applications. Scalable manufacturing techniques provide a substantial reduction in the number of processes and resources required for manufacturing sensors. However, it introduces tremendous challenges such as the ink formulation for conductive and functional patterns, the need for custom-made screens, and the time required in the drying and sintering processes.
In this talk, I will present an array of roll-to-roll laser assisted surface modification and micromachining strategies with two commonly used CO2 and Nd:YAG lasers that can significantly reduce manufacturing costs, increase efficiency, and improve the production rate of wireless sensors for use in food packaging applications. In the first section, I will describe the use of localized CO2 laser irradiation to selectively convert thermoset polymer films (e.g., polyimide) into electrically conductive and highly porous carbon micro/nano structures. This process provides a unique and facile approach for direct writing of carbon-based conductive patterns on flexible polymer sheets in ambient conditions, eliminating complexities of current methods such as expensive CVD processes and complicated formulation/preparation of conductive carbon-based inks used in inkjet printing. In the second part of the talk, I will demonstrate the use of laser ablation for selective patterning of conductive coatings from multilayer films such as ITO-coated PET and metalized paper and plastics as a simple and scalable alternative to conventional photolithography-based processes. I will finally discuss our on-going efforts in utilizing roll-to-roll laser processing approaches to create cost effective wireless sensors that can monitor the food packaging quality and freshness.

We recently demonstrated the high stretch-formability of areca palm leaf-sheath material, a plant-based biological composite, for production of eco-friendly foodware products such as plates and bowls. In the present study, we extend this work to understand various parametric effects on formability using biaxial stretching (Limiting Dome Height Test (LDH)) and uniaxial tension. The principal findings are as follows. Hydration of the sheath prior to the stretching increases the forming limit strains by ~ 400% and reduces deformation forces by as much as 85%. Additional major enhancements in formability are achieved by adding small quantities of NaOH (~ 5%) during the hydration process. Local deformation measurements, based on analysis of distortion of grid-markers inscribed onto the leaf-sheath samples, have enabled characterization of strain field anisotropy and mode of failure in the leaf-sheath. The results also provide a characterization of the types of high-aspect ratio product shapes and structures that can be directly stretch-formed, in a single-step, from this plant material.

A world without plastics, or synthetic organic polymers, seems unimaginable today. Plastics’ largest market is packaging, especially these used for food packaging, which was accelerated by a global shift from reusable to single-use containers, such as straw, coffee cup, lunch boxes. However, due to these disposable plastics’ nonbiodegradability, lack of waste management and low-recycling rate, plastic wastes have been inputting from land into ocean and increasing within our food chain, causing a massive threat to the environment and human health. Therefore, there is an urgent need for an environmentally friendly, fully biodegradable, low cost and biocompatible alternative. To address the challenge, this work used sugarcane bagasse left from sugar industry as a feedstock to prepare fully biodegradable tableware by using a scalable molding method. In addition, long bamboo fibers were mixed with the sugarcane bagasse fibers to enhance the mechanical strength of the resultant plastic alternatives. The fabricated tableware have superior performances required for food packaging, including low heavy metal content (Pb, 0.3633 mg/kg; As, not detected;), oil stability (level 6, TAPPI standard), excellent hydrophobicity (contact angle of 127°), and high mechanical strength (tensile strength 35 MPa). More importantly, our tableware can be mostly biodegraded under natural conditions within 60 days, which is largely shorter that the degradation of synthetic plastics. Furthermore, the impacts of the manufacturing of this biodegradable tableware on environment were evaluated by calculating its CO₂ emission. In comparison with the production of polystyrene (PS) plastic (7.36 kg/kg) and the traditional paper manufacturing (0.51 kg/kg), the manufacturing process of this tableware had much less CO₂ emission (0.22 kg/kg). The tableware made from biomass feedstock thus represents an eco-friendly and biodegradable alternative of synthetic plastics toward food packaging.

