Four-point conductivity measurements

Fig. 4. Four-point conductivity measurements for Nafion 117 and polybenzimidazole films infused with phosphoric acid. Conductivity cell measurements of phosphoric acid shown for comparison. Figure 3 of the first quarter (ending September 1992) project report of the CWRU DARPA methanol fuel cell project...

Figure 2.15 Four-point conductivity measurements of SDS-SWCNT composite films in PS (squares) and in PMMA (rhombi). The molar mass distribution of PS is relatively broad and consists of a mixture of high (about 1,000,000 g/mol for the peak molecular weight) and low molecular weight oligomeric fraction. For the PMMA, the molecular weight distribution is relatively narrow with a main peak located at 1,000,000 g/mol. (From Ref. 100. Reprinted with the authorization of the Royal Society of Chemistry)...

Figure 4.6 Four-point conductivity measurements of MWCNTs/PS composites pressed for 2 min. at 125°C, 150°C, and 180°C. The fittings were determined using the equation given in Table 4.1.

Figure 4.10 Results from [i) Four-point conductivity measurements for SWCNT/PS composites prepared by various processing techniques and ii) respective data fits of the equation given in Table 4.1 (R values of 0.99 for all fittings. Only points close to the percolation threshold were taken into account for the fitting). Lines given in (i) are fittings using the value of t and (pp determined in (//).

Figure 5.9 Results of four-point conductivity measurements as a function of the MWCNT concentration for MWCNT/PPO/PS nanocomposites.

Figure 5.11 Four-point conductivity measurements of MWCNT-polymer composites prepared with various PMMA/PS latex blends and homopolymer...

Figure 5.12 Four-point conductivity measurements of MWCNT-pol3nner composites prepared with a high molecular weight PMMA latex and a blend of this matrix and a low molecular weight PS matrix.

Figure 7.5 Four-point conductivity measurements of graphene/PS nanocomposites as a function of graphene content (Courtesy E. Tkalya).

This transmembrane conductivity method is a two-point measurement. Contact resistance is always a worry with such measurements indeed, we must apply substantial pressure across the membrane (7 x 10 psi) to obtain reproducible resistance data [15]. We recently developed a method for forming thin films from our template-synthesized nanostructures [16,44]. This has allowed us to make four-point conductivity measurements on these nanomaterials (without applying pressure during the measurement). The thin films are prepared by dissolving the template membrane, collecting the conductive polymer nanofibrils or nanotubules by filtration to form a film across the surface of the filter, and then compacting this film in an IR pellet press [16,44]. 

Later on. Song et al. [19] performed a four-point resistivity measurement on a large bundle of CNTs of 60 pm diameter and 350 pm distance between the two voltage probes. They interpreted their resistivity, magnetoresistanee and Hall effect results in terms of semimetallie conduction and 2D weak localisation as for the case of disordered turbostratie graphite. 

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

Conductivity of (BN) iSO F and comparison with Cg SO F. In our early studies (12), a four-probe technique was employed, in which four platinum wires were used for electrical contact, and the samples were prepared by pressing powdered polycrystalline material into pellets. Because the platinum wires and the pellet surface are not ideally flat, a uniform intimate contact could not be assured between the wires and the pellet. The boundary effects due to the polycrystalline nature of the pellet sample also render such conductivity measurements unreliable. Attempts to use a contactless radio frequency inductive technique described by Zeller et al. (22) failed because this technique is not sensitive to low conductivities. A four-point probe measurement (21) on an intercalated highly oriented boron nitride sample was used in the present set of conductivity measurements. The <7295k 1.5Scm . The specific conductivity increased with decreasing temperature (see Fig. 1), it having nearly twice the room temperature value at 77 K. This indicates metallic behavior. 

Contact cuts were plasma etched through the polyimide (using a photoresist mask) and buffered HF was used to etch the silicon dioxide underneath. After aluminum was deposited and patterned, both test and control wafers were sintered in forming gas at 400°C for 10 minutes. A CPI strip was fabricated beside each FET with four aluminum contacts to allow CPI 4 point conductivity measurements. 

Quantitative conductivity of a CP sample is typically measured by a four-point probe technique. CPs for biomedical applications have typically yielded conductivities of between 1 and 200 S cm [44—46,49,50,138]. However, four-point probe measurements can be problematic, as the CP film must be removed from the substrate prior to testing. There have been a number of different methods used for film removal, including doublesided tape, razor blades, and backing the film with polydimethylsiloxane (PDMS) [61]. Fonner et al. found the double-sided tape technique to be most effective, as the CP film was removed firom the substrate undamaged and the presence of the tape did not affect the conductivity measurement [61]. 

Pentacene diquinone (4) was reduced electrochemically with one Faraday/mole, and the semiquinone salt was precipitated. Four-point-probe measurements were made on pressed pellets at room temperature. The lithium salt and tetramethylammonium salt had a = 1 [4] and a = 0.02 S cm-i, respectively. Such high conductivities are not measured on mono-semiquinones. For example, naphthacene quinone has a < S cm-i. 

Bowler, N. and Y. Huang (2005). Electrical conductivity measurement of metal plates using broadband eddy-current and four-point methods. Measurement Science and Technology 16, 2193. 

Figure 7.3 Four-point conductivity ofMWCNT/PS composite as a function of MWCNT content VGCNT2s fo) IPCNTs ( ]. Each point of the curve is the average of several measurements performed several times on several locations on both sides of the nanocomposite films.

The remarkable theoretical predictions mentioned above are even more difficult to verify by experimental measurements in the case of electrical conductivity. Ideally, one has to solve two experimental problems. First, one has to realize a four-point measurement on an individual nanotube. That means four contacts on a sample with typical dimensions of the order of a nm... 

The freezing point lowering of sulfuric acid by acetic anhydride and by benzoic anhydride also corresponds to -factors of four.201 Two explanations are possible in this case, but conductivity measurements favor the second one 202... 

The distance between two cluster molecules is 1.3 nm, i.e., between the naked base and apex of gallium atoms of two clusters, whereby two parallel oriented toluene molecules bridge the intermediate space. Although four-point measurements for electrical conductivity in the temperature range 350 K to 2 K have been carried out, the mechanism of electron conductivity cannot be conclusively explained 83 is... 

The most typical way to measure the in-plane electrical conductivity of a diffusion layer is through the use of the four-point probe method. A small current is applied across the sample material a separate set of voltage measuring probes that are in touch with the material are used to measure the resulting voltage drop in order to calculate the resistance. With these values, the in-plane resistivity, p, can be calculated with the following equation [9,233] ... 

Solid State Properties. Most likely as a result of the limited intermoleeular interactions of these complexes in the solid state, little investigation of their solid-state properties have been reported. However, the electrical conductivity of pressed pellets of 17 have been measured via four-point probe to give a room temperature value of 10 S cm. This relatively low value is likely a result of the lack of significantly strong t-stacking as observed in the X-ray structure. 

To minimize the current flow through the sample, an ac four-point probe technique was used to monitor the conductivity of the sample with a lock-in amplifier (Stanford Research Systems, model SR 830 DSP). The lock-in amplifier enabled us to measure very low voltages without noise problems. 

Sheet resistance can be measured with a four-point probe. The probes may be in line or in a square pattern, as shown in Figure 9. In either configuration, a constant current I is passed through two of the probes, and the voltage difference between the other two is read. Provided the conducting layer is thin (t < 0.60 d), the sheet resistance can be calculated from... 

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