Resistivity of paper
Electrical current passes through paper along fibres. In the fibres, the mechanism of electrical conduction is probably ionic. According to Murphy 1, the ionic charge carriers are cations that move through hydroxyl groups in the polysaccharide chains, as shown in Fig. 1. The ions can move only to hydroxyl groups that are associated with a water molecule. The concentration of mobile cations and moisture in paper therefore control the electrical conductivity. The mobile ions are free, or the applied electric field releases them from carboxyl groups.
Figure 1. Ionic conduction in polysaccharide chains along the hydroxyl groups. The ions can move only to hydroxyl groups occupied by a water molecule1.
Since all the hydroxyl groups along the cation path must be associated with water, conductivity should be proportional to some power of moisture content (mc), or
(1)
The probability for a water molecule in a hydroxyl group is at first approximation linearly proportional to the moisture content. Measured conductivities in Figure 2(a) follow this law very accurately with n ≈ 9. The reason for this particular power is controversial. A 1-percentage point increase in moisture content causes nearly an order of magnitude increase in conductivity.
Figure 2. Resistivity of cellulose vs. temperature at constant moisture content (a) and conductivity vs. moisture content at room temperature (b) 1,2.
The concentration of free charge carriers in paper increases with temperature, since some characteristic activation energy, Ea, controls it:
(2)
As a result, the conductivity of cellulose is an exponential function of temperature, as shown in Figure 2. An increase of 20 °C in temperature will increase the conductivity by one order of magnitude.
Fibre bonding dominates the effects of paper structure on its electrical conductivity. This is seen in Figure 3, where resistivity is plotted against pulp freeness. The microscopic origin of the effect of bonding is in the motion of cations. They can make transitions from one cellulose chain to another only if the neighbouring chains are within a molecular distance.
Figure 3. Bulk conductivity of paper as a function of pulp freeness 3.
In electrophotographic papers, conductivity is sometimes increased by adding salt such as KCl, NaCl, or some other charge control agent to the surface size. The main effect of salt is to increase the number of available charge carriers, but it can also affect the equilibrium moisture content. Fillers have such a small effect on the conductivity of copy papers that other means can easily compensate for them. Conductive or anti-static coatings have occasional use to avoid static electricity. The anti-static agent causes the surface to saturate with moisture so that its resistivity is small.