Cottonid, vulcanized fiber and leather stone - many names exist for one of the oldest known plastics. In 1859, the Englishman Thomas Taylor described for the first time the production of this material on the basis of rag paper, which he produced by soaking cellulose fibers in a zinc chloride bath and pressing several layers under heat. Nowadays, unsized specialty paper made from cotton, pulp or a mixture of both serves as a renewable raw material for industrial production. Chemically, Taylor described the parchmentization of cellulose fibers.
The treatment with zinc dichloride may only last until the fibers have reacted superficially, otherwise the cellulose chains are degraded and the material is damaged. The exact mechanism of parchmentization has not yet been identified in detail. During the process a tremendous swelling can be observed followed by the decomposition of the paper sheet. The result of this conversion process of the cellulose fibers is a considerable change in the material properties, from soft and flexible to horn-like and hard.
The manufacturing process and the material itself is very sustainable. The zinc dichloride, used as a catalyst, can be completely recycled. The washing water is also almost completely reused. The finished material is free from chemical residues and consists only of cellulose and, for marketing purposes in some cases, pigments. Also zinc dichloride is a cost effective and a safe “solvent” compared to commonly used for dissolving cellulose. The industrial manufacturing process is established and optimized for more than 100 years in terms of energy- and resource efficiency.
In this context, the presented talk will provide an overview of the fundamental changes of the cellulose, the resulting customizable properties of Cottonid and its possible applications. Almost all properties of the material can be tuned. Through variation of the parchmentizing process, it is possible to set the crystallinity of the material. With this in mind, we can set the mechanical properties, hygroscopicity, optical properties, electrical properties and even the duration of the biodegradation. The process-structure-property relationship of the resulting material is characterized by infrared spectroscopy, differential scanning calorimetry and x-ray diffraction. In addition, structural properties after manufacturing are analyzed by scanning electron microscopy.
Cottonid can be used for almost every suitable application from packaging to autonomous actuation devices. Due to the adjustable hygroscopicity and the associated swelling, Cottonid can also be used as a functional material. It can work as a humidity sensing actuator as the active layer in a bilayered composite. Because of its good resistance against chemicals, grease and oil, a possible application in the packaging industry can lead to a further development of the material. Furthermore, Cottonid can be joined and machined similar to wood. Cottonid fiber is currently used as a support material for grinding wheels due to its toughness and because of its spark-quenching properties for welding helmets. The oldest use is as a sealing material in the water pipe technology.
In summary, Cottonid is a promising material in the field of biological and sustainable materials. Due to the topicality of the issues of environmental protection and sustainability, these materials are experiencing a renaissance. It has great potential to replace conventional petroleum-based materials as a green alternative. Additionally, the reaction route via zinc dichloride can be transferred to the wide area of all cellulose composites and might lead to a new, more sustainable way for their fabrication.

The sheet strength of cellulose nanofibre sheets is of interest in a wide variety of applications. This study looks at understanding the mechanisms of nanofibre sheet strength by using up to 80% silica nanoparticles as a spacer between the nanoparticles. The silica nanoparticles are largely inert and by varying the amount of silica nanoparticles we can vary the fibre density of the network. The cellulose nanofibre network does not act as a conventional wood fibre network. The data show that the nanofibers are forming a non-woven network with highly efficient stress transfer between the fibres, requiring relatively few fibre-fibre bonds to efficiently transfer load through the network, thus tensile strength was essentially independent of fibre density, while stiffness went up with reduced network density and strain at break went down. These changes may be explained by the nanoparticles physically limiting rearrangement of the fibre network to accommodate the load applied to the network. The results will then be discussed in terms of theories of paper strength and compared with data from the literature.

The utilization of sustainable material feedstocks (such as cellulose, naturally produced by plants) to fabricate advanced materials is the vital area of the research needed to achieve the future independent of fossil fuels and related greenhouse gas emissions. Japan focuses on the energy transition toward a hydrogen society to improve its sustainability profile – a conceptually different energy system with hydrogen (H2) as the primary energy carrier. Fuel cells and specifically polymer electrolyte membrane fuel cells (PEMFCs) – the devices used for efficient transformation of chemical energy into electrical energy are the key technology to achieve this transition. PEMFCs are particularly suited for the transportation sector due to their high power density, durability, and fast start-up time.
PEMFCs are built around an essential core element – the proton exchange membrane (PEM). The main feature of a PEM is the ability to conduct protons through its structure selectively, enabling the controlled reaction between hydrogen and oxygen. In addition, the PEM acts as a barrier to gases and electrons. Currently, the specific class of materials – sulfonated perfluoropolymers (or perfluorosulfonic acids) are benchmarks for PEM. Among them, the most recognized polymer is Nafion® (Du Pont). Its chemical structure and microscopic morphology are responsible for its high proton conductivity of > 100 mS/cm in the fully hydrated state [1]. However, these materials' high-cost and non-recyclable nature are among the main drawbacks that prevented their use on a larger scale and enabled the lower cost of hydrogen fuel cell devices. These factors motivate the research to develop novel materials to substitute the PFSA materials for PEM applications.
Most mainstream research efforts relate to the synthesis of polymers with architectures similar to Nafion®, namely, including acid-bearing functional groups in conventional polymers [2]. Recently, however, considering the synthetic origin of most polymers (made of fossil fuels), it is strongly desired to use more sustainable polymer feedstocks. Therefore, various bio-polymers naturally produced by the biosphere are considered a good option. Nanostructured forms of cellulose (often referred to as nanocellulose) are particularly attractive. Cellulose is a biodegradable polymer; it has numerous advantages over fluorinated polymers, such as exceptional mechanical strength, high gas barrier, and chemical structure convenient for modifications. The utilization of nanocellulose in the form of PEMFCs and the concept of "paper-based" fuel cells was introduced by our research group [3]. However, low proton conductivity and the aqueous stability of pristine nanocellulose membrane are limiting factors for the fuel cell's performance and application.

