Electrical percolation of fibre mixtures

In the development of conductive threads for wearable electronics, nonconductive cotton fibres and conductive stainless steel fibres are mixed to produce composite yarns at a wide range of stainless steel fibre weight fractions. The electrical resistance of the composite yarns is measured at different probe span lengths, ranging from 0.5 to 10 L (ss) (L (ss) = 50 mm is the average length of stainless steel fibres). The percolation threshold and critical exponent are determined for each span length. The critical exponent followed a decreasing trend from 1.87 to 1.17 as the span length was increased. When the conductive fibre loading was expressed in terms of conductive fibre volume fraction, the percolation critical exponent showed a similar trend of change with probe span length. Such a dependence of percolation critical exponent on resistance probe span length has not been previously reported for conductive particle-filled polymer composites, probably because the probe span length used in resistance measurement is orders of magnitude larger than the dimension of the conductive fillers in the composites.