Polymers 2021 , 13 , 2485
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exponential acceleration of diffusion with temperature dominates the setting of wet strength over other factors such as process dynamics or final material density. • The highest solids content before hot-pressing for the TMP sheets was found to give the highest values for wet strength. A possible explanation for this is that when a drier sheet is pressed, a higher temperature is reached, which accelerates the inter-diffusion of the lignin and thus enhance bonding. No significant correlation was observed between the varied solids content before pressing and dry strength. • The elastic modulus increases with the increasing density of the sheets after hot- pressing, as expected. On the other hand, the dry strength does not show the same trend, indicating that the inelastic behaviour after yielding is responsible for the observed differences among the trial points. • For dry strength and elastic modulus, the optimum pressing temperature is lower than for wet strength due to the degradation of hemicelluloses. Author Contributions: Conceptualisation, A.M. (Amanda Mattsson) and J.A.K.; methodology, A.M. (Amanda Mattsson), T.J., A.M. (Arttu Miettinen) and J.A.K.; formal analysis, A.M. (Amanda Matts- son), T.J., A.M. (Arttu Miettinen) and J.A.K.; investigation, A.M. (Amanda Mattsson) and J.A.K.; writing—original draft preparation, A.M. (Amanda Mattsson), T.J., A.M. (Arttu Miettinen) and J.A.K.; writing—review and editing, A.M. (Amanda Mattsson), T.J., A.M. (Arttu Miettinen), J.A.K. and P.E.; visualisation, A.M. (Amanda Mattsson), A.M. (Arttu Miettinen) and J.A.K.; funding acquisition, G.P. and P.E. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by The Kamprad Family Foundation for Entrepreneurship, Research & Charity (grant number 20180234), The KK foundation, and Kempestiftelserna. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data in this study are available on request from the corresponding author. Acknowledgments: The authors thank Licentiate of Engineering Javier Brug é s for the help with editing the figures. Conflicts of Interest: The authors declare no conflict of interest. AppendixA The vapour pressure P v inside a fibre wall at elevated temperatures can be estimated based on the theory developed by Flory and Huggins [33]. We assume that all water is bound to the (hemi)cellulose gel. In a binary polymeric solution (w water, c cellulose) [33], the vapour pressure P v is givenby ln P v P 0 = ln ( φ w )+ 1 − v w v c φ c + χφ 2 c (A1) where P 0 is the vapour pressure of pure solvent, approximated by the Antoine equation log 10 P 0 = A − B C + T ; A = 8.071, B = 1731 ◦ C, C = 233.4 ◦ C ( P 0 inTorr ) (A2) In Equation (A1), φ i is volume fraction, v i is molar volume (molar mass divided by mass density), and χ is Flory–Huggins interaction parameter (for cellulose at moderate water contents). According to reference [34], the specific volume (or density) of cellulose does not vary much with temperature up to 190 ◦ C if the pressure remains below 20 MPa. Assuming that the lignin content of fibre is c l , the cellulose content is 1 − c l . The volumes
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