AN ANALYTICAL MODEL FOR NUMBER OF FIBRE-FIBRE CONTACTS IN PAPER AND EXPRESSIONS FOR RELATIVE BONDED AREA (RBA)

摘要

This paper proposes an analytical model for fibre-fibre contacts relating the number of fibre-fibre contacts per unit fibre length with the cross-sectional dimensions of the fibres in a sheet and the sheet density. This model has been verified with data of the (number of fibre-fibre contacts (N_c) measured directly in hand-sheets using a combined technique of resin embedding and con-focal microscopy. The fibre-fibre contacts in the handsheets were classified into full contacts and partial contacts during measurement. We showed that the model best fits this data when 1.5 partial contacts are treated as equivalent to one full contact, for the purposes of comparison with the model. Using this equivalence, when the model predictions were plotted against the number of measured equivalent full contacts, a linear relationship was found with a slope of 0.99 and a correlation coefficient of R~2 = 0.93. The model for N_c is further substituted into expressions for Relative Bonded Area (RBA) and its validity again checked using experimental data for RBA. The RBA was determined using two different methods, viz. by measuring the BET area of the sheets by nitrogen adsorption technique (RBA_(N_2)) and by measuring scattering coefficients of the sheets (RBA_(sc)). A new method was used in this study for determination of S_0 and two expressions of RBA (corresponding to RBA_(sc) and RBA_(N_2)) are derived from the model for N_c. A graphical comparison of the predicted RBA_(N_2) to the measured RBA_(N_2) shows a slope of 1.01 and a correlation coefficient of 0.88. The predictions for RBA_(sc) and the corresponding measurements showed a very strong linear correlation (slope = 0.94 and R~2 = 0.94)) when they were plotted against each other. It is concluded that the model for the number of fibre-fibre contacts per unit fibre length is valid.