An analytical model for number of fibre–fibre contacts in paper and expressions for relative bonded area (RBA)

This paper proposes an analytical model for calculating the number of fibre–fibre contacts per unit fibre length from the cross-sectional dimensions of the fibres in a sheet and sheet density. This model has been verified with data of the number of fibre–fibre contacts measured directly in handsheets. The measured fibre– fibre contacts in the handsheets were classified into full and partial contacts. The model best fits this data when 1.5 partial contacts are equated to one full contact. A plot of measured versus predicted equivalent full contacts produced a linear correlation with a slope of 0.99 and correlation coefficient of R2 = 0.93. The model was used to derive expressions for the fraction of the available fibre surface, which is bonded to other fibres, a quantity called the Relative Bonded Area (RBA). The validity of the model was checked using experimental data for RBA. RBA was determined both by nitrogen adsorption ( RBAN2) and by scattering coefficient (RBAsc). The extrapolation method of Ingmanson and Thode to determine S0, the scattering coefficient of an unbonded sheet, proved to be inaccurate. We estimated S0 for some samples from their linear relationship between scattering coefficient and nitrogen adsorption. The new model accurately predicted both RBAN2 and RBAsc.