Ex-Situ DC Conductivity of Powders, Films and Fibers

The basic techniques for measurement of conductivity derive from the resistivity relationship in Ohm s law (J = // , E the potential (voltage) difference, / the current, R the resistance). Across two points spaced at a distance d and with a cross sectional area of 4, the resistance is expressed as  

knowing the cross-sectional area, the separation distance, the current flowing and the potential difference between two points, the bulk resistance, R above, can be computed, expressed as specific resistivityy p, in units of 0-cm. The bulk specific conductivity a, in units of Q -cm or Siemens (S) /cm, is then its reciprocal. The surface resistivity of a coating or film, in units of 0/D (square), is just pity with t the thickness of the coating/film. 

When a conventional 2-probe measurement instrument such as an ohmmeter is sought to be applied to a highly resistive sample, the contact resistance between the probe and the sample constitutes a major impediment. To circumvent this, 4-probe techniques, such as those illustrated in Fig. 11-1 are used. In these, a current is applied between the outer probes, and the voltage differential between the inner probes is measured. Such techniques were proposed by van der Pauw, among others [386]. 

A commercially available four point probe, with sharp probe tips of very small diameter, and probe spacing typically ca. 0.2 cm, may be used in conjunction with a current source and a voltmeter (e.g. a digital multimeter). The probe may be lowered onto the sample through a mechanical device. Alternatively, the 4-in-line configuration of Fig. 11-la may be emulated in a permanent fixture into which the sample is lowered or otherwise affixed. If the sample is a powder, it is first compacted into the form of a pellet, using a laboratory hydraulic press or other device. 

Measurements can also be carried out on a thin film on a nonconductive substrate. In such a case, use of four line probes, as shown in Fig. 11-lb. rather than point probes, is recommended, and the conductivity is then given by  

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