This work will report a systematic study of organic-acid-based crosslinking of various nanocelluloses to create the material suitable for PEMs for hydrogen fuel cells. Namely, we demonstrate that crosslinking of nanocelluloses with acid could deliver improved proton conductivity, provide mechanical reinforcement allowing the fabrication of thinner membranes, and enhance the stability in aqueous media. Ultimately these improvements would result in suitable PEMFC performance leading to the expansion of the concept of "paper-based" fuel cells that are low-cost and biodegradable. From the fundamental point of view, this study also aims to clarify what is more important for the proton conduction: "backbone sulfonation" or "sulfonation via added crosslinker". Finally, from the practical point of view – the research aims to create proton exchange membranes that can be used as a low-cost alternative in hydrogen fuel cells.

Papertronics have recently emerged as a next-generation “green” electronic platform with the goal of tackling deformability, cost-effectiveness, electronic waste management, environmental pollutions, and resource shortages. Papertronics possess unique characteristics including foldability, flexibility, lightweight, low cost, biodegradability, renewability, eco-friendliness, and probability for abundance. The potential of papertronics for large-scale manufacturing, system integration, and commercialization has been demonstrated in an increasing number of scientific publications and patents that develop many electronics such as paper-based printed circuit boards (PCBs), displays, touch-pads, and other electronic components. While paper is used for flexible electronics, it has also recently been considered as a promising substrate for microfluidic assays and diagnostics. Paperfluidics have revolutionized public healthcare, both in developed and developing countries and have become a new class of point-of-care (POC) diagnostic devices that are portable, rapid, low-cost, and easy to use. The process of pattering microfluidics in paper has been well established in photolithography, wax printing, laser micromachining and other techniques. Microfluidic channels in paper can be fabricated two-dimensionally or even three-dimensionally to transport the fluids horizontally and vertically. In this invited talk, he will present many innovative papertronic devices that his research group recently developed including paper-based PCBs, paper-based microfluidics, and paper-based batteries. Details of the frontier of research to improve the performance of the devices will be discussed, followed by a critical perspective on strategic future directions.

Lignin is a highly abundant compound that can be extracted in large amounts as a side stream in the pulping process. At neutral pH, lignin is hydrophobic and could thus be a candidate for a bio-based water barrier. However, dispersing a highly hydrophobic substance in water is problematic. In this work, the concept of using emulsions to produce a water barrier was demonstrated using a lignin oil coated on a board substrate.
A lignin oil was prepared with a lignin ester from kraft lignin. Emulsions were then prepared by dispersing water in the oil using an electric homogenizer. The lignin content in the oil was between 35 and 40% and the emulsion had a water to oil ratio between 1:9 to 1:5. The emulsions were then coated onto a board substrate in a laboratory bench coater at different coating weights and dried in an oven. Different drying temperatures were used to dry the emulsions, i.e. 120 to 150 °C.
The coated samples were then screen tested for water barrier properties by applying droplets of water onto the coated surface and measuring the time for the droplets to disappear or to become absorbed by the substrate. Water barrier properties were then characterized by Water Vapour Transmission Rate, WVTR.
The drop tests showed that the water drops stayed on the coated surfaces. It is therefore likely that lignin emulsions formed a continuous barrier film. The WVTR measurements indicated moderate water vapor barrier properties. A higher coat weight decreased the WVTR and a lower drying temperature seemed favorable for the water barrier properties. Increasing the lignin content in the oil from 35% to 40% also decreased the WVTR slightly.

