Effect of fibre properties

The statistical geometry of random fibre networks provides an estimate of the effect of fibre properties on paper roughness. Profilometric measurements of micro roughness show that the local height distribution of the paper surface is near the normal distribution, or Poisson distribution, of a heigh mean value ¹. This is true even after normal calendering.

The Poisson distribution of surface heights suggests that in the first approximation all fibres make the same contribution to paper thickness and that surface height is proportional to local grammage. This leads to the following estimate for the RMS roughness:

(1)

where N is the average number of fibres under the measurement head,
A the area of the measurement head,
b the grammage of paper,
d_eff the effective thickness of paper, and
m_f the mass of a fibre.

According to Eq. 1, at a given grammage, roughness increases with increasing fibre mass and paper thickness. One can understand the effect of fibre mass with the analogy of filling a bucket with small or large stones. In the same way, filler and coating pigments give a smooth surface because of their small size — now consider filling the bucket with sand.

Long fibres give high roughness because of their high mass. Long fibres are often also more coarse than short fibres. Paper thickness increases with fibre coarseness through fibre flexibility. Coarse fibres therefore yield a particularly rough paper surface (see Figure 1 for a demonstration). For this reason, in chemical pulps, hardwood should give better smoothness than softwood, and in mechanical pulps, groundwood should be better than TMP. The beating of chemical pulp increases fibre flexibility and collapse. Beating reduces paper roughness through the loss of paper thickness, d_eff. In mechanical pulping, refining increases the relative proportions of short fibres, which again reduces roughness through the lower average fibre mass, as shown in Figure 2.

Figure 1. Bendtsen roughness vs. kraft content in an LWC base paper. Fibre coarseness, ωf, and mass, m f, are 0.23 mg/m and 0.53 μg for Canadian softwood kraft, 0.23 mg/m and 0.46 μg for Finnish pine kraft, and 0.31 mg/m and 0.84 μg for U.S. Southern pine kraft. Calendering with a constant nip load²

Figure 2. Bendtsen roughness vs. long-fibre content in a TMP pulp. The proportions of the long (lf = 2.43 mm) and middle fraction (lf = 1.45 mm) vary at a constant 30% fines content. Calendering with a constant nip load³