Dielectric properties
Typically, the dielectric constant, εr = ε´/ε0 is 2–3 in paper, and in water it is 80. The high value in water is not surprising considering that water molecules have a permanent dipole moment. One might thus think that moisture content has a strong effect on the dielectric constant of paper. However, in paper, water molecules are associated with polysaccharide chains and cannot rotate freely. Rotation is possible only if the field is parallel to the chain axis. Since the chain orientations in paper are random, only a small fraction of the water molecules have perfect alignment with the electric field. This makes the effective dielectric constant much smaller than it would be with liquid water. In addition, the dielectric constant of paper increases little with increasing moisture content. Instead, moisture can significantly influence dielectric losses or the imaginary part of permittivity, ε´´ (see Electrical properties Eq. 4).
The coupling between the orientation of polysaccharide chains and electric field implies that the dielectric constant of paper is greater in the planar directions than in the z-direction. In sheets with anisotropic fibre orientation, the dielectric constant is largest in the direction of the fibre orientation angle. Fibre orientation measurements can make use of this. Also, the dielectric losses depend on the orientation, and seem to be largest in the MD 1.
With increasing temperature, the dielectric constant of paper increases somewhat, and the loss factor has a minimum around 60 °C. This is due to the decrease in interfacial polarisation and the increase of the loss due to carboxyl groups at high temperatures.
The dielectric constant of paper increases with density, ρ. The behaviour follows the Clausius-Mossotti relation:
(1)
The loss factor increases linearly with density, as shown in Figure 1. Impurities such as metallic ions increase the loss factor. Lignin and hemicelluloses have the same effect. Table 1 provides a summary of the factors affecting the dielectric properties of paper.
Table 1. Dielectric properties of paper and factors that affect them 2.
Dielectric constant, ε’
Paper density
Sheet structure (fibre orientation)
Crystalline cellulose
Pulp components (lignin, hemicellulose, etc.)
Dielectric loss, ε’’
Ionic conduction losses
Inclusion of organic and inorganic ions
Adsorbed ions
Carboxyl groups, etc.
Fibre morphology
Polarisation losses
Rotation and oscillation of polar material
Fine structure of cellulose
Pulp components (lignin, hemicellulos etc.)
Dielectric breakdown strength
Long-term ac breakdown strength
Paper density
Barrier effect of paper
Inclusion of inorganic ions or organic esins
Dielectric loss
Short-term breakdown strength (ac, pulse)
Barrier effect of paper and network structure
Inter-fibre bond structure
Fibre morphology
Bulk structure of paper
Inhomogeneity of paper
Figure 1. Dielectric constant expressed as (εr – 1) / (εr + 2) in (a) and loss tangent tan δ ≡ ε´´/ε´ in (b) vs. density in pulp sheets 2.