Linerboard producers using old corrugated board (OCC) in North America have bene facing two major challenge: 1) reducing basis weight while maintaining or even enhancing compression strength and 2) addressing the lack of availability and rising cost of OCC. Softwood high-yield pulps including TMP, CTMP and BCTMP, with highly fibrillated fibers and high fines content, can help increase the bulk while improving bonding of recycled fibers. On the other hand, high-yield pulps with coarse, stiff fibers help increase bulk and this bending stiffness, leading to the improved box compression strength (BCT). A laboratory study showed that substituting 15-20% OCC with high-yield pulps can increase bulk, bonding and tensile strength, leading to an increase in bending stiffness by more than 50%. The compression strength (SCT) was not negatively affected (in fact, a small positive effect with SW CTMP was observed). The implication of these findings is that for mills with high-yield pulps (e.g. TMP) available on the mill site, substituting OC with HYP would provide a cost-effective solution to enhance the performance of recycled linerboard.

Films were prepared of Nanocellulose (CNF) generation 1 by vacuum filtration and films of poly(butylene succinate) (PBS) were prepared by compression moulding. The water uptake of nanocellulose (cnf) and poly(butylene succinate) (PBS) films was measured at different temperatures, 23°C, 30°C, and 38°C, and relative humidity (RH), 10-90%. The diffusion coefficient was calculated from the absorption data and the GAB model was used to calculate clustering of water.
The cnf films absorbed more water than the PBS films, which was expected due to the hygroscopic nature of cellulose. The diffusion coefficient of water in both materials increased with increasing temperature. The diffusion coefficient in the CNF films increased with increasing relative humidity up to a certain point, i.e. a maximum was observed at a RH of 40%, at all temperatures. The diffusion coefficient of the PBS decreased with increased relative humidity with a steep decrease at a RH above 60%.
Clustering of water was low for CNF at low relative humidities, i.e. below 40%, and increased quite rapidly at RH above 40%. Clustering of water in the PBS films showed an increase with RH in all areas. A steep increase was observed for RH above 60% at 38°C. The clustering of water thus showed a good correlation with the diffusion data. It therefore seemed reasonable to assume that the larger aggregates formed by water due to clustering would pass through slower and that this would decrease the diffusion coefficient at higher RH.

In the papermaking process different fiber with different fiber length is mixed into a pulp. In the process it is possible to steer a paperboard machine to control the density in different plies in a paperboard. This can be done e.g., by the degree of refining or by chemical that are used to attract the fibers. In addition, it is possible to steer the orientation of the fiber by controlling the headbox outlet speed in relation to the web that the fiber is put on.
However, the product paperboard is characterized with respect to its bending stiffness when it is used. To optimize the bending stiffness the through-thickness (ZD) profile can be engineered. The straightforward path to optimize the bending stiffness to make a paperboard with and I-beam structure. The ZD profile in a paperboard will however also affect local failure mechanisms, which contribute to converting behavior of paperboards. For optimal converting behavior it is important to control where the purpose made damage made during creasing develop; this put additional requirements on the paperboard design that needs to be considered.
The aim of this work would be to implement analytical models that can be used to predict the performance of paperboards based on how it is constructed in the thickness direction using different properties in the plies, which hence can be used to investigate the performance of paperboards with different ZD design. This will be done by utilizing laminate theory, a Timoshenko bending model and the rule of mixture, to construct a model that can predict the strength based on papermaking variables such as density, fiber orientation and fiber length.
For paperboard, an in-plane tensile and out-of-plane shear component are needed for good predictions of bending and converting, which are accounted for by a Timoshenko model. The in-plane properties give information about the network structure, and out-of-plane shear is the best measure of bond deformation. The biaxial stress state has been used to formulate a Hill based failure criterion for paperboard.

The material properties and needs to be evaluated from the specific paperboard. For this purpose, about 100 paperboards with various properties have been splitted with a Fortuna sheet splitter such that top, middle and bottom plies have been free-laid and tested in the machine direction (MD), cross machine direction (CD) as well as in ZD. The paperboards were selected to have variation in the different plies, such we could shows the limits and possibilities with respect to density, fiber orientation etc within each layer. The data was used to formulate empirical models of and . A linear model to predict the geometrical strength of a sheet made of a particular fibre will be suggested.

Out-of-plane shear strength can be associated with breaking of bonds within the sheet, for this purpose ZD strength can be used, which are linearly correlated to the out-of-plane shear strength. A valid approximation would be that the shear strength is three times larger than the ZD strength. Hence, by utilizing data from free-laid middle plies the out-of-plane shear strength was be correlated to the geometrical tensile strength by a linear relation. The middle ply of a paperboard normally has a ZD strength that is 3-4 times lower than the top and bottom plies. ZD failure do therefore occur in the middle ply, therefore the ZD strength was only measured for the middle plies. <!--![endif]---->